Question

onsider the following two scenarios for the economy and the expected returns in each scenario for the market portfolio, an aggressive stock A, and a defensive stock D.

Rate of Return

Scenario

Market

Aggressive Stock A

Defensive Stock D

Bust

–7

%

–10

%

–5

%

Boom

19

25

15

a. Find the beta of each stock. (Round your answers to 2 decimal places.)

b. If each scenario is equally likely, find the expected rate of return on the market portfolio and on each stock. (Enter your answers as a whole percent.)

c. If the T-bill rate is 4%, what does the CAPM say about the fair expected rate of return on the two stocks?(Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

d. Which stock seems to be a better buy on the basis of your answers to (a) through (c)?

• Stock D

• Stock A

Answer 1

(a)

​

Where:

Covariance=Measure of a stock’s return relativeto that of the market

Variance=Measure of how the market moves relativeto its mean​

Beta of stock A = 0.02275 / 0.01690 = 1.3462 or 1.35

Beta of stock B = 0.01300 / 0.01690 = 0.7692 or 0.76

Working Notes :

Scenario	Probability (p)	Stock A		Calculation of Covariance Stock A and Market
Return (r )	r x p	r - Σ (r x p)	{r- Σ (rxp)}2	p x {r- Σ (rxp)}2		Scenario	Probability (p)	Rm - Řm	ŘA - ŘA	p (RM-ŘM) (RA - ŘA)
Bust	0.50	-0.10	-0.050	-0.175	0.030625	0.0153125
Boom	0.50	0.25	0.125	0.175	0.030625	0.0153125		Bust	0.50	-0.1300	-0.175	0.01137500
		Σ (r x p) =	0.0750		Variance =	0.0306250		Boom	0.50	0.1300	0.175	0.01137500
										Covariance	0.02275000
Scenario	Probability (p)	Stock D
Return (r )	r x p	r - Σ (r x p)	{r- Σ (rxp)}2	p x {r- Σ (rxp)}2		Calculation of Covariance Stock D and Market
Bust	0.50	-0.050	-0.0250	-0.100	0.01	0.0050000		Scenario	Probability (p)	Rm - Řm	ŘD - ŘD	p (RM-ŘM) (RD - ŘD)
Boom	0.50	0.150	0.0750	0.100	0.000049	0.0000245
		Σ (r x p) =	0.0500		Variance =	0.0050245		Bust	0.50	-0.1300	-0.100	0.00650000
								Boom	0.50	0.1300	0.100	0.00650000
Scenario	Probability (p)	Market				Covariance	0.01300000
Return (r )	r x p	r - Σ (r x p)	{r- Σ (rxp)}2	p x {r- Σ (rxp)}2
Bust	0.50	-0.07	-0.0350	-0.130	0.0169	0.0084500
Boom	0.50	0.19	0.0950	0.130	0.0169	0.0084500
		Σ (r x p) =	0.0600		Variance =	0.0169000

(b)

Stock A = Σ (r x p) = 0.0750 or say 7.50%

Stock B = Σ (r x p) = 0.0500 or say 5.00%

Market = Σ (r x p) = 0.0600 or say 6.00%

All Σ (r x p) calculated in (a)

(c)

ERi​=Rf​+βi​(ERm​−Rf​)

where:

ERi​=expected return of investment

Rf​=risk-free rate

βi​=beta of the investment

(ERm​−Rf​)=market risk premium​

Here Rf = T-bill rate and market return as calculated in (b).

Stock A = 4% + 1.35 (6% - 4%) = 4% + 1.35 x 2% = 4% +2.70% = 6.70%

Stock B = 4% + 0.76 (6% - 4%) = 4% + 0.76 x 2% = 4% + 1.52% = 5.52%

(d)

Stock	CAPM	Expeacted	Valued
A	6.70%	7.50%	Undervalue
D	5.52%	5.00%	Overvalue

As per CAPM model if expected return under more than CAPM return than stock undervalue asn if expected return less than CAPM return than stock overvalued.

So here investor buy the undervalue stock i.e. Stock A, Because stock A's expected return > CAPM return.

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