Measuring Basis Risk Between Cash Government Bonds and Bond Futures
Summary
The document discusses how to measure the risk left when a government bond is hedged with a bond future, even when their DV01s match. Matching DV01 addresses first-order sensitivity to yield changes, but does not make the positions behave identically. The answer identifies the difference in convexity between the cash bond and the futures contract’s cheapest-to-deliver bond as one source of residual risk.
A second source is a change in which bond is cheapest to deliver, which can alter the futures exposure. The suggested analysis is to examine candidate delivery bonds across interest-rate scenarios and track changes in duration and convexity; dynamic futures hedging may be needed. The document also notes that futures pricing requires a convexity adjustment and points to yield-curve trade literature as further reading. A separate response mentions exchange or broker failure and sovereign credit exposure, but gives no method for quantifying these risks. No numerical basis-risk formula or worked calculation is provided.
Key ideas
- Equal DV01s do not remove the convexity mismatch between a cash bond and a bond future.
- The cheapest-to-deliver bond can change across interest-rate scenarios, shifting the futures exposure.
- Scenario analysis of delivery candidates can reveal changes in duration and convexity.
- Futures valuation may require a convexity adjustment in addition to the forward value.
- The discussion offers a qualitative framework rather than a complete numerical risk metric.
Tags
Full text
# What is the basis risk between cash and futures government bonds? # What is the basis risk between cash and futures government bonds? I am currently working in a team responsible for maintaining a simple risk application for our bond desk and I am interested in knowing how to provide some sort of basic basis risk metric. Our desk mainly trades vanilla bonds which are hedged with bond futures. While I will not be implementing this, I am keen to know at a high level how this might be possible. For example, if I have a German Bund maturing in ten years with a DV01 of 100 which I hedge with German Bund futures which also have a DV01 of 100, how might I calculate the basis risk between these two instruments. Any references would also be appreciated. ## Answer by Tal Fishman (score 4) https://quant.stackexchange.com/a/1654 There are (at least) two factors here. One is the difference in convexity between the vanilla bond and the cheapest-to-deliver underlying the futures. The second is potential changes in which bond is cheapest to deliver. The former is simple enough to calculate, and you will need to dynamically hedge with futures to offset that risk For the latter, you will want to create something like a spreadsheet showing which bond is cheapest to deliver under various interest rate scenarios, and how the duration and convexity of the new underlying changes at those points. One added complication is that you will also have to apply a convexity correction to the futures price (on top of the normal value of the forward) to handle the convexity bias. See Salomon Brothers' Understanding the Yield Curve. The Salomon Brothers note series is also a good general reference for yield curve trades. ## Answer by Drhu (score -1) https://quant.stackexchange.com/a/21270 Future is backed by exchange so there is risk of exchange going bankrupt or broker. Bund cash backed by German govt which is different credit risk.
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