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P1.T1.610. Risk-adjusted performance measures (Topic Review)

Nicole Seaman

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610.1. Over a historical period, the broad market index had an excess return of 7.0% with volatility, σ(M), of 20.0%. Please note "excess return" refers to the return in excess of the riskfree rate. Over the same period, the excess returns of a portfolio were regressed against the market index. Where Rf signifies the riskfree rate, the regression result is given by E[R(p) - Rf] = α(i) + β(p,M)*[R(M) - Rf] = 0.02850 + 0.450*[R(M) - Rf]; that is, the regression intercept is +2.850% and the portfolio beta's, β(p,M), is 0.450. The regression R^2 (coefficient of determination) is 0.12960.

What is the portfolio's implied Sharpe ratio?

a. 0.24
b. 0.33
c. 0.59
d. We need the riskfree rate and/or portfolio return


610.2. Which of following statements is TRUE about the information ratio (IR)?

a. The information ration generalizes the Sharpe ratio by replacing the riskfree rate with the benchmark rate of return
b. The monthly information ratio (IR) is the same as its annualized IR because both numerator and denominator are multiplied by 12
c. If a portfolio underperforms the benchmark (e.g., portfolio return is 7% versus market index return of 8%) then the information ratio must be negative
d. Because t-stat = IR*N, where N is number of years, N = t/IR, such that demonstration of alpha-type skill typically requires N = 2/IR years of out-performance


610.3. Consider the following results of an ex-post analysis of a portfolio and its benchmark.
  • The riskfree rate is 1.0% per annum
  • The benchmark (market index) had an average return of 4.0% per annum with volatility of 20.0%
  • The portfolio's average return was 5.0% per annum with volatility of 30.0%
  • The portfolio correlation to the benchmark, ρ(p, M), was 0.60
  • The portfolio's tracking error (aka, active risk not residual risk) was 10.0%
  • The portfolio's minimum acceptable return (MAR) was 3.0% per annum and its downside deviation was 15.0%
Assume all values are already annualized. Which of the following measures gives the HIGHEST value?

a. Sharpe ratio
b. Treynor ratio
c. Information ratio
d. Sortino ratio

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