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	(46%)
Below average	0.4	(8)
Average	0.3	16
Above average	0.1	20
Strong	0.1	53
	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

1.
Expected returns=Sum(probability*returns)
=0.1*(-46%)+0.4*(-8%)+0.3*16%+0.1*20%+0.1*53%=4.300%

2.
Standard deviation=Sqrt(Sum(probability*(returns-expected returns)^2))
=sqrt(0.1*(-46%-4.300%)^2+0.4*(-8%-4.300%)^2+0.3*(16%-4.300%)^2+0.1*(20%-4.300%)^2+0.1*(53%-4.300%)^2)
=24.828%

3.
Coefficient of variation=Standard deviation/Expected returns=24.828%/4.300%
=5.773953488

4.
=(Expected returns-risk free rate)/Standard deviation
=(4.300%-3%)/24.828%
=0.052360238