Question

Question: Evaluation risk and return Bartman Industries’s and Reynolds Inc.’s stock prices and dividends, a... (4 bookmarks) Evaluation 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. Bartman Industries Reynolds Inc. Winslow 5000 Year Stock Price Dividend Stock Price Dividend Includes Dividends 2014 $17.25 $1.15 $48.75 $3.00 $11,663.98 2013 14.75 1.06 52.30 2.90 8,785.70 2012 16.50 1.00 48.75 2.75 8,679.98 2011 10.75 0.95 57.25 2.50 6,434.03 2010 11.37 0.90 60.00 2.25 5,602.28 2009 7.62 0.85 55.75 2.00 4,705.97 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) Calculate the standard deviations of the returns for Bartman, Reynolds, and the Winslow 5000. (Hint: Use the ample standard deviation formulate, Equation 8.2a in this chapter, which corresponds to the STDEV function Excel.) Calculate the coefficients of variation for Bartman, Reynolds, and the Winslow 5000. Construct a scatter diagram that shows Bartman’s and Reynolds’ returns on the vertical axis and the Winslow 5000 Index’s returns on the horizontal axis. Estimate Bartman’s and Reynolds’ betas by running regressions of their returns against the index’s returns. (Hint: Refer to Web Appendix8A.) Are these betas consistent with your graph? 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. If you formed a portfolio that consisted of 50% Bartman and 50% Reynolds, what would the portfolio’s beta and required return be? Suppose an investor wants to include Bartman Industries’ 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. Please show all work

Answer 1

Solution:

Since the question has many parts I have divided the questions into sub parts and answered accordingly.

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)

Data given in the problem are shown below:

	Bartman Industries		Reynolds Incorporated		Winslow 5000
Year	Stock Price ($)	Dividend ($)	Stock Price ($)	Dividend ($)	Includes Dividends ($)
2014	17.25	1.15	48.75	3.00	1,663.98
2013	14.75	1.06	52.30	2.90	8,785.70
2012	16.50	1.00	48.75	2.75	8,679.98
2011	10.75	0.95	57.25	2.50	6,434.03
2010	11.37	0.90	60.00	2.25	5,602.28
2009	7.62	0.85	55.75	2.00	4,705.97

We now calculate the rate of return for the two companies and the index for 2010 – 2014

Year	Bartman Industries	Reynolds Incorporated	Winslow 5000
2014	24.7%	-1.1%	32.8%
2013	-4.2%	13.2%	1.2%
2012	62.8%	-10.0%	34.9%
2011	2.9%	-0.4%	14.8%
2010	61.0%	11.7%	19.0%
Average returns	29.4%	2.7%	20.6%

Note: To get the average, you could get the column sum and divide by 5, or you could also use the function wizard, f_x. Click f_x, then statistical, then Average, and then use the mouse to select the proper range. Do this for Bartman and then copy this cell to put the formula in the other two cells.

b. Calculate the standard deviations of the returns for Bartman, Reynolds, and the Winslow 5000. (Hint: Use the ample standard deviation formulate, Equation 8.2a in this chapter, which corresponds to the STDEV function Excel.)

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

	Bartman Industries	Reynolds Incorporated	Winslow 5000
Standard Deviation of return	31.5%	9.7%	13.8%

c. Calculate the coefficients of variation for Bartman, Reynolds, and the Winslow 5000.

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

Now, divide the Standard Deviation by average return to calculate Coefficient of Variation:

	Bartman Industries	Reynolds Incorporated	Winslow 5000
Coefficient of Variation	1.07	3.63	0.67

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

d. Construct a scatter diagram that shows Bartman’s and Reynolds’ returns on the vertical axis and the Winslow 5000 Index’s returns on the horizontal axis.

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

Year	Winslow 5000	Bartman Industries	Reynolds Incorporated
2014	32.8%	24.7%	-1.1%
2013	1.2%	-4.2%	13.2%
2012	34.9%	62.8%	-10.0%
2011	14.8%	2.9%	-0.4%
2010	19.0%	61.0%	11.7%

Pic of the graph attached.

