Table of Contents

Getting Started

Welcome to the Optimizer:
The Asset Allocation System:
Worksheets:
Sample Cases:

Settings and Tools

The Optimizer Ribbon:
Conventions in the Optimizer:
Options Menu:
Display Menu:
Copying and Pasting:
Instances:
Preferences:

Inputs

Setting an Investment Problem:
Loading:
Portfolios:
Drifting:
Correlation Matrix:
Expense Ratios:
Yield:
Four Moment Resampling Inputs:
Custom Characteristic:
Puts and Calls:
Risk Free Rate:
Information Ratio:
Multi-Period Horizon:
Assets Wizard:
Asset Groups:

Optimization

Optimization:
Forecast Confidence:
Number of Simulations:
Active Weight Optimization:
Options Strategy:
Tolerance:
Rejection Sampling:

Rebalancing

Rebalancing Test:
Trade Advisor:
Trade Advisor and Post-Optimization:
Filter Matching:
Loading and Saving Relative Variance Tables:

Charts

Charts Worksheet:
Editing Charts:
Portfolio Weights Comparison Charts:
Portfolio Bounds Line Chart:
Efficient Frontier Chart:
Portfolio Composition Maps:
Rebalance Probability Chart:
Portfolio Risk Contribution Charts:

Saving

Saving:
Moving to LifeCycle:

Results

Results Worksheet:
Comparison in the Optimizer:
Interpreting the Results:
Significant Results:
Filter Worksheet:
Portfolio Spacing:
Standard Error:
Data Pages:
Reports:

Constraints

Introduction to Constraints:
Asset Bounds:
Transaction Costs:
Customized Constraints:
Maximum Turnover:
Long-Short Optimization:
Quadratic Transaction Costs (Return Penalty):
Quadratic Risk Penalty:
Constraint Analysis:
Constraints Analysis II:

Taxes

Working with Taxes:
Basic Method:
Tax Lots:
Tax Deferred Assets:

Investability Constraints

Post-Optimization:
Investability Constraints:
Asset Anchoring:
Asset Threshold:
Maximum Assets:
Asset Increment:

Simulator

Simulator:

Troubleshooting

Error Handling:
Covariance Fixer:
Troubleshooting Tools:
Debugging Log:
Known Issues:
Add-In Not Loaded:

Welcome to the Optimizer

New Frontier's Optimizer uses Michaud optimization to calculate the Michaud Resampled Efficient Frontier™ from your optimization inputs, producing allocations that are less extreme, more intuitive, and have more reliable risk estimations than the output of traditional optimizers.  

New users may wish to start by familiarizing themselves with these introductory topics:

The Asset Allocation System

The three modules of the Asset Allocation System facilitate the construction of realistic, effectively diversified portfolios with well-managed risk. The software provides a complete system for making asset allocation decisions.

Your relationship manager will be happy to discuss additional licensing and training opportunities.

Worksheets

The primary worksheets:

 

The secondary worksheets:

Sample Cases

New Frontier provides some sample cases for your use in the samples directory. The default location for the samples directory is Program Files/NewFrontier/8.0/samples. The Optimizer can open Estimator cases (*.nfei) and Optimizer (*.nfoi) cases. Estimator cases consist of inputs only when opened in the Optimizer, while the Optimizer cases contain optimization choices and results as well.

Michaud 1998 book

This is the original dataset used to study resampling in Efficient Asset Management by Richard Michaud. The data consists of six country equity indices and two bond indices: Canada, France, Germany, Japan, United Kingdom, United States, a U.S. bond index, and a Eurobond index. The non-U.S. equity indices are all MSCI data and the U.S. equity index is the S&P 500.  The dataset is meant to illustrate a reasonable global asset allocation but is not for investment purposes.

Michaud 2008 paper

The Michaud 2008 case offers the data used by Richard Michaud and Robert Michaud in "Estimation Error and Portfolio Optimization" (Journal Of Investment Management, Q1 2008).  Following Jobson and Korkie (1981), the optimizations are illustrated based on the risk and returns of twenty U.S. stocks randomly chosen from 100 largest capitalization stocks in the S&P 500 index with continuous monthly returns from January 1997 through December 2006. The list of stocks, their annualized average returns, standard deviations and correlations over the period and further details are given in the appendix to the paper.  

Vanguard Data

New Frontier includes data for several index funds provided by Vanguard with the Asset Allocation System. Because Vanguard uses a passive, full-replication approach to managing their index funds, the funds may be expected to serve as good proxies for the underlying indices. The equity funds track their MSCI, CRSP, and FTSE index counterparts. The fixed income index funds track the appropriate Bloomberg Barclays Capital indices. New Frontier provides four Estimator cases using Vanguard data and two Optimizer cases. The Optimizer case started with the monthly Estimator case.  One includes tax lots and one does not. The included funds are:

  1. CPI (seasonally adjusted, as reported by the Bureau of Labor Statistics)

  2. Vanguard Short-Term Bond Index

  3. Vanguard Intermediate-Term Bond Index

  4. Vanguard Long-Term Bond Index

  5. Vanguard Inflation-Protected Securities Index

  6. Vanguard High-Yield Corporate Index

  7. Vanguard REIT Index

  8. Vanguard European Stock Index

  9. Vanguard Pacific Stock Index

  10. Vanguard Emerging Markets Index

  11. Vanguard Growth Index

  12. Vanguard Value Index

  13. Vanguard Small-Cap Growth Index

  14. Vanguard Small-Cap Value Index

 

The Optimizer Ribbon

The NFA ribbon, labelled Optimizer, stretches across the top of each worksheet, providing tools for each step of the optimization process from loading to interpreting the results.

Application Section

File Section

Optimize Section

Rebalance Section

Wizards Section

Trade Section

Edit Menu

Post-Optimize

Case Settings Section

Workbook Section

Report Designer constructs reports that contain Optimizer results.

Help opens this help manual.

Conventions in the Optimizer

Background color indicates the purpose of individual cells within the Optimizer.  White cells can be changed. Cells shaded a light yellow contain calculated information or information that cannot be changed.  For example, the Return and Standard Deviations Columns on the Inputs Worksheet are white, but the Information Ratio Column, calculated by the Optimizer, is light yellow.  A light blue background indicates that the cell conforms to the default value for a constraint.  For example, if you set a default asset bound constraint of 2%, all of the rows that follow the defaults appear in blue.  If you then set a particular asset to have a lower bound of 5%, the 5% appears with a white background.  If you set an individual asset to 2%, thereby matching the default, the cell would appear with a white background because changing the default would not change that constraint.  To revert to the default, enter a letter.  Similarly, blue backing to customized constraint weights indicates that the Optimizer recognizes the source of the weights and will update the constraint if the source material changes.

Numbers appear in blue, black, and red.  Protected, light yellow cells, contain black numbers.  Editable cells (light blue or white) contain blue numbers.  When there are dark blue and light blue fonts, such as with customized constraints, dark blue indicates that the content is enabled while light blue indicates that the content is disabled.  Red indicates negative values.  

Options Menu

The Options Menu offers ways to adjust the optimization problem.  Many of these options are displayed on the information bars at the top and bottom of the each worksheet when they are enabled, and the Info Worksheet provides a summary of your current settings and those used for the most recent optimization.

Optimization Options

Advanced Options Sub-Menu

Miscellaneous Options

You may also want to review the description of the display options:

Display Menu

The Display Menu shows and hides optional worksheets, charts, and information so that you can match your workspace to your workflow.  Your choices will persist as you open future instances of the Optimizer.

Asset Info Columns

Worksheets

 

Charts

Copying and Pasting

For the most part, copying and pasting behaves as you would expect it to in Excel.  However, there is a difference between the normal Excel tools and the NFA versions found in the Edit Menu that appears in the NFA ribbon.  

Use the New Frontier versions to copy the entire case -- all  information in the Optimizer at the time, onto a clipboard, and then paste into another Optimizer instance or into LifeCycle as the efficient frontier.  You can also copy an Estimator case (asset universe, returns, standard deviations, and correlations) into the Optimizer.  The New Frontier versions of copy and paste only work within a single instance of Excel.

To copy a section of the case, utilize the Excel copy and paste functions.  The Excel copy function can also be used to copy portfolios or other data into a blank Excel Spreadsheet for comparison purposes.  

 

Instances

Multiple Instances of Excel

Opening the Optimizer through the Start Menu starts an instance of Excel, accesses Optimizer, and loads the default case.  Alternatively, you can double click on a saved Optimizer info file (*.nfoi), which opens a new instance of Excel, accesses Optimizer, and loads your saved file.  If you perform both of the above actions, or repeat one them, you will have two instances of Excel with Optimizer open.  Opening separate instances of Excel means that closing one instance will not close the others, that you can run two instances of Optimizer simultaneously, and that you cannot use New Frontier’s copy and paste tools between the two.  The same advantages and limitations apply to LifeCycle and Estimator instances operating within separate instances of Excel.

One Instance of Excel

To open multiple instances of LifeCycle, Optimizer, or Estimator within the same instance of Excel, use either the Launch Menu or New on the NFA ribbon.  With only one instance of Excel open, the New Frontier copy and paste works.  However, only one application can run at a time.  

  From Estimator From Optimizer

 

From LifeCycle

Launch Estimator

Copies current Estimator case into a new Estimator instance

Launches Estimator with the default case

Launches Estimator with the default case

Launch Optimizer

Copies Estimator data  into a new Optimizer instance

Copies current Optimizer case into a new Optimizer instance

Launches Optimizer with the default case

Launch LifeCycle

Launches LifeCycle with the default case

 

There are three ways to launch.  Each copies the Optimizer data (frontier and portfolios) into LifeCycle.  The LifeCycle case  depends on the option chosen:

  • LifeCycle - Blank Case: LifeCycle case with minimal data

  • LifeCycle - Choose File: Prompts for a *.nfli or *.nflc file

  • LifeCycle - Sample Case: uses the Endowment LifeCycle sample case

Copies the entire LifeCycle information file except for the efficient frontier

 

New

New Estimator copies the current data into a new Estimator.

Opens a blank, eight asset Optimizer case

Opens a blank LifeCycle case

Preferences

The Preferences Window permits you to adjust the settings for your application.  Preferences save with the case.  Additional settings can be found in the Options Menu.

To access, click the Preferences Button from the ribbon.  The Preferences Window appears.  Choose one of the panes by selecting the appropriate option in the tree to the left.

General Pane

Bloomberg Pane

Once Bloomberg account information is entered here, the Optimizer can drift portfolios according to Bloomberg returns. This requires a file with Bloomberg global ids entered as the ticker, a valid Bloomberg account, and an internet connection.  

Misc. Data Sources Pane (FMP)

The Optimizer can drift portfolios according to FMP returns once the FMP API key has been entered here. Remember to set the ticker source to FMP for each ticker in the Inputs sheet. (If the Ticker Source column is hidden, please expand Asset Info Columns in the ribbon and check Ticker Source).

Optimization Panes

Computation Pane

The Computation panes manage multi-core processing. Choose the appropriate option in the Run Computations On drop down menu. Clicking the Advanced Button brings you to the corresponding sub-pane for specifics.

Contact New Frontier at support@newfrontieradvisors.com for details as required.

Debug Pane

The Debug Pane permits the user to enable debugging. Debugging should only be enabled when a specific problem has been identified, as it creates logs for each action that save to the specified folders.

Reset Pane

The Reset Pane provides the option to return the preferences to the defaults selected by New Frontier. Invoking this option will carry over to your preferences in all modules of the Asset Allocation System.

The Info Worksheet offers a convenient review of your currently selected preferences and options.

Setting an Investment Problem

In order to use the Optimizer, you must set an investment problem. This involves either overwriting the default case, loading a previously prepared Estimator or Optimizer case, or entering a case manually. An Optimizer case must contain a list of assets, a correlation matrix, and estimates of risk and return. An Estimator case includes all of these basic inputs. There are also numerous optional inputs. Optional inputs range from constraints to the currently used portfolio.   

Entering a case is sometimes easier if you start with empty worksheets, instead of the default case. Click the New Button in the File Section of the ribbon to open an empty Optimizer case. Piece together your case by loading files, copying data from other spreadsheets, or entering data manually. Just remember that you must have a list of assets, a correlation matrix, and estimates of risk and return.

After a case is loaded there are many follow-up activities that you may need or want to perform:

Next, enter optimization inputs: the number of simulations (or tolerance) and the forecast confidence level. Then, initiate optimization. After reviewing results, consider post-optimization. Later, use the Optimizer for monitoring and rebalancing your portfolios and consult the Trade Advisor for trade guidance. The Info Worksheet summarizes many of these choices in one location for your review.

Loading

The Load Menu appears in the File Section of the NFA ribbon. Select the Load Option from the drop down. The Load Data File Window appears. Navigate to the folder that contains the desired file. Narrow down the files that appear by changing the file type selection in the drop down menu next to the File Name Field.

Portfolios

Types of Portfolios 

Portfolio Characteristics

You can enter, review, compare, and change portfolios on the Portfolios Worksheet. The Optimizer calculates the return, standard deviation, and Sharpe Ratio for all of these portfolios automatically; if a Rebalance Test score is available, it is shown below the Sharpe Ratio; if four-moment resampling is enabled, an estimated skewness and estimated kurtosis are displayed next; if you have entered asset yields, expense ratios, or a custom characteristic on the Inputs Worksheet, the Optimizer also displays the portfolio-weighted versions of these quantities.  

Note that the standard deviation calculations for the portfolios are affected if quadratic risk penalties are entered and the Add Quadratic Penalty to Risk option is enabled in the Display>>Charts Menu.

Evaluating Portfolios

The optimal portfolios appear on the Results Worksheet after optimization.  The Efficient Frontier Chart on the Results Worksheet presents all portfolios in mean-variance space.  All portfolios appear on the Charts Worksheet for comparison and other analysis. Filtered Portfolios refer to portfolios that match the criteria set up on the Filter Worksheet.

Portfolio Total Value

Portfolio Total Value, enabled through the Options Menu, reveals a row at the bottom of the worksheet for you to enter the monetary value of the portfolios. This can be used for your reference, but more often it is used in consonance with drifting. Drifting can update both the portfolio weights and the portfolio total value according to market activity. The dates that appear directly beneath the portfolio names on the Portfolios Worksheet indicate when the portfolio was last updated.

Reference Portfolios Wizard

Selecting the Reference Portfolios Button in the Wizards Section of the NFA Ribbon, accesses the Reference Portfolios Wizard, which allows reference portfolio management.

 

Drifting

The drift function calculates how portfolio allocations have changed between the date that the portfolio was last updated and a specified date.  For instance, if you entered an initial portfolio a year ago, this tool can calculate how the allocations of that portfolio have changed within that year based on return streams from an Estimator file or from online sources.  This works for the benchmark, initial, and reference portfolios, which simplifies case preparation and allows for more accurate rebalancing.

The Drift Button in the Assets Section of the NFA ribbon opens the Drift Portfolios Window.

  1. If your case includes tickers, you can chose to update from online sources (Yahoo!, Google, and BLS).  If you have set up Bloomberg, enter the BBGID Composite as the ticker.  
    • New Frontier is not responsible for the imported data.  You should review the terms of use of each site. Be aware that sometimes the public sites can lag reality significantly. Google also prefers tickers that identify the exchange, which can lead to significant errors. New Frontier recommends using online sources for quick reviews or for exploring possibilities, not for actual investing.
    • To view/enter tickers, adjust the display using the Display Menu to enable the Ticker and Ticker Source Columns on the Inputs Worksheet.  Enter tickers and select the source. For more information about tickers, access the Estimator Help Manual.
  2. To avoid online sources, enter an Estimator file that contains return streams for the appropriate assets over the desired time frame in the File Field.  Make sure that the asset names match.
  3. Enter the Drift To date.  Remember that it may not be possible to drift to the default current date depending on how performance is reported for your specific assets.
  4. Pick the portfolios that you wish to drift. Checkmarked portfolios will be drifted.  (Note that portfolios only appear in the drift dialog if they are enabled.  Both the benchmark and initial portfolios can be disabled and enabled through the Options Menu. Reference portfolios will only appear if they have a date assigned on the Portfolios Worksheet past the default date of March 1, 1900.)
  5. Review the dates given for the last update of the portfolio.  These mirror the dates that appear beneath the portfolio name on the Portfolios Worksheet.  Ensure that the dates are as expected, clearing up any discrepancies before continuing.  You can enter/update the dates for your portfolios either on the Drift Window or on the Portfolios Worksheet.
  6. When everything is set, click the Drift Button. 
    • If you selected the initial and benchmark portfolios, the drifted portfolios replace the previous portfolios and the date is updated.
    • If you selected reference portfolios, the drifted portfolios appear to the right as additional reference portfolios labeled "Drifted [Portfolio Name]" and the new date. The original reference portfolios remain. You may need to scroll to the right to see the drifted portfolios.
    • If you have enabled Portfolio Total Value, the values entered in that row of the Portfolios Worksheet will also update.
  7. To undo a drift, removing all drifted portfolios, click the Undo Button on the New Frontier ribbon.

The Robot, which automatically runs estimations and optimizations, makes use of the drift tool to update cases.  Instructions for the Robot appear in the Start Menu--All Programs--NFA Asset Allocation System 8.0--Documentation folder.

