Test of Benchmark Quality

SAMURAI

The choice of benchmark often has a significant effect on the assessment of manager performance. Investment managers should be compared only with benchmarks that reflect the universe of securities available to them. A valid benchmark must satisfy certain criteria. The following are characteristics of a valid benchmark by using the definitive list from Bailey and Tierney (1998). (Together they spell SAMURAI)

• Specified in advance: The benchmark must be constructed before the evaluation period so the manager is not measured against benchmarks created after the fact.
• Appropriate: The benchmark must be consistent with the manager's investment style or area of expertise.
• Measurable: It must be possible to measure the benchmark's return on a reasonably frequent and timely basis.
• Unambiguous: The individual securities and their weights in a benchmark should be clearly identifiable. For example, we should be able to identify whether any firm is included in a global equity benchmark and its weight.
• Reflective of current investment opinions: The manager should be familiar with the securities that constitute the benchmark and their factor exposures. Managers should be able to develop an opinion regarding their attractiveness as investments; they should not be given a mandate of obscure securities.
• Accountable: The manager should accept ownership of the benchmark and its securities and be willing to be held accountable to the benchmark. The benchmark should be fully consistent with the manager's investment process, and the manager should be able to demonstrate the validity of his or her benchmark. Through acceptance of the benchmark, the sponsor assumes responsibility for any discrepancies between the targeted portfolio for the fund and the benchmark. The manager becomes responsible for differences between the benchmark and her performance.
• Investable: It must be possible to recreate and invest in the benchmark to earn its return (at least gross of expenses). The sponsor should have the ability to move assets from active management to a passive benchmark. If the benchmark is not investable, it is not an investment alternative.

Testing Benchmark Quality

Once a benchmark is constructed, its quality can be tested using the following formula, which will be built up piece by piece for understanding.

First, state the identity where a portfolio's return (P) is equal to itself:

$$ P = P $$

Then, add an appropriate benchmark (B) to, and subtract this benchmark from, the right-hand side of the equation:

$$ P = B + (P − B) $$

The term \(P – B\) is the result of the manager's active management decisions, which we denote as A. Thus:

$$ P = B + A $$

The portfolio return is a function of the benchmark and the manager's active decisions. Next, add market index return (M) to and subtract it from the right-hand side of the equation:

$$ P = M + (B – M) + A $$

The manager's style return is the difference between the benchmark return and the market index (B – M):

$$ P = M + S + A $$

The final equation states that the portfolio return (P) is a result of the market index return (M), a style return (S), and the active management return (A).

If the manager's portfolio is a broad market index where S = 0 and A = 0, then the portfolio earns the broad market return: P = M.

If the benchmark is a broad market index, then S is assumed to be zero and the prediction is that the manager earns the market return and a return to active management: P = M + A.

Question

Assume that an account has a return of 6.9% in a given month, during which the portfolio benchmark has a return of 6.2% and a market index has a return of 3.2%.

Calculate the return due to active management for the account:

1. 7.0%.
2. 0.7%.
3. 3.7%.

Solution

The correct answer is B.

The return due to active management is \(A = P – B = 6.9\% – 6.2\% = 0.7\%.\)

A is incorrect. It misapplies the decimal in the answer as 7.0%.

C is incorrect. It uses the market index return rather than the portfolio benchmark returns \(6.9\% – 3.2\% = 3.7\%.\)

Performance Measurement: Learning Module 1: Portfolio Performance Evaluation; Los 1(k) Discuss tests of benchmark quality