QUESTIONBartman Industries’s and Reynolds Inc.’s stock prices and dividends, along with the Winslow 5000 Index, are shown here for the period 2010–2015. The Winslow 5000 data are adjusted to include dividends.
$$
\begin{align*}
\begin{array}{c|cc|cc|c}
\text{} & \text{ Bartman Industries} & & \text{Raynolds Inc.} & & \text{Windslow 5000} \\\\ \hline
\text{Year} & \text{Stock Price} & \text{Dividend} & \text{Stock Price} & \text{Dividend} & \text{Includes Dividends} \\\\
\text{2015} & \text{ 17.25} & \text{ 1.15} & \text{48.75} & \text{3.00} & \text{11.663.98}\\\\
\text{2014} & \text{14.75} & \text{10.6} & \text{52.30} & \text{2.90} & \text{8.785.70}\\\\
\text{2013} & \text{16.50} & \text{1.00} & \text{48.75} & \text{2.75} & \text{8.679.98}\\\\
\text{2012} & \text{10.75} & \text{0.95} & \text{57.25} & \text{2.50} & \text{6.434.03}\\\\
\text{2011} & \text{11.37} & \text{0.90} & \text{60.00} & \text{2.25} & \text{5.602.28}\\\\
\text{2010} & \text{7.62} & \text{0.85} & \text{55.75} & \text{2.00} & \text{4.705.97}\\\\
\end{array}
\end{align*}
$$
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.
b. Calculate the standard deviations of the returns for Bartman, Reynolds, and the Winslow 5000.
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.
f. Assume that the risk-free rate on long-term Treasury bonds is $4.5\%$. 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 10$\%$ 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 $C$.