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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

CAPM, PORTFOLIO RISK. AND RETURN Consider the following information for Stocks X, Y, and Z. The returns on the three stocks arc positively correlated, but they are not perfectly correlated. (That is, each of the correlation coefficients is between 0 and 1.)

Stock Expected Return Standard Deviation Beta
X 9.00% 15% 0.8
Y 10.75 15 1.2
Z 12.50 15 1.6

Fund Q has one-third of its funds invested in each of the three stocks. The risk-free rate is 5.5%, and the market is in equilibrium. (That is, required returns equal expected returns.)

  1. a. What is the market risk premium (rM − rRF)?
  2. b. What is the beta of Fund Q?
  3. c. What is the required return of Fund Q?
  4. d. Would you expect the standard deviation of Fund Q to be less than 15%, equal to 15%, or greater than 15%? Explain.

a.

Summary Introduction

To determine: The market risk premium.

The Required Rate of Return:

The required rate of return is the rate, which should be earned on an investment to keep that investment running in the market. When the required return is earned, only then the users and the companies invest in that particular investment.

Market risk premium:

The amount of returns that exceeds the risk-free rate on an investment is known as market risk premium. The slope of the security market line represents the market risk premium.

Explanation

For stock X:

Given,

The risk-free rate is 5.5%.

The expected return is 9%.

The value of beta is 0.8.

The formula to calculate the market risk premium is,

(rMrRF)=rirRFbi

Where,

  • ri is the required return on the stock.
  • rRF is the risk-free return.
  • rM is the market return.
  • bi is the value of the stock’s beta.

Substitute 5.5% for rRF, 9% for ri, and 0.8 for bi in the above formula.

(rMrRF)=9%5.5%0.8=4.375%

The market risk premium for stock X is 4.375%.

For stock Y:

The risk-free rate is 5.5%.

The expected return is 10.75%.

The value of beta is 1.2.

The formula to calculate the market risk premium is,

(rMrRF)=rirRFbi

Where,

  • ri is the required return on the stock.
  • rRF is the risk-free return.
  • rM is the market return

b.

Summary Introduction

Portfolio beta:

The portfolio beta is a measure that reflects the relativity to market. 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.

To determine: The beta of Fund Q.

c.

Summary Introduction

To determine: The required return of Fund Q.

d.

Summary Introduction

Standard deviation:

The standard deviation refers to the stand-alone risk associated with the securities. It measures how much a data is dispersed with its standard value. The Greek letter sigma represents the standard deviation.

To explain: The expected value of standard deviation of Fund Q.

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