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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?

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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

The amounts that will be invested in Bay Corp. and City Inc. will be $33500 and $16500.

  • Let the weight invested in Bay Corp be x.
  • Therefore the weight invested in City Inc. will be 1 - x.

Therefore, the equation to solve the question will be:

( x × 11.2%) + [(1 - x) × 14.8%)] = 12.4%

Open the brackets

0.112x + 0.148 - 0.148x = 0.124

Collect like terms

-0.036x = -0.024

x = -0.024 / 0.036

x = 0.67

The portfolio beta will be:

= 0.67 * 1.2 + ( 1 - 0.67) × 1.8

= 1.398 .

Therefore, the amount invested in Bay Corp will be:

= 0.67 × $50,000

= $33,500

Therefore, the amount in City Inc. will be:

= $50,000 - $33,500

= $16,500

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