Question

You want to invest $50,000 in a portfolio with a beta of no more than 1.4 and an expected return of 12.4%. Bay Corp. has a beta of 1.2 and an expected return of 11.2%, and City Inc. has a beta of 1.8 and an expected return of 14.8%. The risk-free rate is 4%. You can invest in Bay Corp. and City Inc. How much will you invest in each?

Answer 1

Answer:

Assume the weight to be invested in Bay Corp is x. That means (1 - x) will be the weight for City Inc. The expression for the expected return will be;

(x * 11.2%) + ( (1 - x) * 14.8%) = 12.4%

0.112x + 0.148 - 0.148x = 0.124

-0.036x = -0.024

x = 0.67

Portfolio beta is;

= 0.67 * 1.2 + ( 1 - 0.67) * 1.8

= 1.398 so beta condition is satisfied.

Amount in Bay Corp.;

= 0.67 * 50,000

= $33,500

Amount in City Inc.;

= 50,000 - 33,500

= $16,500