Constrained Benchmarks

The constrained benchmark allows you to constrain, or limit, the weight of a security or segment level of a vendor-supplied index and:

• Proportionately reweight the remaining securities and segments.

• Recalculate the returns above the constrained level using the new constraint-weighted returns.

• Reweight the securities and segments below the constrained level using the new constrained weights.

Two types of constraints are supported:

• Cap constraint. Sets the upper limit that the weight of a segment or security can take in the target custom benchmark. If the CAP is not reached, the vendor-supplied benchmark weight for the segment is used for the period.

• Fixed constraint. Sets the exact weight that a segment or security takes in the target custom benchmark.

You can set constraints at more than one level of the structure. For example, you can constrain a segment to a particular weight and a security within a different segment to a particular weight. The software does not support constraining a segment and a security within that segment.

Calculate Weights and Returns

The methodology for calculating constrained benchmarks follows:

1. Calculate the Total Constrained Weight = (Sum of all the constrained weights).
   Constrained weights = (the newly assigned weight for the segment or security – the vendor-supplied weight for the segment or security).
   Sum the constrained weights from Step 1.

2. Calculate the Sum of the Total Original Source Weight at all constrained levels.
   Sum the original source weight before the constraints.

3. Calculate the New Weights for the constrained securities and segments and the securities and segments below the constrained level using:
   Weight Change = (Source weight for segment or security * That Segment or Security's Constrained Weight) / (That Segment or Security's Total Original Source Weight)
   New Weight = Weight Change + Original Source Weight

4. Calculate the New Weights for all remaining (non constrained) levels.
   Weight Change = –1*((Source weight for segment or security * Total Constrained Weight (Step  1b)) / (1 – (Sum of the Total Original Source Weight at all Constrained Levels (Step 2))
   New Weight = Weight Change + Original Source Weight

5. Copy all the security and segment returns, except those for the constrained level and above, from the source to the target (custom benchmark).

6. Calculate the New Returns for the segments above the constrained segment.
   Reproportion the New Weights (calculated in Steps 3 and 4) to 100 percent for the target benchmark.
   Calculate the New Returns: Sum (Return * New Weight) of all the underlying segments or securities.

Constrained Benchmark Example

For the purposes of example, assume the source index (vendor-supplied index) and constraints listed in the following table.

The following table lists the data for the source index for this example constrained benchmark.

In the following table, the resulting target data for the constrained benchmark is listed.

Complete the following:

1. Calculate Total Constrained Weight = 10% - 17.97% = -7.97%.

2. Calculate the Sum of the Total Source Weight at all Constrained Levels = 17.97%.

3. Calculate the New Weights for the constrained segments/securities and those below the constraints. For example:
   Total Australia Weight Change = (17.97% * -7.97%) / (17.97%)
   Total Australia New Weight = -7.97 + 17.97% = 10%

4. Calculate the New Weights for the remaining (non constrained) levels. For example:
   Total UK Weight Change =1*((21.65% * -7.97%)/(1 17.97%)) = 2.10%
   Total UK New Weight = 2.10% + 21.65% = 23.75%

5. Copy all security and segment returns, except those for the constrained level and above.
   For example: Total UK Return = 3.475919
   Returns above the constrained node are recalculated — in the example in the following table, only the Total return is recalculated.