Chapter 8, Problem 22SP

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14th Edition

Eugene F. Brigham + 1 other

ISBN: 9781285867977

Textbook Problem

**EVALUATING RISK AND RETURN** Bartman Industries’s and Reynolds Inc.’s stock prices and dividends, along with the Winslow 5000 Index, are shown here for the period 2009–2014. The Winslow 5000 data are adjusted to include dividends.

- a. Use the data to calculate annual rates of return for Bartman, Reynolds, and the Winslow 5000 Index. Then calculate each entity’s average return over the 5-year period. (Hint: Remember, returns are calculated by subtracting the beginning price from the ending price to get the capital gain or loss, adding the dividend to the capital gain or loss, and dividing the result by the beginning price. Assume that dividends are already included in the index. Also, you cannot calculate the rate of return for 2009 because you do not have 2008 data.)
- b. Calculate the standard deviations of the returns for Bartman, Reynolds, and the Winslow 5000. (Hint: Use the sample standard deviation formula, Equation 8.2a in this chapter, which corresponds to the STDEV function in Excel.)
- c. Calculate the coefficients of variation for Bartman, Reynolds, and the Winslow 5000.
- d. Construct a scatter diagram that shows Bartman’s and Reynolds’s returns on the vertical axis and the Winslow 5000 Index’s returns on the horizontal axis.
- e. Estimate Bartman’s and Reynolds’s betas by running regressions of their returns against the index’s returns. (Hint: Refer to Web Appendix 8A.) Are these betas consistent with your graph?
- f. Assume that the risk-free rate on long-term Treasury bonds is 6 04%. Assume also that the average annual return on the Winslow 5000 is
*not*a good estimate of the market’s required return—it is too high. So use 11% as the expected return on the market. Use the SML equation to calculate the two companies’ required returns. - g. If you formed a portfolio that consisted of 50% Bartman and 50% Reynolds, what would the portfolio’s beta and required return be?
- h. Suppose an investor wants to include Bartman Industries’s stock in his portfolio. Stocks A, B, and C are currently in the portfolio; and their betas are 0 769, 0 985, and 1 423, respectively. Calculate the new portfolio’s required return if it consists of 25% of Bartman, 15% of Stock A, 40% of Stock B, and 20% of Stock C.

**a.**

Summary Introduction

**To determine:** The average rate of return.

**Risk and Return:**

The risk and return are two closely related terms. The risk is the uncertainty attached to an event. In case of any investment, there is some amount of risk attached to it as there can be either gain or loss. While return in the financial term is that percentage which represents the profit in an investment.

Higher risk is associated with higher return and lower risk has a probability of lower return. The investor has to face a tradeoff between risk and return in terms of an investment.

**Annual Rate of Return:**

The annual rate of return refers to that return which is charged or is earned on an investment for a year. This rate is expressed in percentage.

Explanation

**Calculation of annual rates of return in the excel spreadsheet:**

**b.**

Summary Introduction

**To prepare:** The standard deviation for the given data.

**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.

**c.**

Summary Introduction

**To determine:** The coefficient of variation.

**The coefficient of variation:**

The coefficient of variation is a tool to determine the risk. It determines the risk per unit of return. It is used for measurement when the expected returns are same for two data.

**d.**

Summary Introduction

**To prepare:** A scatter diagram showing the company’s returns and the index returns.

**e.**

Summary Introduction

**To determine:** The beta of the B Industries and R Inc. by running regressions of their returns.

**f.**

Summary Introduction

**To determine:** The required returns of the two companies by security market line equation.

**g.**

Summary Introduction

**To determine:** The beta and the required return for a newly constructed portfolio.

**h.**

Summary Introduction

**To determine:** The new portfolio’s required return.

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