The pro-cyclical nature of linear VaR measures: Should a risk measure be reactive or anticipative?

by Ilija Zovko and Raphael Douady, 2009

It is often thought that a reactive VaR measure is a good one. We will argue the contrary. Reactivity of a VaR measure means that upon a sudden market event, for example a jump in one of the factors relevant to the risk of a fund, the risk measures immediately increases. It is perceived that such a risk measure will let the manager react quickly to changing market conditions and adjust her/his positions accordingly. However, quite the contrary is true. Reactivity of a VaR measure only shows that it does not in fact reveal all the hidden risks of a fund and leads to a very dangerous circle.

A reactive VaR creates a mechanism that leads to a dangerous cyclical cascade of market events as shown in the figure: Factor jump -> Risk increase -> Sell order -> Liquidity crisis -> Factor jumps further

This is the typical risk adjustment chain that induced the 1987 crisis, as well as a number or other crisis, including the 2008 credit squeeze.

On a wider scale this pro-cyclical nature of a reactive VaR encourages the deepening of a crisis. For a manager it induces the cancelation of risky positions in illiquid times that are least favorable.

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