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# Treasury Bonds

Treasury bonds, like the T-notes, are also debt instruments that are issued by the U.S. Treasury. With a maturity of more than 10 years, these semiannual coupon bonds are auctioned in the months of February, May, August, and November, although they are reopened during the other months of the year. The computations associated with accrued interest, yield-to-maturity, quoted price, settlement, and so on are identical to those used for T-notes.

# Eurodollar Futures

Eurodollars refer to U.S. dollar deposits in a U.S. or a foreign bank that is domiciled outside the United States.[1] A Eurodollar futures contract is

TABLE 2.2B Calculating Bond Yield Using Newton's Method

a futures contract on a 3-month Eurodollar deposit. The last trading day associated with a Eurodollar futures contract tends to be two business days (at 1100 hours London time) prior to the third Wednesday of the months of March, June, September, and December of the first 10 years. In addition to this, the four nearest serial months (which are not in the March quarterly cycle) are also included as expiry dates.[2]

Given how a Eurodollar futures contract is constructed, the Eurodollar futures interest rate is defined to be 100 – QP, where QP represents the quoted Eurodollar futures price. Furthermore, the contract or settlement price associated with this QP is given by the expression 10,000* [100 – 0.25 * (100 – QP)]. Thus, a QP of 99.25 gives rise to a Eurodollar futures interest rate[3] of 0.075 percent and a contract price of USD998,125 where each contract results in a maturity value of USD1,000,000.

Since Eurodollar futures contracts provide a market expectation where the underlying 3-month LIBOR rates will be in the future, practitioners use them as a proxy for 3-month forward rate agreements[4] with some adjustments. To do this, practitioners use the approximation[5]

(2.5)

to correct the futures rate, where the futures rate represents the rate of a 3-month Eurodollar futures contract rate maturing at time tl that is continuously compounded, , represents the standard deviation of the change in the interest rate, and forward rate represents the continuously compounded forward rate for a 3-month LIBOR setting on tl and settling on t2. The reader is referred to Hull (2012) for further details. Table 2.3 shows how these calculations are implemented in practice.

• [1] The origin of these types of deposits goes back to the Cold War. More precisely, before the Cold War, it was customary to make deposits in the country of the denominated currency (e.g., to make a U.S.-dollar-denominated deposit one would need to deposit U.S. dollars in a bank that is domiciled in the United States and to make a yen-denominated deposit one would need to deposit yen in a bank that is domiciled in Japan). During the Cold War, the former Soviet Union bloc nations had to use U.S. dollars to do their import and export. Due to the fear of getting their assets frozen, the Soviet Union invested its U.S. dollars in a British bank (which was owned by the Soviet Union) that had a British charter, which in turn made the deposit into a U.S. bank that was domiciled in the United States – thereby creating the first-known transaction of a Eurodollar deposit.
• [2] For further details on the contract specifications associated with the Eurodollar futures contract, see cmegroup.com/trading/interest-rates/stir/eurodollar_ contract_specifications.html.
• [3] This can be obtained by simply computing the quantity (100 – QP) %.
• [4] Forward rate agreements (FRAs) are also considered as single period swaps, which are essentially bilateral financial contracts trading in the over-the-counter market in which one party agrees to exchange the interest payments linked to the then- prevailing 3-month LIBOR for those linked to a prespecified forward rate.
• [5] There are two reasons for the need of the correction in equation (2.5). The first stems from the fact that in a forward rate contract there is no concept of marked-to- market compared to a Eurodollar futures contract in which the positions are marked- to-market daily until the contract matures at time tt. The second stems from the fact that, unlike a forward contract where the parties only settle up at time t2, in a Eurodollar futures contract, assuming it is held to expiry date, the parties settle up at time t1.

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