Skip to content
All library documents

How Conversion Factors Affect Treasury Futures Implied Repo Returns

Article Quant Q&A · Author: Saiyo
Read the original

Summary

The document addresses how daily mark-to-market settlement fits into the implied repo rate calculation for a cash-and-carry trade in Treasury futures. The key point in the accepted answer is that the hedge assumes a position of shorting a number of futures equal to the bond’s conversion factor. The futures mark-to-market and delivery payment then offset: the terminal futures price terms cancel, leaving the initial futures price scaled by the conversion factor, together with accrued interest at delivery, in the invoice proceeds.

This explains why the conversion factor matters to the hedge ratio and why the single-stock futures analogy, which has no conversion factor, does not directly carry over. The discussion is brief and offers no worked numerical example or treatment of funding cash flows, coupon payments, or delivery options. It therefore clarifies the cancellation underlying the textbook expression, but is not a complete valuation procedure for every Treasury futures trade.

Key ideas

  • The implied repo setup pairs the cash bond with a short futures position sized by the conversion factor.
  • Daily variation settlement accumulates the futures price change through delivery.
  • The terminal futures price cancels against the delivery settlement when the conversion-factor hedge is used.
  • The resulting invoice proceeds depend on the initial futures price scaled by the conversion factor and delivery-date accrued interest.

Tags

Fixed incomeFuturesCarryDerivatives pricing
Full text
# Implied Repo Rate and Treasury Futures MTM Process


# Implied Repo Rate and Treasury Futures MTM Process












I am a little confused about the Treasury futures mtm process and its impact on the Implied repo rate.

The definition of the IRR on most text book is the theoretical return you would obtain if you bought the cash bond, sold futures short against, and then delivered the cash bond into the futures.

Let T be the delivery date, and 0 be the date we start to open the position.

$$IRR = \frac{Invoice Price - Purchase Price}{Purchase Price}\frac{360}{n}=\frac{F_0*CF+AI_{T}-(Bond Clean Price+AI_{0})}{Bond Clean Price+AI_{0}}$$

Since the futures is settled daily, assuming on delivery date, the future price is $F_{T}$, we collect $F_0-F_T$ in total in daily settlement process up to delivery date

On delivery date, we should deliver the bond and get paid $F_{T}*CF + AI_{T}$

So in this case our return should be

$$\frac{F_T*CF + AI_{T}+F_0-F_T-PurchasePrice}{PurchasePrice}$$

and I don't know how to cancel the $F_T$ term and get the IRR formula.

For single stock futures without the conversion factor, the pnl from mark to market and the final settlement price should cancel each other easily at time T, e.g $$\text{Delivery Date Settlement Price} + MTM = S_T+(S_0-S_T) = S_0$$ hence lock in the sell price as $S_0 $

But in the scenario with conversion factor, I am not sure how to cancel the $F_T$ term as if we lock in the sell price. And if we can't lock in the price, how to understand the definition of IRR?

I feel that I might miss something here. Could somebody help me out?

## Answer by user68819 (score 1, accepted)

https://quant.stackexchange.com/a/82413

The formula assumes you have sold 'CF' futures versus the cash bond, so the F(T) term cancels out, leaving you with F(0) x cf + AI(T)

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.