Question

Bartman Industries’ and Reynolds Incorporated’s stock prices and dividends, along with the Wilshire 5000 Index, are shown below for the period 1996-2001. The Wilshire 5000 data are adjusted to include dividends.

Year Bartman Industries Reynolds Incorporated Wilshire 5000 Stock Price Dividend Stock Price Dividend Includes Divs.

2001 $ 17.250 1.15 $ 48.750 3.00 52.300 2.90 48.750 2.75 57.250 2.50 60.000 2.25 55.750 2.00 11,663.98 8,785.70 8,679.98 6,434.03 5,602.28 4,705.97 2000 1999 1998 1997 1996 14.750 1.06 16.500 1.00 10.750 0.95 11.375 0.90 7.625 0.85

1. Use the data given to calculate annual returns for Bartman, Reynolds, and the Wilshire 5000 Index, and then calculate average returns 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 1996 because you do not have 1995 data).

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

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

4. Construct a scatter diagram graph that shows Bartman’s, Reynolds’ returns on the vertical

   axis and the market index’s returns on the horizontal axis.

5. Estimate Bartman’s and Reynolds’ betas by running regressions of their returns against the

   Wilshire 5000’s returns. Are these betas consistent with your graph?

6. The risk-free rate on long-term Treasury bonds is 6.04 percent. Assume that the market risk premium is 5 percent. What is the expected return on the market? Now use the SML

   equation to calculate the two companies’ required returns.

7. If you formed a portfolio that consisted of 50 percent of Bartman stock and 50 percent of

   Reynolds stock, what would be its beta and its required return?

8. Suppose an investor wants to include Bartman Industries’ stock in his on 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.

Answer 1

a) To compute annual return:
Subtract beginning price from ending price, add dividends, divide sum by beginning price

Formula:
Annual return= ((ending price-beginning price)+dividends)/beginning price

Bartman Industries

Reynolds Incorporated

Wilshire 5000

b) Average returns over the 5-year period

c) &d ) Standard deviations of the returns and coefficients of variation

Bartman Industries

Reynolds Incorporated

Wilshire 5000

e) Scatter diagram graph that shows Barton’s, Reynolds’ returns

.

Blue-Bartman

Orange-Reynold

f) Estimate Bartman’s and Reynolds’ betas by running regressions of their returns against the Wilshire 5000’s returns

Beta of Bartman

For Bartman, the beta is 1.539151936 (red text). Comparing this to the scatter diagram above, we see that the beta we computed is consistent. Since the beta is positive, the returns are moving along with the market (if market returns increase, stock return also increases).

Regression analysis of Bartman

Beta of Reynold

For Reynolds Inc., the beta is -0.560355859 (red text). Comparing this to the scatter diagram above, we see that the beta we computed is consistent. Since the beta is negative, the returns are moving opposite of the market (if market returns increase, stock return also decrease).

Regression analysis of Reynold

g)

Bartman's required rate of return

Reynold Inc required rate of return

To find portfolio beta

h)

Amount                  Weighted

Stock Weight x Beta¹ = Average²

Bartman               50%         x 1.53915 = 0.769575

Reynold                50%     x -0.56035 = -0.280175

Portfolio beta (b_p) = 0.4894

Steps:

1. Multiply the weights by the stock beta

Stock Bartman = 50% x 1.53915 = 0.769575

Stock Reynold = 50% x 0.56035 = 0.280175

2. Find the sum of the weighted beta of each stock to find portfolio beta.

Portfolio beta = 0.769575 + (-0.280175) = 0.4894

Then plug the portfolio beta to CAPM:

Required return of portfolio = risk-free rate + (market risk premium)(portfolio beta)

= 4.5% + (10% — 4.5%)(0.4894)

= 4.5% + (5.5%)(0.4894)

= 4.5% + 2.6917%

= 7.1917%

i)

Amount Weighted

Stock             Weight x Beta¹ = Average²

Bartman             25% x 1.53915 = 0.3847875

A                        15%           x 0.769 = 0.11535

B                        40%         x 0.985 = 0.394

C                        20%          x 1.423 = 0.2846
Portfolio beta (b_p) = 1.17873

Steps:

1. Multiply the weights by the stock beta

Stock Bartman = 25% x 1.53915 = 0.3847875

Stock A = 15% x 0.769 = 0.11535

Stock B = 40% x 0.985 = 0.394

Stock C = 20% x 1.423 = 0.2846

2. Find the sum of the weighted beta of each stock to find portfolio beta.

Portfolio beta = 0.3847875 + 0.11535 + 0.394 + 0.2846 = 1.17873

Then plug the portfolio into to CAPM:

Required return of portfolio = risk-free rate + (market risk premium)(portfolio beta)

= 4.5% + (10% — 4.5%)(1.17873)

= 4.5% + (5.570(1.17873)

= 4.5% + 6.483015%

= 10.983015%