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	0.2	(36%)
Below average	0.1	(7)
Average	0.3	18
Above average	0.2	27
Strong	0.2	48
	1.0

Assume the risk-free rate is 3%. 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

Stock's expected return = Summation of (Probability of the scenario*Expected return in that scenario)

Stock's expected return = 0.2*(-36%)+ 0.1*(-7%) + 0.3*18% + 0.2*27% + 0.2*48%

Stock's expected return = 12.5%

Variance = Summation of (Probability of the scenario*(Expected return in that scenario-Expected return)^2)

Variance = 0.2*(-36%-12.5%)^2 + 0.1*(-7%-12.5%)^2 + 0.3*(18%-12.5%)^2 + 0.2*(27%-12.5%)^2 + 0.2*(48%-12.5%)^2

Variance = 0.081165

Standard deviation = Variance^0.5 = 0.081165^0.5

Standard deviation = 0.2849 = 28.49%

Coefficient of variation = Standard deviation/Expected return = 0.2849/0.125

Coefficient of variation = 2.2792

Sharpe's ratio = (Expected return-Riskfree rate)/Standard deviation

Sharpe's ratio = (0.125-0.03)/0.2849

Sharpe's ratio = 0.3334