Question

# 14. Expected Returns. Consider the following two scenarios for the economy and the expected returns in...

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)?

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