Estimating Implied Repo from a Bond Future and CTD Bond
Summary
The document questions whether a bond’s carry, estimated from changes in dirty price and yield, can be used to infer its implied repo rate. The response instead defines implied repo through the cash-and-carry trade: buy the cheapest-to-deliver bond and sell the corresponding futures contract. The rate is the return implied by that position over the delivery period.
A formula is given that relates the futures price, conversion factor, bond price, accrued interest at spot and delivery, and the time fraction to delivery. The response suggests checking a proposed method by entering the implied rate into a repo pricer and comparing the resulting forward price with the futures price adjusted by the conversion factor. This provides a practical consistency check. The formula explicitly ignores interim coupons, so it is a simplified treatment; users must account for coupon cashflows and contract-specific conventions when relevant. The numerical carry example is a question, not evidence that its proposed rate is correct.
Key ideas
- Implied repo is the return from buying the cheapest-to-deliver bond and selling the related future.
- The futures price must be adjusted by the bond’s conversion factor when comparing it with a forward price.
- Accrued interest at both spot and delivery enters the calculation.
- A repo pricer can check whether a proposed implied repo rate reproduces the futures-implied forward price.
- The stated formula omits interim coupon payments.
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Full text
# Implied repo rate from carry component
# Implied repo rate from carry component
Carry is coupon income + pull-to-par - financing cost. Pull to par is derived as ytm-coupon. So carry can be rewritten as ytm - financing costs. Carry cash value is the current dirty price minus the cash flows in period x discounted at the current yield to maturity. So let's say you have a bond with annual coupon $2.5$, $5$ years remaining maturity and a ytm of $1\%$. The dirty price of this bond is $104.7826$. The dirty price for the cashflows in 6m time is $105.5656$. So an increase of $0.782945$.Ytm for 6m equals a value of $104.7826 \cdot 1.5\% \cdot 0.5 = 0.78587$. Can you say that the difference of $-0.00293$ is the implied repo value which implied a repo rate of $- 0.00293/104.7826/0.5 = -0.0058\%$?
## Answer by oronimbus (score 1)
https://quant.stackexchange.com/a/63823
I've never seen Implied Repo defined like this but there's a way to check whether your reasoning is correct. The implied repo is called implied repo for a reason: take your favorite Repo pricer of choice, load the current CTD bond with delivery date equal to the future's expiration (e.g. first delivery date) and plug the IR rate as the repo cost. If the calculated Forward price is equal to the bond future price divided by the CTD conversion factor, then your methodology is correct.
The implied repo rate is simply the return that you get from selling the future and buying the CTD bond. Ignoring interim coupons:
$$IR = \frac{CF\times P_{fut} - P_{bond} + (a_2-a_1)}{(P_{bond}+a_1)t}$$
where $a_1$ is the accrued at the spot and $a_2$ the accrued at the delivery date, $CF$ is the conversion factor and $t$ the day count fraction from spot to delivery date.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.