Why an Inverted Treasury Curve Can Imply Negative Bond Carry

Summary

The document explains the link between a downward-sloping Treasury yield curve and negative carry on a vanilla Treasury bond. Carry is framed as coupon income less financing costs, with repo as the financing rate. The answer argues that repo rates should remain close to short-term Treasury rates because short-term lending to the US government is nearly risk-free. Consequently, when a bond’s yield is below the short-term rate, its yield less repo financing cost is likely to be negative; the response treats these conditions as nearly equivalent.

It supports the relationship with a basic arbitrage intuition. If repo rates were materially below Treasury bill yields, an investor could finance bill purchases through repo and seek to earn the spread. If repo rates were materially above bill yields, an investor could buy bills through reverse repo and sell them into the market. These trades would tend to limit the gap. The explanation is intentionally simplified: it does not address transaction costs, collateral specifics, funding constraints, or differences between a bond’s coupon and its yield.

Key ideas

• Bond carry is described as coupon income minus repo financing costs.
• Repo rates tend to track short-term Treasury rates because Treasury bills are close to risk-free investments.
• When a bond’s yield is below the short-term rate, financing can exceed the bond’s yield and produce negative carry.
• Arbitrage trades can constrain large gaps between repo rates and Treasury bill yields.
• The explanation omits practical frictions and does not cover all details of Treasury bond financing.

Tags

# Negative Carry when Yield Curve is Downward Sloping


# Negative Carry when Yield Curve is Downward Sloping












I am currently reading "The Treasury Bond Basis", and have a question regarding negative carry. The book states that the carry of a vanilla treasury bond will be negative when the yield curve is negatively sloped. I understand that carry is defined as the coupon income on an investment minus the financing costs (repo rate). What the book does not explain is why the carry will be negative in an environment where the yield curve is negatively sloped. I have searched around for an explanation but have not found one. The only think that I could think of is that, as the demand for longer maturity debt increases relative to that of short term debt (which causes the YC to invert), the demand for longer term repo will increase, which will spike repo rates. Any input is greatly appreciated.

## Answer by Chris Taylor (score 4)

https://quant.stackexchange.com/a/59537

Repo rates will be very close to short-term treasury rates so "the yield curve is downward sloping" and "bond yield minus repo rate is negative" mean very nearly the same thing.

The reason that repo rates must be close to short-term treasury rates is that lending money to the US government for short periods is nearly risk-free. If repo rates were significantly below treasury bill rates, you could buy treasury bills financed with repo and earn the difference between the bill yield and the repo rate. Similarly if repo rates were significantly above treasury bill rates you could purchase the bills in a reverse repo and sell them into the market, earning the difference between the repo rate and the yield on the bill.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.