Discuss the tests used to judge whether a benchmark is sound
The idea
A valid benchmark is specified in advance, appropriate, measurable, unambiguous, reflective of the manager's current opinions, accountable and investable. Write the portfolio return as P = M + S + A, where M is the market, S = B − M is style and A = P − B is active return. Low systematic bias: the portfolio's beta against the benchmark is close to 1 and the correlation of A with S is close to zero. Tracking error against the benchmark should be lower than against a broad index. Size and value exposures should match. Coverage, the share of the portfolio held in benchmark securities, should be high; benchmark turnover low; and most active positions positive for a long-only manager. Failures mean the benchmark misstates skill.
Formulas
Portfolio return split by benchmark
P = M + S + A
- M
- the market index return
- S
- the style return: the benchmark less the market
- A
- the active return: the portfolio less the benchmark
A sound benchmark leaves A uncorrelated with S and gives the portfolio a beta near one against it. A misspecified benchmark pushes style into A, where it looks like skill.
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