Question

An investor is considering making an investment into a stock which has a beta of 1.6 and an expected return of 13%. The investor is a rational and risk averse person who likes to diversify if there are other assets available for investing. Currently, there is a risk-free asset available for investing with a 2% return. The investor has $1,000 available for investing purposes.

(a) (If investor invests $150 into the risk-free asset and $850 into the risky stock, what would be the expected rate of return on her portfolio?

(b) ( Let’s assume that the investor invests all of her $1,000 into the risky stock and risk-free asset, but we do not know the portfolio weights. If she tells us that the beta of her portfolio is 0.9, can we find the portfolio weights? If yes, then compute the weights.

Answer 1

a).

Given the investment in the portfolio is $150 of risk free asset and $850 of the risky stock. So weights of risk free asset is 150/1000= 15% and of risky stock is 850/1000= 0.85

So, expected return on portfolio= 0.15*2%+(0.85*13%)=

b).

Let the portfolio weights be w1 and w2. Beta of portfolio is weighted average of individual securities. we know that beta of risk free asset is 0.

So, w1*(0)+(w2*1.6)= 0.9. This gives w2= 0.5625 and w1= 1-0.5625= 0.4375

So, weights of risk free asset and risky stock are 43.75% and 56.25% respectively.