Assume we have two stocks, A and B. Stock A has expected return 12% and stock B

Question

Assume we have two stocks, A and B. Stock A has expected return 12% and stock B
has expected return 15%. The beta for stock A is 0.8 and the beta for B is 1.2. The
expected returns of both stocks lie on the SML line.

(a) What is the expected return of the market?
(b) What is the risk-free rate?
(c) What is the beta of a portfolio made of these two assets with equal weights?
(d) Stock A is currently selling for $37 per share. A put option with an exercise price
of $45 sells for $8 and expires in four months. If the risk-free rate of interest is
2:3% per year, compounded daily, what is the price of a call option with the same
exercise price?

Explanation / Answer

Let X be market return and Y be risk-free rate

According to CAPM,

Stock A

Expected return = Risk-free rate + beta A (Market return – Risk-free rate)

12% = Y + 0.8 (X – Y)

0.12 = Y + 0.8X – 0.8Y

0.12 = 0.8X + 0.2Y------------- (1)

Stock B

Expected return = Risk-free rate + beta A (Market return – Risk-free rate)

15% = Y + 1.2 (X – Y)

0.15 = Y + 1.2X – 1.2Y

0.15 = 1.2X - 0.2Y------------- (2)

Solving (1) and (2), we get

X = 0.135 and Y = 0.06

a) Expected market return = 13.5%

b) Risk-free rate = 6%

c) Given equal weights in stock A and Stock B, therefore

Beta of the portfolio = 0.5*0.8 + 0.5*1.2

                              = 1

d) We have S = 37, X = 45, P = 8, r = 2.3% and t = 4/12 = 0.25

Using Put-call parity

C + Xe-rt = S + P

C + 45e-0.023*0.25 = 37 + 8

C + 44.74 = 45

C = $0.26       

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