To make the graph, we first select the range with the returns and columns heads, then clicked the chart wizard, then choose the scatter diagram without connected lines. That gives us the data points. We then use the drawing toolbar to make free-hand (“by eye”) regression lines, and changed the colour of the lines and weights to match the dots.

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

e. Estimate Bartman’s and Reynolds’ betas by running regressions of their returns against the index’s returns. (Hint: Refer to Web Appendix8A.) Are these betas consistent with your graph?

We can use the data just above the graph to do the regression. Click on Tools, Data Analysis, Regression and then follow the menu. We first calculate Bartman Industries beta and then Reynolds Incorporated.

Bartman’s Calculations

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.68
R Square	0.46
Adjusted R Square	0.28
Standard Error	0.27
Observations	5

ANOVA

	df	SS	MS	F	Significance F
Regression	1	0.18	0.18	2.52	0.21
Residual	3	0.22	0.07
Total	4	0.4

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-0.02	0.23	-0.09	0.93	-0.76	0.72
X Variable 1	1.54	0.97	1.59	0.21	-1.55	4.63

Bartman’s Beta = 1.54

RESIDUAL OUTPUT

Observation	Predicted Y	Residuals
1	0.48	-0.23
2	0	-0.04
3	0.52	0.11
4	0.21	-0.18
5	0.27	0.34

Reynold’s Calculations

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.8
R Square	0.64
Adjusted R Square	0.51
Standard Error	0.07
Observations	5

ANOVA

	df	SS	MS	F	Significance F
Regression	1	0.02	0.02	5.24	0.11
Residual	3	0.01	0
Total	4	0.04

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0.14	0.06	2.42	0.09	-0.04	0.33
X Variable 1	-0.56	0.24	-2.29	0.11	-1.34	0.22

Reynold’s Beta = -0.56

RESIDUAL OUTPUT

Observation	Predicted Y	Residuals
1	-0.04	0.03
2	0.14	0
3	-0.05	-0.05
4	0.06	-0.06
5	0.04	0.08

Note that these betas are consistent with the scatter diagrams we constructed earlier. Reynold’s beta suggests that it is less risky than average in a CAPM sense, whereas Bartman is more risky than average.

f. 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.

Market return = 11.000%

Risk-free rate = 6.040%

Required return = Risk-free rate + Market risk premium * Beta

Bartman:

Market risk premium = 4.960%

Risk-free rate = 6.040%

Beta = 1.539

Required return = Risk-free rate + Market risk premium * Beta

                                = 6.040% + 4.960% * 1.539

                                = 13.675%

Reynold:

Market risk premium = 4.960%

Risk-free rate = 6.040%

Beta = -0.560

Required return = Risk-free rate + Market risk premium * Beta

                                = 6.040% + 4.960% * -0.560

                                = 3.260%

This suggests that Reynold’s stock is like an insurance policy that has a low expected return, but it will pay off in the event of a market decline. Actually, it is hard to find negative-beta stocks, so we would not be inclined to believe the Reynold’s data.

g. If you formed a portfolio that consisted of 50% Bartman and 50% Reynolds, what would the portfolio’s beta and required return be?

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:

[1.539 + (-0.560)] / 2 = 0.489

Market risk premium = 4.960%

Risk-free rate = 6.040%

Beta = 0.489

Required return on portfolio = Risk-free rate + Market risk premium * Beta

                                                         = 6.040% + 4.960% * 0.489

                                                         = 8.468%

h. Suppose an investor wants to include Bartman Industries’ 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.

	Beta	Portfolio weight
Bartman	1.539	25%
Stock A	0.77	15%
Stock B	0.99	40%
Stock C	1.42	20%
		100%
Portfolio Beta	1.179

Market risk premium = 4.960%

Risk-free rate = 6.040%

Beta = 1.179

Required return on portfolio = Risk-free rate + Market risk premium * Beta

                                                        = 6.040% + 4.930% * 1.179

                                                         = 11.89%