Chapter 8, Problem 14P

### Fundamentals of Financial Manageme...

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

Chapter
Section

### Fundamentals of Financial Manageme...

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

# PORTFOLIO BETA Suppose you held a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio’s beta is 1.12. Now suppose you decided to sell one of the stocks in your portfolio with a beta of 1.0 for$7,500 and use the proceeds to buy another stock with a beta of 1.75. What would your portfolio’s new beta be?

Summary Introduction

To determine: The portfolio’s beta.

Portfolio beta:

The portfolio beta is a measure of the volatility of the portfolio. It measures how the stock moves in the market. A high portfolio 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 diversified portfolio investment held is of $7,500 in each of 20 different common stocks. The beta on investment is 1.12. The one stock of portfolio is sold for$7,500 which has a beta of 1.0.

The proceeds are used to buy another stock of beta 1.75.

Compute the new portfolio beta.

The formula to calculate the new portfolio beta is,

Substitute 1.12 for portfolio’s current beta, 0.05 for weight of selling stock and buying stock, 1.0 for the beta of selling stock and 1.75 for the beta of buying stock.

Portfolio'sNewBeta=[1.12(0.05×1)+(0

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