$($ Please answer part d and e$)$ You are the manager of a stock portfolio. On October $1,$ your holdings consist of the eight stocks listed in the table shown in the associated. You are concerned

about the state of the market over the next three months, so you would like to

temporarily adjust your portfolio risk without having to change your holdings. The

spreadsheet provides the number of shares held, each stock$$s beta, and the prices of each stock both on October $1$ and three months later on December $31.$ There is a liquid futures contract that settles in March on the index that the stock's betas are based on; its multiplier is $$500$ per unit of the settlement price.

Stock Shares Beta $10/1$ Price $12/31$ Price

RRD $10,0001\mathrm{.}00$ $$19\mathrm{.}63$ $$27\mathrm{.}38$

BFG $6,2001\mathrm{.}05$ $$31\mathrm{.}38$ $$32\mathrm{.}88$

Ray $15,8001\mathrm{.}15$ $$49\mathrm{.}38$ $$53\mathrm{.}63$

May $8,9000\mathrm{.}90$ $$55\mathrm{.}38$ $$77\mathrm{.}88$

Kro $11,0000\mathrm{.}85$ $$42\mathrm{.}13$ $$47\mathrm{.}88$

Comd $14,5001\mathrm{.}45$ $$19\mathrm{.}38$ $$28\mathrm{.}63$

Ces $9,9001\mathrm{.}20$ $$29\mathrm{.}75$ $$30\mathrm{.}13$

Fox $4,5000\mathrm{.}95$ $$24\mathrm{.}75$ $$26$

a$.$ What are the beta and market value of your portfolio on October $1?$

b$.$ On October $1,$ the contract$$s settlement price is $376\mathrm{.}20.$ How many contracts would

you need to enter into $($and in which direction, long or short$)$ to set your combined

portfolio$$s beta to:

i$.0\mathrm{.}0?$

ii$.1\mathrm{.}0?$

iii. $1\mathrm{.}5?$

c$.$ What is the portfolio of stocks alone worth on December $31?$

d$.$ What is the value of the total portfolio on December $31$ given each of the three

scenarios in part b$?$ Assume the settlement price for the futures contract has risen

to $424\mathrm{.}90$ on December $31.$

e$.$ What is the return for each of the four scenarios in parts c and d$?$ Remember that entering into a futures contract is a net zero cash flow, so the denominator for the return should only be the initial value of the stock portfolio on October $1.$

f$.$ Plot these returns in Excel with the betas as your horizontal axis using a scatter plot without lines connecting each point, but add a trendline. Set up the data in Excel that is plotted as follows:

Beta Return

$[$stock portfolio beta, place in table in $[$enter values from part e in this column$]$

appropriate row so this column is

sorted in ascending order$]$

$0\mathrm{.}0$

$1\mathrm{.}0$

$1\mathrm{.}5$