What is Bond Futures?
Bond Futures is a contract that puts liability on the holder to purchase and sell a fixed amount of bonds as specified in the contract agreement at a price which is predetermined by the contract holder where the other side is the exchange. It can be bought and sold in the exchange market, the price and dates are standardized at the time when an agreement is entered into by the holder.
How the Bond Future is Priced?
One of the most popular bond futures is treasury bond futures contracts traded by CME Group. In this, any government bond that has more than 15 years to maturity on the first day of the delivery month and is not callable within 15 years from that day can be delivered. The 10, 5, and 2-year Treasury note futures contracts in the united states are very popular.
Future price for the treasury bond is difficult to determine because the short party’s options concerned with the timing of delivery and the choice of the bond that is delivered cannot be easily valued. However, if we assume that both the cheapest to deliver bond and the delivery date is known, the treasury bond future contract is a futures contract on traded security that provides the holder with known income. Below equation shows that future price (F0) of Bond is related to the Spot price (S0)
- I – present value of the coupons during the life of the futures contract
- T – is the time until the maturity futures contract
- r – is the risk-free rate
Suppose an investor enters into a treasury contract to deliver a bond @ 12 % coupon with a conversion factor of 1.6000 where the delivery will take place in 270 days. Coupons are payable semi-annually on the bond and the last coupon date was 60 days ago, the next coupon date is in 122 days, the coupon date thereafter is in 305 days. The term structure is flat and the interest rate is 10% per Annum. Assume that the current quoted bond price is $115.
The cash price of the bond is obtained by adding quoted price the proportion of the next coupon payment that accrues to the holder.
- = $115+(60/ (60+122)) * 6
- = $116.978
A coupon of $6 will be received after 122 days (.3342 years) The present value of this
- = 6*e(-.1*0.3342)
- = 5.803
The future contract lasts for 270 days (0.7397) The cash future price if the contract is written on 12 % bond would be
- = (116.978-5.803) e (0.1*.7397)
- = $119.711
There are 148 days of accrued interest from delivery. If the contract is written on a 12 % bond accrued interest is excluded in order to calculate quoted future price.
- = (119.711-6) + 148/(148+35)
- = $114.859
The quoted futures price is given below considering 1.6000 conversion factor equivalent to a 12% standard bonds
- = 114.859/1.6000
- = 71.79
How to derive Cheapest to deliver Bonds in Bond Futures Contact?
The party with the short position or the writer of the bond chooses the bond that is cheapest to deliver among a wide variety of bonds. And his decision is based on below derivation :
And the cost of purchasing the bond is,
The cheapest to deliver bond is one for which below is least.
The number of factors determines the cheapest to deliver the bond. If bond yields reach 6%, the conversion factor system enables the writer to deliver long maturity low coupon bonds. When yields are below 6%, then high short-term coupon bonds are favored.
Also, when the yield is upward sloping there is a tendency for bonds with long maturity to be favored, whereas when it is downward sloping bonds with short term maturity will be delivered.
What are Bond Futures Conversion Factors?
- This contract allows the party with the short position to choose to deliver any bond that has a maturity of more than 15 years and is not callable within 15 years. A conversion factor is applicable at the time of delivery of a particular bond in exchange for the price received by the short position for the bond. The applicable quoted price is the product of the recent settlement price for the futures contract and the conversion factor. Taking accrued interest into account the cash received for each $100 face value of the bond delivered is:
- Each contract is for the delivery of $100000 face value of bonds. Suppose that the most recent settlement price is 90-00 the conversion factor for the bond delivered is 1.3800 and the accrued interest on this bond at the time delivery is $3 per $100 face value.
- The cash received by the party with the short position is then(1.3800*90.00) +3 = $127.20 per $ 100 face value. A party with the short position is one contract that would deliver bonds with a face value of $10,000 and receive $127,200.
How it is Quoted?
This contract is quoted in dollars and thirty seconds of dollar per $100 face value. This is similar to the way bonds and notes are quoted in the spot market. Let’s say the settlement price of this contract for June 2017 delivery is specified as 124-150. This means 124 (15/32) or 124. 46875. Taking the next example if the settlement price of September 2017 is quoted as 120-105 means 120 (10.5/32) or 120.328125.
One of the important interest rate contracts is Treasury bond contracts traded in the United States. The party with the short position has a number of interesting delivery options:
- Delivery can be made any day during the delivery month.
- There is a number of alternative bonds that can be delivered.
- On the day of the delivery month, the notice of intention is to deliver at 2.00 pm and settlement price can be made any time up to 8.00 pm.
This has been a guide to What is Bond Futures. Here we discuss what are bond future conversion factors and how it is quoted along with an example. You can learn more about from the following articles –