Question

1. Expected return on two stocks for two particular market returns:

                        Market Return             Aggressive Stock          Defensive Stock

                             4%                               -5%                              6%

               20%                             30%                             15%

1. What are the betas of the two stocks?
2. What is the expected rate of return on each stock if the market return is equally likely to be 4% or 20%?
3. If the T-bill rate is 5% and the market return is equally likely to be 4% or 20%, draw the SML for this economy.

Please show in excel with formulas. thank you!

Answer 1

a) Beta can be found by finding the slope of Market returns and the stocks

Aggressive stock Beta	2.1875
Defensive stock Beta	0.5625

b) Expected return on aggressive stock in % = 0.5*(-5) + 0.5*(30) = 12.5%

Expected return on defensive stock in % = 0.5*(6) + 0.5*(15) = 10.5%

c) Expected return on the market in % = 0.5*(4) + 0.5*(20) = 12%

The required rate of return on aggressive stock R(A) is calculated by CAPM model

R(A) = r(f) + Beta*(R(m) - r(f))

R(m) is the market return =12%

r(f) is the risk-free rate = 5%

Beta of aggressive stock = 2.1875

R(A) = 0.05+2.1875*(0.12-0.05)

R(A) = 0.203125= 20.31%

The required rate of return on defensive stock R(D) is calculated by CAPM model

R(D) = r(f) + Beta*(R(m) - r(f))

R(m) is the market return =12%

r(f) is the risk-free rate = 5%

Beta of defensive stock = 0.5625

R(D) = 0.05+0.5625*(0.12-0.05)

R(D) = 0.089375= 8.94%

Expected return on the market in % = 0.5*(4) + 0.5*(20) = 12%

SML =  r(f) + Beta*(R(m) - r(f))

SML = 0.05 + Beta*(0.12 - 0.05)

SML = 0.05 + Beta*0.07

Beta	SML
0.1	5.70%
0.2	6.40%
0.3	7.10%
0.4	7.80%
0.5	8.50%
0.6	9.20%
0.7	9.90%
0.8	10.60%
0.9	11.30%
1	12.00%
1.1	12.70%
1.2	13.40%
1.3	14.10%
1.4	14.80%
1.5	15.50%
1.6	16.20%
1.7	16.90%
1.8	17.60%
1.9	18.30%
2	19.00%
2.1	19.70%
2.2	20.40%
2.3	21.10%
2.4	21.80%
2.5	22.50%
2.6	23.20%
2.7	23.90%
2.8	24.60%
2.9	25.30%
3	26.00%
3.1	26.70%
3.2	27.40%
3.3	28.10%
3.4	28.80%
3.5	29.50%
3.6	30.20%
3.7	30.90%
3.8	31.60%
3.9	32.30%
4	33.00%