Interest Rate FuturesChapter 6*

*

Day Count Conventions in the U.S. *

Treasury Bonds:Actual/Actual (in period)Corporate Bonds:30/360Money Market Instruments:Actual/360

*

*Treasury Bond Price Quotesin the U.S Cash price = Quoted price + Accrued Interest

It is January 9, 2013. The price of a Treasury bond with a 12% coupon (issue date October 12, 2012) that matures on October 12, 2020, is quoted as 102-07. What is the cash price?

*

*Treasury Bond FuturesAn interest rate future is a financial derivative (a futures contract) with an interest-bearing instrument as the underlying asset.

Examples include Treasury-bill futures and Eurodollar futures.

*

*Treasury Bond FuturesInterest rate futures are used to hedge against the risk of that interest rates will move in an adverse direction, causing a cost to the company.

For example, borrowers face the risk of interest rates rising. Futures use the inverse relationship between interest rates and bond prices to hedge against the risk of rising interest rates. A borrower will enter to sell a future today. Then if interest rates rise in the future, the value of the future will fall (as it is linked to the underlying asset, bond prices), and hence a profit can be made when closing out of the future (i.e. buying the future).

*

*Treasury Bond FuturesIt's Important to note that interest rate futures are not directly correlated with the market interest rates. When one enters into an interest rate futures contract (like a bond future), the trader has ability to eventually take delivery of the underlying asset. In the case of notes and bonds this means the trader could potentially take delivery of a bunch of bonds if the contract is not cash settled. The bonds which the seller can deliver vary depending on the futures contract. The seller can choose to deliver a variety of bonds to the buyer that fit the definitions laid out in the contract. The futures contract price takes this into account, therefore prices have less to do with current market interest rates, and more to do with what existing bonds in the market are cheapest to deliver to the buyer.

*

*Treasury Bond Futures

Cash price received by party with short position = Most recent settlement price Conversion factor + Accrued interest

*

*ExampleMost recent settlement price = 90.00Conversion factor of bond delivered = 1.3800Accrued interest on bond =3.00Price received for bond is 1.380090.00+3.00 = $127.20

per $100 of principal

*

*Conversion Factor The conversion factor for a bond is approximately equal to the value of the bond on the assumption that the yield curve is flat at 6% with semiannual compounding

*

Cheapest to deliver Bond(Most recent settlement price * Conversion factor) + Accrued interest

and the cost of purchasing a bond is

Quoted bond price + Accrued interest

the cheapest-to-deliver bond is the one for which

Quoted bond price - Most recent settlement price * Conversion factor*

Cheapest to deliver BondSuppose that the Treasury bond futures price is 101-12. Which of the following four bonds is cheapest to deliver?

*

*CBOTT-Bonds & T-NotesFactors that affect the futures price:Delivery can be made any time during the delivery monthAny of a range of eligible bonds can be deliveredThe wild card play

*

Determining the future priceIn a Treasury bond futures contract, it is known that the cheapest to-deliver bond will be a 12% coupon bond with a conversion factor of 1.6000. Suppose that it is known that delivery will take place in 270 days. Coupons are payable semiannually on the bond. The last coupon date was 60 days ago, the next coupon date is in 122 days, and the coupon date thereafter is in 305 days. The term structure is flat, and the rate of interest (with continuous compounding) is 10% per annum. Assume that the current quoted bond price is $115. The cash price of the bond is obtained by adding to this quoted price the proportion of the next coupon payment that accrues to the holder. The cash price is ??*

*A Eurodollar is a dollar deposited in a bank outside the United States Eurodollar futures are futures on the 3-month Eurodollar deposit rate (same as 3-month LIBOR rate)One contract is on the rate earned on $1 millionA change of one basis point or 0.01 in a Eurodollar futures quote corresponds to a contract price change of $25

Eurodollar Futures

*

*Eurodollar Futures continuedA Eurodollar futures contract is settled in cashWhen it expires (on the third Wednesday of the delivery month) the final settlement price is 100 minus the actual three month deposit rate

*

*ExampleSuppose you buy (take a long position in) a contract on November 1The contract expires on December 21The prices are as shownHow much do you gain or lose a) on the first day, b) on the second day, c) over the whole time until expiration?

*

*Example

DateQuoteNov 1 97.12Nov 297.23Nov 396.98.Dec 2197.42

*

*Example continuedIf on Nov. 1 you know that you will have $1 million to invest on for three months on Dec 21, the contract locks in a rate of

100 - 97.12 = 2.88%In the example you earn 100 97.42 = 2.58% on $1 million for three months (=$6,450) and make a gain day by day on the futures contract of 30$25 =$750

*

*QuestionAn Investor wants to lock in the interest rate for 3 months period beginning September 19, 2012, on a principal of $100 million. The September 2012 Eurodollar futures quoted is 96.50 per annum. Suppose that on September 19, 2012 the 3 month Eurodollar rate turns out to be 2.6%. Calculate the final settlement amount gain/ loss.

*

*Formula for Contract ValueIf Q is the quoted price of a Eurodollar futures contract, the value of one contract is 10,000[100-0.25(100-Q)]

*

*Duration MatchingThis involves hedging against interest rate risk by matching the durations of assets and liabilitiesIt provides protection against small parallel shifts in the zero curve

*

*Duration-Based Hedge Ratio

FCContract price for interest rate futuresDFDuration of asset underlying futures at maturityPValue of portfolio being hedgedDPDuration of portfolio at hedge maturity

*

*Example It is August. A fund manager has $10 million invested in a portfolio of government bonds with a duration of 6.80 years and wants to hedge against interest rate moves between August and DecemberThe manager decides to use December T-bond futures. The futures price is 93-02 or 93.0625 and the duration of the cheapest to deliver bond is 9.2 yearsThe number of contracts that should be shorted is

*

*Limitations of Duration-Based HedgingAssumes that only parallel shift in yield curve take placeAssumes that yield curve changes are smallWhen T-Bond futures is used assumes there will be no change in the cheapest-to-deliver bond

*

*

**

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*