Correlation Matrix

The correlation matrix on the Inputs Worksheet describes the relationship between individual assets.  Correlation values range from -1 to 1.  Values of 1 populate the diagonal within the matrix, indicating each asset's correlation with itself.  We strongly recommend estimating correlation matrices all at once through a valid statistical procedure, guaranteed to create a positive definite or positive semi-definite (valid) correlation matrix. This is normally the case when inputs are generated in the Estimator. However, it is possible in the Optimizer to input your own asset correlations manually.  If you do enter the correlations manually, you only need to complete the correlations either above or below the diagonal progression of 1s as the Optimizer automatically populates each cell's duplicate.  

Note that the Optimizer expects the matrix of Full Correlations as the input, not the matrix of Partial Correlations, which is available in the Estimator via a drop-down menu. 

Manual alterations to correlation matrices often result in inconsistent values and poorly conditioned matrices.  These will lead to numerical problems or even infeasible optimizations.  We do not recommend making manual tweaks to individual values in the correlation matrix.  However, in the case that a correlation matrix is badly specified, the Covariance Fixer can be licensed to find the nearest well-conditioned matrix.

Expense Ratios

An expense ratio measures the operational costs, including fees, of mutual funds, exchange traded funds, etc.  Operating expenses are taken out of a fund's assets and lower the return to a fund's investors.  Expense ratios can have a marked impact on optimization.  

The Expense Ratio Column is an optional column that appears on the Inputs Worksheet when enabled through the Display Menu. If you enter expense ratios, the Optimizer deducts the expense ratio from each asset's return when optimizing.  

The expense ratios are available for customized constraint construction as well.

See Loading for instructions on how to import expense ratios from online sources.

Yield

The Yield Column is an optional column that appears on the Inputs Worksheet when enabled through the Asset Info Columns submenu within the Display Menu. If you are working with taxes (basic taxes, not tax lots), yield information is used to calculate after-tax expected return.

Yield is available for customized constraint construction and reference purposes. If you do not apply a customized constraint based on this data or work with taxes, this column will not impact the optimization.

The yield of a portfolio is the weighted sum of the assets' yields. It is displayed at the bottom of the Portfolios Worksheet, optionally on the Efficient Frontier Chart, and in tables on the Results and Charts Worksheets. Portfolio yields calculate automatically when an asset yield is changed. When basic taxes are enabled, portfolio yields will update but will not reflect optimal portfolios based on the new information until after you optimize.

See Loading for instructions on how to import yields from online sources.

Four Moment Resampling Inputs

Since a normal or t distribution doesn't approximate all asset return distributions equally well (e.g. hedge funds), the Optimizer offers non-normal distribution. If you enable four moment resampling in the Options Menu, Skew and Kurtosis Columns appear on the Inputs Worksheet, and the Optimizer uses a multivariate distribution for resampling that matches these higher moments. Keep in mind that it is not possible for assets with significantly different kurtosis to be highly correlated; if the correlation matrix is incompatible with the given kurtosis and skewness, the Optimizer adjusts the correlation matrix as needed.  

For details on New Frontier's approach to non-normal optimizations, access "Non-Normality Facts and Fallacies" and other articles from our website (www.newfrontieradvisors.com).

Custom Characteristic

The Custom Column is an optional, renameable column that appears on the Inputs Worksheet when enabled through the Asset Info submenu within the Display Menu. It allows you to enter a numerical characteristic that is not normally included in the Optimizer (e.g. an asset liquidity measurement).  This column is available for customized constraint construction and reference purposes. If you do not apply a customized constraint based on this data, this column will not impact the optimization.

The custom characteristic of a portfolio is the weighted sum of the values input of the assets' custom characteristic.

Puts and Calls

Puts and calls are inputs when you've enabled the options strategy.  Options strategy can be activated through the Options Menu in the Optimizer ribbon.  Upon activation, six new columns appear on the Inputs Worksheet between the Annualized Market Forecasts and the Correlations.  Three of these columns are for puts, the other three for calls. To assign a put or call to an asset, the user must input the strike price, cost, and coverage. New Frontier puts and calls apply generally to the resampling procedure in both optimizations and rebalance tests.  They remain in place and always affect the return distribution in all resampled returns.  In the resampling process, during optimization or calculation of the rebalancing test, resampled returns beyond the strike price are converted to the strike price if the coverage is set at 100%.  For less than 100% coverage, the designated percentage coverage is moved to the strike price, producing a return that is as weighted combination of the strike price and the resampled return.  The strike is given as a percentage relative to the current price, rather than an absolute price as is the case in most real-world puts and calls.  They are also assumed to be repeated for each time period.  This is in contrast to real-world options, which expire on a particular date and are only used once.

The three fields are similar for puts and calls; more detailed descriptions follow:

Strike:

The strike is specified as an annualized return.  Note that this may require a conversion if the units of return are monthly or quarterly.  If a one-period annualized return is less than the strike, any existing put option is exercised. Similarly, if the one-period annualized return is greater than the specified strike, any existing call option is exercised. There is no general restriction on strike prices.  Out-of-the-money puts and calls can be entered into the Optimizer.  It is up to the user to make sure that these investments are sensible, since they can dramatically alter the resulting allocations and be dangerous if used recklessly.

Cost:

The cost is again specified as an annualized percentage.  Note that this too may require a conversion.  Mispriced options may force an asset to be overused or underused in an asset allocation; correct pricing is important when entering options into the optimizer.  It is the user’s responsibility to ascertain and enter correct pricing for any options entered.

Coverage:

Coverage is expressed as a percentage of holdings of the underlying asset and is unrestricted.  Positive coverage implies buying, and negative coverage implies selling the option. Note that ordinary coverage for call sales is measured in negative percentages. The designated percentage of the holdings covered by an option, if exercised, will be bought/sold at the strike price.

Risk Free Rate

The risk free rate is the expected rate of return for a risk free asset, such as a savings account. Enter the Risk Free Rate through the Options Menu. The Optimizer uses the risk free rate to calculate the information ratio. You may also wish to add the risk free asset to the investment problem.

Information Ratio

The information ratio appears on the Inputs Worksheet. Also known as the Ex Ante Sharpe Ratio, the information ratio is calculated as follows: (estimated return - risk free rate of return) / (standard deviation). It provides a rough indicator of how much an investor knows about an asset.

The Sharpe ratio that appears on the Charts Worksheet reflects the Sharpe Ratio for the portfolios.

Multi-Period Horizon

The classic optimization framework is a single-period model.  Geometric return implies a multi-period time frame, but investing is still a series of single period decisions.  If you want to show the efficient frontier over multiple periods, enter a Multi-Period Horizon in the Options Menu.  The Multi-Period Horizon must be greater than 0 and less than 100 years.  The multi-period horizon does not change the optimization results, but it does set the time frame for the displayed multi-period efficient frontier on the Efficient Frontier Chart on the Results Worksheet.  Though not a true multi-period analysis, the multi-period line uses the geometric mean to help you determine a sensible amount of risk over time.

The financial validity of multi-period return depends on assumptions about the nature of single-period return. Employing active weight optimization, specifically calculating return relative to a benchmark, generally invalidates multi-period return; so, the Optimizer does not permit multi-period horizons to be above one while active weight optimization is enabled. However, in many situations that do not involve active weight optimization, multi-period return can be helpful in understanding the consequences of an optimization, particularly in the case of leveraged investment strategies. For more detailed multi-period calculations, access LifeCycle.

Assets Wizard

The Assets Wizard provides functionality to select and sort assets.  Access the Assets Wizard by clicking the Assets Button in the ribbon.

Add an asset

In general, it is wise to add an asset in the Estimator so that the impact of the new asset on the correlations matrix and any contrasts will be accounted for. If you add an asset in the Estimator, use NF copy to bring the case over to the Optimizer.

If you are not working with the Estimator, click the Add Button. A highlighted row will appear with a placeholder name (starting with A1). Click the OK Button to accept the change and close the Asset Wizard, then return to the Inputs Worksheet to fill in the columns pertaining to the new asset.

Sort the assets by clicking on the column headings. For example, clicking on the Asset Name heading sorts the assets by name. This duplicates the sorting functionality found on the worksheets (double clicking on the Asset Name heading on the Inputs Worksheet will also sort assets by name.) The difference is that here you can select an asset row and use the Move Up and Move Down Buttons to customize the sort. You can also save a particular sort by clicking on the Store Order Button. Clicking on the Restore Order Button at a later point will sort the assets according to that previous sort.

Exclude assets from the optimization by removing the checkmark in the appropriate row. Excluded assets remain as options in the Asset Wizard, but do not appear in the Optimizer. If you exclude an asset from the investment universe after optimization has already taken place, the portfolios do not total 100% until you optimize again. Return excluded assets to the investment problem by returning to the Asset Wizard and checking the appropriate asset. Saving a case in Excel format removes any excluded assets permanently. Saving a case in NFA format keeps excluded assets in the Asset Selector so they can be returned to the investment universe at a later date. 

Asset Groups

Assets in the Optimizer can be assigned to groups, such as stocks and bonds, to facilitate sorting and constraints.  

Display Groups

To display or hide fields pertaining to groups, select Asset Groupings in the Display Menu.

Assign and Add Groups

Assign groups on the Inputs Worksheet.  Add a new group by typing the name in one of the cells of the Asset Group column.  Once a group has been added to the list, you can select the appropriate group for each asset from the drop down menu.  For instance, in the default sample case, the assets are assigned as either a stock or a bond.  Those two options appear in the drop down menu when a cell in the Asset Groups column of the Inputs Worksheet is selected.  You can select either of those, or you could type in a third group name instead, which would make that group appear in the drop down menu.

Using Groups

After assigning each asset to a group on the Inputs Worksheet, you can sort by groups in the Asset Selector, use the group column to guide your constraint application, or review results on the Portfolio Weights Pie and Portfolio Allocation Charts by group.  The very bottom of the Charts Worksheet also displays the results by group.

Optimization

Michaud optimization refers to the patented process used to find the Michaud Resampled Efficient Frontier™. Before you optimize, two steps are required. First, you need to choose how optimization will take place by reviewing and adjusting your options.  (The Info Worksheet provides a convenient review of your current selections.) Second, you must set up an investment problem.

After preparing an investment problem, initiate the optimization process by clicking the Optimize Button on the NFA ribbon.  The Optimizer begins to run the simulations necessary for resampling; a progress meter appears. This progress meter displays the progress of all steps that occur when you click the Optimize Button: running the simulations, averaging the simulations, etc. If you have multiple cores, progress made on alternate cores is displayed in a lighter blue.

When the simulations begin, a progress meter for the entire process appears at the bottom left. When the efficient frontier simulations begin, the NFA Optimizer Running Window appears with an optimization progress meter, a portfolio convergence measurement, and a Stop Button. When the More Button has been toggled, the optimization progress bar exhibits the convergence to the final Michaud Resampled Efficient Frontier on two simplified charts: an Efficient Frontier Chart (showing the Classical Markowitz Mean Variance Frontier, the converging Michaud Resampled Efficient Frontier, and a few of the simulated efficient frontiers) and a converging Portfolio Composition Map. At the end of optimization, the NFA Optimizer Running Window disappears, but the progress meter in the lower left indicates the remaining functions that the application must perform before you can see the results.  

For large and complicated optimization cases it can be beneficial to test the optimization on a small number of simulations. It is worth examining results to check that they make intuitive sense, i.e. assets with high returns and/or lower standard deviations or lower correlations should be receiving more portfolio weight. If this is not the case, check the constraints to make sure the weights are not being unintentionally coerced to unreasonable values. Constraint Analysis I is useful for this purpose. Remember that a limited number of simulations limits the usefulness of the results for anything other than a cursory review.

See Interpreting the Results for tools in understanding the optimal portfolios.  

For more information about Michaud optimization, visit New Frontier's website.

Forecast Confidence

Forecast confidence, also known as forecast certainty, indicates your confidence in the input investment forecast. (The forecast includes risk and return estimates, but not trading costs, quadratic penalties, or constraints).  Numerically it is on a scale with 0 representing no information (FC must technically be greater than 0, but 0.1 or greater is allowed), and 11 representing perfect confidence, i.e. Markowitz Classical Mean-Variance optimization. The numerical setting is displayed in the Forecast Confidence Field on the New Frontier ribbon.

The Optimizer relies on the forecast confidence level to determine the degree of dispersion of the resampling distribution and thus the variability among simulated efficient frontiers.  With a high level of confidence, generally 8 and above, the optimal portfolios resemble the classical and the rebalance test applies small statistical indifference regions and a narrow resampling dispersion.  This means that the rebalance test will be less tolerant of deviations from optimality and the confidence interval for portfolio weight ranges will narrow.  With a low level of confidence, the Optimizer applies large regions of equivalence and a wide resampling dispersion.  See the Information Correlation and Forecast Confidence description below for more information.

Toggle the Forecast Confidence drop down menu in the Optimize Section of the ribbon to adjust the confidence level.  You can also type in your forecast confidence, which permits you to enter a decimal point and specify non-integer values for forecast confidence.

If you set a classical confidence level (11), the Optimizer doesn't perform any simulations to correct for estimation error; you do not have to set the number of simulations in that situation.

The Ledoit Covariance Estimation option is enabled automatically when you have low forecast confidence in a case where the number of assets might exceed the number of simulated returns to determine resampled inputs.

Number of Simulations

The Simulations Field on the ribbon displays the number of simulations that the Optimizer runs during the optimization process.  The number of simulations is a very important optimization input.  Larger numbers produce more accurate approximations to the correct frontier portfolios for the given case, but take longer to run.  When building a case and experimenting, you may wish to use fewer simulations (50 to 100) for the sake of speed.  However, when the time has come to find the Michaud Resampled Efficient Frontier™ that you will actually invest in, run a greater number of simulations (1000+) to produce an accurate answer without any unnecessary simulation error.  The margin of error for each asset can be found in the Standard Error Column on the Results Worksheet.  Increasing the number of simulations will generally reduce the standard errors. We recommend making sure that the standard error for each asset is an amount that could be tolerated as error in the final portfolio. The greatest standard error appears on the progress bar as the optimization is running as the Portfolio Convergence statistic.

If you wish the Optimizer to automatically run enough simulations so that margin of error is below a specified number, use the Optimization Tolerance feature.

After optimization, both the number of simulations requested and the number of simulations run appear in the Simulations Run/Requested Field on the Info Worksheet.  If the numbers are different, something occurred to halt the optimization in the middle, probably you hitting the Stop Button on the progress meter.  Whether or not the simulations were completed, review the standard error of the asset weights to determine whether or not more simulations would be helpful.

If you select a classical optimization when you set the forecast confidence, the Optimizer ignores number of simulations as it only needs to run one simulation.

Related Topics:

Note: Rebalancing simulations is a separate field within the Rebalancing drop down menu.

Active Weight Optimization

You can choose to run an active weight optimization in order to optimize your portfolio's performance relative to a benchmark portfolio.  If you enable active weight optimization through the Options Menu, optimality is determined based on risk-return characteristics of the active weights of the portfolio, and the Optimizer displays portfolio risk and return relative to the benchmark.  To illustrate this, the benchmark portfolio always has active weights of zero for all assets.  In general, if the vector of absolute portfolio weights is given by p, the vector of benchmark weights is given by b, the vector expected absolute returns of assets by μ, and the covariance matrix of absolute returns by Σ; then the active weights of a portfolio are given by p-b, the active return of the portfolio is μ' * (p-b), and the active variance is (p-b)' * Σ * (p-b).  Active standard deviation, more commonly called tracking error, is the square root of the active variance.

For example, an initial portfolio with a 7% absolute return changes to a 0% active return when active weight optimization is employed, given that the benchmark portfolio has a return of 7%. However, the risk transformation is not so straightforward. If a portfolio and the benchmark both have a 10% standard deviation, the active risk of the portfolio might be anywhere from 0 to 20% depending on the cross-correlation between initial and benchmark portfolios. Furthermore, very low risk assets in absolute terms can become highly risky relative to the benchmark.

When active weight optimization is enabled, the following conditions occur:

 

Options Strategy

Options strategy allows simple one-period rolling put and call options to be assigned to assets.  This is a very powerful feature and can lead to drastic changes in portfolio allocations.  Option-based allocation, like any asset allocation, should be approached cautiously and thoughtfully.  The technology behind this feature is pending US patent approval.  This feature is in beta testing, so please send us your feedback.  In order to ensure that options are used properly, the feature requires a key update.  Contact your relationship manager for a license update.

Substantial knowledge of options trading is assumed here, but in order to standardize terminology going forward, we provide the following basic definitions:

Put options are contracts that, when bought, guarantee an investor the right, but not the obligation, to sell a covered portion (at a fixed coverage rate) of an asset’s holdings at a guaranteed fixed strike price on or before a fixed date. Buying a put at a low strike price is like an insurance policy against the asset’s price falling below that price.

Call options are contracts that, when bought, guarantee an investor the right, but not the obligation, to buy a covered portion (at a fixed coverage rate) of an asset’s holdings at a guaranteed fixed strike price on or before a fixed date.

The type of options allowed in the Optimizer can be thought of as applying to every simulated or real return.  When such an option is purchased, it will always be exercised according to its coverage when the corresponding return falls beyond its strike price.  Thus, these are one-period options renewed at each period or some other long-term contract with similar payout characteristics. Strike prices are expressed as annualized returns in the same units as the forecasts.  Coverage indicates what percentage of the asset is covered by the option.  So, when the price is outside of the strike price, exercising the option means that the covered percentage will be at the strike price and the remaining percentage will be unaffected by the option.  Options like these fit well into the simulation framework of the Michaud Resampled Efficient Frontier.  The Optimizer currently can accept any level of coverage on a single put and/or call option for each asset, with user-input cost and strike price.  Options with longer periods or multiple overlaid puts or calls are not currently implemented.

