Pro‐cyclicality beyond business cycle

We show that pro‐cyclicality is inherent in risk measure estimates based on historical data. Taking the example of VaR, we show that the empirical VaR measure is mean‐reverting over a 1‐year horizon when the portfolio is held fixed. It means that a capital requirement rule based on historical measurements of VaR tends in calm times to understate future required capital and tends in volatile times to overstate it. To quantify this pro‐cyclicality, we develop a simple and efficient methodology, which we apply to major equity market indices. We make the interesting point that the pro‐cyclicality property holds true even in a world with constant volatility, though the empirical magnitude of the mean‐reversion is greater than what would be observed in that special case.