Forecast Contrasts

Displaying Forecast Contrasts

Display of forecast contrasts is toggled through the Display Menu.  When displayed, forecast contrast entry fields and intermediate result tables appear on the Forecasts Worksheet as well as on the Results Worksheet.  When forecast contrasts are hidden, they are disabled and do not impact the Estimator case.

You enter up to 50 contrasts.  Individual contrasts can be turned on or off by checking or unchecking the boxes on top of the column.  Contrasts are also considered off if they have no standard deviation or weights.  When they are on, they appear in a darker blue font.  When they are off, they appear in lighter blue font.  

The tops of the columns indicate how the contrast has been weighted.  If a contrast is weighted according to the market portfolio, the top of the column states "Market Weighted".  Similarly, the Estimator labels contrasts with equally weighted groups of assets as "Equal". If either of these labels appears, the contrast's weights will update automatically if the case changes (market portfolio changes, added asset, etc.).  If no label appears, the contrast has been weighted manually and it will not update automatically.

The Vanguard sample cases include sample contrasts to explore.

What Are Forecast Contrasts?

Forecast contrasts are forecasts for groups of assets that are applied to your assets along with any entered single asset forecasts when the Run Bayes button in the Estimator Ribbon is clicked.  

Forecast Contrasts provide a way to include investor views in an estimation process. These investor views are merged with historical information as well as any other forecast information to form the final estimates, which balance all information sources to give final estimates. Contrasts may be familiar to practitioners through the Black-Litterman procedure, and NFA’s implementation of contrast forecasts is entirely analogous to the “investor views” in that procedure.

When a view target (mean) differs from its corresponding historical prediction, a contrast will bend the estimator results towards that target. The strength of the view’s influence on the answer can be adjusted through the contrast standard deviation. Thus a vague view which is not tightly focused is assigned a large standard deviation and has a less pronounced effect on final estimates than a specifically focused, high-certainty view, which has a small standard deviation.

A complete specification of a contrast includes a portfolio (which may sum to 0% or 100%), a mean (target for the expected return of that portfolio), and a standard deviation, which controls the influence of the view on the result. Larger standard deviations signify less focus and less influence on the result.

Although contrast portfolios may legally sum to any number, it is fully general and simpler to consider only contrast portfolios that sum to zero or 100%, since contrast portfolios summing to any other number can be converted into another equivalent contrast with a portfolio summing to 100% by dividing portfolio, mean, and standard deviation by that sum.

Sum-to-zero contrasts are useful for comparing one asset, or basket of assets, to another single asset or basket. The portfolio weights can be broken into one sum-to-100% portfolio minus another. The contrast mean then represents the expected difference in returns, or expected premium of the positive portfolio over the negative one. The standard deviation controls the influence on the results.

Sum-to-100% contrasts are views on portfolios. A suitably weighted basket of assets is assigned an expected return and standard deviation.

Example: Global Market Forecast (Portfolio view: sum-to-100% contrast)

A manager might have information about which way the total market is headed, above and beyond what history tells us. A market-capitalization weighted portfolio would be assigned a target, e. g. somewhat more positive than the historical forecast, if a particularly good quarter is expected for the entire market. Standard deviation could be assigned to be equal to the historical estimate for the market portfolio, to influence the result roughly equally to history. If historical estimates are present, the NFA software displays the historical mean and standard deviation of the contrast portfolio, once entered, for reference.

Example: Risk Premium (Group difference view: sum-to-zero contrast)

A manager likely has personal outlooks on various risk premia. Risk factors have been an important subject of study for estimation in finance. To specify a particular risk premium, a basket would be chosen to represent those assets possessing the risk factor, and another basket representing assets without the factor. For example, for the size premium, baskets of small-cap equities and large cap equities can be created. The small assets would be assigned the positive weights of their basket, and the large assets would be assigned negative weights. The mean would target the actual target premium, and the standard deviation would be assigned relative to the historical standard deviation. The estimator results would then show a size premium (expected return of the contrast portfolio) pulled toward the contrast mean.

Entering Forecast Contrasts Manually

When forecast contrasts are displayed, one forecast contrast entry column appears on the Forecasts Worksheet.  

• Enter a name for the contrast in the column heading.

• Enter a percentage for each asset to be included in the contrast.  The percentage reflects the asset's weight in the group.

• • Positive, negative, or zero values are allowed.

  • Contrasts with all zero weights will be eliminated from the estimation procedure.

• Enter your forecast for the group of assets in the Mean and Standard Deviation Fields.    

• • These two entries are analogous to the Forecast Mean and Standard Deviation of Forecast columns for Bayes Forecasting. In fact, with 100% in an asset’s row and 0% in all other assets, any mean and standard deviation entered here is equivalent to entering the mean and standard deviation Forecast Mean and Standard Deviation of Forecast columns for that asset.  

  • All values are legal for the mean and positive values are legal for the standard deviation.

• To enter additional forecast contrasts, click the “+” button and repeat the steps above, or use the Contrasts Wizard (see below).

• To delete the rightmost forecast contrast, click the “-” button.  To delete other contrasts, without deleting the rightmost contrast, access the Contrasts Wizard (see below).

