How Bond Futures Basis Relates to Yields, Repo, and Convexity
Summary
The discussion considers whether a widening gap between a bond futures price and its spot price causes the bond yield to rise. The answers describe the price gap as related to financing carry and argue that changes in yields or financing conditions generally drive the futures–spot relationship, rather than the basis serving as a reliable signal for government yields. A positive carry environment with an upward-sloping curve is given as a setting where futures may trade above spot.
The explanation distinguishes the repo rate, which is directly relevant to spot-forward financing arbitrage, from other meanings of “yield.” It also cautions that basis movements can reflect liquidity limits and transaction costs that prevent arbitrage, without a corresponding move in yields. For futures, the forward relationship also requires a convexity adjustment; changes in volatility could therefore affect futures prices even if spot and repo rates stay unchanged. The answers are qualitative and do not provide a pricing equation or quantify these effects.
Key ideas
- The futures–spot price difference is linked to financing carry and related rates.
- Changes in yields or financing conditions are generally drivers of the basis, not necessarily consequences of it.
- Repo is the rate most directly relevant to spot-forward financing arbitrage in the discussion.
- Liquidity frictions and transaction costs can move the basis without a related yield change.
- Bond futures pricing includes a convexity adjustment that can respond to volatility changes.
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Full text
# Is there an inverse relationship between (future-spot) price and yield? # Is there an inverse relationship between (future-spot) price and yield? If the difference between futures and spot prices rises will the yield for the current bond increase as well? ## Answer by VanillaCall (score 1) https://quant.stackexchange.com/a/45180 The difference between futures and spot is related by the carry. Assuming a positive carry environment where the yield curve is upward sloping, then the spot price is less than the futures price. If prices rise, the yields will change. ## Answer by bhutes (score 1) https://quant.stackexchange.com/a/45674 The cause-effect relation is the other way round. The driver is the change in yields, and the effect is the change in the difference between futures and spot. The fixed income markets (specifically the government bond markets) are among the deepest (i.e. highest volumes and notional balances) and most liquid. I do not believe anyone tracks the difference between futures and spot (for any underlying security - stocks, FX or commodities) to take a cue that risk-free yields (govie bond yields) to react to a change in future-spot difference. It is quite possible, for a variety of reasons that the future-spot difference changes while yields show no related changes - because the futures/spot difference can change to due to limitations in the liquidity of the underlying so that any arbitrage opportunity cannot be effected due to large transaction costs. Lastly, when you say yields you need to be more specific as interest rates come is quite a few flavours. The interest rate most relevant to spot-futures arbitrage argument is the repo rate. This is the rate which is likely to be most responsive to the change in the difference between futures and spot. And one more really last thing, the arbitrage argument is really for the spot-forward-repo rate trinity. For futures, a convexity adjustment (on top of the forward price) is also relevant. So a change in underlying volatilities could theoretically increase the futures price (while spot and repo rates remain unchanged). Although, to my best understanding is will normally be quite small to bother.
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