## Bond Futures

Bond futures are futures contracts where the commodity for delivery is a government bond. There are established global markets for government bond futures. Bond futures provide a liquid alternative for managing interest-rate risk.

In the U.S. market, the Chicago Mercantile Exchange (CME) offers futures on Treasury bonds and notes with maturities of 2, 5, 10, and 30 years. Typically, the following bond future contracts from the CME have maturities of 3, 6, 9, and 12 months:

The short position in a Treasury bond or note future contract must deliver to the long position in one of many possible existing Treasury bonds. For example, in a 30-year Treasury bond future, the short position must deliver a Treasury bond with at least 15 years to maturity. Because these bonds have different values, the bond future contract is standardized by computing a conversion factor. The conversion factor normalizes the price of a bond to a theoretical bond with a coupon of 6%. The price of a bond future contract is represented as:

$InvoicePrice=FutPrice×CF+AI$

where:

FutPrice is the price of the bond future.

CF is the conversion factor for a bond to deliver in a futures contract.

AI is the accrued interest.

The short position in a futures contract has the option of which bond to deliver and, in the U.S. bond market, when in the delivery month to deliver the bond. The short position typically chooses to deliver the bond known as the Cheapest to Deliver (CTD). The CTD bond most often delivers on the last delivery day of the month.

Financial Instruments Toolbox™ software supports the following bond futures:

• U.S. Treasury bonds and notes

• German Bobl, Bund, Buxl, and Schatz

• UK gilts

• Japanese government bonds (JGBs)

The functions supporting all bond futures are:

Function

Purpose

`convfactor`

Calculates bond conversion factors for U.S. Treasury bonds, German Bobl, Bund, Buxl, and Schatz, U.K. gilts, and JGBs.

`bndfutprice`

Prices bond future given repo rates.

`bndfutimprepo`

Calculates implied repo rates for a bond future given price.

The functions supporting U.S. Treasury bond futures are:

Function

Purpose

`tfutbyprice`

Calculates future prices of Treasury bonds given the spot price.

`tfutbyyield`

Calculates future prices of Treasury bonds given current yield.

`tfutimprepo`

Calculates implied repo rates for the Treasury bond future given price.

`tfutpricebyrepo`

Calculates Treasury bond futures price given the implied repo rates.

`tfutyieldbyrepo`

Calculates Treasury bond futures yield given the implied repo rates.