Basis Risk Example

[lanlan666]

Hi Dave,

Just a quick question on Define and Compute the basis example:

The Sep-09 in this case is near/close to expiration of the future contract correct? My understanding is that the spot and future will always converge on the expiration date. So the basis risk only occurs when offsetting the existing future contract prior to expiration date.

Can you help to confirm?

Thanks,

 

[David Harper CFA FRM]

Hi lanlan,

Yes, in terms of textbook theory, I think you have found an elegant statement. My paraphrase (in agreement) would be: as basis risk is really the risk of unexpected basis strengthening/weakening (Hull), a basis that converges to exactly zero upon futures maturity should allow for a perfect hedge and therefore present no basis risk; i.e., the basis risk should manifest in close-out rather than delivery (where, convergence --> zero basis which is predictable). I am very much enamored of your angle on its textbook definition!

But that's only under the no-arbitrage (textbook) model, right?, which depends on a model that excludes frictions and further does not include certain technical factors (namely, liquidity and supply/demand)?

The thing about "basis risk" is, unlike say the cost of carry, its own definition includes reality and the frictions of reality. In fact, basis risk is sort of like "convenience yield:" they a variable that bridges between a no-arbitrage (unrealistic) model and friction-full reality. We have not really defined "basis risk" very well by stopping with the model .... we need to list all of the frictions to give it full definition.

In this way, in practice, often there is not a convergence to zero. My favorite oldie-but-goodie is econbrowser http://www.econbrowser.com/archives/2008/04/commodity_arbit.html
but also (e.g.) http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1950262

so you've got frictions like delivery cost that interfere with zero convergence such that:

"... it is better to think of a zone of convergence between cash and futures prices during delivery periods, with the bounds of convergence determined by the cost of participating in the delivery process." -- Scott Irwin

okay, so as soon as we allow for a zone of convergence, we've allowed for basis risk at convergence (alas, basis risk at delivery, if for no other reason than a delivery must occur). Which is always going to be true, if for no other reason than the hedge instrument is not identical to the underlying exposure. Basis risk is forever b/c we never really get to hedge X with X, we hedge X with ~ X. Even though, despite, the textbook truth of your original statement, thanks,

 

[lanlan666]

Thanks David for the detailed explanations!