Question

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

Portfolio	RP		σP		βP
X	14.0	%	39	%	1.50
Y	13.0		34		1.15
Z	8.5		24		0.90
Market	12.0		29		1.00
Risk-free	7.2		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

SHARPE RATIO:
= (RP-Rf)/SD of the portfolio.
Portfolio X = (14%-7.2%)/39% =	0.17436
Portfolio Y = (13%-7.2%)/34% =	0.17059
Portfolio Z = (8.5%-7.2%)/24% =	0.05417
TREYNOR RATIO:
= (RP-Rf)/Beta of the portfolio.
Portfolio X = (14%-7.2%)/1.5 =	0.04533
Portfolio Y = (13%-7.2%)/1.15 =	0.05043
Portfolio Z = (8.5%-7.2%)/0.90 =	0.01444
JENSEN'S ALPHA:
= Portfolio Return − [Risk Free Rate + Portfolio Beta * (Market Return − Risk Free Rate)]
Portfolio X = 14.0% -((7.2%+1.5*(12%-7.2%)) =	-0.40%
Portfolio X = 13.0% -((7.2%+1.15*(12%-7.2%)) =	0.28%
Portfolio X = 8.5% -((7.2%+0.9*(12%-7.2%)) =	-3.02%