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	(12)
Average	0.4	12
Above average	0.3	30
Strong	0.1	58
	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=Respective return*Respective probabiity

=(0.1*-44)+(0.1*-12)+(0.4*12)+(0.3*30)+(0.1*58)

=14%

probabiity	Return	probabiity*(Return-Expected Return)^2
0.1	-44	0.1*(-44-14)^2=336.4
0.1	-12	0.1*(-12-14)^2=67.6
0.4	12	0.4*(12-14)^2=1.6
0.3	30	0.3*(30-14)^2=76.8
0.1	58	0.1*(58-14)^2=193.6
		Total=676%

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

=(676)^(1/2)

=26%

Coefficient of variation=Standard deviation/Expected return

=26/14

=1.86(Approx)

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

=(14-4)/26

=0.38(Approx)