Question

You are given the following information about Stock 1 and Stock 2.

		Rate of return if State Occurs
State of economy	Probability of State of Economy	Stock 1	Stock 2
Recession	0.25	0.11	-0.4
Normal	0.5	0.29	0.1
Boom	0.25	0.13	0.56

The market risk premium is 8% and the risk-free rate is 4%.

(a) Use an appropriate computing tool to help you work out the following.

(i) Calculate the expected returns of Stock 1 and Stock 2.

(ii) Appraise which stock has the higher systematic risk.

(iii) Compute the total risk of each stock.

(iv) Appraise which stock is riskier.

(b) Discuss whether a risky asset can have a negative beta and what the CAPM predicts about its return.

Answer 1

Probability	Stock 1	Stock 2
0.25	0.11	-0.4
0.5	0.29	0.1
0.25	0.13	0.56

a)

i)   Expected return

E(Stock1) = 0.25*0.11 + 0.50*0.29 + 0.25*0.13 = 0.205

E(Stock2) = 0.25*(-0.4) + 0.50*0.10 + 0.25*0.56 = 0.09

ii) Using CAPM, E(Stock) = Risk free rate + Beta * Market risk premium

Beta(stock1)= (0.205 – 0.04) / 0.08 = 2.0625

Beta(stock1)= (0.09 – 0.04) / 0.08 = 0.625

Hence, Stock 1 has higher systematic risk (i.e. Beta).

iii) Risk of stock

SD(Stock1) = [0.25*(0.11-0.205)² + 0.5*(0.29-0.205)²+ 0.25*(0.13-0.205)²]^0.5= 0.08529

SD(Stock2) = [0.25*(-0.4-0.09)² + 0.5*(0.10-0.09)²+ 0.25*(0.56-0.09)²]^0.5= 0.33956

iv)

Since Stock2 has higher Standard deviation than Stock1, Stock2 is riskier than stock1.

b)

Yes risky assets can have negative beta. As per CAPM, Negative Beta implies that the stock carries a negative risk premium i.e. the stock with negative beta will have opposite return as compare to market return i.e. positive return in case there is decline in market.