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	(38%)
Below average	0.2	(15)
Average	0.3	12
Above average	0.3	36
Strong	0.1	61
	1.0

Assume the risk-free rate is 2%. 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=Respective return*Respective probabiity

=(0.1*-38)+(0.2*-15)+(0.3*12)+(0.3*36)+(0.1*61)

=13.7%

probabiity	Return	probabiity*(Return-Expected Return)^2
0.1	-38	0.1*(-38-13.7)^2=267.289
0.2	-15	0.2*(-15-13.7)^2=164.738
0.3	12	0.3*(12-13.7)^2=0.867
0.3	36	0.3*(36-13.7)^2=149.187
0.1	61	0.1*(61-13.7)^2=223.729
		Total=805.81%

Standard deviation=[Total probabiity*(Return-Expected Return)^2/Total probability]^(1/2)

=(805.81)^(1/2)

=28.39%(Approx)

Coefficient of variation=Standard deviation/Expected return

=28.39/13.7

=2.07(Approx)

Sharpe ratio=(Expected return-risk free rate)/Standard deviation

=(13.7-2)/28.39

=0.41(Approx)