## risk-return

Assignment 2 | |||||

a. Use the year-end stock price data given to calculate annual returns for Bartman, Reynolds, and the Market Index, and then calculate average returns over the five-year period. Remember, returns are calculated by subtracting the beginning price (previous year year-end price) from the ending price (current year year-end 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 (previous year year-end price). Assume that dividends are already included in the index., so in your calculation of index return, you don’t need to add the dividend. Also, you cannot calculate the rate of return for 2002 because you do not have 2001 data.) | |||||

Data as given in the problem are shown below: | |||||

Bartman Industries | Reynolds Incorporated | Market Index | |||

Year | Stock Price | Dividend | Stock Price | Dividend | Includes Divs. |

2007 | $17.250 | $1.150 | $48.750 | $3.000 | 11,663.98 |

2006 | 14.750 | 1.060 | 52.300 | 2.900 | 8,785.70 |

2005 | 16.500 | 1.000 | 48.750 | 2.750 | 8,679.98 |

2004 | 10.750 | 0.950 | 57.250 | 2.500 | 6,434.03 |

2003 | 11.375 | 0.900 | 60.000 | 2.250 | 5,602.28 |

2002 | 7.625 | 0.850 | 55.750 | 2.000 | 4,705.97 |

We now calculate the rates of return for the two companies and the index: | |||||

Bartman | Reynolds | Index | |||

2007 | |||||

Kenneth D. Jackson: Change in stock price plus any dividends, divided by the previous stock price | 2006 | ||||

2005 | |||||

2004 | |||||

2003 | |||||

Average | |||||

Note: To get the average, you could get the column sum and divide by 5, but you could also use the function wizard, fx. Click fx, then statistical, then Average, and then use the mouse to select the proper range. Do this for Bartman and then copy the cell for the other items. | |||||

b. Calculate the standard deviation of the returns for Bartman, Reynolds, and the Market Index. (Hint: Use the sample standard deviation formula given in the chapter, which corresponds to the STDEV function in Excel.) | |||||

Use the function wizard to calculate the standard deviations. | |||||

Bartman | Reynolds | Index | |||

Standard deviation of returns | |||||

c. Now calculate the coefficients of variation Bartman, Reynolds, and the Market Index. | |||||

Bartman | Reynolds | Index | |||

Coefficient of Variation | |||||

d. Estimate Bartman’s and Reynolds’s betas as the slope of a regression with stock return on the vertical axis (y-axis) and market return on the horizontal axis (x-axis). (Hint: use Excel’s SLOPE function.) | |||||

Bartman’s beta = | |||||

Reynolds’ beta = | |||||

e. The risk-free rate on long-term Treasury bonds is 6.04%. Assume that the market risk premium is 5%. What is the expected return on the market? Now use the SML equation to calculate the two companies required returns. | |||||

Market risk premium (RPM)= | 5.000% | ||||

Risk-free rate = | 6.040% | ||||

Expected return on market = | Risk-free rate | + | Market risk premium | ||

= | + | ||||

= | |||||

Bartman: | |||||

Required return | = | + | x | ||

= | |||||

Reynolds: | |||||

Required return | = | + | x | ||

= | |||||

f. If you formed a portfolio that consisted of 50% Bartman and 50% Reynolds, what would be its beta and its required return? | |||||

The beta of a portfolio is simply a weighted average of the betas of the stocks in the portfolio, so this portfolio’s beta | |||||

would be: | |||||

Portfolio beta = | |||||

g. Suppose an investor wants to include Bartman Industries’ stock in his or her 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 percent of Bartman, 15 percent of Stock A, 40 percent of Stock B, and 20 percent of Stock C. | |||||

Beta | Portfolio Weight | ||||

Bartman | 25% | ||||

Stock A | 0.769 | 15% | |||

Stock B | 0.985 | 40% | |||

Stock C | 1.423 | 20% | |||

100% | |||||

Portfolio Beta = | |||||

Required return on portfolio: | = | Risk-free rate + | Market Risk Premium * | * Beta | |

= | |||||

= | |||||