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	(44%)
Below average	0.1	(15)
Average	0.3	10
Above average	0.3	23
Strong	0.2	45
	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*-44%+0.1*-15%+0.3*10%+0.3*23%+0.2*45% =13%
Standard Deviation =(0.1*(-44%-13%)^2+0.1*(-15%-13%)^2+0.3*(10%-13%)^2+0.3*(23%-13%)^2+0.2*(45%-13%)^2)^0.5=25.314% or 25.31%

Coefficient of variation =Standard Deviation/Expected Return =25.314%/13% =1.9472 or 1.95
Sharpe Ratio =(Expected return -Risk Free rate)/Standard Deviation =(13%-4%)/25.314%=0.3555 or 0.35