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Explanation:
B is correct. Tracking error (TE) is defined as the standard deviation of a portfolio's active return, where active return is the difference between the portfolio's return and the benchmark's return (RP - RB). This measure quantifies how consistently a portfolio deviates from its benchmark over time.
A is incorrect because the Sharpe ratio calculates the ratio of the portfolio's excess return (portfolio return minus risk-free rate) to the portfolio's total standard deviation, not the ratio of portfolio return to benchmark return.
C is incorrect because the Sortino ratio uses the standard deviation of returns below the target return (downside deviation), not above the target return.
D is incorrect because the information ratio is calculated as the ratio of active return to tracking error (active return divided by the standard deviation of active returns), not simply the difference between portfolio and benchmark returns.
Key Formulas:
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The CIO of a pension fund is assessing several actively managed equity funds to add to the pension fund's portfolio. As part of this assessment, the CIO examines the suitability of various measures to evaluate the performance of outside managers and considers how each measure is calculated. Which of the following statements is correct regarding the given performance measure?
A
The Sharpe performance index calculates the ratio of the return of a portfolio to the return of the benchmark against which the portfolio is compared.
B
The tracking error calculates the standard deviation of a portfolio's active return.
C
The Sortino ratio calculates the ratio of the return of a portfolio to the standard deviation of returns above the portfolio's target rate of return.
D
The information ratio calculates the difference between the return of a portfolio and the return of the benchmark against which the portfolio is compared.