# Spreads price constraints

Craig Pirrong writes on his Streetwise Professor blog that “Spreads price constraints.” Though Pirrong is talking about natural gas calendar spreads, I think this is an excellent way of thinking about many other spreads even for financial assets. In commodities, the constraints are obvious: for calendar spreads, the constraint is that you cannot move supply from the future to the present, for location spreads, the constraints are transportation bottlenecks, for quality spreads, technological constraints limit the elasticity of substitution between different grades (in case of intermediate goods), while inflexible tastes constrain the elasticity in case of final goods.

But the idea that “spreads price constraints” is also true for financial assets where the physical constraints of commodities are not applicable. The constraints here are more about limits to arbitrage – capital, funding, leverage and short-sale constraints, regulatory constraints on permissible investments, and constraints on the skilled human resources required to implement certain kinds of arbitrage.

Thinking of the spread as the shadow price of a constraint makes it much easier to understand the otherwise intractable statistical properties of the spread. Forget about normal distributions, even the popular fat tailed distributions (like the Student-t with 3-10 degrees of freedom) are completely inadequate to model these spreads. Modelling the two prices and computing the spread as their difference does not help because modelling the dependence relationship (the copula) is fiendishly difficult (see my blog post about Nordic power spreads). But thinking about the spread as the shadow price of a constraint, allows us to frame the problem in terms of standard optimization theory. Shadow prices can be highly non linear (even discontinuous) functions of the parameters of an optimization problem. For example, if the constraint is not binding, then the shadow price is zero, and changing the parameters makes no difference to the shadow price until the constraint becomes binding, at which point, the shadow price might jump to a large value and might also become very sensitive to changes in various parameters.

This is in fact quite often observed in derivative markets – a spread may be very small and stable for years, and then it can suddenly shoot up to very high levels (orders of magnitude greater than its normal value), and can also then become very volatile. If the risk managers had succumbed to the temptation to treat the spread as a very low risk position, they would now be staring at a catastrophic failure of the risk management system. Risk managers would do well to refresh their understanding about duality theory in linear (and non linear) programming.

Posted at 17:43 on Thu, 15 Nov 2018 View/Post Comments (0) permanent link