ch random A share has a beta of 090 and an expected return o

ch random A share has a beta of 0.90 and an expected return of 13 per cent. A risk-free asset currently earns 7 per cent ets. We ce of urns. ts. Required a) Calculate the expected return on a portfolio that is equally invested in the two b) If the portfolio of the two assets has a beta of 0.6 calculate the portfolio weights c) If a p assets. ortfolio of the two assets has an expected return of 11 per cent, calculate its beta. If a portfolio of the two assets has a beta of 1.80, calculate the portfolio weights. How do you interpret the weights for the two assets in this case? d)

Solution

a) Expected return=(Wt of A*return on A)*(Wt of B*return on B)
=(0.5*13%)+(0.5*7%)=10%
b)Beta for stock=0.9 and beta for risk free asset=0
let wt of stock be x then for risk free=1-x
0.6=(x*0.9)+(0*(1-x))
x=66.67% and for risk free asset it is 1-66.67%=33.33%
c)let the wt of stock be x and other is 1-x
11%=(13%*x)+((1-x)*7%)
x=66.67% and 1-x =33.33%
beta of portfolio=(66.67%*0.9)+(33.33%*0)=0.6
d)1.8=(x*0.9)+(1-x)*0
x=2 and 1-x=-1. Here it means we have to double our investment in stock and short risk free asset