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 93% and 7%, respectively. The risk-free rate of return was 2%.

One-Year Trailing Returns
	Miranda Fund			S&P 500
Return		10.4	%		−20.9	%
Standard deviation		35.0	%		40	%
Beta		1.20			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

a. Sharpe ratio = (Portfolio return - risk-free rate)/Standard deviation of portfolio returns

Sharpe ratio for Miranda fund = (0.104 - 0.02)/0.35 = 0.084/0.35 = 0.2400

Sharpe ratio for S&P 500 = (-0.209 - 0.02)/0.40 = -0.229/0.40 = -0.5725

b. M² measure = Risk-free rate + [(Portfolio return - risk-free rate)/Standard deviation of portfolio returns] * market standard deviation

M² measure for Miranda fund = 0.02 + [(0.104 - 0.02)/0.35] * 0.40 = 0.02 + (0.084/0.35) * 0.40 = 0.02 + 0.24*0.40 = 0.02 + 0.096 = 0.116 or 11.60%

c. Treynor measure = (Portfolio return - risk-free rate)/Beta of portfolio returns

Treynor measure for Miranda fund = (0.104 - 0.02)/1.2 = 0.084/1.2 = 0.0700

Treynor measure for S&P 500 = (-0.209 - 0.02)/1 = -0.229/1 = -0.2290

d. Jensen measure = Portfolio return - [Risk-free rate + beta of portfolio*(market return - risk-free rate)]

Jensen measure for the Miranda Fund = 10.4% - [2% + 1.2*(-20.9% - 2%)] = 10.4% - [2% + 1.2*-22.9%] = 10.4% - (2% -27.48%) = 10.4% - (-25.48%) = 10.4% + 25.48% = 35.88% or 0.3588