• To turn a contrast off, enter a zero, a negative number, or a non-numerical entry in the Standard Deviation Field.  "N/A" appears in the field, and the column turns a lighter blue.  Contrasts that are off are not included during estimation.  

• When NFA Bayes or Forecasts is selected in the Bayes Forecasting drop down menu, click the Run Bayes button in the ribbon in order to combine all forecasts with the historical results.  The results will appear on the Results Worksheet.

• The historical numbers are presented below each contrast on the worksheet for guidance as to how to set the forecast mean and standard deviation.  

• • Historic Mean indicates the historical return for the portfolio with the same weights as the contrasts for comparison purposes.  For instance, if you entered a contrast with 100% in Euro Bonds, this field would show the historic return of Euro Bonds.

  • Historic Standard Deviation indicates the historical standard deviation for the contrasts.  For instance, if you entered a contrast with 100% in Euro Bonds, this field would show the historic standard deviation of Euro Bonds.

  • Result Mean shows the final result of expected return for the contrast, including historical estimates, single asset forecasts, and contrasts.  

  • Contrast Effect shows the difference in estimates with and without that contrast, the estimate with all contrasts minus the estimate with all contrasts except the one in question.

Equity Premium Example

One way to forecast an equity premium, where the bond weights sum to -100% and the equity weights sum to 100%, is to equally weight the bonds and weight the equities in proportion to their market weights.  Using this method, the contrast portfolio for the default sample case would be:

• Euro Bonds: -50%

• US Bonds: -50%

• Canada: 5%

• France: 10%

• Germany: 10%

• Japan: 30%

• UK: 10%

• US: 35%

If you believe that the equity premium will be 8%, enter 8% as the mean. The historic mean for this portfolio is shown as 5.9% and the historic standard deviation is 13.7%. So, entering 8% as the standard deviation would represent a view which is relatively strong when compared to the historical information only. Indeed, with these settings the result mean is 7.5% and the contrast effect is 1.5%, moving the result mean from 6.0% to 7.5%.

The Vanguard data sample cases provide additional examples of forecast contrasts.

Contrasts Wizard

Click the Edit Contrast button on the ribbon. The Edit Contrasts Window appears. If you want to enter a view (forecast) on a single portfolio, click the Add Portfolio Forecast button.  A dialog window the opens with the complete list of available assets in the left pane. Use the Add and Remove buttons to move the desired assets into the Selected Assets Box.  Select either the Equal Weight or the Market Weight option. Fields then must be entered for the Mean (target value) and Standard Deviation (dispersion) for the contrast. For reference the historical mean and standard deviation of the chosen contrast are displayed. A name for the contrast can be added in the top field. Click the OK button. The contrast weight for the ith asset is then proportional to the market weight. In mathematical terms this is equal to (1iwi)/(Σj1jwj) where

• 1i={1 if the asset is in the contrast, 0 otherwise

• wi={1 if equal weighting is selected and the ith market weight if market weighting is selected and the summation in the denominator is over the entire asset set.

A view (forecast) contrasting two portfolios can be entered by clicking on the Add Contrast Forecast button. A dialog appears with the list of available assets at the top center.  Add assets to a group by using the appropriate Add button. At least one asset must be on each side. Select either the Equal Weight or the Market Weight option.  Complete Forecast Mean (target value) and Forecast Standard Deviation (dispersion) Fields. Watch the sign of the forecast mean. The return of group A is forecast to exceed the return of group by the forecast mean. For reference the historical mean and standard deviation of the chosen contrast are displayed. A name for the contrast can be added in the top field. Click the OK button. The contrast weight for the ith asset is then proportional to the market weight within its portfolio. This is mathematically equal to (signiwi)/(Σj1sign j = sign iwj) where

• signi={1 for the positive assets, 0 for assets not included in the contrast, and -1 for negative assets

• 1sign j = sign i = {1 if signj = sign i, 0 otherwise

•  wi={1 if equal weighting is selected, the ith market weight if market weighting is selected and the summation in the denominator is over the entire asset set.

Maintaining Contrasts

• You can edit contrasts manually at any time, by making changes directly on the Forecasts Worksheet. Alternately, access the Contrasts Wizard, select a contrast, and click the Edit Button. If the Estimator recognizes the contrast type, either the Portfolio Forecast or Contrast Forecast Window will appear with the current contrast data. Make the desired changes. Click the OK button.

• Market portfolio weighted and equally weighted contrasts automatically update when the market portfolio changes or the number of assets in the case changes. (Note that if you load an older case, the source of the weightings may not appear above the contrast.  In those situations, you will need to update the contrast manually.) The "market-weighted" or "equal" indicator at the top of the column tells you whether or not the contrast will update automatically.

• Managed contrasts, marked with either "equal" or "market-weighted", must be edited with the wizard in order to maintain their managed, automatically-updating status. If you change the weights manually, the contrast will no longer update automatically.

• To delete a contrast,access the Contrasts Wizard, select a contrast, and click the Remove Button.

• Rather than delete contrasts, some users prefer to deactivate the contrast so that it will be available later. To do so, remove the checkmark from the box above. The contrast will appear in a lighter blue to indicate that it is inactive. To reactivate, re-check.