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	(26%)
Below average	0.3	(8)
Average	0.4	15
Above average	0.1	36
Strong	0.1	62
	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

Final answers

Stock's expected return = 10.80 %

Standard deviation = 23.96 %

Co-efficient of variation = 221.87 %

Sharpe ratio = 0.33

Explanation

Let ......... X ...... represents the returns, P ....... represents probability

Dx = Deviation in returns = (X - Expected return )

Dx² = Dx * Dx

X	P	X*P	Dx	Dx2	P * Dx2
-26	0.1	-2.6	-36.8	1354.24	135.424
-8	0.3	-2.4	-18.8	353.44	106.032
15	0.4	6	4.2	17.64	7.056
36	0.1	3.6	25.2	635.04	63.504
62	0.1	6.2	51.2	2621.44	262.144
Sum(P*X) =		10.8	Sum ( P * Dx2) =		574.16

Expected return = Sum (P*X) = 10.80

Standard deviation = Square root [ Sum(P*Dx² ) = Square root [ 574.16] = 23.96

Coefficient of variation = Standard deviation / Expected return * 100 = 23.96 / 10.80 * 100 = 221.87 %

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

= ( 10.80 - 3 ) / 23.96

= 0.33