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.
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.