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Nicole Seaman

Director of FRM Operations
Staff member
Learning outcome: Determine the statistical significance of a performance measure using standard error and the t-statistic. Describe style analysis. Explain the difficulties in measuring the performance of actively managed portfolios.


21.11.1. Jane Dart is a portfolio manager (she happens to be happily married to Joe Dart who is mentioned in the Bodie reading). Her performance has been dazzling. Her portfolio provided an alpha of 190 basis points per month, or +22.80% per year before compounding. Her portfolio beta is 1.30 and the monthly standard deviation of the residual is σ(e) = 4.0% per month; assume this is also the monthly standard deviation of the alpha such that σ(e) = σ(α). We certainly think Jane is skilled! The null hypothesis is that her alpha is due to luck. We only require 90.0% confidence; put another way, the two-sided significance level is 10.0%. Approximately how many years of this outperformance do we require in order to consider Jane skillful; that is, to reject the null hypothesis?

a. 1.0 year
b. 5.0 years
c. 12.0 years
d. 25.0 years

21.11.2. Peter manages a portfolio and his performance is measured against a hypothetical benchmark (aka, Bogey Portfolio). The Bogey Portfolio has an allocation of 50.0% to equity, 30.0% to bonds, and 20.0% to cash. During the period the Bogey Portfolio's return was +5.40% (see top panel below).

Peter's active portfolio outperformed the Bogey portfolio by +4.0% because his portfolio returned +9.40%. His asset allocation was 80.0% to equity (i.e., +30% over the Bogey), 10.0% to bonds (i.e., -20.0% under the Bogey) and 10.0% to cash (-10.0% under the Bogey). His equity return was +11.0% (versus 8.0% for the Bogey) and his bond return was +5.0% (versus +4.0% for the Bogey). Of the +4.0% excess return, how much should be attributed to security selection?

a. 0.75%
b. 2.50%
c. 3.40%
d. 4.0-% (the entire excess)

21.11.3. Robert manages a portfolio and his part of his compensation is based on performance over a three-year period. During the first 18 months, his performance was significantly below his benchmark; aka, bad. Based on this reality, he decides to greatly increase the leverage in his portfolio with the aim of boosting returns in the second 18-month sub-period (this also magnifies the risk, of course). His firm employs several candidate performance metrics, including: Sharpe ratio, Jensen's alpha, Treynor ratio, information ratio, and Morningstar's risk-adjusted rating (aka, MRAR). Among these metrics, which is BEST suited to Robert's situation?

a. The information ratio is best because it incorporates investor risk aversion
b. Because we are evaluating the manager's entire risky portfolio rather than a (sub-) component, the Treynor ratio is best
c. The Sharpe ratio is the best and most robust measure to handle (i.e., adjust for) the manager's mid-cycle adjustment
d. Morningstar's risk-adjusted rating (MRAR) is the best measure to handle (i.e., adjust for) the manager's mid-cycle adjustment.

Answers here:
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