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	(22%)
Below average	0.1	(13)
Average	0.3	16
Above average	0.2	23
Strong	0.2	71
	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:

Please help and example !:)))))

Answer 1

Solution:

a)Calculation of expected return

Expected return=Return*Probability

=-22%*0.2+(-13%)*0.10+16%*0.30+23%*0.20+71%*0.20

=17.90%

b)Calculation of Standard deviation

Standard deviation=SQRT[sum of (return-expected return)^2*probability]

=SQRT[(-22-17.90)^2*0.2+(-13-17.90)^2*0.10+(16-17.90)^2*0.30+(23-17.90)^2*0.20+(71-17.90)^2*.20

=SQRT(318.402+95.481+1.083+5.202+563.922)

=31.37%

c)Calculation of Coefficient of variation

Coefficient of variation=Standard deviation/Mean

=31.37%/17.90%

=1.75

d)Calculation of Sharpe ratio

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

=17.90-2/31.37

=0.51