Question

Question 4 (25 marks / Risk & Return and Equity Valuation)
(a) Donald is considering the merits of two securities. He is interested in the common shares of A Co. and B Inc. The expected monthly rate of return of securities is shown below:

State of Affair Probability Stock A Stock B Boom 0.1 40% -20% Normal 0.5 20% 8% Recession 0.4 -10% 15%

At the time of purchase, the market value is $70/share for A and $50/share for B. Donald plans to invest 10,000 shares of Stock A and 6,000 shares in Stock B.

(i) Compute the portfolio weights of Stock A and Stock B.
(ii) Compute the expected returns of Stock A and Stock B.

(iii) Assume that the covariance between Stock A and Stock B is -28%2 (0.0028). Compute the expected rate of return and variance of rate of return of Donald’s portfolio.
(iv) If the risk-free rate is 2%, the market risk premium is 18% and the beta of Stock A is 0.75, estimate the required and expected rates of return of Stock A. Should Donald invest in Stock A? Show the calculations.

(b) Assume that Stock X is fairly priced today. Stock X just distributed a per share dividend of $1. It is expected that the company will increase its dividend by 20% in the coming year, 15% in the second year, 10% in the third year, and 5% in the fourth year. Starting from the fifth year, the company will maintain the dividend growth rate to be 5% per year forever. How much is Stock X worth today if its equity cost of capital is 10%?

Answer 1

1.
portfolio weights
Stock A=10000*70/(10000*70+6000*50)=70.000%

Stock B=6000*50/(10000*70+6000*50)=30.000%

2.
expected returns
Stock A=0.1*40%+0.5*20%+0.4*(-10%)=10.000%

Stock B=0.1*(-20%)+0.5*8%+0.4*15%=8.000%

3.
portfolio returns=0.70*10%+0.30*8%=9.400%

standard deviation of Stock A=sqrt(0.1*(40%-10%)^2+0.5*(20%-10%)^2+0.4*(-10%-10%)^2)=17.321%

standard deviation of Stock B=sqrt(0.1*(-20%-8%)^2+0.5*(8%-8%)^2+0.4*(15%-8%)^2)=9.899%

portfolio variance=0.70*(17.321%)^2+0.30*(9.899%)-2*0.70*0.30*0.0028=0.049522193

4.
required return=2%+0.75*18%=15.500%

expected return=10%

Dont invest as expected return is less than required return

5.
=1*(1.20/1.10)+1*(1.20/1.10)*(1.15/1.10)+1*(1.20/1.10)*(1.15/1.10)*(1.10/1.10)+1*(1.20/1.10)*(1.15/1.10)*(1.10/1.10)*1.05/(10%-5%)
=27.32231