$3.$ Mod. $5$: Hedging with Interest Rate Futures $($Chapter $8,$ pp$.191$ to $193).$

In October, a bank short$-$term investment manager has $$1$ million in $90-$day T$-$bills on its balance sheet that it plans to sell in December for liquidity purposes, and is worried about interest rates rising $($i$.$e$.$ T$-$bill prices falling$)$ in the next few months, which would cause the value of the Bank$$s holdings of T$-$bills to fall.

The current $($spot$)$ discount yield is $5\mathrm{.}32\%($i$.$e$.$ a Discount $\%$ price of $94\mathrm{.}68\%)$ for a $90-$day T$-$bill.

Hint: $ Price for T$-$bills or Price for T$-$bill Futures Contract

$ Price $=$ $ Amount $\{1[($d x n$)/360]\}$

where d $=$ discount yield as a fraction; n $=$ maturity, usually $90$ days$]$

a$.$ What is the price for the $ $1$ million of T$-$bills in dollars?

T$-$bill Price in Dollars $\_\_\_\_\_\_\_\_$

On the CME Group website, a December $90-$day T$-$bill Futures contract gives a price of $94\mathrm{.}615\%($i$.$e$.,$ a discount yield of $5\mathrm{.}385\%)$ for a $$1$ million, $90-$day Eurodollar Futures contract.

b$.$ What is the contract price for the T$-$bill Futures Contract in dollars?

T$-$bill Futures Price in Dollars $\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

What type of T$-$bill futures contract should be purchased $($long or short$)?$ Explain why.

Long or Short $\_\_\_\_\_\_\_$ Why?$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

c$.$ Suppose in December the T$-$bill discount yield goes up by $100$ basis points to $6\mathrm{.}32\%,$ and the T$-$bill Futures yield goes up by $100$ basis points to $6\mathrm{.}385\%,$ what is the new dollar price for the $1$ mil. T$-$bills, and what is the new contract dollar price for the T$-$bill Futures Contract?

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

New T$-$bill Futures Price in Dollars $\_\_\_\_\_\_\_\_\_\_\_\_$

d$.$ What is the loss or gain for respectively the T$-$bills and the T$-$Bill Futures contract? What is the net hedging result?

T$-$bill Position Spot Loss $\_\_\_\_\_$T$-$bill Futures Gain$\_\_\_\_\_\_\_\_\_$

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