Question

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             

Answer 1

	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%