Options are activated through by enabling Options Strategy in the Advanced Options sub-menu of the Options Menu in the Optimizer ribbon.  When activated, the blue Optimization Options bar indicate that options are enabled and additional columns appear on the Inputs Worksheet.  Enter data for puts and calls.  

Optimization proceeds with option overlays much the same as without.  However, drastic changes in allocations may result from option overlays, as the risk inherent in an asset is clipped from above or below.  A formerly risky equity, for example, may behave more like a bond when puts and calls are taken out to eliminate the tail risk of the equity.  Options overlays can produce some curious results. The displayed frontier may fold back on itself to produce multiple portfolios with the same level of nominal risk.  We leave it to the user to determine the appropriate use of these portfolios.

A Note on the Classical M-V Frontier

When classical frontiers are requested from the optimizer, the simulation framework which provided a natural framework for calculating allocations with options is no longer available.  The classical frontier calculation requires only a set of means and variances, so the means and variances adjusted for any existing option overlays are  recalculated within the software.  This can be done analytically or through Monte Carlo, and depends on the choice of resampling function (normal, T, or 4-moment resampling). Currently, the Monte Carlo solution is implemented, with a high number of simulations to ensure convergence.  Non-normal resampling distributions such as T or 4-moment with greater skewness or excess kurtosis will generally put more probability mass on certain extreme returns for which options are exercised, thus more drastically altering the behavior of the assets and the resulting portfolio.

How Means and Variances are Affected

There are two types of means and variances with option overlay.  Applying an option will not affect the return on an asset. Thus the return observed on the asset price remains the same with or without the option overlay.  However, the holder of the portfolio with the option has a guaranteed return and risk which is different from the nominal returns of the portfolio of assets. We refer to this as the portfolio means and variances, as opposed to the asset means and variances.

All reference portfolios are assumed in the software to be option-free, so the reference portfolio means and variances will reflect only asset means and variances.  Similarly, individual assets, when plotted on a mean-variance frontier diagram, are plotted with their option-free means and variances.  The optimal frontier, classical frontier, and simulated frontier portfolios will all be displayed with options-included means and variances.

Calculating the Value of an Option

The cost of returns are calculated as follows:  result mean = simulated mean - put cost * put coverage - call cost * call coverage + put coverage * (put strike - min (put strike, simulated mean)) + call coverage * (max (call strike, simulated mean) - call strike) = simulated mean - coverages * costs associated with buying options + coverages * difference in prices if options are exercised.

Example 1: 50% coverage on a call at +5% strike price, cost of 2%

Raw Simulation: 3%  Adjustment: 3% - 50%*2% = 2% (Pay 1% for option not exercised)

Raw Simulation: 6%   Adjustment: 3% - 50%*2% + 50%*(6%-5%) = 2.5% (Pay 1% for option, benefit of 0.5% from option exercise)

Raw Simulation: 10%  Adjustment: 3% - 50%*2% + 50%*(10%-5%) = 4.5% (Pay 1% for option, benefit of 2.5% from option exercise)

Example 2: 50% coverage on a call at +5% strike price, cost of 2%;  80% coverage on put at -3% , cost 2%)

Raw Simulation: 3%   Adjustment: 3% - 50%*2% - 80%*2% = 0.4% (Pay 1% for call and 1.6% for put)

Raw Simulation: -6%    Adjustment: 3% - 50%*2% - 80%*2% + 80%*(-3% - (-6%)) = 2.8% (Pay for options as above and get 80% of difference between -3% and -6% for exercise of put option)

Raw Simulation: +10%  Adjustment: 3% - 50%*2% - 80%*2% + 50%*(10%-5%) = 2.9% (Pay for options as above and get 50% of difference between 10% and 5% for exercise of call option)

Unsupported Features

Please remember that this feature as a whole is relatively new and extremely powerful. Caution is strongly recommended when using this new technology for investment purposes.

Tolerance

Tolerance, the simulation error tolerance, is an alternative to choosing the number of simulations for controlling the precision of the solution. To implement, enable Optimization Tolerance in the Advanced Options sub-menu within the Options Menu, then enter the desired maximum standard error in the Tolerance Field in the ribbon. The Optimizer will run simulations until that standard error is met  as shown on the Portfolio Convergence statistic on the progress bar. A 1% standard error provides a rather rough solution. New Frontier recommends starting experimentation with 1% and narrowing it down to 0.5% or even 0.1% for investment purposes. Note that an optimization with a 0.1% tolerance may require many simulations, take a long time to complete, and even cause out-of-memory errors on some computers.

If the Rebalance Simulations Field is set to N/A, enabling optimization tolerance automatically sets the number of rebalance simulations to 500.

Rejection Sampling

Rejection sampling is designed to measure certain characteristics of each simulation in the resampling procedure, and replace them with new simulations if they fail a test. This test measures the filter score of the maximum return portfolio. Normally the filter is set up so that the higher risk assets, perhaps the stocks, obtain higher scores when the total portfolio weight of these assets is greater. If a particular simulation assigns a greater expected return to an asset which does not add to the filter score, this simulation may not attain a high filter score at the top of its frontier, since the optimal assets to load on for that frontier do not add to the filter score. This could be construed to mean that the simulation in question is “upside down”, i. e. assigns more attractive inputs to assets which are less attractive in the main inputs.

The rejection sampling feature will replace simulations whose maximum filter scores (at the top of the frontier) are less than a specified threshold with new simulations that attain a filter score greater than or equal to the threshold. This means that all of the simulations will be “pointing in the same direction,” at least with respect to the filter score metric. Under many circumstances this can increase the out-of-sample performance of the Michaud optimal portfolio.

Rebalancing Test

Rebalancing should only take place when the optimal portfolio is testably distinct from the current allocations. This policy limits unnecessary trades and their attendant costs. New Frontier's second patented process, the rebalance test, helps you determine when rebalancing is necessary.  

The underlying theory for the calculations appears in "Portfolio Monitoring in Theory and Practice" (Journal Of Investment Management Q3 2012, available in draft form on the New Frontier website).  

Rebalancing Section of the Ribbon

Rebalance Probability (Results)

The rebalance probability or score is a comparison of the distance (tracking error/relative variance) between one portfolio and an optimal portfolio to the distances of statistically equivalent alternative optimal portfolios from the same optimal portfolio. Specifically, the rebalance probability is the rank of the distance of the initial portfolio from the optimal, among the distances of the optimal portfolio from a set of meta-resampled (statistically similar) optimal portfolios with the same portfolio rank, or the same filter score if filter matching is enabled. A rebalance score of 100% means that all of the portfolios simulated during the rebalance test fall closer to the target optimal portfolio than the portfolio with the 100% rebalance probability does, which is quite strong evidence that the portfolio is not optimal, at least for the targeted risk or return as indicated by the selected optimal portfolio in the rebalance test. As the rebalance probability decreases, the two portfolios become closer to one another. So, a high rebalance percentage indicates that rebalancing could be beneficial. The Optimizer highlights especially high rebalance probabilities, above 80%, by coloring the selected portfolio's rebalance probability red on the Results Worksheet. Similarly, green signals an especially low rebalance probability in which rebalancing is unlikely to be helpful, from a statistical perspective.  

Viewing Results

The rebalance probability appears in charts and tables:

Trade Advisor works with the rebalance test to help you decide how to trade if a full rebalance to optimal is undesirable. This feature can ensure that a low rebalance score is maintained under partial trading.

 

Trade Advisor

The Optimizer finds optimal portfolios, indicates when you should trade, and now advises you on how to trade. Subject of our latest patent application, the separately licensed Trade Advisor offers guidance as to what trades most efficiently bring your held portfolio closer to a targeted optimal, filtered, or directly input portfolio. In the case of a targeted portfolio on the efficient frontier with a corresponding previously run rebalance test, it also calculates rebalance scores, thus laying out the trades with minimum turnover necessary to reach a portfolio that is statistically equivalent to the targeted portfolio. (For information about using the Trade Advisor with investable portfolios, see the Trade Advisor and Post-Optimization topic.)

How to Use the Trade Advisor:

  1. Optimize and run the rebalance test first for best results.

  2. Access the Trade Worksheet and Trade section of the NFA ribbon by enabling the Trade Advisor in the Worksheet Section of the Display Menu.

  3. Choose a held portfolio (either initial or reference) from the Choose Held Portfolio drop down menu in the ribbon, or complete the column manually. The held portfolio is the starting point for the trade advice. If you enter the portfolio manually, the weights should normally sum to 100%. Otherwise a jump will appear between the held and first advised portfolios since all the advised portfolios are constrained to sum to 100%.

  4. Select a target portfolio.

    • Choose the portfolio type from the drop down menu: direct input, a portfolio from the optimal frontier, or a reference portfolio.

    • If you chose optimal, use the slider to target the desired portfolio or type the desired portfolio rank in the cell beneath the slider and above the portfolio weights.

    • If you chose direct input, enter asset weights of the desired portfolio in the Target Portfolio column.  The portfolio should normally sum to 100%.

  5. To find trades which simply minimize turnover for a given tracking error or rebalance property, leave all of the entries in the Relative Trading Cost column at 100%. To prioritize trading of an asset, lower this number, and to discourage trading, raise the number corresponding to the asset in question. Note that this column replaces the "Constrain to held" column from versions of the AAS prior to 6.6, which did not allow for prioritizing an asset.

  6. Select a portfolio on the trade advice frontier. There are three criteria you can use to select a portfolio.  After you do so, the Trades column displays the differences from the held portfolio and the Advised Portfolio column shows the selected portfolio.

    • Turnover Percentage: Use the turnover percentage slider in the Advised Portfolio column, or enter a turnover percentage in the cell beneath the slider, to select the portfolio with the turnover percentage closest to your input percentage.

    • Tracking Error: Enter the desired tracking error in the field at the bottom of the page to select the portfolio with the tracking error closest to your input tracking error.

    • Rebalance Percentage: Enter a rebalance probability in the cell beneath the slider to select the portfolio with the rebalance probability closest to your input probability.

  7. Sometimes the minimum turnover minimum tracking error path to the target portfolio is such that one or more portfolio weights travels outside of the interval bracketed by the held and target portfolios. Trading to such a portfolio and subsequently trading to optimal will incur more total turnover than trading directly to optimal. If you wish to disallow trades with weights outside held and target, check the Enforce Trade Bounds box in the ribbon.  All advised portfolios then will have asset weights bounded by held and target asset weights.

  8. Interpret results. The Advised Portfolio Composition Map appears to the left, and the Advised Portfolio Statistics plot, a plot of the tracking error against turnover, appears to the right. If the target is an optimal portfolio and a valid rebalance procedure has been run, the rebalance score for each portfolio on the trade advice frontier will also be plotted in the right graph.

  9. Once you have the Trade Advisor set up, you can run it with the Robot if you have that licensed.

What the Trade Advisor Does:

The Trade Advisor finds the set of portfolios which minimize turnover, or total relative trading cost, for given tracking error from the target portfolio between held and target, or equivalently, which minimize tracking error from the target portfolio for given turnover, or total relative trading cost, between held and target. This produces a frontier of portfolios which are efficient in the sense of solving the optimization problem which we call the trade advisor frontier.

Technically, Trade Advisor performs a calculation having the form of a Markowitz mean-variance optimization. The quadratic component of the Trade Advisor’s optimization criterion is identical to the squared tracking error from the target portfolio. This is convenient since the Michaud-Esch rebalance score is a monotone function of this quantity, when the target is a portfolio on the Michaud efficient frontier. In that case, if the Michaud-Esch rebalance procedure has been run, rebalance scores are available for the entire trade advisor frontier. The software then plots the rebalance scores for the frontier in a separate chart, and displays the score for the selected trade-advised portfolio. When the target is a Michaud-efficient optimal portfolio, the Trade Advisor shows the minimum turnover portfolio that passes the rebalance test. Because of the nature of positivity-constrained Markowitz optimization, the trade path breaks the trades into separate components, and often many assets will not need to be traded to achieve optimality in a statistical equivalence sense. This property is useful to client management in recommending only a few trades to bring the client portfolio back into line with minimal operational complexity. Managers may prefer to go a little further on the trade advisor frontier towards the target to push the rebalance score below the threshold and leave room for drift so the portfolio stays in the “optimal zone” for a longer period of time. Choosing a suitable trade target is at the discretion of the manager, but the Trade Advisor can be helpful in showing the most efficient path to Michaud optimality.

Additional flexibility is provided to the manager using Trade Advisor with the Enforce Trade Bounds checkbox and Relative Trading Cost column. The Enforce Trade Bounds checkbox adds upper and lower bounds at the upper and lower of the held and target portfolio weights for all assets not constrained to the held weights, and the Relative Trading Cost column can prioritize or deprioritize the trading of assets relative to others. The Enforce Trade Bounds feature is useful when designing an incremental trading strategy for the client. It is occasionally possible for some asset weights on the trade advisor frontier to be larger or smaller than their weights in either the held or target portfolio. If the goal is to ultimately have the client hold the target portfolio exactly, the manager may not wish for a partial rebalance which moves asset weights further away from those in the target portfolio, as such trades will have to be undone in remaining rebalances, incurring unnecessary round-trip trading costs. In such instances, Enforce Trade Bounds will be useful in order to ensure that all asset weights move in the direction of the target portfolio’s asset weights, and never in the opposite direction.

Trade Advisor and the Rebalance Test:

The Trade Advisor shows the fastest trading path to statistical optimality as determined by the rebalance test. The "fastest trading path" is defined by total relative trading cost, or turnover if all the relative trading costs are equal. The optimization within the trade advisor minimizes the tracking error for optimal for a given turnover/total relative trading cost. Since tracking error from optimal also determines the rebalance score, the need-to-trade score is also shown on the trade advisor graph, keyed to the axis on the right-hand side. Rebalance scores can be especially useful in determining a threshold for trading on the trade advisor frontier. This could be used to design a policy to keep the portfolios under a particular score at all times via regular monitoring the score in tandem with judicious trading and partial trades determined by the trade advisor. These types of policies must be determined appropriately for each strategy by the manager.

Trade Advisor and Post-Optimization

The Trade Advisor offers guidance as to what trades most efficiently bring your held portfolio closer to a targeted portfolio. Additionally, it allows the application of investabilty constraints similarly to the postoptimize algorithm, i.e., results subject to threshold and interval constraints, as well as any other investability constraints, including asset anchoring but not including any turnover constraint, as turnover forms the horizontal axis of the trade advice frontier.  In other words, the results sought by establishing a turnover constraint are the same as exacting the trade advice for that particular turnover setting. The threshold and interval constraints can be applied relative to the held portfolio (trades will obey interval and threshold constraints), or in an absolute sense (trade advised portfolios will adhere to these constraints). 

To switch to Trade Advisor with the investability constraints, select the Enable Investability Constraints Option within the Trade Menu.  To choose whether the investability constraints will be applied relative to the held portfolio or to zero, pick Absolute or Relative to Held from the Select Investability Constraint Type sub-menu.

Since the computation for postoptimized Trade Advisor is considerably slower than for the non-postoptimized version, computation does not take place until the Calculate Button within the Trade Menu is clicked. A progress bar indicates the progress of the computation.

All of the settings that normally apply to postoptimize apply to postoptimized Trade Advisor as well, as do the preferences for time limit on each portfolio in the Trade Advisor frontier.

Filter Matching

The filter Matching feature is a new and experimental feature that applies only to the rebalance test. It is useful for making sure that a rebalance test only compares against simulated alternative portfolios with the same filter scores.

When executing a rebalance test, the tracking error (relative variance) of the portfolio being tested against an optimal frontier portfolio is compared with the tracking error (relative variance) of portfolios from simulated alternative Michaud frontiers, created with perturbed alternative outputs. Normally these alternative efficient frontier portfolios are selected by associating portfolio rank, e. g. if the optimal portfolio point was portfolio 31 by arc length on the Michaud frontier, the simulated alternative frontier points for comparison will also be portfolio 31 by arc length on their corresponding efficient frontiers.

However, when filter matching is enabled, the alternative frontier portfolio is selected by matching the filter score. This means that in the rebalance test, the tracking error between the portfolio being tested and an optimal portfolio will be compared to tracking errors between that optimal portfolio and simulated alternative portfolios with the same filter scores, or the nearest available if no portfolio exists on the alternative frontier which exactly matches the filter score. This can be useful when the filter score is used to select the optimal portfolio for a particular strategy, and may help tame the alternative tracking errors and boost the rebalance signal at the top of the frontier where sometimes the rebalance signal is weak, especially in cases with non-homogenous assets such as multi-asset-class models.

This feature can be useful for certain cases to calibrate the relative sensitivities of rebalance tests across multiple strategies on the same frontier. Many cases may show little difference in the rebalance probabilities generated with or without this feature, but in certain cases, the normally more sensitive lower risk strategies can be made less sensitive relative to the upper strategies with this feature on. In these cases all strategies may be less sensitive in absolute terms, which can be corrected by adjusting the typical rebalance periods to a lower number, thereby lowering the relative variances between simulated alternative frontiers and the main optimal frontier, and increasing the sensitivities of all rebalance tests across the frontier. Clearly a lot of calibration is necessary to determine the operating characteristics of a rebalance test and the correct settings.

Loading and Saving Relative Variance Tables

Saving and loading a lookup table for the rebalance test can save considerable time, allowing the user to bypass the lengthy simulation process normally involved in running the rebalance test, and simply use the rebalance portfolios feature to quickly recalculate the rebalance probabilities. This feature also allows the user to run a more precise test with more simulations, since the compute-intensive part of running the test can be precalculated.

