# 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.

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In the example, is the first German bond a government bond or a corporate bond? In other words, are you looking for the corporate-government basis or the government cash-futures basis? – Tal Fishman Aug 10 '11 at 18:03
I was referring to government cash-futures basis in the example. – Mr Smith Aug 11 '11 at 7:52

## 2 Answers

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.

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What are the possible deliverables in the german bond futures contracts? Is it like the US (i.e. multiple bond issues satisfy the criteria)? – Foo Bah Sep 12 '11 at 18:04

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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