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Explanation:
B is correct. Tracking error (TE) is the measure of the difference between a portfolio's returns and those of a benchmark it was meant to mimic or to beat. The first step to calculate TE is simply to calculate: R_P − R_B where R_P is the return on the portfolio under consideration and R_B is the return on the client-specified benchmark portfolio. This difference is referred to as the active return. Tracking error is then the standard deviation of the active returns over some time period.
A is incorrect. The Sharpe performance index calculates the ratio of the difference of the return of a portfolio and the risk-free interest rate to the standard deviation of the portfolio returns.
C is incorrect. The Sortino ratio calculates the ratio of the return of a portfolio to the standard deviation of returns below the target (i.e., downside deviation), not above.
D is incorrect. The information ratio is calculated as the ratio of the active returns to the tracking error. The difference between the return on the portfolio under consideration and the return on the client-specified benchmark portfolio is referred to as the active return.
Learning Objective: Calculate, compare, and interpret the following performance measures: the Sharpe, Treynor, Jensen's alpha, information ratio, and the Sortino ratio.
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Q-14. 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.