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.

• Absolute bounds refer to the amount of a particular asset in the resulting portfolio.  If you enter a lower bound of 2% and an upper bound of 10% for asset A, every resulting portfolio on the efficient frontier will contain between 2% and 10% of asset A.

• • When negative asset bounds are specified, they appear in red.  Negative bounds and bounds above 100% are permissible without enabling Long-Short Optimization.

  • To exclude an asset entirely, enter zeroes in both the Min% and Max% columns.

  • Consider leaving the minimum bounds at zero, even if you want to insist on an allocation to each asset.  Then, use investability constraints (either asset bounds or the asset threshold constraint) to perform a similar function during the post-optimization process.  This allows you to see what the allocations would be with and without the forced allocation, which can be useful.

• Benchmark-relative asset bounds reference the benchmark portfolio on the Portfolios Worksheet.  For example, asset bounds of -2% and 2% when the benchmark weight of that asset is 4%, means that the resulting portfolios must contain between 2% and 6% of the asset in absolute terms.

• • A benchmark-relative asset bound of 0% (either upper or lower) results in a one portfolio efficient frontier--the benchmark.

  • Negative lower bounds permit dipping below the benchmark asset weights.

• You can set one bound as absolute and another as benchmark-relative.  One possibility is to set the minimum bound to an absolute 0, while having a maximum bound that is benchmark-relative.

• Investable asset bounds, entered on the Investability Constraints Worksheet, restrict the asset allocations after optimization.  Optimal asset bounds, entered on the Constraints Worksheet, restrict the asset allocations on the optimal efficient frontier.

• To assign the same asset bound to each asset, enter the desired minimum and maximum weights in the row directly below the Asset Bounds header on the Constraints Worksheet (light blue fields).  The default bounds populate the Min% and Max% columns for all assets.

• Enter asset bounds for particular assets as you desire; individually entered bounds appear with a white background to differentiate them from the defaults.

• Entering a non-numeric key or delete changes the bound from an individually entered bound to tracking the default bound; this change is indicated by the changed background color. 

• Asset bounds can be loaded or saved as part of a constraint set.

• Keep in mind that if you set asset bounds you are insisting that all simulations be between those bounds, which can greatly affect your results.  For example, it is easy to have a case where an unconstrained allocation of 10% becomes a 6% allocation by setting a 15% maximum asset bound.  In the unconstrained version there were a lot of simulations that went above 15%, thus bringing the average up. For Michaud optimization, it is unlikely that portfolio weights will attain the bounds, unlike Classical Mean-Variance optimization, in which constrained assets frequently attain the constraint bounds.