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:
- 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. - Calculate the Sum of the Total Original Source Weight at all constrained levels.
Sum the original source weight before the constraints. - 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 - Calculate the New Weights for all remaining (nonconstrained) 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 - Copy all the security and segment returns, except those for the constrained level and above, from the source to the target (custom benchmark).
- 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.
Dictionary Level | Fixed |
|---|---|
Total | |
Australia | 10% |
Unknown | |
Canada | |
Foreign Gov. | |
UK | |
Petroleum | |
Unknown | |
US | |
Capital Goods | |
Technology | |
Petroleum |
The following table lists the data for the source index for this example constrained benchmark.
Perf Rollup Returns ID | Description | ABAL | Return |
|---|---|---|---|
1 | Total | 100.000000000000 | 2.337512614320 |
2 | Total – Canada | 0.186961567780 | 1.167482994596 |
3 | Total - Canada - Foreign Govt. | 0.186961567780 | 1.167482994596 |
4 | Total – UK | 21.654973670853 | 3.475919376493 |
5 | Total - UK - Petroleum | 16.356854652918 | 3.800720520895 |
6 | Total – US | 60.189112766022 | 2.149367889086 |
7 | Total - US - Capital Goods | 16.928285677007 | 0.954101703137 |
8 | Total - US - Technology | 17.933412208518 | 2.922672275580 |
9 | Total - US - Petroleum | 2.960736862858 | 3.768148149908 |
10 | Total - US - Basic Industries | 16.596291716438 | 2.654587081941 |
11 | Total – Australia | 17.968951995345 | 1.607967908012 |
12 | Total - Australia - Unknown | 17.968951995345 | 1.607967908012 |
13 | Total - UK - Unknown | 5.298119017935 | 2.473162531641 |
14 | Total - US - Unknown | 5.770386301202 | 0.968905089765 |
In the following table, the resulting target data for the constrained benchmark is listed.
Description | ABAL (%) | Return | Fixed (%) | Wt. Chg. (%) | New Weight (%) | Return Recalc | New Returns |
|---|---|---|---|---|---|---|---|
Total | 100.00 | 2.337513 | 100.00 | 2.408385 | 2.408385 | ||
Total – Canada | 0.19 | 1.167483 | 0.02 | 0.21 | 1.167483 | ||
Total – Canada – Foreign Govt. | 0.19 | 1.167483 | 0.02 | 0.21 | 1.167483 | ||
Total – UK | 21.65 | 3.475919 | 2.10 | 23.76 | 3.475919 | ||
Total – UK – Petroleum | 16.36 | 3.800721 | 1.59 | 17.95 | 3.800721 | ||
Total – US | 60.19 | 2.149368 | 5.85 | 66.04 | 2.149368 | ||
Total – US – Capital Goods | 16.93 | 0.954102 | 1.64 | 18.57 | 0.954102 | ||
Total – US – Technology | 17.93 | 2.922672 | 1.74 | 19.68 | 2.922672 | ||
Total – US – Petroleum | 2.96 | 3.768148 | 0.29 | 3.25 | 3.768148 | ||
Total – US – Basic Industries | 16.60 | 2.654587 | 1.61 | 18.21 | 2.654587 | ||
Total – Australia | 17.97 | 1.607968 | 10 | -7.97 | 10.00 | 1.607968 | |
Total – Australia – Unknown | 17.97 | 1.607968 | X | -7.97 | 10.00 | 1.607968 | |
Total – UK – Unknown | 5.30 | 2.473163 | 0.51 | 5.81 | 2.473163 | ||
Total – US – Unknown | 5.77 | 0.968905 | 0.56 | 6.33 | 0.968905 | ||
Sum of Total Source Weight at Constrained Levels | 17.97 | ||||||
Total Constrained Weight | -7.97 |
Complete the following:
- Calculate Total Constrained Weight = 10% - 17.97% = -7.97%.
- Calculate the Sum of the Total Source Weight at all Constrained Levels = 17.97%.
- 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% - Calculate the New Weights for the remaining (nonconstrained) 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% - 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.
Description | Return | New Weight | Target Return |
|---|---|---|---|
Total | 2.408384642 | ||
Total - Australia | 1.607968 | 10.00% | 0.160796791 |
Total - Canada | 1.167483 | 0.21% | 0.002394788 |
Total - UK | 3.475919 | 23.76% | 0.825831804 |
Total - US | 2.149368 | 66.04% | 1.41936126 |
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