Exporting/Saving a Relative Variance Table

In order to save a table, you must first run a rebalance test normally with the desired settings and number of simulations. Only then is it possible to export a file in comma-separated-value text format. This file will be saved with a .nfrv (New Frontier Relative Variance) extension. Under the Save Menu in the File Section of the Optimizer ribbon, select the icon labeled "export relative variances" to export the file. This file then can be loaded to bypass the usual rebalance test workflow and go straight to rebalancing portfolios, a compute-efficient procedure that consists of calculating the relative variance of the portfolios to the new optimal frontier, and comparing this calculation to the pre-loaded table rather than separately computing a new table for comparison.

Loading a Relative Variance Table

To load a previously saved .nfrv table, select the Load Relative Variances option from the Load Menu in the File section of the Optimizer ribbon. Then select the file in the dialog box and click the Open Button to load the file. The relative variance table will then be loaded and "rebalance portfolios" will be enabled in the rebalance menu.

A note about Asset Bound Confidence Intervals and Loading Tables

One by-product of the normal calculation of the rebalance test is to provide more accurate portfolio bounds than the quick computation that results from the optimization procedure. However, upon loading a relative variance table, these more accurate bounds are not available, so the bounds calculated from the optimization procedure are shown instead.

Charts Worksheet

The Charts Worksheet provides analysis and direct comparison.  Select the portfolios to compare at the top of the worksheet.  The Portfolio 1 drop down menu offers either the optimal or investable portfolios on the Michaud Resampled Efficient Frontier™.  Use the Portfolio Control Slider to select the particular portfolio; the rank of the selected portfolio along the efficient frontier appears to the right.  (The rankings depend on the number of frontier portfolios you have set.)  Optionally, select another portfolio for contrast in the Portfolio 2 drop down menu and slider.  For reference portfolios, utilize the drop down menu that appears to select the specific reference portfolio.  The initial and benchmark portfolios are static.  Stored results and filtered portfolios can also be analyzed.

As soon as two portfolios are selected, the Charts Worksheet populates for the selected portfolio(s).  The risk, return, information ratio, and yield for the two selected portfolios populate the top of the worksheet.  The rebalance probability appears when applicable.  If non-normal resampling is enabled, the skewness and kurtosis appear there as well.  A table at the bottom of the worksheet compares the asset weights of the two selected portfolios, accompanied by an iteration of the assets' returns, standard deviations, standard errors, and information ratios.  If you used the basic tax optimization method, these numbers are tax-adjusted. If the Add Quadratic Risk Penalty to Risk option has been selected in the Display>>Charts Menu, standard deviations will be calculated to include the quadratic risk penalty. At the very bottom of the worksheet, a table splits the assets by group.  To the side of this table, the Asset Ranges Table indicates the significance of each asset allocation.  The Percentile Field similarly indicates significance.

Select the following charts from the Chart Type drop down menu:

You can edit all of these charts using Excel functionality.  To view the numbers used to produce the charts, access the Data Worksheets.

Editing Charts

All of the charts included in New Frontier's applications can be edited using Excel's chart editing tools.  Add legends, change colors, switch axes, edit the title, include additional labels, etc.  Right click with either the entire chart or part of the chart selected depending on what you want to format.  A menu appears.  Select options such as Format Data Series, Chart Options, etc.  See an Excel manual for details.

Portfolio Weights Comparison Charts

The Portfolio Weights Comparison Charts appears on the Charts Worksheet.  Once you select Portfolio Weights Comparison from the Chart Type Menu, two submenus appear.  The first allows you to pick between displaying assets or groups of assets.  The second lists different types of comparison charts: bar, stack, pie, and doughnut charts.

Each of these charts compares the weights allocated to each asset or group in the two selected portfolios. For instance, if you select optimal in both Portfolio 1 and Portfolio 2, you can compare two different optimal portfolios to see how the portfolios change as risk increases.  Or select an investable portfolio and an optimal portfolio at the same risk level to see how the allocations changed when you post-optimized.  There are many possible analyses to perform with these tools.

Portfolio Bounds Line Chart

The Portfolio Bounds Line Chart appears on the Charts Worksheet.  It shows the selected percentile bounds for each asset weight in the selected optimal portfolio to facilitate determining significant results.  Check the box at the top left corner of the chart to force the axis to end at 100%.

Proper bounds should be constructed from Michaud Resampled Efficient Frontiers generated from statistically equivalent inputs.  Calculation of a separate resampled frontier for each simulation requires meta-simulation, which is performed during the rebalance test.  In order to streamline the workflow, this meta-resampling is removed from the first optimization pass when the Optimize Button is pressed.  Thus, the intervals shown after an optimization are a fast approximation and not precise.  These intervals will normally be substantially wider than the intervals produced after the second step and should not be taken literally as confidence ranges for the asset weight.  These intervals should be taken to show the operating characteristics of the simulated optimizations in the resampling process. Also note that loading a relative variance table for the rebalance test will bypass the meta-resampling stage of the computation, so that the more accurate intervals will be unavailable. The fast-approximated intervals will be shown instead when relative variance tables are loaded instead of a full meta-resampling computation of the rebalance test.

After a rebalance step, the intervals will reflect the overlapping data or information between initial and optimal portfolios as entered in the Typical Rebalance Periods Field in the Rebalance section of the ribbon and can be interpreted as valid confidence intervals for the portfolio weights.  However, each interval is a test on its own, so at the 50% confidence level, only half of the assets would be expected to be within the bounds under the null hypothesis of statistical equivalence of initial and optimal portfolios.  A better and statistically valid indication of global portfolio significance is found from the result of the rebalance test.

One peculiarity of the Excel implementation of interval graphs is that the central value of each interval must lie within the outer two values.  Because of the skewed distribution of portfolio weights, the mean of all the simulations can easily be outside of the quantiles, when the upper tail of portfolio weights is long.  Excel displays this case by extending the interval limit to the value.  Thus, for example, a quantile range of 10%-20% with a portfolio weight of 25% will be shown as an interval of 10%-25% with the central value of 25%.  The distinct behavior of mean versus quantiles combined with Excel's extension of all intervals to contain the mean can occasionally explain some curious-looking intervals.

Efficient Frontier Chart

The Efficient Frontier Chart, which appears on both the Results and Charts Worksheets, displays the Michaud Resampled Efficient Frontier™ and additional data according to your preferences. The Display Box to the right of the chart provides numerous options that can be added to the chart. Checking a display option on either the Results or Charts Worksheet causes that option to activate or inactivate on both worksheets.  

If a segment of the frontier appears in red, this means that the maximum return portfolio is not at the end of the frontier, and the red segment is actually lower in expected return than the maximum return portfolio, which is at the point where the transition from blue to red occurs.

 

By default, the chart plots the Michaud Resampled Efficient Frontier in blue on the axes measuring standard deviation (horizontal) and expected return (vertical). A legend with checkboxes that can be checked or cleared to enable or disable additional elements on the chart appears to the right.  The table below details those checkboxes.

Selected Portfolio

the optimal portfolio currently selected in the Selected Column of the Results Table (Results Worksheet) or in the portfolio selection section of the Charts Worksheet. If Show Standard Deviation Confidence Intervals is selected in the Charts Menu in the Display section of the Optimizer Ribbon, a horizontal bar showing the confidence region for the risk of the selected portfolio will appear on the graph, with confidence limits set according to the selected percentile bounds in the Options menu in the Case Settings section of the Optimizer Ribbon.

 RE Simulations

A scatter plot of the individual resampled portfolios appears in light blue.  After a rebalance procedure is run, the meta-resampled portfolios appear in purple.

This option helps to display the degree of variation among the alternative simulations.  After rebalancing, the points are typically in a tighter arrangement around the parent frontier points.

You can adjust the number of points displayed in the Preferences Menu.

You can switch between the simulations corresponding to the entire frontier and those only corresponding to the selected portfolio in the Display--Charts Menu.  The one-portfolio display is more informative in showing where the simulated equivalent portfolios are landing on the mean-variance chart, since they are no longer mixed in with simulations from other points on the frontier. After a rebalance procedure is run, the meta-resampled points are typically in a tighter arrangement around their parent frontier points, especially when typical rebalance periods are set to a small number. The cloud display on the efficient frontier chart shows simulations coming from a meta-resampled rebalance procedure in purple, instead of the light blue color used for optimization simulations.

Assets

the risk and return position of each individual asset
If basic tax optimization is enabled, the assets' positions on the chart are tax-adjusted.

Initial Portfolio

the initial portfolio's risk and return position

Reference Portfolios

the risk and return position of each reference portfolio

Result Portfolios

the six representative optimal portfolios displayed on the Results Worksheet, if you change the selections in the table below, the result portfolios change

Rebalance Test

the rebalance probability graph overlay
Note that the rebalance probability is graphed with respect to the vertical axis on the right (0-100%), not the left vertical axis (return).

Classical Frontier

the classical mean variance efficient frontier

Multiperiod Frontier

the efficient frontier over the multi-period horizon selected on the Inputs Worksheet

Stored RE Frontier

the efficient frontier stored during a previous optimization (Store Results option in the Edit Menu)

Max SR Portfolio

the maximum Sharpe ratio portfolio

Filtered Portfolios

the position of each of the portfolios that result from filtering
Yield

the yield of each optimal portfolio from the optimal frontier, if yield has been activated

If you have checked the Show Standard Deviation Confidence Intervals Option in the Charts Menu in the Display Section of the ribbon, confidence intervals appear around the standard deviation of the selected portfolio on the Efficient Frontier Chart. (To adjust the confidence interval limits, change the percentile bounds in the Options Menu.  Also, you may need to re-run the optimization to calculate these intervals in order to enable them after an optimization is run without them.) This feature facilitates analysis of the standard deviation of the optimal portfolios, but disabling this option speeds up the optimization.

If you are using Quadratic Risk Penalties, the standard deviation calculations for this chart are affected by whether or not the Add Quadratic Risk Penalty to Risk option in the Charts sub-menu within the Display Menu on the ribbon is enabled.

Portfolio Composition Maps

Portfolio Composition Maps display the allocations along an efficient frontier. Each color represents a particular asset class. A vertical slice on the left of the composition map portrays the composition of a low risk portfolio.  A vertical slice on the right of the composition map portrays the composition of a high risk portfolio. The height of each asset's color segment equals that asset's portfolio weight at the risk level from which the slice is taken. Composition maps illustrate the changing portfolio make-up across the frontier.

The order of the assets in the composition map mirrors the order in the Inputs Worksheet. Sorting the assets there or in the Asset Selector changes the order in the chart.

Three varieties of Portfolio Composition Map are available in the Optimizer. All three are available on the Charts Worksheet. If you select the Portfolio Composition Option from the Chart Type drop down menu, an additional drop down menu appears. The two "Stored" options display either the optimal or investable results stored to the clipboard.

Rebalance Probability Chart

The Rebalance Probability Chart displays the rebalance probability for the initial portfolio or reference portfolio against each optimal portfolio along the Michaud Resampled Efficient Frontier.  Select the Rebalance Probability Option from the Chart Type drop down menu on the Charts Worksheet.  A vertical gold line shows the risk of the current portfolio selection and a red dot marks the rebalance probability of the optimal portfolio selected as Portfolio 1.  If the reference or initial portfolio selected is not too far from the optimal frontier, you will notice that the rebalance probability is generally close to 100% and dips down for a range of values close to the target risk level of the optimal portfolio. The width and depth of this dip depends on the individual characteristics of the case.

Portfolio Risk Contribution Charts

Portfolio standard deviation can be decomposed into component risk contributions for each asset in the portfolio. These risk contributions can then be displayed in a stacked bar chart for an entire efficient frontier (map chart), or a bar chart comparing two selected portfolios (bar chart). Both charts appear as options on the Charts Worksheet.

Mathematics

The standard deviation of an N-asset portfolio P with weights w = {wi } i = 1,…,N, and assets Ai and covariance matrix Σ, with elements {σji } is defined as √(w' Σw)=(w' Σw)/√(w' Σw)=w'{Σw/√(w' Σw)}.

The vector MCR=Σw/√(w'Σw) is called the vector of marginal risk contributions.  It can be shown that the ith component of this vector is equal to the following:

 {Σw/√(w' Σw)}i=(∂σ(P))/(∂Ai )=corr(Ai,P)σi.

Thus, the risk contribution of the ith asset to the portfolio P can be expressed as wi MCRi = wi∙corr(Ai,P)∙σi, although it is far more convenient in practice to compute it using the formula (∑j [σji wj])/√(w'Σw).

More Information

Menchero, J. and Davis, B. (2011) “Risk Contribution Is Exposure Times Volatility Times Correlation: Decomposing Risk Using the X-Sigma-Rho Formula.” Journal of Portfolio Management. 37(2): 97-106.

Menchero, J., and Hu, J. (2006). “Portfolio Risk Attribution.” Journal of Performance Measurement. 10(3): 22-33.

Saving

Please note that options and settings that affect the results of a case are always stored with the corresponding case file.  Other options, such as display options, are stored locally for each user.

Access the Save Data File Window by selecting the Save As Button in the File Section of the NFA ribbon.

To save a complete case, select the OptimizerInfoFiles Option in the Save Data File Window.  Navigate to the appropriate folder.  Enter a name for the saved Optimizer case.  Click the OK Button.  The case (*.nfoi) saves to the designated folder and remains open.  The file compresses as it saves according to your preferences.  Be aware that changes to the Reporter Worksheet do not save in the NFA format.  A complete case includes the investment universe, portfolios, constraints, any results, and the current portfolio selections on the Results Worksheet.

To save transaction costs, select the Transaction Cost Files Option from the Save As Type drop down menu in the Save Data File Window. Navigate to the appropriate folder. Enter a name for the saved transaction costs. Click the OK Button. The transaction cost (*.nftc) saves to the designated folder.

To save a portfolio, select the Portfolio Files Option from the Save As Type drop down menu in the Save Data File Window. Navigate to the appropriate folder. Enter a name for the saved portfolio. Click the OK Button. The Choose Portfolio Window appears. Select the portfolio that you wish to save: reference, initial, optimal, or benchmark. If you wish to save a reference or optimal portfolio, select the appropriate portfolio name/number from the drop down menu. Click the OK Button. The portfolio (*.nfp) saves to the designated folder.

To save a model portfolio set, select the Model Portfolios Option in the Save Data File Window. Navigate to the appropriate folder.  Enter a name for the saved set. Click the Save Button. Select the desired portfolios from the window that appears.  You can select up to six portfolios. Name the portfolios if desired. Click the OK Button. This file format saves the selected portfolios as well as the efficient frontier. If loaded to LifeCycle, the model portfolios appear as named options along the efficient frontier.  

Alternately, pick the Model Portfolio Comma Separated Value Files Option. This option permits you to make changes to the portfolios before loading them in to LifeCycle, which can be useful when you're working with a short-term optimization, yet want to explore the long-term implications in LifeCycle. Navigate to the appropriate folder. Enter a file name. Click the Save Button. Select the desired portfolios in the window that appears. Name them if you wish. Click the Ok Button. This saves two CSV files for importation to Optimizer.

To save a constraint set, select the Constraint Files Option from the Save As Type drop down menu in the Save Data File Window. Navigate to the appropriate folder.  Enter a name for the saved constraint set (*.nfcs). Click the Save Button. Constraint sets (*.nfcs) include asset bounds, customized constraints, quadratic risk penalties, investable asset bounds, and investable customized constraints.

To save investable constraints, select the Investable Constraint Files Option from the Save As Type drop down menu in the Save Data File Window. Navigate to the appropriate folder. Enter a name for the saved investable constraint set (*.nfic). Click the OK Button. Investable constraint sets (*.nfcs) include asset thresholds and asset increments.

To save default constraints, click the Save Default Constraints Button on the Constraints Worksheet (or Investability Constraints Worksheet). The current default asset bound, transaction cost, investable asset bound, asset increment, and asset threshold constraints save to a clipboard. Clicking the Apply Default Constraints Button returns the most recently saved default constraints to the Optimizer and applies them to the current asset set.

To save an efficient frontier within the Optimizer, select the Store Results Option in the Edit drop down menu. This stores the current efficient frontier to a clip board for comparison against a future case.

To save in Excel, access the Excel saving functionality. If you have enabled the Warn Before Attempting to Save in Excel Option in the Preferences Window, a ConfirmDialog Window appears. Though saving in Excel is supported, there are several limitations. First, future versions of the Optimizer may not open the case correctly. Second, cases saved in Excel contain only what is included on the Inputs Worksheet. Any assets currently removed from the investment universe in the Asset Selector do not save in Excel cases.  

To export a tax lot file, select the Export Tax Lots Option from the Taxes Menu. This saves the tax lots information in a CSV file.

To export a relative variance table, select Export Relative Variances from the Save as Menu. Navigate to the appropriate folder. Enter a name for the exported relative variance table (.nfrv). Click the Save Button. A saved relative variance table is a comma-separated text file with the numerical values of the relative variances, used for the rebalance test. Loading this saved table enables the Rebalance Portfolios command in the Rebalance menu, allowing the user to bypass the compute-intensive rebalance test meta-resampling step.

You can also move directly to LifeCycle.

Moving to LifeCycle

LifeCycle is the NFA financial planning software included in the Asset Allocation System.  Moving an Optimizer case into LifeCycle permits you to examine its multi-period implications.  Depending on what you are doing, any of the options below could be helpful for moving your efficient frontier into LifeCycle.

