Question

ch18

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 91% and 9%, respectively. The risk-free rate of return was 3%.

One-Year Trailing Returns
	Miranda Fund			S&P 500
Return		9.9	%		−21.4	%
Standard deviation		30.0	%		35	%
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

	Miranda Fund	S&P 500
Return ('r)	9.9%	-12.4%
Standard deviation (σ)	30.0%	35.0%
Beta	1.20	1.00
risk-free rate (rf)	3%	3%

a). Sharpe ratio:

	Miranda Fund	S&P 500
(r-rf)	6.9%	-15.4%
Sharpe ratio = (r-rf)/σ	0.2300	-0.4400

b). M2 measure for Miranda Fund:

M2 = (Sharpe ratio for Miranda Fund)*(Standard deviation for the benchmark) + (risk-free rate)

= (0.2300*35%) + 3% = 0.11

c). Treynor measure:

	Miranda Fund	S&P 500
(r-rf)	6.9%	-15.4%
Treynor ratio = (r-rf)/beta	0.0575	-0.1540

d). Jenson measure for Miranda Fund:

Jensen's measure is that part of a rate of return which exceeds the return as calculated/expected by models like a CAPM model. So,

returnMiranda = rf + beta(rm - rf) + Jensen measure

Jensen measure = returnMiranda - rf - beta(rm - rf)

= 9.9% - 3% - 1.2(-12.4%-3%)

= 0.2538