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 90% and 10%, respectively. The risk-free rate of return was 3%.

One-Year Trailing Returns
	Miranda Fund			S&P 500
Return		9.7	%		?21.6	%
Standard deviation		38.0	%		43	%
Beta		1.50			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

Sharpe ratio= (r_p-r_f)/?_p

r_p Expected portfolio return

r_f = Risk free rate= 3%

?_p = Portfolio standard deviation

For Miranda fund, Sharpe ratio= (9.7%-3%)/38%= 0.1763

For S&P 500, Sharpe ratio= (-21.6%-3%)/43%= -0.5721

M2 measure = Sharpe ratio x standard deviation of benchmark (S&P 500 in this case) + risk free rate

= 0.1763 x 43% + 3% = -0.8084%

Treynor measure = (Portfolio return – risk free rate)/beta of portfolio

For Miranda fund, Treynor measure= (9.7%-3%)/1.5= 4.4667%

For S&P 500, Treynor measure= (-21.6%-3%)/1= -24.6%

Jensen measure= r_p – (r_f + Beta x (r_m - r_f))

r_p Expected portfolio return

r_f = Risk free rate= 3%

r_m = return of market index (S&P 500 in this case)

=9.7% - (3% + 1.5 x (-21.6% - 3%))

=0.436

Summarized results:

	Sharpe ratio	M2 measure	Treynor measure	Jensen measure
Miranda fund	0.1763	-0.8084%	4.4667%	0.4360
S&P 500	-0.5721	NA	-24.6000%	NA