Due on Feb$\mathrm{.}25$

Chapter: $6$

See the Example for the estimation of standard deviation and beta.

a$.$ Use the data given to calculate annual returns for Goodman, Landry, and the Market 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 $2010$ because you do not have $2009$ data.$)$

Data as given in the problem are shown below:

Goodman Industries Landry Incorporated Market Index

Year Stock Price Dividend Stock Price Dividend Includes Divs.

$2016$ $$25\mathrm{.}88$ $$1\mathrm{.}73$ $$73\mathrm{.}13$ $$4\mathrm{.}5017,495\mathrm{.}97$

$2015$ $$22\mathrm{.}13$ $$1\mathrm{.}59$ $$78\mathrm{.}45$ $$4\mathrm{.}3513,178\mathrm{.}55$

$2014$ $$24\mathrm{.}75$ $$1\mathrm{.}50$ $$73\mathrm{.}13$ $$4\mathrm{.}1313,019\mathrm{.}97$

$2013$ $$16\mathrm{.}13$ $$1\mathrm{.}43$ $$85\mathrm{.}88$ $$3\mathrm{.}759,651\mathrm{.}05$

$2012$ $$17\mathrm{.}06$ $$1\mathrm{.}35$ $$90\mathrm{.}00$ $$3\mathrm{.}388,403\mathrm{.}42$

$2011$ $$11\mathrm{.}44$ $$1\mathrm{.}28$ $$83\mathrm{.}63$ $$3\mathrm{.}007,058\mathrm{.}96$

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

DON'T FORGET TO ADD DIVIDENDS WHEN CALCULATING A COMPANY'S RETURN.

Goodman Landry Index

$2016$

$201524\mathrm{.}1\%$

$2014$

$2013$

$2012$

Average

b$.$ Calculate the standard deviation of the returns for Goodman, Landry, 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.

Goodman Landry Index

Standard deviation of returns

c$.$ Estimate Goodman$$s and Landry$$s betas as the slopes of regression lines with stock returns on the vertical axis $($y$-$axis$)$ and market return on the horizontal axis $($x$-$axis$).($Hint: use Excel$$s SLOPE function$)$

Goodman's beta $=$

Landry' beta $=$

d$.$ The risk$-$free rate on long$-$term Treasury bonds is $6\mathrm{.}04\%.$ Assume that the market risk premium is $5\%.$ What is the expected return on the market? Now use the CAPM model to calculate the two companies' required returns.

Market risk premium $($RPM$)=5\mathrm{.}000\%$

Risk$-$free rate $=6\mathrm{.}040\%$

Required return on the market? $=$

Goodman:

Required return $=$

Landry:

Required return $=$

e$.$ If you formed a portfolio that consisted of $50\%$ Goodman stock and $50\%$ Landry stock, what would be its beta and its required return?

Portfolio beta $=`$

Expected return$=$