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In: Finance

You manage a $100 million portfolio has a beta of 0.92 and an expected return of...

You manage a $100 million portfolio has a beta of 0.92 and an expected return of 9.8% per year. You intend to invest an additional $40 million in the portfolio so that the expected return increases to 10.8% per year. If the market risk premium is 5.0% per year, what does the beta of the new investment need to be?

Solutions

Expert Solution

Step-1:Calculation of risk free rate
As per Capital asset pricing model,
Expected return = Risk free rate + Beta *Market risk premium
0.098 = Risk free rate + 0.92*0.05
0.098 = Risk free rate + 0.046
Risk free rate = 0.052
So, risk free rate is 5.20%
Step-2:Calculation of expected return of new investment
Increased return = (Return of existing investment*weight of existing investment)+(Return of additional investment*Weight of additional investment)
0.108 = (0.098*0.7143)+(return of addiitonal investment*0.2857)
0.108 = 0.07 + return of addiitonal investment*0.2857
Return of addiitonal investment*0.2857 = 0.038
Return of addiitonal investment = 0.133007
So, return of new investment is 13.30%
Working:
Existing investment $        100 Million
Additional investment $          40 Million
Total investment $        140 Million
Weight of:
Existing investment $        100 / $        140 =      0.7143
Additional investment $          40 / $        140 =      0.2857
Total      1.0000
Step-3:Calculation of beta of additional investment
As per Capital asset pricing model,
Expected return = Risk free rate + Beta *Market risk premium
             0.1330 = 0.052+beta*0.05
             0.0810 = beta*0.05
beta =           1.62
Thus,
Beta of new investment need to be           1.62

jeff jeffy answered 1 year ago
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