Question

You are given the following information concerning three portfolios, the market portfolio, and the risk-free asset:

Portfolio	Rp		σp		βp
X	12.5	%	38	%	1.45
Y	11.5		33		1.15
Z	9.4		23		.80
Market	11.9		28		1.00
Risk-free	6.2		0		0

What are the Sharpe ratio, Treynor ratio, and Jensen’s alpha for each portfolio? (A negative value should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Round your ratio answers to 5 decimal places. Enter your alpha answers as a percent rounded to 2 decimal places.)

Answer 1

Required Return of X =Risk Free Rate+Beta*(Market Return-Risk Free Rate) =6.2%+1.15*(11.9%-6.2%) =14.465%
Sharpe Ratio of X=(Expected Return-Risk Free)/Standard Deviation =(12.5%-6.2%)/38% =0.16579
Treynor ratio of X=(Expected Return-Risk Free)/Beta =(12.5%-6.2%)/1.45 =0.04345
Jensen Alpha of X =Expected Return -Required rate of A =12.5%-14.465% =-1.97%

Required Return of Y =Risk Free Rate+Beta*(Market Return-Risk Free Rate) =6.2%+1.45*(11.9%-6.2%) =12.755%
Sharpe Ratio of Y=(Expected Return-Risk Free)/Standard Deviation =(11.5%-6.2%)/33% =0.16061
Treynor ratio of Y=(Expected Return-Risk Free)/Beta =(11.5%-6.2%)/1.15 =0.04609
Jensen Alpha of Y =Expected Return -Required rate of A =11.5%-12.755% =-1.26

Required Return of Z =Risk Free Rate+Beta*(Market Return-Risk Free Rate) =6.2%+0.8*(11.9%-6.2%) =10.76%
Sharpe Ratio of Z=(Expected Return-Risk Free)/Standard Deviation =(9.4%-6.2%)/23% =0.13913
Treynor ratio of Z=(Expected Return-Risk Free)/Beta =(9.4%-6.2%)/0.8 =0.04
Jensen Alpha of Z =Expected Return -Required rate of A =9.4%-10.76% =-1.36%

Required Return of Market =Risk Free Rate+Beta*(Market Return-Risk Free Rate) =6.2%+1*(11.9%-6.2%) =11.90%
Sharpe Ratio of Market=(Expected Return-Risk Free)/Standard Deviation =(11.9%-6.2%)/28% =0.20357
Treynor ratio of Market=(Expected Return-Risk Free)/Beta =(11.9%-6.2%)/1 =0.057
Jensen Alpha of Market =Expected Return -Required rate of A =11.90%-11.90% =0