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Fundamentals of Financial Manageme...

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977

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BuyFindarrow_forward

Fundamentals of Financial Manageme...

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977
Textbook Problem

PORTFOLIO BETA A mutual fund manager has a $20 million portfolio with a beta of 1.5. The risk-free rate is 4.5%, and the market risk premium is 5.5%. 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 13%. 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.

Portfolio beta:

The portfolio beta is a measure of the volatility of the portfolio. 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 1.5.

The risk-free rate is 4.5%.

The market risk premium is 5.5%.

The additional amount expected to be received is $5 million.

The required rate of return is 13%.

Calculated,

The portfolio’s new beta is 1.54 (refer working note).

Calculation of the average beta of the newly added stocks:

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

Newstock'sbeta=[Portfolio'snewbetaPortfolio'soldbeta×(Portfolio'soldvaluePortfolio'snewvalue)Newinvestmentvalue×Portfolio'snewvalue]

Substitute 1.54 for portfolio’s new beta, 1.5 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.

Newstock'sbeta=[(1.541

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