Question

Company X has a beta of 0.70, while Company Y's beta is 1.20. The required return on the stock market is 11.00%, and the risk-free rate is 4.25%. A fund has $3500 invested in company X stock and $4500 invested in the stock of company Y. a) What is the difference between X's and Y's required rates of return? b) What is fund's beta? c) What is fund's required rate of return? d) Suppose inflation decreases by 1.5%, what is the fund's required rate of return now? e) Suppose risk aversion decreases by 2.5%, what is the fund's required rate of return now?

Answer 1

a). Using CAPM, required return = risk-free rate + beta*(market return - risk free rate)

Company X return = 4.25% + 0.70*(11% - 4.25%) = 8.98%

Company Y return = 4.25% + 1.20*(11% - 4.25%) = 12.35%

Difference between X and Y returns = 12.35% - 8.98% = 3.38%

b). Fund beta = sum of weighted betas

Weight of X = amount invested in X/total amount = 3,500/(3,500+4,500) = 43.75%

Weight of Y = 100% - weight of X = 100% - 43.75% = 56.25%

Fund beta = (Company X beta*weight of X) + (Company Y beta*weight of Y)

= (0.70*43.75%) + (1.20*56.25%) = 0.9813

c). Fund's required return (using CAPM) = 4.25% + 0.9813*(11%-4.25%) = 10.87%

d). If inflation decreases by 1.5% then fund's required return will be 10.87% -1.5% = 9.37%

e). If risk aversion decreases by 2.5% then fund's required return will be 10.87% - 2.5% = 8.37%