Results Worksheet

Optimization results appear in the table on the Results Worksheet.  The Optimizer calculates the Michaud Resampled Efficient Frontier as a numbered set of separate optimal portfolios, where 1 represents the minimum risk portfolio. (The total number of portfolios on the frontier can be adjusted through the Options Menu.) The default version of the Optimal Portfolios Section of the Results Table displays six of these optimal portfolios, moving up the efficient frontier in equally-spaced increments of expected return, frontier arc length, or standard deviation as possible, depending on what is selected in the Options Menu. These representative portfolios permit you to review the return, risk, information ratio, yield (if entered), and rebalance probability for portfolios along the efficient frontier in order to narrow down the range of optimal portfolios that best meet your needs.  Focus return, standard deviation, or rank by selecting the appropriate radio button to the left, which copies that particular row immediately beneath the header for easier review. Use the slider in the Selected Column to obtain information about one of the other portfolios on the efficient frontier.

Results Table

Choose representative portfolios other than the six that automatically appear by entering either a return, standard deviation or rank (depending on which is currently selected in the radio buttons to the left) in the header row.  The portfolio closest to that return, standard deviation, or rank populates that representative portfolio column.  Use this function to display particular optimal portfolios that match your purposes.  If you choose to save a model portfolio set for use in LifeCycle, the Save Window picks up your selections here as the best guess at the six portfolios you're interested in.  

Note also that the filter provides a more sophisticated algorithm for choosing frontier portfolios based on more advanced criteria.

The Results Table provides the portfolio weights, expected return of the portfolio, expected risk of the portfolio, portfolio yield, rebalance probabilities, and information ratios calculated during the optimization process for each of the optimal portfolios.  The Totals row confirms that each portfolio's allocations total 100%.  If you excluded an asset from the investment universe after optimizing, these totals may not equal 100%.  The Optimizer also presents the initial portfolio weights, each asset's risk and return estimates, tax method, number of simulations (both requested and actually performed), and forecast confidence level on the sides and beneath the optimal portfolio data as tools for evaluating the optimization results.  The Efficient Frontier Chart above the Results Table contains much of the same information in a more visual form.

Two standard deviation rows with percentile bounds populate if you have selected the confidence intervals option in the Charts Menu.

The View Optimal and View Investable buttons switch the Results Table between optimization and post-optimization results.  A blue background indicates investable portfolios.

The Results Worksheet also displays Portfolio Composition Maps according to your selections in the Charts Section of the Display Menu.  Additional charts illustrate the results on the Charts Worksheet.

Related Topics:

Comparison in the Optimizer

Comparing various portfolios and results is essential while using the Optimizer. Comparison is a very effective method for reviewing your data, constraints, and results. The Optimizer provides several tools to ease comparisons within its worksheets, but you can always copy the desired data into a blank Excel spreadsheet. This capability is useful for comparing data between optimizations, such as optimal portfolios produced with different constraints.

Interpreting the Results

Optimization and post-optimization produce portfolios for your evaluation and eventual use. The Results Worksheet displays the optimization results: the optimal portfolios along the efficient frontier.  

To continue optimal portfolio evaluation, save your optimized case for later, or move your case into LifeCycle. To share your evaluation with others, use the reporting functions.

Significant Results

The ability to distinguish significant assets in an optimization result is another benefit of resampled optimization.  New Frontier provides percentile bounds to illuminate how much variability exists in the optimization results and therefore the significance of a particular recommended weight. You can change the percentile bounds through the Options Menu.  The default of 25%/75% indicates the 25th and 75th largest asset weights if 100 simulations are performed.  In other words, the default displays lower bounds for which 25% of the simulations are below and the upper bound for which 25% of the simulations are above in both the Asset Range Table and the Portfolio Bounds Line Graph, both of which appear on the Charts Worksheet.

Individual asset significance is most properly assessed using meta-resampled portfolios which are simulated to be equivalent to the main result optimal portfolios. Therefore, to obtain valid confidence ranges for asset weights, a rebalance test must be run first. Meta-resampled simulations should be set to standard or refined to obtain the most reliable and accurate confidence ranges. The confidence limits shown after an optimization only are a quick approximation and are not very accurate. They are an illustration of the operating characteristics of the Michaud resampling algorithm. Note also that if a relative variance table is loaded to bypass calculation of the rebalance test, the confidence limits shown will remain the quick approximation; to show accurate confidence intervals a full rebalance test must be run.

An asset's significance is also influenced by the assumptions used in the rebalance test - notably the forecast confidence, the resampled returns distribution, the and the typical rebalance periods. Generally, reducing the dispersion of the sampling distribution will tighten the intervals.

An individual asset is significant at the level of coverage of the percentile bounds if the interval shown for the asset and the selected optimal portfolio rank does not touch zero. Otherwise, a substantial number of simulations had zero portfolio weight for that asset and that target optimal portfolio, and the evidence that that asset matters to the portfolio is weaker. Of course the numerical values of the simulated portfolio weights also enter the decision process - an asset whose confidence limits are greater than zero, but all of the simulated weights are small, is less important than an asset whose confidence limits may touch zero, but the range extends to rather large portfolio weights.

Note also that assets often have significance in one part of the frontier versus another; the asset bounds chart applies to only one efficient frontier portfolio at a time. Low-risk assets may tend to be more significant in the lower parts of the frontier, whereas high return assets are more likely to be significant in the upper range of a Michaud Efficient frontier. Mid-range assets may be significant in the middle of the frontier but not at either end.

Overall significance of an arbitrary (reference or initial) portfolio is best assessed using the rebalance test.

If you have checked the Show Standard Deviation Confidence Intervals Option in the Charts Menu in the Display Section of the ribbon, confidence interval bars appear around the standard deviation of the selected portfolio on the Efficient Frontier Chart and in two rows of the Results Table. This feature facilitates analysis of the standard deviation of the optimal portfolios, but disabling this option speeds up the optimization.

 

For more information about the Michaud Resampled Efficient Frontier™, review New Frontier's website.

Filter Worksheet

The Optimizer’s Filter Worksheet shortens your workflow by helping you find the portfolios on the efficient frontier that match your criteria.  These portfolios then appear as options for charts, constraint analysis, and saving model portfolio sets.  

  1. Choose to base the filter on asset score or portfolio standard deviation from the drop down menu in the top left corner.  
    • If you select portfolio standard deviation, the filter locates the chosen standard deviations of portfolios on the efficient frontier.  
    • If you select asset scoring, an additional column will appear to allow you to customize the filter according to one characteristic. (See below for instructions.)
    • If you select advanced asset scoring, two additional columns will appear to allow you to customize the filter according to the ratio of two characteristics.  (See below for instructions.)
  2. Pick either the optimal frontier or (if you've post-optimized) the investable frontier by clicking either the View Optimal or View Investable Button just below the chart.
  3. In the twenty drop down menus, select whether you want the filter to look for the minimum, the maximum, the nearest value, or the exact value.  
    • Selecting minimum or maximum will show the portfolio that has the minimum or maximum value of whatever criteria you have selected.  
    • Selecting nearest value will show the numbered portfolio that most closely matches your criteria.  Note that the closest portfolio to your filter might be the first or last frontier point.
    • Selecting exact value will linearly interpolate the neighboring portfolios to exactly match your criteria, if possible.  This can be helpful when you are considering rebalancing probabilities across the frontier, allowing you to compare the appropriate portfolios. If no exact match is found, the filter will show all zero portfolio weights and N/A in the actual and Portfolio Number rows.
    • Selecting exact or nearest will show the exact match if possible, or the nearest match otherwise. This is useful because it always produces a portfolio on the efficient frontier.
    • Selecting off will disable that particular filter column without overwriting its settings. It can be turned back on later if desired.  
  4. If you select nearest, exact, or exact or nearest, you will need to enter numbers for the filter to match.  If you enter "0.04" after selecting portfolio standard deviation and nearest value, the filter will find the portfolio that is closest to having a 4% portfolio standard deviation.  
  5. Review filtered portfolios.  The Actual Row shows how near the filtered portfolios are to the number you entered if you chose to look for nearest portfolios.  The Portfolio Number Row indicates the portfolio's position along the efficient frontier.
  6. If there are reference portfolios with the same names as filters, and rebalance scores are available, the rebalance score and drifted rebalance score for the reference portfolios with matching names will be shown in rows beneath the filtered portfolios, below the Score type and Desired value rows.

Asset Scoring

The asset score is the criterion for the filter's selection process. The score is generated by multiplying the coefficients in the Asset Score column by the optimal portfolio weights across the frontier, and summing. This results in a range of portfolio-weighted scores across the frontier, which the filter then searches to match the desired number.   The pulldown menu for the Asset Score can populate the column with asset means, yields, expense ratios, benchmark weights, or a custom characteristic.  Portfolio-weighted scores corresponding to the selected choice will then be used to find matches to the desired portfolio score.  For an example, if you select mean from the Asset Score drop down menu, the assets' means will populate the column.  If you then set up a filter for the nearest value and enter "0.07" in the desired row, the filter shows the portfolio with a portfolio mean closest to 7%.  

A few considerations for working with means, yields, expense ratios, and benchmark weights.

Direct input can be used to model the global character of the portfolios and is often used to locate desired stock/bond ratios. For example, if you enter "1" for every equity asset in the Asset Score Column, and then enter "0.2" in the desired row with nearest value selected, the filter will look for the portfolio that has 20% stocks.

The advanced version of the asset score permits assigning both numerator and denominator coefficients to each asset and calculating the ratio as the score.  One way to use this ratio is to assign a numerator of 1 for each equity asset and a denominator of 1 for everything that you want to include as either a stock or a bond, leaving other asset classes in the case out of the calculation.  Then the filter can find the portfolios nearest to various stock/bond ratios.  For instance, "0.6" would indicate a 60/40 portfolio.  (In this scenario, any alternative assets would be given a score of zero to be excluded from the ratio.)  When the asset score curve is non-monotone, in other words it goes up and back down again, the filter will select the lower risk portfolio of the two possibilities closest to that score.

The Robot, a separately licensed module which automatically runs estimations and optimizations, uses the Filter to help match the appropriate portfolio on the frontier for rebalance statistics. Information about the Robot appears in the Start Menu--All Programs--NFA Asset Allocation System--Documentation folder.

The Portfolio Score Chart graphs filtered portfolios along the efficient frontier according to their asset scores.

Portfolio Spacing

Sometimes the optimal portfolios do not appear to be evenly spaced along the efficient frontier.  The portfolios could be spaced according to standard deviation, arc-length, or return, depending on what is set in preferences.  If you've selected return in preferences, the uneven spacing occurs because the Optimizer computes the portfolios to move up the frontier in increments of expected return.  At a classical confidence level, the increments are exactly equal, but estimation error prevents exact increments at other confidence levels.  The portfolios within the high risk section (the right) of the frontier appear to be more spread out because a slight increase in expected return results in a large increase in risk. 

Standard Error

The standard error that appears on the bottom of the Charts Worksheet is the standard deviation of the simulation error in calculating the corresponding optimal portfolio weight. This is sampling error, which is intrinsic to any simulation result. More simulations decrease standard error, generally by the square root of the number of simulations done. For example, increasing the number of simulations from 250 to 1000 should reduce the standard error of a typical asset weight by half.  Assets with high uncertainty, or that are highly correlated to other combinations for assets tend to have higher standard errors and converge to their final value more slowly. A moderate amount of standard error of portfolio weights is rarely a concern for the behavior of the optimal portfolio, but it might be useful to run enough simulations for a small standard error if replicating the optimal portfolio is a concern.  

During optimization, the NFA Optimizer Running Window displays the maximum standard error among all assets and all portfolios on the efficient frontier. This gives a good indication of the worst case simulation convergence for any asset. Optimization tolerance can also be used to bound the standard error of an optimal solution.

Data Pages

Advanced users may desire to see all the numbers behind the optimization solution displayed on the Results and Charts Worksheets.  Access the additional worksheets that contain this data by selecting the Show Data Pages option in the Display Menu.  Two additional worksheet tabs appear.

The wksChartData Worksheet shows the numbers used to produce the charts on the Results and Charts Worksheets.  The opOutput Worksheet contains a table with one column for each of the selectable optimal portfolios on the Michaud Resampled Efficient Frontier™.  The chart below explains how each of the row headings corresponds to results from the Optimizer.

Row

Description

Comment

3

N (maxAssets)

number of assets in the optimization problem

4

optimalPortfolioMean

resampled portfolio expected return

5

optimalPortfolioStdev

resampled portfolio expected standard deviation

6

multiPeriodMean

resampled efficient frontier multi-period mean of input horizon

7

optimalPortfolioYield

yield of the efficient frontier portfolios

8

optimalPortfolioSkew

skew of the efficient frontier portfolios

9

optimalPortfolioKurtosis

kurtosis of the efficient frontier portfolios

10

classicalMean

traditional MV portfolio expected return

11

classicalStdev

traditional MV portfolio expected standard deviation

12

classicalYield

traditional MV portfolio expected yield

13

classicalSkew

traditional MV portfolio skew

14

classical Kurtosis

traditional MV portfolio kurtosis

15

postOptimizePortfolioMean

expected return of the post-optimized portfolios

16

postOptimizePortfolioStdev

expected standard deviation of the post-optimized portfolios

17

postOptimizePortfolioYield

expected yield of the post-optimized portfolios

18

postOptimizePortfolioSkew

expected skew of the post-optimized portfolios

19

postOptimizePortfolioKurtosis

expected kurtosis of the post-optimized portfolios

20-219

optimalPortfolio

resampled portfolio weights

220-419

investablePortfolio

post-optimize portfolio weights

420-619

classicalPortfolio

mean variance portfolio weights

619-819

optimalPortfolioRangeLow

portfolio weights at the lower percentile bound

820-1019

optimalPortfolioRangeHigh

portfolio weights at the higher percentile bound

1020-1219

optimalPortfolioRiskContribution

each asset's contribution to the optimal portfolio's risk

1220-1419

postOptimizePortfolioRiskContribution

each asset's contribution to the investable portfolio's risk

1420-1619

longPortfolios

resampled efficient portfolio weights greater than and equal to zero

1620-1819

shortPortfolios

resampled efficient portfolio weights less than zero

1820-2019

asset Mean Stdev SelectionFlag Correlation

information for each asset (mean, stdev, selection, name, correlation)

2020

outputReferencePortfolioNames

names of reference portfolios including the initial portfolio

2021

 outputReferencePortfolioDates reference portfolio dates

2022

referencePortfolioCalcMean

derived expected return of initial and reference portfolios

2023

referencePortfolioCalcStdev

derived expected standard deviation of initial and reference portfolios

2024

referencePortfolioYield

derived yield of the reference portfolios

2027-2226

referencePortfolioWeights

initial and reference portfolio weights

2227-2426

referencePortfolioRiskContribution

each asset's contribution to the reference portfolio's risk

2427

initialPortfoliorebalanceProbability

rebalance probability relative to the initial

2428-2527

rebalanceProbability

rebalance probability for reference portfolios

2528-2727

optimalPortfolioStdError

standard error of the optimal portfolios

2728

lotOptimalShares

pertains to tax lots

The in-sample and out-of-sample results for the Simulator start at line 3729.

Reports

The Reports button in the Run Section of the NFA ribbon opens the Reports Designer. The Reports Designer provides a list of prepared charts, tables, and paragraphs that can be used in generating a report. Start a report from scratch, or open a previously prepared template. Use the tools and elements described below to develop the correct report for you.

Report Format:

Choose the format of the resulting report from the Report Format drop down menu. The Reporter can generate both Word documents and PowerPoint presentations. Switching between Word and PowerPoint destroys any formatting, such as page breaks, that you may have set up.

After picking the PowerPoint format, you can set the background of your PowerPoint report by instructing the Reports Designer to use the master slides of another presentation.  

Report Elements provided by NFA:

For users who have used previous versions of the Reporter, don't be confused if your User Defined Report Sections Box populates with a different list than the one above.  The User Defined Report Sections Box populates with the report elements that you imported and saved while using the previous version.  This feature protects the material you may have edited in the Reports Designer previously (master slides and user defined report elements).  Sections prepared by NFA can be imported into Reports Designer from C:\Program Files\NewFrontier\8.x\reports (or wherever you installed the Asset Allocation System) using the importing tool described below.  Until these elements have been imported, you will be unable to access them or use them in templates.

Reporting Tools:

Introduction to Constraints

Michaud optimization, while significantly reducing the need for traditional tight constraints, may benefit from constraints. Constraints are also useful for ensuring compliance with investment policy.  Still, we recommend setting up your case without constraints so that you are aware of the unconstrained solution before implementing constraints.

Adding too many constraints lessens the available solution space for the optimized portfolios and thus may diminish the optimality of the resulting efficient frontier. Keep in mind that constraints impact all of the simulations run during optimization, so they have a larger impact than you may anticipate. For instance, a maximum asset bound of 15% means that none of the simulated portfolios can have an asset allocation over 15%, which can drop the average allocation to that asset significantly.

Another caution: it is extremely easy to enter conflicting constraints. For example, entering a small maximum turnover and a maximum asset bound when your initial portfolio includes a large allocation to an asset necessitates using much of the allowed turnover to bring the large allocation down to the required level. The Constraint Analysis and Constraint Analysis II Worksheets help identify the impact and possible conflicts within linear constraints. Conflicting constraints will generally produce an error message indicating that the optimization is infeasible.

Constraint sets provide the capability to save and load asset bounds, quadratic risk penalties, customized constraints, and investability constraints (except max assets and maximum turnover) in one file (*.nfcs). Transaction costs can be saved and loaded separately (*.nftc).

