Question

Consider the following information about stocks I and II. Assume both stocks are correctly priced. The market risk premium is 7.5 percent, and the risk-free rate is 4 percent.

		Rate of return if state occurs
State of the economy	Probability of state of the economy	Stock I	Stock II
Recession	0.15	0.11	-0.25
Normal	0.55	0.18	0.11
Irrational exuberance	0.30	0.08	0.31

a) Compute the systematic risk and total risk for each of the two stocks.

b) From the perspective of a risk-averse, well-diversified investor, which stock is riskier? Explain.

Answer 1

stock 1
state of economy	probability	return	probability*return	( return-averagereturn)	square of (return-average return)	probability* square of (return-average return)
Recession	0.15	11	1.65	-2.95	8.7025	1.305375
Normal	0.55	18	9.9	4.05	16.4025	9.021375
irrational exuberance	0.3	8	2.4	-5.95	35.4025	10.62075
average return			13.95
variance	sum of probability*(square of return-average return)					20.9475
total risk = standard deviation = square root of variance						4.576844
stock 2
state of economy	probability	return	probability*return	( return-averagereturn)	square of (return-average return)	probability* square of (return-average return)
Recession	0.15	-25	-3.75	-36.6	1339.56	200.934
Normal	0.55	11	6.05	-0.6	0.36	0.198
irrational exuberance	0.3	31	9.3	19.4	376.36	112.908
average return			11.6
variance	sum of probability*(square of return-average return)					314.04
total risk = standard deviation = square root of variance						17.72117
Systematic risk stock -1	required rate of return = risk free rate+(market risk premium)*beta	13.95 = 4+(7.5)*beta	7.5 beta = 9.95	beta = 9.95/7.5	1.32666667
systematic risk stock-2	required rate of return = risk free rate+(market risk premium)*beta	11.6 = 4+(7.5)*beta	7.5 beta = 7.6	beta = 7.6/7.5	1.01333333
From the risk averse well diversified investor stock A is a better option as its return is higher and total risk is low
stock 1	coefficient of variance	standard deviation/average stock	33%
stock 2			153%