Harcourt, Inc. items and derived items copyright © 2002 by Harcourt, Inc.

a. Use the data given to calculate annual returns for Bartman, Reynolds, and the Wilshire 5000 Index, and then calculate average returns over the five-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 1995 because you do not have 1994 data.)

Data as given in the problem are shown below:Bartman Industries Reynolds Incorporated Wilshire 5000

Year Stock Price Dividend Stock Price Dividend Includes Divs.

2000 $ 18.00 $ 1.15 $ 49.25 $ 3.00 $ 11,773.98

1999 $ 15.25 $ 1.06 $ 53.10 $ 2.90 $ 8,895.70

1998 $ 17.00 $ 1.00 $ 49.25 $ 2.75 $ 8,689.98

1997 $ 11.25 $ 0.95 $ 58.25 $ 2.50 $ 6,444.03

1996 $ 12.75 $ 0.90 $ 61.00 $ 2.25 $ 5,612.28

1995 $ 8.60 $ 0.85 $ 56.05 $ 2.00 $ 4,815.97

We now calculate the rates of return for the two companies and the index for 1996-2000:

Bartman Reynolds Index2000 25.6% -1.6% 32.4%1999 -4.1% 13.7% 2.4%1998 60.0% -10.7% 34.9%1997 -4.3% -0.4% 14.8%1996 58.7% 12.8% 16.5%

Avg Returns 27.2% 2.8% 20.2%

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 Bartmanand then copy the cell for the other items.

b. Calculate the standard deviation of the returns for Bartman, Reynolds, and the Wilshire 5000. (Hint: Use the sample standard deviation formula given in Footnote 5 to this chapter, which corresponds to the STDEV function in Excel.)

We will use the function wizard to calculate the standard deviations.

Bartman Reynolds IndexStandard deviation of returns 31.8% 10.4% 13.4%

On a stand-alone basis, it would appear that Bartman is the most risky, Reynolds the least risky.

c. Now calculate the coefficients of variation Bartman, Reynolds, and the Wilshire 5000.

Divide the standard deviation by the average return:

Bartman Reynolds IndexCoefficient of Variation=Std dev / Mean 1.17 3.76 0.67

Reynolds now looks most risky, because its risk (SD) per unit of return is highest.

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Harcourt, Inc. items and derived items copyright © 2002 by Harcourt, Inc.

d. Construct a scatter diagram graph that shows Bartman’s and Reynolds’ returns on the vertical axis and the market index’s returns on the horizontal axis.

It is easiest to make scatter diagrams with from a data set that has the X-axis variable in the left column, so we reformatthe returns data calculated above and show it just below.

Year Index Bartman Reynolds2000 32.4% 25.6% -1.6%1999 2.4% -4.1% 13.7%1998 34.9% 60.0% -10.7%1997 14.8% -4.3% -0.4%1996 16.5% 58.7% 12.8%

To make the graph, we first selected the range with the returns and the column heads, then clicked the chart wizard,then choose the scatter diagram without connected lines. That gave us the data points. We then used the drawingtoolbar to make free-hand ("by eye") regression lines, and changed the lines color and weights to match the dots.

It is clear that Bartman moves with the market and Reynolds moves counter to the market. So, Bartman has a positivebeta and Reynolds a negative one.

e. Correlations

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Stock Returns Vs. Index

Bartman

Reynolds

Index Returns

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