Risk measurement for hedge funds and CTA's: VaR vs. SPAN margin

Abstract

The past decade has seen the explosive growth in the technology and techniques of quantitative risk assessment, usually under the rubric of "Value at Risk (VaR)". What is novel about VaR is that it tries to do two things, viz.: 1) provide an integrated methodology for the risk measurement of portfolios of diverse financial assets, and 2) to describe that risk in probabilistic terms. However, despite the growth of VaR as a risk measurement tool, it is still the case that the bulk of risk management is conducted using risk metrics that are not specifically cast in or are reducible to probabilistic quantities. Specifically, most risk management is conducted not through direct VaR constraints, but through margin constraints or other techniques that seek to limit the quantity of capital allocated to a particular position or positions. An important issue is, therefore, the relationship between these two types of constraints. In the present article, I investigate the relationship between generic parametric and non-parametric VaR measures and a set of futures margins set by various derivatives exchanges. I develop a number of useful results, including some rules of thumb that should be of value to risk managers and others responsible for managing positions in markets for various assets. VaR and margin ratio are closely related. Most exchanges use the Standard Portfolio Analysis of Risk (SPAN) system to set margins, and SPAN-based margins are determined using a Value at Risk methodology. However, while VaR is based on the risk of the entire portfolio, margins are set for each commodity in the portfolio without regard to the correlation between that position and the other positions in the fund. As such, the margin required for a given portfolio will almost always be larger than the VaR. However, it is possible that the margin ratio contains much the same information about the volatility of a fund as the VaR. If this is the case, then the margin ratio would cleJrrly be preferable to VaR as a risk measure given its ease of computation and low reliance on estimates of historical correlation between assets.