The concept and role of conversion factors

The design of a basket of deliverable bonds means that on the maturity date of Treasury bond futures, there are often many bonds that meet the delivery standards in the spot market. This prevents the occurrence of forced positions to the greatest extent. However, for bonds with different coupon rates and maturities, their spot prices are also very different due to the different cash flows they bring to investors. In this case, it is obviously unreasonable to deliver at the same settlement price of Treasury futures. One question that arises from this is, under the given final settlement price of futures, at what price will bonds with different maturity dates and different coupon rates be delivered?

In order to help investors calculate the final delivery price at delivery, Treasury bond futures have designed a conversion factor system during delivery. For the spot market, there is always co-movement in the prices of different bonds. Since the essence of Treasury bond futures is a reflection of the forward price of the underlying bond, the price of Treasury bond futures should also be linked to bonds with different maturity dates and coupon rates. This is especially true on the expiration dates of Treasury futures. Therefore, we can calculate the delivery price of other deliverable bonds from the price of Treasury bond futures through a certain price comparison relationship. In the Treasury futures market, this system is the conversion factor system. Under the conversion factor system, each deliverable bond has its corresponding conversion factor. Given the conversion factor, the delivery price of the deliverable bond can be calculated. The main purpose of the conversion factor is to calculate the invoice price of the corresponding deliverable bond under a given futures price. That is: market price of deliverable bonds = conversion factor * futures price + bond accrued interest.

In treasury bond futures trading, the conversion factor is usually calculated and announced by the futures exchange, and its calculation method is also public. The formula for calculating the conversion factor is a little complicated, and the calculation of the conversion factor is slightly different on different futures exchanges. For example, on Eurex, the conversion factor is calculated using a precise formula, while on the Chicago Board of Trade in the United States, an approximate method is used. However, no matter what calculation method is used, the principle is the same. That is, when calculating the conversion factor of a certain deliverable bond, you must first determine the remaining term of the bond on the maturity date of the treasury bond futures, and then use the nominal bond interest rate of the futures contract as the discount rate, and put the bond with a face value of 1 yuan in its futures contract. All cash flows during the remaining period are converted into present values, and this present value is the conversion factor of the bond. Therefore, intuitively speaking, the conversion factor is actually a bond price, but this bond price is the bond price corresponding to the deliverable bond calculated by assuming that the market yield is the futures coupon rate and the yield curve is horizontal. .

The rationality of the conversion factor is that if on the maturity date of Treasury bond futures, the market interest rate level is equal to the coupon rate level of the Treasury bond futures contract, and the market yield curve is horizontal, the delivery price is actually the bond spot price. In this case, no matter what type of bond the short seller chooses for delivery, it is impossible to obtain risk-free profits, and the arbitrage opportunity of buying spot bonds and selling bond futures is zero. At this time, each bond type is equivalent. This greatly reduces the possibility of a squeeze in the bond futures market.