Measuring Returns on Bond Futures Using Price Changes and Cash Flows
Summary
The document compares two proposed denominators for measuring returns on a bond futures contract: the contract’s stated face value and the futures price at the start of the period. It favors the starting price as the more appropriate basis, consistent with a general asset-return measure that includes price change and the present value of net cash flows relative to starting value. The contract notional establishes the contract’s scale but is not itself the market value used as the return denominator.
The discussion notes that variation margin can create interest income or funding costs for a futures position, depending on rate movements and the investor’s source of margin cash. That effect can make realized returns nonlinear, although the answer treats it as a refinement that may be omitted for a practical approximation. A second answer emphasizes the cheapest-to-deliver bond as a key influence on futures price changes. The document does not provide a detailed return calculation or account for all contract-specific financing and delivery effects.
Key ideas
- A futures return is generally measured relative to the position’s starting market value rather than its face-value notional.
- A fuller return measure can include price gains and the value of net cash flows.
- Variation margin can generate interest income or funding costs for a futures position.
- The cheapest-to-deliver bond is an important driver of the futures contract’s price dynamics.
- Using price change divided by starting futures price is presented as a practical approximation.
Tags
Full text
# Convention for computing returns on bond futures
# Convention for computing returns on bond futures
From the CME website, we know that the contract unit for bond futures is "face value at maturity of $100,000".
Which of the following is more appropriate the convention to compute "returns" on a 10-year bond future?
a) $\frac{Change in Price}{$100,000}$
b) $\frac{Change in Price}{Previous Price}$
Any help is very much appreciated.
## Answer by kurtosis (score 2)
https://quant.stackexchange.com/a/57719
Answer B is the closest. You can compute returns for any asset over one period as: $$ r = \frac{\text{change in price} + FV(\text{net cashflows received})}{\text{starting price}}. $$ This basically breaks your returns into capital gains (term 1) and dividend and interest income (term 2).
It might seem that you do not have interest income for a bond futures contract; however, that is not exactly true. Suppose you are long the futures. When interest rates go up, you will receive money in your margin account. You can withdraw that excess cash and earn interest on it. When interest rates go down, you will need to withdraw cash from an interest-earning account or investment to add to your futures margin account.
This creates a non-linearity: for equal rises or falls in interest rates, you earn more in interest when interest rates are higher than you lose in interest when interest rates are lower.
That might be a bit fussy to compute, however, so you can just stick with four formula B for an approximation.
## Answer by demully (score 2)
https://quant.stackexchange.com/a/57731
B. The change in the price of the cheapest-to-deliver behind that future is the key.
The 100k is a notional required convention, to allow the future to exist. It has no real relevance in the real world, except in the choice of which bond is the cheapest to deliver for that contract, whose dynamics absolutely set the price for that same contract.
The “complication” here is that the future’s returns might not EXACTLY mirror those of any of the bonds in the potential sample universe. But no actual user of The futures has ever complained thus, because the reasons why are so academic and immaterial, that they become irrelevant to market participants.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.