Question

Consider the following information on a stock and the market portfolio: For the next year, there will be two possible scenarios: Good and Bad. The probability of Good scenario happening is 0.6 and the probability of Bad scenario happening is 0.4. The return on the stock is 30% in Good scenario and -8% in Bad scenario. The return on the market portfolio is 20% in Good scenario and -5% in Bad scenario. Calculate the expected return for the stock and the market portfolio.

Select one:

a. 7.20%; 5.00%

b. 14.00%; 8.80%

c. 18.00%; -3.20%

d. 14.80%; 10.00%

For the above question, calculate the standard deviations for the stock and the market portfolio.

Select one:

a. 0.2378; 0.1581

b. 0; 0

c. 0.1862; 0.1225

d. 0.1960; 0.1127

For the above questions, calculate the covariance between the stock and the market portfolio.

Select one:

a. 0.03440

b. 0.03760

c. 0.02280

d. 0.02208

For the above questions, calculate the beta for the stock

Select one:

a. 1.7391

b. 0.5750

c. 0.6579

d. 1.5200

e. The questions do not provide enough information to calculate beta

For the above questions, suppose the risk-free rate of return is 5 percent. Use CAPM to calculate the required rate of return for the stock. Do you recommend purchasing the stock based on your calculation of required rate of return?

Select one:

a. The required rate of return for the stock is 12.60%. I do not recommend buying the stock

b. The required rate of return for the stock is 12.60%. I recommend buying the stock

c. The questions do not provide enough information to do the recommendation

d. The required rate of return for the stock is 11.61%. I recommend buying the stock

e. The required rate of return for the stock is 11.61%. I do not recommend buying the stock

Answer 1

1. Answer is d.14.8% ;10%

2.Answer is c.1862;0.1225

Stock					deviation
State of economy	Probability	Returns	Expected Returns		Return-14.80%
			(Return*Probability)		Devtaion^2	Devtaion^2*Probability
Good	0.6	0.3	0.18		0.1520	0.0231	0.0139
Bad	0.4	-0.08	-0.032		(0.2280)	0.0520	0.0208
			14.80%			Variance	0.0347
					Standard Deviation	Variance^0.5	0.1862
Market Portfolio				deviation
State of economy	Probability	Returns	Expected Returns		Return-10.00%
			(Return*Probability)		Devtaion^2	Devtaion^2*Probability
Good	0.6	0.2	0.12		0.1000	0.0100	0.0060
Bad	0.4	-0.05	-0.02		(0.1500)	0.0225	0.0090
			10.00%			Variance	0.0150
					Standard Deviation	Variance^0.5	0.1225

3. Answer c.0.02280

State of economy	Probability	Return-14.80%	Return-10.00%	Covariance
P*(A-Mean A)*(B-Mean B)
Good	0.6	0.1520	0.1000	0.00912
Bad	0.4	(0.2280)	(0.1500)	0.01368
				0.0228

4. Answer is d.1.5200

Beta of the stock = Covariance / Variance of the market

= 0.0228/0.0150

= 1.5200

5. Answer is b.The required rate of return for the stock is 12.60%. I recommend buying the stock.

CAPM required rate of return for the stock = E(R) = Rf+Beta(Rm-Rf)

= 0.05+1.5200(0.1-0.05)

=0.05+1.5200(0.05)

=0.05+0.076

=0.126 = 12.6%

As the return on stock is more than the required rate of return i suggest to buy the stock.