Chapter 8, Problem 6P

### Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250

Chapter
Section

### Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250
Textbook Problem

# EXPECTED RETURNS Stocks A and B have the following probability distributions of expected future returns: Probability A B 0.1 (10%) (35%) 0.2 2 0 0.4 12 20 0.2 20 25 0.1 38 45 a. Calculate the expected rate of return, r ^ B , foe stock B ( r ^ A = 12%). b. Calculate the standard deviation of expected returns, σA, for Stock A(σB = 20.35%). Now calculate the coefficient of variation for Stock B. Is it possible the most investors will regard Stock B as being less risky than Stock A? Explain. c. Assume the risk–free rate 2.5%. What are the Sharpe ratios for Stocks A and B? Are these calculations consistent with the information obtained from the coefficient of variation calculations in part b? Explain.

a)

Summary Introduction

To determine: The expected rate of return for the mentioned stock.

Introduction:

The expected return on the stock refers to the weighted average of the expected returns on those assets, which are held in the portfolio.

The portfolio refers to a group of financial assets like bonds, stocks, and equivalents of cash. The portfolio is held by investors and financial users. A portfolio is constructed in accordance with the risk tolerance and the objectives of the company.

Explanation

Given information:

There are two Stocks A and B.

The expected rate of return for Stock A is 12%.

For the Stock B:

The weights are 0.1, 0.2, 0.4, 0.2, and 0.1 for the given distribution and the rate of return is (35%), 0%, 20%, 25%, and 45% for the different demands.

The formula to calculate the expected return is as follows:

rBā§=āi=1Nwiriā§

Here

rBā§ is the expected rate of return for Stock B.

wi is theweight of the stock.

ri is the estimated rate of return.

N is the number of stocks.

Calculate the expected rate of return on the Stock B:

rBā§=[(0

b)

Summary Introduction

To determine: The standard deviation and coefficient of variation for Stock B and the possibility of Stock B being less risky than Stock A.

Introduction:

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.

The coefficient of variation is a tool to determine the investment’s volatility.

c)

Summary Introduction

To determine: The Sharpe ratio for stocks A and B

Introduction:

Sharpe ratio helps to determine the performance of the investment.

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