Interpreting Yield Quotes for Cash-Settled Bond Futures
Summary
The document distinguishes a bond futures contract’s expected return from the yield associated with its underlying bond. A futures price is set so the contract’s expected payoff at settlement is zero under the pricing measure; that does not make the bond’s yield irrelevant. The yield is an equivalent way to interpret the bond price implied by the futures contract, accounting for conversion factors and contract characteristics.
This measure helps compare bonds with different coupons and maturities, including eligible bonds in a delivery basket. The cheapest-to-deliver bond can determine the economics of a contract, and expressing its implied price as a yield makes comparisons more meaningful than raw bond prices alone. The explanation is conceptual rather than a calculation guide: it gives no numerical example or formula for computing the implied yield. It also notes that the yield describes the underlying bond economics, not an investment return earned directly on the futures position, which requires no purchase price paid upfront.
Key ideas
- A bond futures contract’s quoted yield refers to the underlying bond economics, not the futures position’s expected return.
- The futures price can be translated into an equivalent yield using the relevant bond’s terms and contract conversion factors.
- Yield helps compare eligible bonds with different coupons and maturities.
- The cheapest-to-deliver bond can shape the yield interpretation of a bond futures contract.
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Full text
# Why do people speak of yields on bond futures when their expected return is 0? # Why do people speak of yields on bond futures when their expected return is 0? There are several questions on this site asking about the "yield" of a bond futures contract. See e.g. How do I calculate yield from a bond futures contract? However, the expected return of a bond futures contract is zero. Let's say it matures at time $T$ with cash settlement. Since the futures price is the fair price that makes the expected time $T$ payoff equal to zero, then, when entering a futures contract, I don't expect to "earn" anything. Why then does the yield of a bond futures contract matter? What is it used for? If the delivery was physical, I'd understand it, since then you can answer the question of "ok, when I actually get this bond, what will the yield be?", but due to cash settlement, you're not getting anything. ## Answer by D Stanley (score 3) https://quant.stackexchange.com/a/80381 The "yield" on a Bond Futures trade is based on the yield of the underlying bond that you get (or would get for cash settlement), accounting for conversion factors and other characteristics of the future. It is not the "yield" in terms of return on investment that you get from the future itself, since there is no cash spent upfront. > Why then does the yield of a bond futures contract matter? What is it used for? It's used to evaluate what type of yield you can expect from the bond that you would buy, to evaluate what the fair futures price would be. Individual bonds are commonly valued in terms of "yield" rather than price, so you could think of the "yield" as analogous to the "price" of, say, an oil futures contract, where you enter into a contract to buy (or sell) oil at a specific price sometime in the future. With a bond future, you are entering into a contract to buy or sell a bond at a specific price, which translates to an equivalent yield based on the price, term, and coupon rate of the bond. A bond future is not always for one specific bond only, but from the "Cheapest to Deliver" of several eligible bonds, which have different coupons and maturities. Since the "price" of two bonds with different coupons or maturities are not directly comparable, but yield is, the "yield" of a bond future allows one to see what type of return they can expect from the bond regardless of what price is actually paid.
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