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Risk Measurement: Weight Overlap

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A portfolio’s weight overlap (with a benchmark) is a non-risk model specific measure of the extent to which holding weights in a portfolio coincide with those in a benchmark.

 

Suppose that the value of the portfolio is  and the value of an individual security  in the portfolio is . Then its weight in the portfolio is given by:

 

 

The corresponding weight in the benchmark is  say.

 

Occasionally, the portfolio and/or benchmark can be unfunded, in which case these weights are not well-defined. In such circumstances there must be some positions with positive value and some with negative value (if the portfolio is not trivially to equal zero). We might then calculate, say, the gross portfolio value as follows, and express values by reference to it instead.

 

 

The security’s active weight is   (or more generally  if there are several possible portfolios and benchmarks under consideration.  The active weights satisfy .

 

The weight overlap, , then measures the proportion of the value between two portfolios that is identical, calculated as follows (where the summation covers all securities which appear in both  and ):

 

 

See also the MnWeightOverlap web function.

 

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