Cyclicality and Term Structure of Value-at-Risk within a Threshold Autoregression Setup

This paper explores empirically the link between stocks returns Valueat- Risk (VaR) and the state of financial markets across various holding horizons. The econometric analysis is based on a self-exciting threshold autoregression setup. Using quarterly French and US data from 1970Q4 to 2012Q4, it turns out that the k-year VaR of equities is actually dependent on the state of the market: the expected losses as measured by the VaR are smaller in bear market than in normal or bull market, whatever the horizon. It also turns out that the longer the holding horizon, the smaller the expected losses as measured by the VaR, whatever the state of the market. These results suggest that the rules regarding the solvency capital requirements should adapt to the state of the financial market as well as to the investors holding period.
JEL Codes: G11.
Keywords: Expected Equities Returns; Value at Risk; Financial Cycle; Holding Horizon; Threshold Autoregression.