A standard set of constraints used on multiple cases can be saved as default constraints (both optimal and investable) using the Save Default Constraints Button on the Constraints Worksheet or Investability Constraints Worksheet. The current default asset bounds, transaction costs, investable asset bounds, asset increment, and asset threshold save to a clipboard. Clicking the Apply Default Constraints Button returns the most recently saved default constraints to the Optimizer and applies them to the current asset set. Since this only applies to the default constraints, so only fields with a blue background will update.

The Optimizer contains the functionality for the following constraints:

The Optimizer also offers Investability Constraints for post-optimization.

Asset Bounds

Asset Bounds limit or ensure the amount of a particular asset in the resulting portfolios, either optimal or investable.  They can be either absolute bounds or benchmark-relative.

 

Transaction Costs

Entering transaction costs on the Constraints Worksheet allows you to consider the effect of trading costs and fees. (To access the Transaction Cost columns, activate transaction costs in the Constraints Menu.)  The Optimizer applies transaction costs to trades away from the initial portfolio, so you must enter an initial portfolio in order to utilize this function.  If you do not enter an initial portfolio, the Optimizer loads an empty portfolio, and transaction costs are applied as if you were trading from cash.

Linear transaction costs penalize the optimization as follows:  (Initial Portfolio Weight – Optimal Portfolio Weight) x Linear Transaction Cost Value = Penalty

For example, changing an asset’s allocation from an initial weight of 0% to an optimal weight of 15%, with a 2% linear transaction cost assumption, results in a 0.3% transaction cost penalty [(0.00 – 0.15) x 0.02 = -0.003 or -0.3%].  To continue this example, 0.3% of the expected return is subtracted from the expected return during the optimization process.  The Optimizer includes trading costs when calculating which trades improve the overall value of the portfolio.  A buy transaction cost is applied to the difference in portfolio weights of the asset being purchased.  A sell transaction cost is applied to the difference in portfolio weights of the asset being sold.

Default transaction costs work as the other defaults on the Constraints Worksheet. Entering a default (in the cells below the Transaction Costs header) populates all unchanged cells in the column below with the default value. Defaults are indicated by a light blue background. Entering a different value for a specific asset in a particular row overrides the default and appears with a white background. Return the cell to the default by entering a letter.

Transaction costs can be saved and loaded in an NFA format (*.nftc).  

Do not confuse transaction costs with expense ratios.  These transaction costs are also distinct from the Relative Transaction Costs of the Filter.

Customized Constraints

Customized constraints allow you to create customized constraints that restrict optimization and post-optimization for specific purposes. For optimization, New Frontier provides the functionality of both "hard" constraints (linear constraints with upper and lower bounds that must hold) and "soft" constraints, a target for the Optimizer to reach for. (Post-optimization does not accept soft customized constraints, though it does include linear customized constraints.) You can dictate the percentage of the portfolio devoted to equities, require that the sum of two assets equal the total of a third asset, or assess a penalty if the weight of a particular asset or group of assets strays from a target weight. All of these constraints and many more can be developed. However, constraints limit the effectiveness of the optimization and easily render an investment problem infeasible.

Appearance of Customized Constraints

Customized constraints appear on the right of the Constraints Worksheet. A checkbox on the top activates or inactivates the constraint. The row below indicates whether or not the constraint coefficients will automatically update if their source changes. Managed constraints rely on expense ratios, the benchmark portfolio, yields, or custom characteristics for their coefficients. Since these inputs can be updated, the Optimizer will automatically change the constraint if you change the input. For example, a managed constraint that is weighted according to expense ratios would change slightly if you entered new expense ratios. Most often, managed constraints are created in the Constraints Wizard, described below. (The Optimizer will also treat customized constraints as managed if it recognizes the pattern of coefficients entered manually.) Beneath that row is a name for the customized constraint, followed by rows for each asset. If the asset will be included in the constraint, a coefficient of some sort will appear in that asset's row. At the bottom are the bounds on those assets.  

If a constraint is inactive, whether because "N/A" appears for both bounds, there are no coefficients, or they are unchecked, it will appear in a lighter blue. Constraints can be individually activated or deactivated from the Constraints Wizards, and they can all be activated or deactivated from the Wizards as well.

How to Set Up a Customized Constraint

First, determine how to express your constraint.  Customized constraints are written mathematically as:  Min ≤ C1W1 + C2W2 + …. CnWn ≤ Max, where C is the Constraint Value, W is the weight of the asset, and there are n assets in the problem.  Coefficients appear in each asset row, indicating which assets are affected and how the assets relate to each other within the constraint.  The Min% and Max% Fields provide the limits.

Examine a model constraint.  The portfolio constraint, also known as the budget constraint, ensuring that all assets in a portfolio sum to 100%, appears automatically.  For the portfolio constraint, all assets are included equally, so each asset has a coefficient of 1.  Since the portfolio constraint dictates that the assets sum to 100%, both the Min% and Max% Fields contain “100%”.  Note that you can compose constraints that do not total 100%.  

To add a constraint, select the Customized Constraints Option in the Constraints Menu in the Case Settings Section of the NFA ribbon.  The Customized Constraints Wizard appears.  To work directly with the coefficients, add as many blank constraints as you wish and return to the Constraints Worksheet to work with them.  If not, click the Add Customized Constraint button to access the Design Customized Constraint Window (see directions below).

The constraints are automatically assigned an alpha-numeric name starting with "C001".  You can change the names directly on the Constraints Worksheet. A checkbox will appear before the constraint name which can be used to activate or deactivate the constraint.

The simplest customized constraints involve only the coefficients. To ensure that Asset A always has the same weight as Asset B, add a blank constraint, and then enter “1” in one asset’s row and “-1” in the other. To ensure that the sum of Assets A & B always equals the weight of Asset C, enter “-1” for Assets A & B and “1” for Asset C.  

Examples:

Constraints Wizard

If you want the Optimizer to set up the constraint for you, select the Customized Constraints option in the Customized Constraints Wizard and then clicking on the Add Customized Constraint Button. The Design Customized Constraint Window will appear. (For investability constraints, select the Investability Customized Constraints Wizard instead.)

  1. Enter a name in the Constraint Name Field (optional).

  2. Chose whether you want the constraint to apply to one or two groups of assets by selecting the One Group or the Two Groups radio button. Do you want to bound a set of assets to within certain parameters (one group) or set up a relative constraint, sometimes called an inequality constraint (two groups)?

  3. Enter the Lower and Upper Bound. For example, if you want the group of assets A, B, and C to fall within 10% and 40% of the portfolio, enter 10 and 40.

  4. Assign assets to groups by highlighting the asset(s) in question and then adding them to the group boxes by using the Add buttons.

  5. Chose how the assets should be weighted in each group.

    • Coefficient -- Assign a coefficient to apply to all of the assets in the group. The default is "1".  Note that for two group constraints, the assets in the right-hand box will receive the opposite sign coefficient as the one entered in the box; the default coefficient of 1 and 1 means that the assets to the right will be marked as "-1" in the final constraint.

    • Benchmark portfolio -- If you have a benchmark portfolio, you can weight the assets according to their weights in the benchmark portfolio.

    • Yield -- If you have entered yields, you can weight the assets according to their yield.

    • Expense Ratio -- If you have entered expense ratios, you can weight the assets according to their expense ratios.

    • Custom -- If you entered a custom characteristic on the Inputs Worksheet, you can weight the assets according to that characteristic.

  6. Review the formula that appears at the bottom of the window to review the constraint that will be applied.

 

Blue Background and Updating Customized Constraints

If you set up a customized constraint in the wizard, the cell background for the weights will be blue. This indicates that you can edit them in the Customized Constraints Wizard/Investability Customized Constraints Wizard and that the Optimizer automatically updates the weights as the source material is updated. For instance, yield-weighted constraints change when yields are updated. Constraints without the blue background have either been entered or updated manually; they require manual updating going forward and cannot be edited in the wizard.  

Customized Quadratic Constraints

To enable quadratic customized constraints, select the Quadratic Constraints option in the Constraints Menu.  Two rows will appear at the bottom of the Customized Constraints section of the Constraints Worksheet. The Quadratic Target field holds the target for the asset or the specific group of assets designated by the coefficients.  he Quadratic Penalty field indicates the quadratic return penalty that the Optimizer assesses when the target is not met. In other words, the Optimizer applies the penalty to the deviation of the optimal portfolio's constraint value from the target.

Here's an example of the simplest type of constraint that involves more than coefficients. Perhaps you want the sum of Assets A, B & C to be close to 20% of the portfolio, with the outer limits at 10% and 30%. First you would put a coefficient of "1" for Assets A, B, & C. Then you would enter "10" as the lower bound and "30" as the upper bound.  At this point, the sum of Assets A, B, & C must be 10-30% of the optimal portfolio. However, the stated goal is for the sum of the assets to be close to 20%.  If you want to be more precise, you have two options. You can tighten the bounds—forcing the optimization solution nearer to twenty by restricting the weight to between 15 and 25%, or you can enter a target and penalty—encouraging the optimization solution to be nearer to twenty. The penalty is a quadratic function applied to portfolio returns when the optimal portfolio strays from the desired target. For our example, enter “20” in the Quadratic Target Field below the new constraint. Enter “0.001” to enter a 0.1% quadratic return penalty on the optimization if the portfolio strays from the target of 20% in assets A, B & C. This is in addition to the impermeable bounds of 10-30%, but a quadratic penalty on a group of assets does not require the addition of impermeable bounds. Quadratic penalties provide you with the ability to encourage an optimization outcome without forcing it.

Though customized constraints become easier to construct with practice, remember that constraints should be used sparingly to ensure a meaningful optimization result. It is also wise to review your asset bounds and other constraints to confirm that they do not conflict with your customized constraints. You can save customized constraints as part of a constraint set.

Maximum Turnover

The Maximum Turnover Constraint controls the deviation of the resulting portfolios, either optimal or investable, from the initial portfolio weights. This constraint is often used to limit trading, though the transaction cost constraints can be a more effective method of considering trading costs.  

Long-Short Optimization

Long-short strategies are popular among investment managers, so New Frontier has provided several tools to facilitate long-short optimization. Enabling long-short optimization through the Options Menu permits long-short optimization in the Optimizer. The Optimizer reminds users that long-short has enabled by listing it on the Optimization Options Bar. The distinguishing characteristic of long-short is the ability to constrain the total long and short portfolios.

Long-short optimization has far-reaching effects:

You can provide guidelines as to what percentage of the entire portfolio that can be long and short sold in the Portfolio Bounds Fields at the bottom of the Constraints Worksheet. These are soft constraints, so the final portfolios may not fall within the bounds exactly. Enter the approximate maximum percentage of all shorted stocks in the Short Portfolio Max % field, etc. Entering 100-200% as long bounds indicates that the total of all long assets will be close to 100% of the total portfolio and less than 200% of the portfolio.  

Examples:

Shorted assets appear as negative weights within the optimal portfolios.

Quadratic Transaction Costs (Return Penalty)

Quadratic transaction cost constraints (return penalties) impose quadratic penalties to the return in the case of larger transactions in addition to any linear transaction cost constraints. Both types of transaction cost constraints can be saved and loaded in transaction cost files (*.nftc). (To access the Quadratic Transaction Cost column, activate the transaction cost option in the Constraints Menu.)

Use quadratic transaction cost constraints to consider the effect of liquidity factors. Enter quadratic transaction cost constraints in the Quadratic Column in the Transaction Costs Section of the Constraints Worksheet. Quadratic transaction cost constraints require an initial portfolio and a quadratic reference point.  

Define what makes a large transaction in the Quadratic Reference field below the Quadratic Transaction Cost Column. The quadratic reference point indicates the change in an asset's weight between the initial and optimal portfolios where a quadratic transaction cost penalty and a regular, linear transaction cost constraint of the same percentage are equal. In all the examples below, the asset's weight changed by 10% from the initial to the optimal portfolio. In the third row, the reference point is also 10%, so there is no difference between a 2% quadratic or a 2% linear transaction cost. Before the reference point, the quadratic transaction cost constraint penalizes the return of the optimal portfolio less than a linear transaction cost constraint does; after the reference point, the quadratic penalty is greater than a linear transaction cost constraint. A lower reference point forces a higher level of quadratic restraint as the quadratic return penalty surpasses the linear transaction cost sooner. See the chart below for a demonstration in how changing the reference point changes the penalty.

Initial Weight

Optimal  Weight

Reference Point

Quadratic Constraint

Return Penalty

2%

12%

2%

2%

1.00%

2%

12%

6%

2%

0.33%

2%

12%

10%

2%

0.20%

2%

12%

14%

2%

0.14%

The Optimizer calculates the quadratic transaction cost penalty that will be subtracted from the expected return along with any linear transaction costs as follows:

(Initial Portfolio Weight – Optimal Portfolio Weight)2 x (Quadratic Transaction Cost Constraint/Reference Point) = Penalty

So, changing an asset's allocation from an initial weight of 0% to an optimal weight of 15%, with a 2% quadratic transaction cost constraint and a 10% Quadratic Reference Point, results in a 0.45% transaction penalty: [(0.00-0.15)2 X 0.02/0.1=.0045].  A 2% linear transaction cost constraint in the same situation calculates to 0.3%. If you impose both a quadratic and a linear transaction cost constraint, both penalties are exacted from the return.

Quadratic Risk Penalty

Appearing on the Constraints Worksheet, the risk penalty is a quadratic function that raises the effective risk of an asset by adding an independent risk factor to that asset. (To access the Quadratic Risk Penalty column, activate the quadratic risk option in the Constraints Menu.)  he new effective standard deviation in each simulation will be the square root of the exact quadratic risk penalty, squared, plus the simulated resampled standard deviation, squared.  

The quadratic risk penalty is generally used to increase the risk for assets where historical risk is underestimated and heuristic estimates are required, such as, for example, private equities, hedge funds, and real estate. In these and other cases, historical risk estimates may be poorly measured, or limited by lack of transparency, appraisal data, and lockup periods. A risk penalty may also be sensible for emerging market and other indices where long-term return data may be limited or inadequate as an estimate of future risk.  

Normally, the Optimizer calculates portfolio risk with respect to the standard deviations and correlations specified in the inputs.  However, if quadratic risk penalties are present, it may be advantageous to calculate total risk for portfolios and assets, which includes quadratic risk penalties in the risk calculation. This alternative calculation of risk will affect portfolios with nonzero weights of assets with nonzero quadratic risk penalties, as well as the assets themselves. To visualize the impact of quadratic risk penalties, enable the Add Quadratic Risk Penalty to Risk option in the Charts sub-menu within the Display Menu on the ribbon. The results can be seen on the Efficient Frontier Chart on either the Results or Charts Worksheets.  

Considerations

Enter any risk penalties in the Quadratic Risk Penalty column.  

Quadratic risk penalties can be saved and loaded as part of a constraint set.

A Note about the Mathematics of Quadratic Risk Penalties:

Quadratic Risk Penalties add additional variance to the covariance matrix. The diagonal elements of the covariance matrix corresponding to any nonzero Quadratic Risk Penalties are increased by the square of the specified Quadratic Risk Penalty. To the Optimizer, this has the effect of reducing the importance of the correlations, since the recalculated correlations with respect to the total risk including Quadratic Risk Penalties will be dividing each off-diagonal element of the covariance by a greater number, thereby reducing the value of that correlation with respect to total risk.

A consequence of this additional component of the total risk is that portfolio risk will be increased.

Portfolio Risk without Risk Penalties is calculated as , where

o     equation is the portfolio standard deviation,

o     P is the vector of portfolio weights,

o     equation  is the covariance matrix of assets,

o     N is the number of assets in the portfolio,

o     equation and equation are the portfolio weights of assets i and j,

o     equation  is the correlation between assets i and j, and

o     equation and equation are the standard deviations of assets i and j.

With the Quadratic Risk Penalties, the Total Risk is calculated as , where

o     Q is the N by N matrix with the squares of the Quadratic Risk Penalties on the diagonal, and

o     equation is the Quadratic Risk Penalty corresponding to asset i.

Note that the second calculation, of total risk, is mathematically always greater than the first calculation.

Constraint Analysis

The optimization process and the post-optimization process both allow constraints.  In addition to bounding individual assets to values between lower and upper bounds, the user can limit arbitrarily weighted combinations of assets to values between lower and upper bounds using customized constraints.  When many assets and many constraints are involved, the full set of asset and linear bounds imply combined bounds for each asset, which may not be simple to determine from a cursory examination of the full set of bounds. Furthermore, it becomes progressively easier to specify an infeasible set of bounds.  

To facilitate construction, as well as understanding, of a large constraint set, we offer two tools.  This worksheet uses numbers to show the combined effect of constraints.  Another worksheet, the Constraint Analysis II Worksheet, graphically displays where the simulated frontier portfolios are in constraint space and how often each constraint is binding.

Select a Customized Constraint and Portfolio

Choose which customized constraint to examine with the two drop down menus at the top left of the Constraint Analysis Worksheet.  The first menu selects between optimization and post-optimization constraints, and the second one selects a specific constraint by the name assigned to it on the Constraints or Investability Constraints Worksheet.  The tables on the Investability Constraints Worksheet display the analysis of the selected constraint.  The third drop down menu, Portfolio Type, in concert with the Portfolio slider, permits you to choose a portfolio to compare to the implied bounds.  The portfolio selected does not impact the displayed implied bounds in any way.

