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 95% and 5%, respectively. The risk-free rate of return was 3%.

One-Year Trailing Returns
	Miranda Fund			S&P 500
Return		10.7	%		?20.6	%
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

a)MF=(.107-.03)/.38=.2026

S&P=(-.206-.03)/.43=-.5488

b)To compute M²measure, blend the Miranda Fund with a position in T-Bills such that the “adjusted” portfolio has the same volatility as the market index. Using the data, the position in the Miranda Fund should be .43/.38 = 1.1316 and the position in T-Bills should be 1 ? 1.1316 = -.1316. (assuming borrowing at the risk free rate)

The adjusted return is:r_p= (1.1316) × 10.7% ? (.1316) ×3% = .1250 = 12.50%

Calculate the difference in the adjusted Miranda Fund return and the benchmark:M²=rP?r_M=12.5%?(?20.60%)=33.10%

c)MF=(.107-.03)/1.5=.0513

S&P=(-.206-.03)/1.0=-.436

d)MF:?P = E(rp) ? {rf + ?p[E(rM) ? rf]}

=.107-[.03+1.5(-.206-.03)]

=.431