Kelli Blakely is a portfolio manager for the Miranda Fund (Miranda), a core large-cap equity fund. The market proxy and benchmark for performance measurement purposes is the S&P 500. Although the Miranda portfolio generally mirrors the asset class and sector weightings of the S&P, Blakely is allowed a significant amount of leeway in managing the fund. Her portfolio holds only stocks found in the S&P 500 and cash.
Blakely was able to produce exceptional returns last year (as outlined in the table below) through her market-timing and security selection skills. At the outset of the year, she became extremely concerned that the combination of a weak economy and geopolitical uncertainties would negatively impact the market. Taking a bold step, she changed her market allocation. For the entire year her asset class exposures averaged 50% in stocks and 50% in cash. The S&P’s allocation between stocks and cash during the period was a constant 97% and 3%, respectively. The risk-free rate of return was 2%.
| One-Year Trailing Returns | ||||||
| Miranda Fund | S&P 500 | |||||
| Return | 9.6 | % | −21.7 | % | ||
| Standard deviation | 37.0 | % | 42 | % | ||
| Beta | 1.40 | 1.00 | ||||
a. What are the Sharpe ratios for the Miranda Fund and the S&P 500? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 4 decimal places.)
| Sharpe Ratio | |
| Miranda fund | |
| S&P 500 | |
b. What is the M2 measure for Miranda? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
M2 Measure %
c. What is the Treynor measure for the Miranda Fund and the S&P 500? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 4 decimal places.)
| Treynor Measure | |
| Miranda | |
| S&P 500 | |
d. What is the Jensen measure for the Miranda Fund? (Do not round intermediate calculations. Round your answers to 4 decimal places.)
Jensen measure
| Miranda | S&P | |
| Returns | 9.60% | -21.70% |
| S.D. | 37% | 42% |
| Beta | 1.40 | 1.00 |
| Sharpe | 0.2054 | -0.5881 |
| M2 | 10.63% | |
| Treynor | 0.0543 | -0.2370 |
| Jensen | 0.4078 |
Sharpe Ratio = (Rp - Rf) / SDp, where Rp - Returns, Rf - Risk-free rate = 2% and SDp - Standard Deviation of portfolio
Sharpe for Miranda = (9.60% - 2%) / 37% = 0.2054
M2 = Rf + Sharpe Ratio x SDm = 2% + 0.2054 x 42% = 10.63%
Treynor = (Rp - Rf) / Beta
Jensen = Rp - [Rf + beta x (Rm - Rf)], where Rm - Market Return = -21.70%
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