Question

14. Expected Returns. Consider 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	-8%	-10%	-6%
Boom	32	38	24

1. Find the beta of each stock. In what way is stock D defensive?

2. If each scenario is equally likely, find the expected rate of return on the market portfolio and on each stock.

3. If the T-bill rate is 4%, what does the CAPM say about the fair expected rate of return on the two stocks?

4. Which stock seems to be a better buy on the basis of your answers to parts (a), (b), and (c)?

Answer 1

a ) Beta = Defference in stock return - Defference in market return

Stock A = Boom of Stock A - (Bust of Stock A ) / (Boom of market - Bust of Market)

= (0.38 - (-0.10)) / (0.32 - (-0.08))

= 0.48 / 0.4

= 1.20

Stock B = Boom of Stock B - (Bust of Stock B ) / (Boom of market - Bust of Market)

= (0.24 - (-0.06)) / (0.32 - (-0.08))

= 0.3 / 0.4

= 0.75

b )

  

Scenario	Market	Aggressive stock A	Defensive Stock B
Bust	-8%	-10%	-6%
Boom	32	38	24
Expected return	0.5 *-0.08 + 0.5 *0.32	0.5 *-0.10+0.5 *0.38	0.5 *-0.06+ 0.5 *0.24
	12 %	14 %	9 %

c ) If the T-bill rate is 4% , the required rate of return

= Risk free rate + Beta * (Market return - Risk free rate )

Stock A = 5 +1.20 * (12 - 5 )

= 13.4

Stock B = 5 + 0.75 * (12 - 5 )

= 10.25

d ) Expected return of stock A IS 14%.it is greater than Required return of stock A (10.25%).so Stock A is better to

invest