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Homework answers / question archive / Assume the risk-free rate is 3% and the market return is 10%
Assume the risk-free rate is 3% and the market return is 10%. Stock X Stock Z 0.90 Beta Current price Correlation Stock Y 0.65 $26.50 (X/Z) = 0 $13.50 (X/Y) = 0.35 (Y/Z) = 0.55 a) Most equity research concludes that Stock X is much more volatile compared to the market”. On average, Stock X’s volatility is about 1.5 times that of the stock market. Based on CAPM, estimate the required return of Stock X. (5 marks) b) It is expected that Stock Y will pay a per share dividend of $0.43 one year from now, and the dividend will increase by an average of 6% per year in the foreseeable future. According to CAPM, is Stock Y overvalued or undervalued? (9 marks) c) Assume that Stock Z is fairly-priced today. Stock Z has just paid a dividend of $2. It is expected that its dividend will increase by 50% in the first year, 0% in the second year, 10% in the third year, and starting from the fourth year, the company will maintain the dividend growth rate to be 5% forever. How much would Stock Z be worth today if its required rate of return is 10% per year? (9 marks) d) Which pair of stocks (refer to the bottom row of the table) used to form a 2-asset portfolio would achieve the largest diversification effect? Explain the answer.
a)
The beta of the market is always 1
Beta is a measure of volatility
The beta of stock X would be 1.5 x 1 = 1.5
Using CAPM, Required return = Risk free rate + Beta x (Market Return - Risk Free Rate) = 3 + 1.5 ( 10 - 7) = 13.5%
b)
Required return using CAPM = 3 + 0.65 x (10 - 7) = 7.55%
Dividend one year from now D1 = $0.43
Growth rate = 6%
Price of the stock = D1 / (r - g) = 0.43 / (0.0755 - 0.06) = $27.74
The intrinsic price of the stock is greater than the market value, so the stock is undervalued.
c)
Dividend paid todday D0 = $2
D1 = D0 x (1 + 0.5) = 2 x (1 + 0.5) = $3
D2 = D1 x (1 + 0) = $3
D3 = D2 x (1 + 0.10) = 3 x 1.1 = $3.3
Termial Value P3 = D3 x (1 + g) / (r - g) = 3.3 x (1 + 0.05) / (0.1 - 0.05) = $69.3
Value of the stock today = D1 / (1 + r) + D2 / (1 + r)2 + (D3 + P3) / (1 + r)3
= 3 / (1 + 0.1) + 3 / (1 + 0.1)2 + (3.3 + 69.3) / (1 + 0.1)3 = $59.75
d)
The largest diversification effect is acheived with the lowest correlation between two assets. The lowest correlation is 0 between stocks X and Z, so a 2 asset portfolio with them wuld acheive the highest diversification effect.