A Note on the Budget Constraint

The first optimization and post-optimization constraint is always specified by default as a vector of ones with upper and lower bounds equal to 100%.  Labeled "[portfolio]" on the Constraints and Investability Constraints Worksheets, this constraint is also known as the budget constraint.  It essentially specifies that the sum of asset allocations must be 100%, as 100% of your budget will be allocated into the various assets available in the investable universe.  This constraint should not normally be modified, and is treated differently from other constraints in the constraint analysis.  The list of selectable constraints in the constraint analysis worksheet does not include the budget constraint, because it will be assumed present on all of the analyses except for the bounds implied by the selected constraint and portfolio.

Analysis

The middle columns show any asset bounds entered and the currently selected customized constraint (see above).

The right side of the display shows the results of the analysis, summarized here sequentially:

Note that it is possible for a constraint to limit the available combinations of weights without changing the smallest bounding box, which is shown in these analyses. Thus, even if a constraint does not show a difference between the analysis without that constraint and the all-constraint analysis, it is still possible that some combinations of asset weights are disallowed by the constraint. For example, with three assets, the unconstrained bounding box will be in the shape of a cube. A constraint might limit values on one vertex of that cube, effectively slicing off a corner of that cube. The smallest bounding box with the constraint, however, will remain the same cube as without the constraint.

Infeasible Constraints

When problems arise with constraint sets, an error message will be shown when optimization or post-optimization is attempted. This is often the result of a recently added constraint.  In such cases, the recently added constraints can be examined on this worksheet. When a constraint is found which has no N/A values in the Bounds Implied by All Constraints Except the [Constraint Name] Columns, this is the constraint causing the problems. The bounds for that constraint can then be relaxed until a suitable bound is determined where the N/A values in the other rows disappear.

For a more visual, rather than numerical review of your constraints, see the Constraint Analysis II Worksheet.

Constraints Analysis II

The Constraint Analysis II Worksheet is a useful tool for visualizing the effect of customized constraints on the optimal portfolios and thereby determining the appropriate bounds for customized constraints and asset bounds.  (The other Constraint Analysis Worksheet provides a numerical approach to some of the same concerns.)

Select a customized constraint or a particular asset's bounds in one of the two drop down menus at the top of the worksheet.

A set of M constraints on N-asset portfolios with weights P (N by 1) are specified mathematically in the form L ≤ AP ≤ U, where L and U are vectors (M by 1) of lower and upper bounds, and A is a matrix (M by N) whose rows form the linear combinations for each constraint.  

Practical application of constraints requires setting the upper and lower bounds appropriately. Because of the unique resampling framework of the NFA Optimizer, some of the simulations may trigger certain constraint bounds while others may not. Since the final optimal portfolio averages the individual simulations, adjusting a customized constraint bound will have a “soft” effect on the corresponding portfolio weight. Rather than pushed up against the hard boundary, the optimal portfolio weight will be gently moved but remain inside the constraint bounds as long as less than 100% of the resampled simulations are binding.

In order to set the constraint bounds properly, it is of interest to know how often simulated portfolios are hitting the constraint values. The Constraint Analysis II Worksheet shows this information graphically, showing a contour map of the frequencies of the simulated constraint portfolios AP on the vertical axis, charted for the portfolios spanning the efficient frontier on the horizontal axis. The contour map shows one constraint (one row of the matrix A and one scalar value each from L and U) at a time, selected by drop-down menu. The vertical axis ranges from the lower bound to the upper bound and shows the frequencies for simulated portfolios P whose constraint values AP fall between the bounds. Above and below this main contour map graphs display the percentage of time the corresponding bounds are attained. Particularly binding constraints will show a high percentage of simulations attaining that bound. This information can be extremely useful in adjusting the constraint bounds.

 

The figure shows the constraint chart for the Growth to Value constraint in the Vanguard Sample Case. As portfolio risk increases from left to right, the values of the constraint fan out rapidly, with the number of cases attaining the upper and lower bounds steadily increasing across the frontier. This constraint is somewhat binding both above and below, and is likely to have some impact on the optimal portfolio weights.

Working with Taxes

Taxes are a vital consideration when preparing asset allocations.  The Optimizer offers two methods for working with taxes in an optimization framework: the Basic Method, which adjusts returns and standard deviations based on taxes, and Tax Lots. In addition, the Optimizer offers a tax deferment tool that works in concert with the basic method. New Frontier developed these methods based on client suggestions and welcomes additional client input on this subject. Access the various tax methods through the Taxes Menu.  

The Optimizer handles taxes assuming a single period optimization framework, but another NFA application forecasts the multi-period implications. NFA's LifeCycle application produces a multi-period forecast based on single period return and risk expectations. So, if you load a tax-optimized Optimizer case, LifeCycle automatically applies taxes to the multi-period forecast.

Do use taxes thoughtfully. A model that includes municipal bonds may forecast a capital gain in addition to the normal yield of the bonds. However, in early 2009 many municipal bonds were trading at a significant discount and only the coupons were tax-exempt, so some users adjusted the after-tax mean and standard deviation for these bonds as well. Tax models do not currently account for options, so proper care must be exercised when using these features with options in interpreting the results. They can still be used, but must be interpreted carefully.

Basic Method

In the Basic Method of tax optimization, the Optimizer adjusts asset level returns and standard deviations to explicitly consider the effect of marginal income and capital gains taxes. The key to the Basic Method of tax optimization is that total return consists of several components (the first two components sum to the yield):

1. ordinary interest and non-qualified dividend income
2. qualified dividend income

3. realized short-term capital gain or loss

4. realized long-term capital gain or loss
5. unrealized gain or loss

The Basic Method adjusts the return of each component separately and then combines them to find the after-tax return of each asset. It also adjusts the risk based on how taxes affect the returns, lessening large gains, and ameliorating large losses. However, the Optimizer treats correlations as if they do not change with taxation.

Enabling the Basic Tax Method in the Taxes Menu calls up the Taxes Worksheet. Begin by entering the federal and state tax rates on different income types in the Tax Rates Table.  

The Pre-Tax Return, Pre-Tax Standard Deviation, and Pre-Tax Yield columns populate from the data entered on the Inputs Worksheet. If you have not entered yields on the Inputs Worksheet, do so now. Several other components of capital gains and income calculation must be entered directly on the Taxes Worksheet. As you enter data, the protected columns update automatically; the calculations are explained below.

 

Capital Gains Columns

 

Pre-tax capital gains are the portion of the pre-tax total return that came from capital gains or losses.  The Pre-Tax Capital Gains column automatically populates by subtracting the yield from the return.  Correct or complete as necessary.  Pre-tax capital gains and losses split into three elements that are entered separately: unrealized, short term, and long term capital gains.  Begin by identifying what portion of the pre-tax total return comes from capital gains/losses, generally by subtracting the pre-tax yield from the pre-tax total return.  Enter the percentage of pre-tax capital gains that comes from assets held for less than a year in the Short Term Capital Gains column of the appropriate asset.  Enter the percentage of the pre-tax capital gains/losses that come from assets held for at least a year in the Long Term Capital Gains column of the appropriate asset.  The Unrealized Capital Gains column populates by subtracting the short term capital gains and the long-term capital gains from 100%. The Combined Cap Gain Tax Rate column populates according to the following formula:  

 

ST Capital Gains x (Federal + State ST Tax Rates) + LT Capital Gains x (Federal + State LT Tax Rates).

 

The Optimizer applies this rate in order to display the after-tax capital gains total return in the After Tax Capital Gain Column.

 

Income Assumptions Columns

 

Bearing in mind that the Optimizer assumes a single period optimization, indicate whether federal and state taxes apply to each asset in the Income Assumptions columns.  Entering "No" prevents the Optimizer from applying that particular tax to the asset.  You can designate an asset as subject to federal tax, state tax, neither tax, or both taxes.  Tax deferred assets, if any, are automatically listed as tax free.

 

Income Columns

 

Ordinary income (non-qualified, such as from interest) and income from qualified dividends have separate tax rates. Enter the portion of the yield attributable to qualified dividends in the “% of Yield as Qualified Dividend” column.  The “% of Yield as Ordinary Income” subtracts the qualified dividend from each asset's yield.  The Combined Income Tax Rate column displays the weighted average of the federal and state tax rates for interest and dividends.  The After Tax Yield column populates with the total yield after taxes.

 

Additional Columns

 

The After-Tax Standard Deviation column displays the impact of taxes on standard deviation.  Tax bills offset large gains, and tax gains offset large losses.  In tax optimization, this effect of taxes should not be missed.  For most investable assets, the standard deviation of the yield is negligible compared to the standard deviation of the capital gains.  Therefore, the Optimizer calculates the after-tax standard deviation with the following approximation: the pre-tax standard deviation multiplied by (100% - Combined Cap Gain Tax Rate).  The After-Tax Return column aggregates the after-tax returns, both capital gains and income.  The Effective Tax Rate column presents the impact of taxes on returns: 1 - (After Tax Return)/(Pre-Tax Return).  

 

Results

 

The resulting tax-adjusted risk and return estimates appear on the Results Worksheet as well as the Taxes Worksheet.  When enabled, the Optimizer uses the adjusted risk and return estimates for optimization.  

Tax Lots

If you have tax lot information and current prices, you can optimize by tax lot. The Optimizer tracks the impact of gains and losses and applies them as an additional adjustment to the return of the portfolio, like a transaction cost. The difference is that the tax lots can have a positive effect on the return of the portfolio given that there are sufficient losses. If you do not apply capital gains constraints, the Optimizer sells losers and holds on to winners. If you want to hold some losses for later, utilize the capital gains constraints to limit the losses taken at this time. Be aware that tax lots and the capital gains constraints act in concert with any other constraints you may apply, so be careful to watch for conflicting constraints. (For an example, access the Vanguard Tax case in the samples directory.)

Overview of Optimizing with Tax Lots

  1. Begin by enabling Tax Lots in the Taxes Menu.

  2. Create a tax lots CSV file.

  3. Import your tax lots CSV file.

  4. Review the Tax Lots Worksheet.

  5. Optimize.

  6. Review the results.

Create a Tax Lot CSV File

The only way to enter tax lots information is to create a CSV file and import it.

  1. Open a spreadsheet.

  2. Enter the column headings from the table below.

  3. Complete the spreadsheet with tax lots information.

  4. Include all assets in the investment universe.

    • To include price information for assets not included in the initial portfolio, add an entry with a valid price, but no shares or basis. For example, if the initial portfolio contains no Japanese stock, but you included Japanese stock in the optimization problem, you should include a tax lot for Japanese stock in order to import the current share price and tax rate.  

    • Alternately, wait for the Optimizer to create blank tax lots for these assets during optimization. The Optimizer automatically assigns a price of $1/share for assets excluded from the tax lots file. You may then export the tax lots information, change the prices and tax rates, and re-import the tax lots file.

  5. Save the spreadsheet as a *.CSV file.

 

Column Header

Content

AssetID

the unique identifier of the asset (Asset Name), also used on the other worksheets

LotName

the unique identifier of the tax lot

LotDescription

(optional column) further information about the tax lot

BuyDate

the date of purchase for this particular tax lot in MM/DD/YYYY hh:mm format  (Hour and minute are optional.)

Basis

the price of the entire lot on the date of purchase including commissions (not price/share)

TaxRate

the tax rate to be applied to the specific tax lot

Price

current price/share

Shares

the number of shares included in the tax lot

 

Import a Tax Lots CSV File

Select the Import Tax Lots Option from the Taxes Menu.  The Import Tax Lots from CSV Window appears.  Navigate to where you saved the CSV file.  Click the Open Button.  The tax lots file populates the Tax Lots Worksheet.  

 

Capital Gains Tax Bounds

Capital Gains constraints restrict the amount of realized capital gains tax to within the set range.  For example, if you want to pay between $1000 and $2000 in capital gains taxes for the year, enter "1000" in the Capital Gain Tax Lower Bound Field and "2000" in the Capital Gain Tax Upper Bound Field.  

 

Optimizing with Tax Lots

After reviewing the Tax Lots Worksheet for completeness and setting the rest of your investment problem, optimize.  After optimization, you can slide through the optimal portfolios in the top left of the Tax Lots Worksheet in order to view the tax implications.  

 

Results of Optimizing with Tax Lots

After optimization, new lots appear for each recommended buy, and the following fields populate with information concerning the tax implications of the currently selected optimal portfolio:

 

Export a Tax Lots CSV File

Exporting a tax lot file allows you to make changes such as updating the prices, move tax lots into a different Optimizer case, or save tax lot information for a future Optimizer case.  (When you save a complete case, tax lots are included, but you may wish to save tax lots separately.)  Select the Export Tax Lots Option from the Taxes Menu.  The Export Tax Lots to CSV Window appears.  Navigate to where you wish to save the CSV file.  Click the Save Button.  The Optimizer creates a CSV file that includes all assets, even those that were removed from the investment universe in the Asset Selector.  

 

Feedback

This is a beta version of the tax lots feature.  We welcome your feedback.  Please contact your relationship manager or e-mail support@newfrontieradvisors.com.

Tax Deferred Assets

Choosing assets for taxable and non-taxable accounts can complicate optimization problems.  The Optimizer offers a Tax-Deferment tool to assist with this decision.  

Add a Tax-Deferred Asset

  1. Activate the tool by selecting the Create Tax Deferred Assets option in the Taxes Menu.  

  2. The Choose Tax Exempt Percentage Window appears to ask what percentage of the optimal portfolio you want to devote to tax-deferred assets. Enter the percentage, and then click the OK Button. The Optimizer duplicates all of the assets in the current case. The duplicates appear above the original assets with "T/D" following the asset name in all asset lists.  

  3. Enable the basic method of tax optimization in order to utilize these additional assets. Enter additional tax inputs on the Taxes Worksheet.

  4. The Optimizer automatically labels the tax deferred assets as tax free and applies the entered percentage as a customized constraint, which appears on the Constraints Worksheet. During optimization, the constraint forces the chosen percentage of the optimal portfolio to be in tax-deferred assets.  

Disabling Basic Taxes deletes all assets that have "T/D" in the asset name.

Post-Optimization

Post-Optimization polishes the optimal portfolio produced by the optimization process to produce a portfolio that is both practical to invest and near to optimal. You can think about it as the Optimizer's rounding capability, but it is more complicated than that. Specifically, running New Frontier's post-optimization algorithms adjusts the optimal portfolios according to the investability constraints, choosing the nearest such portfolios to the optimal frontier portfolios. The resulting portfolios are referred to within the application as “investable”.

"Nearness" is determined by a portfolio distance metric, which is the tracking error, or the variance of the difference between the optimal and investable portfolios. This choice of metric means that moving portfolio weight between highly correlated assets will incur less penalty than moving weight between less correlated ones, and moving weight toward an asset with smaller standard deviation will reduce the penalty, all other things held equal.  

Set the length of time that you want post-optimize to run on the Optimization Tab of the Preferences Window. This allows you to force a more thorough or quicker post-optimization depending on your goals. The default length of time is based on the problem size, but is also greater than or equal to 120 seconds.  ote that this option only controls the time spent on the actual post-optimization, not on pushing the information into the fields, so post-optimization may feel longer than the set time. Moving the slider all the way to the right will select an unlimited time for post-optimization; this option will fully explore all possibilities before returning the nearest result that satisfies the post-optimization constraints and conditions.

Please note that though post-optimization is available when the options strategy is enabled, it will not use the options-overlaid means and variance. Thus caution should be exercised with postoptimizing, in order to avoid drastically altering the portfolios with extreme investability constraints.

To view the results, click the View Investable Button on the Results Worksheet.  You can also select portfolios according to set criteria on the Filters Worksheet, just click on the View Investable Button. You also can examine the investable portfolios in many charts.

The Investability Constraints Worksheet includes a table that enables the post-optimization of a portfolio selected by the user. This is intended to allow the post-optimization of reference portfolios or a portfolio picked by an exact filter. Copy the portfolio you want to post-optimize into the Target Column (or enter it manually).  Click the Post-Optimize Target Button. The Investable Column populates with the investable version (complies with the investable constraints as described above) of the target portfolio. The Difference Column shows the impact of the post-optimization along with turnover and tracking error. You can also copy a regularly post-optimized portfolio from the Results Worksheet for the same analysis. This method of running post-optimize can save time since it is applying the procedure to just one portfolio instead of the entire frontier.

Related Topics:

Investability Constraints

Post-Optimization polishes the optimal portfolio produced by the optimization process to produce a portfolio that is both practical to invest and near to optimal. Specifically, running New Frontier's proprietary post-optimization algorithms adjusts the optimal portfolios according to the investability constraints entered on the Investability Constraints Worksheet (accessed through the Display Menu). The resulting portfolios are referred to within the application as “investable”.  

Investability Constraint Types:

Considerations:

For further data on post-optimization, review the article "Optimal and Investable Portfolios," available at http://www.newfrontieradvisors.com.

Asset Anchoring

Since the post-optimization process chooses the set of portfolio weights on the lattice of points that satisfy all of the investability constraints and are closest to the optimal portfolio on a distance metric determined by the covariance matrix, assets with small standard deviations and higher correlations to the others are free to drift away from their optimal values, more so than other assets.  

In some cases, it may be desirable to keep such an asset’s weight close to its optimal value. To achieve this end, enter a positive value into the Asset Anchoring Column in the specific asset's row. This adds a penalty to the covariance matrix’s diagonal for that asset, which in turn penalizes distance for that asset from the optimal to investable portfolio. This penalty is quite similar to the quadratic risk penalty in optimization. Entering larger values will create more of an anchoring effect in the post-optimization process. In other words, increasing the anchoring of an asset will increase the penalty of changing the weight for that asset between optimal and investable, thus anchoring the investable portfolio to the optimal weight for that asset. Numerically, the anchoring coefficient adds to the diagonal of the covariance matrix. New Frontier recommends using "20" as a default value in order to explore the impact of anchoring an asset. Even with a very high positive value, post-optimization will shift assets according to asset increments and thresholds.

