How Yield-Curve Slope Affects Treasury Futures Carry and Implied Repo
Summary
The document explains the carry on a long cash bond and short futures position through the relationship between implied repo and the bond’s actual repo financing cost. If the bond is cheapest to deliver and the net basis is zero, delivery leaves the investor with the financing economics accrued before expiry. The position earns the implied repo embedded in the futures price and pays the daily repo rate on the bond. An upward-sloping curve can therefore produce a gain when the implied rate exceeds the financing cost over the holding period.
The discussion distinguishes coupon income from net carry: a coupon above zero does not by itself determine whether financing the bond is profitable. The example in the question highlights that actual repo assumptions matter. The answers are brief and do not derive a full pricing relationship or quantify curve effects; the conclusion depends on delivery assumptions and on comparing implied repo with actual repo.
Key ideas
- A long bond and short futures position earns the implied repo rate and pays the bond’s actual repo financing cost.
- An upward-sloping yield curve can be associated with positive carry when implied repo exceeds the financing cost.
- Coupon income alone does not determine net carry because financing costs also matter.
- The delivery argument assumes the bond is cheapest to deliver and the net basis is zero.
Tags
Full text
# Implied repo rate and slope of the yield curve # Implied repo rate and slope of the yield curve In page 34 of "Treasury Bond Basis" (Third Edition) by Burghardt et al, it says: > If the yield curve has a positive slope, carry for someone who is long bonds and short futures is positive. Every day that goes by is money in the bank. The implied repo rates simply confirm this. Why is this the case? Up to that point in the book, the implied repo rate (IRR) is defined (simple version) as: IRR = (Futures Invoice Price / Bond Purchase Price - 1) x (360 / n) where n is number of days to delivery. It seems to be a function of coupon and actual term repo rate (i.e. carry), or at least it's not clear from this formula how the slope of yield curve impacts IRR. E.g. if we have a bond with coupon=5% and meanwhile a negatively sloped yield curve with spot rate starting at 0%. Then carry should be actually positive, but using the conventional wisdom of looking at yield curve will say negative carry. ## Answer by user68819 (score 1) https://quant.stackexchange.com/a/76602 Think he means for holding onto your basis for longer in a positive sloped curve the irr should increase. This is just because you will carry positively. Carry is measured versus your repo. If your term repo is 5.5% with a coupon of 5% you will carry negatively to term. Your futures invoice price is a function of accrued interest since last coupon. You should compare irr to repo to get an idea of the gain versus cost of holding bonds and delivering into the future at term ## Answer by dm63 (score 1) https://quant.stackexchange.com/a/76922 I think it just means the implied repo rate is higher than the actual repo rate. Explanation: if you are long bonds and short futures, what do you have? Well assuming that the bond is the CTD and the net basis is zero, then your economics are zero after the futures has expired since you just deliver the bond. All you have left is the economics between now and expiration, which is that you are receiving the implied repo rate (fixed) and you are paying the daily repo on your bond. If the curve is upward sloping , then you have a daily gain.
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.