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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 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.
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.
