Question

The market is expected to yield 12% and the risk free rate is 2%. You currently hold a portfolio with a beta of 0.75 worth $25,000. You want to invest in another portfolio with a beta of 2.9. How much will you have to invest in the new risky asset so that the resulting portfolio will have an expected return of 16%?

Answer 1

Given that,

Return on market Rm = 12%

Risk free rate Rf = 2%

$25000 is invested in a portfolio with beta Bo = 0.75

a new risky asset with beta of B1 = 2.9 is available

required expected return of resulting portfolio is 16%

So, beta of new portfolio can be calculated using CAPM model

Beta of new portfolio Bn = (E(r) - Rf)/(Rm - Rf) = (16 - 2)/(12 - 2) = 1.4

Let weight in old portfolio be W, then weight is new risky asset is 1 - W

Beta of new portfolio is weighted average return on its assets

=> Bn = W1*B1 + Wo*Bo

=> 1.4 = (1-W)*2.9 + W*0.75

=> 1.4 = 2.9 - 2.9W + 0.75W

=> W = 0.6977

=> 25000 is 69.77% of new portfolio

So, new portfolio value = 25000/0.6977 = $35833.33

So, investment in new risky asset = 35833.33 - 25000 = $10833.33