Asset Threshold

The Asset Threshold investability constraint eliminates positions below the specified percentage. For example, a 5% asset threshold prevents 2% asset allocations without forcing a 5% allocation to each asset as the minimum asset bound constraint does. If the optimal portfolio has a 2% allocation to an asset, post-optimization with a 5% asset threshold results in either no allocation or a 5% allocation to that asset. An asset threshold of 0% turns this constraint off. The effective threshold is the minimum multiple of the increment that is greater than or equal to the threshold. For instance a 2.5% asset threshold when the asset increment is 1%, results in a smallest possible allocation of 3%.  

Maximum Assets

The Maximum Assets investability constraint controls the number of assets in a solution. For example, a value of 5 results in a portfolio with no more than 5 assets in the investable portfolio. Determining the number of assets is rarely useful with smaller asset universes, but may prove useful with larger asset universes. The default value of 0 shuts this constraint off.

Asset Increment

The Asset Increment investability constraint smooths the asset allocations by rounding allocations. Entering 1% as the asset increment results in asset allocations rounded to the nearest whole number. Entering 2% results in asset allocations rounded to the nearest even whole number. The effective threshold is the minimum multiple of the increment that is greater than or equal to the threshold. For instance a 2.5% asset threshold when the asset increment is 1%, results in a smallest possible allocation of 3%. Asset increments can be saved as part of a constraint set.

Simulator

Enable the Simulator by selecting the Simulator Worksheet in the Display-Worksheets menu.

Purpose

The Simulator allows users to compare competing methods or assumptions over a variety of simulated inputs derived from the main optimizer inputs, and evaluate the "out-of-sample" performance, assuming that the optimizer inputs are the truth. The canonical comparison, seen in Richard Michaud's book Efficient Asset Management (1998, 2nd ed. 2008), is between Markowitz mean-variance (MV) efficient frontiers and Michaud Resampled Efficient (RE) Frontiers.  In the comparison from the book, the in-sample curves show the MV frontier dominating the Michaud frontier, but the out-of-sample curves reverse this, demonstrating the advantage of Michaud optimization on average in the presence of estimation error. One such display is shown below. Many such displays can be generated with different settings, constraints, and datasets.

Procedure

  1. The Simulator starts with the correlations, risk, and return estimates currently entered into the Optimizer to find both the MV and the RE frontiers.  All constraints remain in effect, and the forecast confidence determines the magnitudes of the error distributions over which resampling takes place throughout the procedure.
  2. Next, the Simulator randomly generates correlations, risk, and return estimates based on the original inputs, using a resampling process identical to that used in Michaud optimization. This step represents estimation error.
  3. The Simulator takes the simulated inputs to create new versions of both the MV and RE frontiers.
  4. Steps 2 and 3 repeat to calculate the stipulated number of simulated frontiers, or until the user stops calculation on the progress bar.
  5. The Simulator averages the MV frontiers and the RE frontiers to create the average MVF and the average REF.

Inputs

A Note about Optimizer and Simulator Forecast Confidence:  Within a resampled optimization, the forecast confidence determines the size of the error distribution used to create each Michaud Efficient Frontier portfolio. Greater forecast confidences imply smaller error distributions. Perfect forecast confidence generates the Markowitz frontier, since there is no error in estimating the input mean and covariance.  The Simulator Forecast Confidence occupies a similar role in the Simulator; it determines the size of the error distribution from which inputs for each simulation are drawn. In this situation, high Forecast Confidence corresponds to a smaller error distribution. Lower Forecast Confidence in the Simulator will increase the separation between the averaged frontiers and the current frontiers, just as lower Forecast Confidence increases the separation between Michaud and Markowitz frontiers. The flexibility of being able to separately choose Optimizer and Simulator Forecast Confidence means that it is possible to simulate effects of performing optimizations with the “wrong” forecast confidence – i. e. high confidence in a volatile market, or low confidence in a stable market.

Results

The Simulator chart, also available on the Charts Worksheet, demonstrates the relative investment value of the four different efficient frontiers. The current Markowitz and Michaud frontiers are derived from the current optimization case. The averaged Markowitz and Michaud frontiers are the averages of optimizations from simulations of the inputs (mean and variance) over an error distribution. The equal-weighted portfolio is also plotted with respect to the mean and variance of the case.

The relative positions of the curves demonstrate the performance of the methods. Since the current Markowitz frontier is optimally efficient with respect to the current inputs, by construction it will be above and to the left of the other curves.  The current Michaud frontier lies somewhat below this curve, depending on the forecast confidence chosen to run the optimization.  However, this relationship is misleading since the true mean and variance of the assets is unknown.  A more realistic representation of the relative performance of the two methods is demonstrated by the averaged frontiers.  Each simulation begins with a mean vector and covariance matrix sampled from an error distribution for the current optimization inputs.  This error distribution can be chosen to have low, medium, or high volatility.  

Checkboxes on the side of the chart allow the four frontiers (current Markowitz and Michaud, and average Michaud and Markowitz) as well as the Equal Weight Portfolio, Reference Portfolios, and Assets to be shown or hidden on the chart. If a case is stored, then the four stored frontiers can also be shown or hidden on the chart. Note that if the input return or risk assumptions are changed between storing a case and running a new one, the stored frontier risks and returns will show as calculated with their original risk and return assumptions, not the new ones. Also, for a portfolio to appear on the Simulator Chart when the Reference Portfolios checkbox is checked, the portfolio must appear as a reference portfolio on the Portfolios Worksheet.

Figure 1: A simulation chart created with medium volatility from the default case.*

 

The graph shown in Figure 1 was created from the default case with medium volatility.  fter all the simulations complete their optimizations, the resulting portfolios are averaged together and plotted on the same axes with respect to the current input mean and covariance matrix. We can see in Figure 1 that the averaged REF dominates the averaged MVF, lying significantly to the left with lower risk.

The placement of the equal weight portfolio provides an indication of the level of information in the optimization case.

The Simulator should be viewed as a demonstration of the value of the procedure of Michaud optimization.  It is not meant to predict the out-of-sample performance of the MVF or REF, since the averages are made over many portfolios with respect to the current mean and variance, rather than averaging the current frontiers of portfolios over the correct error distribution, which itself is not well-known.

Stored Results

If you click the Store Results Button, the Simulator stores the current results for comparison. After running the Simulator again, click the Display Stored Results box on the chart. Both sets of results become visible. You can compare simulations of the same optimization to check that you have enough simulations, or you can change the case between simulations, just remember to optimize the main case as well.

*Twenty simulations were used.  The RE frontiers were created with 500 simulations at a forecast confidence of 4.

Error Handling

An error message appears when the Optimizer recognizes an incongruity, generally during the optimization or post-optimization process.  Infeasible constraints are the most common cause of errors.

If an error message appears and the cause of the error is not immediately apparent, click the More Information Button.  A more thorough description appears.  Some of the less common errors have incomplete descriptions.  Later versions will have more complete error descriptions.  You may also find it useful to review topics in this help manual.

Common error resolutions:

The Copy to Clipboard Button on the error message window can help you report the error to NFA.  Clicking that button copies the text of the error message into your clipboard, so you can easily paste into an email message.  In order to provide version information as part of a support request, click on the Copy to Clipboard Button on the About Window, accessed by clicking on the logo in the top left hand corner of the application.

Covariance Fixer

The Covariance Fixer is a separately licensed application that appears as a page in the Optimizer if you enable it in the Display Menu. The Covariance Fixer adjusts matrices to be positive definite (no negative eigenvalues), rounds correlations to a set number of decimal places, and improves the condition of badly-conditioned correlation matrices.  It is useful for those who create their own matrices or make adjustments manually, rather than using the historical correlations computed by the Estimator. If you are interested in licensing the Covariance Fixer, please contact your relationship manager.

Reasons to use the Covariance Fixer

  1. Negative or zero eigenvalues.  Correlation matrices by definition are positive semidefinite and may not contain any negative eigenvalues, since all portfolio variances must be by definition nonnegative.  In order for solutions to be unique and well-defined, optimization requires no perfect correlations among assets, or no negative eigenvalues.  The covariance fixer finds a nearby valid covariance matrix to the input matrix, if it has any negative or zero eigenvalues.

  2. High condition numbers.  Condition indicates how close a matrix is to zero.  Even historical correlations prepared in the Estimator may not be well-conditioned, though they will be technically valid.  A well-conditioned correlation matrix has a low condition number, meaning that the ratio of the largest eigenvalue to the smallest is low.  Optimization involves inverting the matrix and multiplying according to it.  A high condition number indicates that your matrix is close to zero and that multiplying by the inverse of the matrix would magnify errors.  A matrix with a low condition number is therefore easy to invert and multiply during optimization, because it is far from zero.

  3. Excessive precision.  If your correlation matrix displays full machine precision in the relationships between assets, you can lower the number of significant digits. In other words, you can dictate how many decimal places considered during optimization.

Covariance Matrices

Covariance matrices are square matrices whose diagonal entries are variances and whose off-diagonal entries correspond to covariances. Covariances are defined as correlations times the standard deviations of the two correlated assets. Thus, a covariance matrix V can be factored as V = DCD, where D is a diagonal matrix of standard deviations and C is a correlation matrix.  he matrices simplify the notation and organize the calculations for converting covariances to standard deviations and correlations, and vice-versa. The Estimator and Optimizer allow modifications on D and C rather than V directly, since it is useful to separate the covariance forecasting process into these two parts. The standard deviations can often be interpreted as a variability of the return forecast, where larger standard deviations indicate more uncertainty in the return forecast. However, New Frontier does not normally recommend exogenous forecasting of correlation matrices. Nevertheless, the capability exists for advanced users to change entries of the forecast correlation matrix. Users who opt to modify correlation matrices face the danger that the specified correlations are not consistent with each other and do not form a valid correlation matrix. In terms of linear algebra, the consequences of this are that one or more of the eigenvalues of the correlation and covariance matrices may be negative. This is equivalent to saying that the covariance matrix may not be positive semidefinite, a requirement for valid covariance matrices.  

 

Eigenvalues and Eigenvectors

A covariance matrix can be factored into its spectral decomposition V = QΛQT, where Q is a matrix whose columns are the eigenvectors of V and Λ is a diagonal matrix of the eigenvalues of V.  The n-by-n matrix of eigenvectors Q can be thought of as a rotation through n-dimensional space, preserving distances, and the n-by-n diagonal matrix Λ can be thought of as a rescaling of distances, preserving rotation. Thus a zero eigenvalue would represent a complete collapse of the variance of the data along the direction of the corresponding eigenvalues.

 

Since the covariance is a measure of dispersion in space, negative eigenvalues do not make sense, and in fact are prohibited by the definition of covariance. The consequences of attempting an optimization with a covariance matrix with negative eigenvalues are that the optimization will not represent a valid optimal portfolio since the input covariance cannot represent a true set of assets. Zero eigenvalues can be problematic as well, since they correspond to an eigenvector with zero variance. This means that some linear combination of assets is constant, a situation which occurs if returns are relative to a benchmark which is a linear combination of the assets. If there is only one such zero eigenvalue, the optimizer can find a solution, and will assume that the optimization is relative to a benchmark whose weights are proportional to the eigenvector corresponding to the zero eigenvalues. Covariance matrices with more than one zero eigenvalue will generate an error in the Optimizer and should be run through the covariance fixer if the problem at the root of the negative eigenvalue cannot be addressed. Often a negative eigenvalue may indicate a more fundamental problem with the process. It is always preferable to address the direct cause of the problem than to smooth it over with the covariance fixer.  

 

Although negative and zero eigenvalues usually occur under specific circumstances, historically estimated covariance matrices frequently have eigenvalues close to zero. When this is just a result of legitimately highly correlated assets, it is only a numerical concern. However, the greater the number of assets and the shorter the history, the more likely certain combinations of assets will have serious correlations that result in small eigenvalues.  Small positive eigenvalues can also cause problems for the Optimizer, since some of the calculations involve total or partial inversion of the covariance matrix. Small eigenvalues can occur when assets are highly correlated, and can cause numerical instability in the optimization process. “Smallness” is measured with respect to the largest eigenvalues of the covariance matrix, and is stated in terms of the condition number, or ratio of smallest to largest eigenvalues, of the matrix. Because of the numerical instability when the condition number is high we recommend use of the covariance fixer in this case.

For further information on eigenvalues, consult a good linear algebra text, such as Mike Artin's Algebra. For correlation matrix computation, consult a good multivariate statistics book, such as Johnson and Wichern's Applied Multivariate Analysis. Convex Optimization by Boyd and Vandenberghe and New Frontier's own Efficient Asset Management provide insight into how these apply to optimization.

How to use the Covariance Fixer

  1. Access the Covariance Fixer through the Display Menu.

  2. Click the Copy from Inputs Button to populate the Input Correlations table with the correlations you entered on the Inputs Worksheet.

  3. Enter the number of decimal points that you wish the Optimizer to consider in the Significant Digits field.

  4. Enter the minimum eigenvalue in the Minimum Eigenvalue field.

  5. Click the Fix Covariance Button.

  6. Review the Fixed Correlations Table and the Differences in Correlations Table.

  7. If the matrix is acceptable, click the Copy to Inputs Button to transfer the correlations into the case.

  8. Proceed with your optimization.

Troubleshooting Tools

Several troubleshooting tools appear in Windows Start Menu, NFA Asset Allocation System folder.

Launch Preferences brings you to the Preferences Window.  Within the Preferences Menu, you can:

HASP Key Firmware Upgrade updates the firmware if necessary. This should be unnecessary for most users.  Make sure that your HASP key is attached to the computer before applying.  

Use the NFA Key Updater to request and receive updates to the license on your HASP key.   

  1. The Sentinel HASP RUS Window appears.   
  2. Select the Collect Key Status Info tab.  
  3. Click the Collect Information button.  The Save Key Status As window appears.  
  4. Change the file destination as desired; the default is the Desktop.  Assign a name to the file (*.c2v).  Click the Save button.  
  5. A status message appears on the Collect Key Status Info tab.  If successful, the file appears at the designated file destination.  E-mail the file to licensing@newfrontieradvisors.com.
  6. When NFA replies with a HASP update file (*.v2c), save the file to the Desktop or another folder.  (We recommend that you don't use Outlook Web Access to download the file).  
  7. Right click on the file.  Select the Update NFA HASP Key option. The Sentinel HASP RUS Window appears with the file name in the Update File field of the Apply License File tab.  
  8. Click the Apply Update button.  

System Information opens the System Information application that contains information about your computer that will enable you to answer questions from support personnel.  The buttons at the bottom of the window allow you to copy the data or e-mail it directly to New Frontier.  

Debugging Log

Only prepare a debugging log if NFA asks you to do so as part of a support operation. If NFA requests a debugging log, access the Preferences Window or Toolbox. Select the Debug Tab. Check the Enable Debugging Box. The rest of the window activates. Enter the folder in which you want to save the debugging log.

Known Issues

When the assets have been flipped in the Display--Charts Menu, hovering over the first asset in the Portfolio Composition Map causes the Optimizer to display "Plot Area" rather than the asset name.  (Internal Reference #11002)

When you ask the application to identify available cores in preferences, the "best settings for my computer", your computer selects the number that are currently available, which can change within seconds.  This means that depending on when the application checks the preferences, your computer could be running on fewer cores than are available.  If you have a multi-core machine, we recommend entering your number of physical cores manually on the same tab in preferences. (Internal Reference # 9366)

Double clicking or triple clicking on a button on the ribbon causes the operation to run two or three times.  To avoid this problem, use a single click. (Internal Reference #9349)

The Asset Allocation System is incompatible with Bloomberg Excel Tools v.3 build 6284.  When this add-in is enabled, the Asset Allocation System will start to open before crashing without an error message.  The solution is to disable the Bloomberg Excel Tools add-in.

Sometimes when you access the Constraints Analysis II Worksheet, you will see an Excel alert asking you to remove lines between colors.  Select No. Also, sometimes the chart fails to display properly when first accessed in that the three charts are misaligned, and an error dialog will pop up. Switching to another worksheet and switching back will generally fix this problem.

Add-In Not Loaded

  1. When the NFA add-in does not load, first check to see if the New Frontier add-in is disabled.

    • Access the File menu on the ribbon.  

    • Click on the Options option at the bottom of the list to the left.  The Excel Options Window appears.

    • Click on the Add-Ins option at the bottom of the list to the left.  

    • Select Disabled Items in the Manage drop down menu at the bottom of the window.  

    • Click the Go Button.  

    • Select any New Frontier items that appear in the Disabled Items Window.  

    • Click the Enable Button.  

    • Close all Excel windows.  

    • Launch the application.

  2. If New Frontier add-ins did not appear in the disabled items list, try closing and restarting the application.

  3. If restarting the application does not work, try rebooting the computer.

  4. If you got the add-in not loaded error immediately after installing version 8.x and rebooting didn't fix the problem, try a repair.  This option is found in your program list, usually right next to the uninstall option.  Restart your computer before trying to open the application.

  5. If you got the add-in not loaded area immediately after installing version 8.x and repairing didn't fix the problem, uninstall and reinstall the software.  Restart your computer before trying to open the application.

  6. If the problem persists, contact New Frontier at support@newfrontieradvisors.com.