Question

A stock's returns have the following distribution:

Demand for the Company's Products	Probability of This Demand Occurring	Rate of Return If This Demand Occurs
Weak	0.1	(48%)
Below average	0.1	(15)
Average	0.3	11
Above average	0.3	40
Strong	0.2	65
	1.0

Assume the risk-free rate is 4%. Calculate the stock's expected return, standard deviation, coefficient of variation, and Sharpe ratio. Do not round intermediate calculations. Round your answers to two decimal places.

Stock's expected return:   %

Standard deviation:   %

Coefficient of variation:

Sharpe ratio:

Answer 1

Expected Return =0.1*-48%+0.1*-15%+0.3*11%+0.3*40%+0.2*65%=22%
Standard Deviation =(0.1*(-48%-22%)^2+0.1*(-15%-22%)^2+0.3*(11%-22%)^2+0.3*(40%-22%)^2+0.2*(65%-22%)^2)^0.5
=33.6184% or 33.62%
Coefficient of Variation =Standard Deviation/Expected Return =33.6184%/22% =1.53
Sharpe Ratio=(Expected Return-Risk Free rate)/Standard Deviation =(22%-4%)/33.6184%=0.54