Question

An analyst has determined that a particular stock's return will vary depending on what will happen to the economy. Utilizing the information below, what is the coefficient of variation of the company's stock?

STATE OF THE ECONOMY	PROBABILITY OF STATE OCCURRING	STOCKS EXPECTED RETURN IF THIS STATE OCCURS
Recession	.10	(35)
Below Average	.20	(20)
Average	.40	15
Above Average	.20	40
Boom	.10	90

Answer 1

Expected returns=Sum(probability*returns)

Standard deviation=Sqrt(Sum(probability*(returns-expected returns)^2))

Coefficient of variation=Standard deviation/Expected returns

Expected returns=0.10*(-35%)+0.20*(-20%)+0.40*15%+0.20*40%+0.10*90%=15.50%

Standard deviation=sqrt(0.10*(-35%-15.50%)^2+0.20*(-20%-15.50%)^2+0.40*(15%-15.50%)^2+0.20*(40%-15.50%)^2+0.10*(90%-15.50%)^2)=34.38%

Coefficient of variation=34.38%/15.50%=2.21806