$9$

It is now October $2014.$ A company anticipates that it will purchase $1$ million pounds of copper in each of February $2015,$ August $2015,$ February $2016,$ and August $2016.$ The company has decided to use the futures contracts traded in the COMEX division of the CME Gronp to hedge its risk. One contract is for the delivery of $25,000$ pounds of copper. The initial margin is $$2,000$

per contract and the maintenance margin is $$1,500$ per contract. The company's policy is to hedge $80\%$ of its exposure. Contracts with maturities up to $13$ months into the future are considered to have sufficient liquidity to meet the company's needs. Devise a hedging strategy for the company. $($Do not make the "tailing" adjustment described in Section $3\mathrm{.}4.)$

Assume the market prices $($in cents per pound$)$ today and at future dates are as follows. What is the impact of the strategy you propose on the price the company pays for copper? What is the initial margin requirement in October $2014?$ Is the company subject to any margin calls?

$\backslash$table$[[$Date$,$Oct $2014,$Feb $2015,$Aug $2015,$Feb $2016,$Atrg $2016],[$Spot Price,$372\mathrm{.}00,369\mathrm{.}00,365\mathrm{.}00,377\mathrm{.}00,388\mathrm{.}00],[$Mar $2015$ Futures Price,$372\mathrm{.}30,369\mathrm{.}10,,,],[$Sep $2015$ Futures Price,$372\mathrm{.}80,370\mathrm{.}20,364\mathrm{.}80,,],[$Mar $2016$ Futures Price,,$370\mathrm{.}70,364\mathrm{.}30,376\mathrm{.}70,],[$Sep $2016$ Futures Price,,,$364\mathrm{.}20,376\mathrm{.}50,388\mathrm{.}20]]$

$10$

The cash prices of six$-$month and one$-$year Treasury bills are $94\mathrm{.}0$ and $89\mathrm{.}0.$ A $1\mathrm{.}5-$year bond that will pay coupons of $$4$ every six months currently sells for $$94\mathrm{.}84.$ A two$-$year bond that will pay coupons of $$5$ every six months currently sells for $$97\mathrm{.}12.$ Calculate the six$-$month, one$-$year, $1\mathrm{.}5-$year, and two$-$year zero rates.

$11$

When compounded annually an interest rate is $11\%.$ What is the rate when expressed with $($a$)$ semianmual compounding, $($b$)$ quarterly compounding, $($c$)$ monthly compounding, $($d$)$ weekly compounding, and $($e$)$ daily compounding.

$12$

$\backslash$table$[[$Maturity $($years$,$Zero rate,Coupon payment,Principal$],[0\mathrm{.}5,2\mathrm{.}0\%,$$$20,],[1\mathrm{.}0,2\mathrm{.}3\%,$$$20,],[1\mathrm{.}5,2\mathrm{.}7\%,$$$20,$$$1000$