Chapter 8, Problem 17P

### Fundamentals of Financial Manageme...

9th Edition
Eugene F. Brigham + 1 other
ISBN: 9781305635937

Chapter
Section

### Fundamentals of Financial Manageme...

9th Edition
Eugene F. Brigham + 1 other
ISBN: 9781305635937
Textbook Problem
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# PORTFOLIO BETA A mutual fund manager has a $20 million portfolio with a beta of 1.7. The risk-free rate is 4.5%, and the market risk premium is 7%. The manager expects to receive an additional$5 million, which she plans to invest in a number of stocks. After investing the additional funds, she wants the fund’s required return to be 15%. What should be the average beta of the new stocks added to the portfolio?

Summary Introduction

To determine: The average beta of the newly added stocks.

Introduction:

Portfolio beta:

The portfolio beta is a measure of the portfolio’s volatility. It measures how the portfolio moves with the movement in the market. A high portfolio beta shows that securities are more volatile in the price movements while a low beta represents that securities are less volatile in the price movements.

Explanation

Given,

The amount of portfolio is $20 million. The value of beta is 1.7. The risk-free rate is 4.5%. The market risk premium is 7%. The additional amount expected to be received is$5 million.

The required rate of return is 15%.

Calculated (working note),

The portfolio’s new beta is 1.5.

Calculation of the average beta of the newly added stocks:

The formula to calculate the average beta of the newly added stocks is,

Portfolio'snewbeta=(Portfolio'soldbeta×(NewinvestmentvaluePortfolio'snewvalue)+Portfolio'snewbeta×(Portfolio'soldvaluePortfolio'snewvalue))

Substitute 1.5 for portfolio’s new beta, 1.7 for the portfolio’s old beta, $20 million for the portfolio’s old value,$25 million for the portfolio’s new value and $5 million for the new investment in the above formula. Portfolio'snewbeta=[(1.7×$20,000,000$25,000,000)+(bA×$5,000,000\$25,000,000)]1

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