Question

1. Based on the following information for mutual funds A and B, find Jensen’s alpha, Sharpe ratio, Treynor ratio, and Information ratio. Which fund is preferable based on each performance measure? Can you make an overall recommendation between the two? (10 points)

	A	B
Beta	1.3	1.6
Standard deviation	8%	14%
Standard deviation of nonsystematic risk	5%	10%
Expected return	14%	17%
Market return	10%	10%
Risk-free rate	2%	2%

Answer 1

For Mutual Fund A
Capm Required Rate of A =Risk Free Rate+Beta*(Market Return -Risk Free Rate) =2%+1.3*(10%-2%) =12.4%
Jensen Alpha =Expected Return -Required rate of A =14%-12.4% =1.6%
Sharpe Ratio =(Expected Return-Risk Free)/Standard Deviation =(14%-2%)/8% =12%/8% =1.50
Treynor ratio =(Expected Return-Risk Free)/Beta =(14%-2%)/1.3 =0.092
Information Ratio =(Expected Return A -Required rate of A)/Standard deviation of nonsystematic risk =(14%-12.4%)/5% =0.32

For Mutual Fund B
Capm Required Rate of A =Risk Free Rate+Beta*(Market Return -Risk Free Rate) =2%+1.6*(10%-2%) =14.80%
Jensen Alpha =Expected Return -Required rate of A =17%-14.8% =2.2%
Sharpe Ratio =(Expected Return-Risk Free)/Standard Deviation =(17%-2%)/14% =15%/14% =1.07
Treynor ratio =(Expected Return-Risk Free)/Beta =(17%-2%)/1.6 =0.094
Information Ratio =(Expected Return A -Required rate of A)/Standard deviation of nonsystematic risk =(17%-14.8%)/10% =0.22

Based on Jansen alpha Mutual Fund B is better.
Based on Sharpe ratio Mutual Fund A is better.
Based on Treynor ratio Mutual Fund B is better
Based on Information Ratio Mutual Fund a is better

Based on overall recommendation Mutual Fund A is better because the return to risk ratio is less for Mutual Fund A.