$3.$ It is February and, Max McMillian, Treasury Manager for the Excelsior Corporation, recognizes the need to purchase $$10,000,000$ of $91-$day T$-$bills for the company$$s short$-$term portfolio when that amount of cash comes in to the company in June. At this time, the $91-$day T$-$bill discount rate is $5\mathrm{.}21\%,$ implying a price of $$1,000,000[1(\mathrm{.}0521$ x $91/360)]=$ $$986,830\mathrm{.}28.$

At this time, on the CME Group website, the June $2024$ futures price for a $3-$ month $(90$ day$)$ Eurodollar CD$,$ the IMM index price is quoted as $96\mathrm{.}180($implying a discount rate of $100\%-96\mathrm{.}18\%=3\mathrm{.}82\%,$ and each contract is for $ $1$ million, implying a contract price of $$1,000,000[1(\mathrm{.}0382$ x $90/360)]=$

$ $990,450$ per contract.

a$.$ Suppose Max wants to hedge his spot position against a fall in rates $($rise T$-$bill prices$),$ that would make the purchase of the T$-$bills more expensive in June by taking on $10$ Eurodollar CD futures contracts as a hedge.

What position should he take short or long, and explain why?

Long or Short Position $\_\_\_\_\_\_\_\_\_\_\_$ Explain why $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

b$.$ Suppose in June, the T$-$bill discount rate falls to $3\mathrm{.}82\%$ and the Eurodollar CD May futures contract discount rate falls to $2\mathrm{.}105\%.$ What are the new T$-$bill and Eurodollar futures contracts?

New T$-$bill Price $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

New EurCD Futures Price $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

c$.$ What is the gain or loss on the spot position and on the futures position, and the net hedging result? Be sure to multiply by the $10$ T$-$bills and $10$ futures contracts.

Spot Opportunity Loss $\_\_\_\_\_\_\_\_\_\_\_\_\_$ Futures Gain $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Net Hedging Result $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$