# Treasury bonds

- The prices for treasury bonds are quoted in dollars and 1/32nd of a dollar
- $82â€“27 is equivalent to $82.84375

- Cash price / dirty price is the price at which the investor buys a bond from the market
- Cash price = Quoted price + accrued interest
- Accrued interest is the interest which the nearest coupon that is due, generates

- Cash price = Quoted price + accrued interest

# Treasury Bond Futures

- Treasury bond futures are the most commonly traded futures contract on the Chicago board of trade (CBOT)
- When the Treasury bond futures contract expires, any government bond with maturity more than 15 years on the first day of the delivery month and is not callable for the next 15 years from that day can be delivered

**Conversion price**

- When a bond is delivered the party with the short position, the amount transacted is:
- Quoted futures price + accrued interest
- Where, Quoted futures price = settlement price * conversion factor

- The conversion factor is equal to the quoted price the bond would pay per dollar or principal on the first day of the delivery month on the assumption that the interest rate for all maturities equals 6% per annum (with semi annual compounding)

Example

The last coupon payment of $10 was paid on a treasury bond on June 19, 2009. The next coupon is due on December 19, 2009 and we are currently on September 1, 2009. If the quoted price is $82â€“27 then the cash price would be?

Solution

The number of days for which the December coupon has accrued interest is the time period between June 19 to September 1 (74 days). The actual time period between June 19 and December 19 is 183 days. Hence the interest the December coupon accrues is:

$10 * (74/183) = 4.04

Hence, cash price = 82.84375 + 4.04= $86.887