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	(34%)
Below average	0.2	(14)
Average	0.3	14
Above average	0.3	40
Strong	0.1	64
	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

From above calculation :

1. The expected rate of return = 16.4%

2. The standard deviation is 28.88%

Now the coefficient of variance is defined as the ratio of standard deviation and expected return and is written as under:

Coefficient of variance (Cv) = Standard deviation / Expected return

= 28.88 / 16.4

= 1.7609

As Cv measures standard deviation per unit of expected return , lower the Cv (coefficient of variance), better it is.

Calculation of Sharpe ratio:

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

Given risk free rate is 4%

and from above calculations Expected rate of return = 16.4%

Standard deviation = 28.88%

Thus Sharpe ratio = (16.4%-4%) / 28.88%

= 12.4% / 28.88%

= 0.4293

As Sharpe ratio measures the excess of return compared to risk free return against per unit of risk (measured in terms of variability as standard deviation). Higher the shapre ratio indicates better measure of performance.