How important is that footnote on page 3? Understanding the effect of autocorrelation on the calculation of expected shortfall

The failure of the efficient market hypothesis has a direct bearing on the Geometric Brownian Motion model of asset returns. The current paper aims to investigate the effect that the autocorrelation in the time‐series of returns has on the calculation of expected shortfall (ES) for an asset‐liability investor.

The regression model is selected according to the Akaike and the Schwarz information criterion. A series of tests are used to insure the stability of the autocorrelation parameters. Autocorrelation‐adjusted formulas for volatility and cross‐asset correlations are then employed for the computations.

The presence of autocorrelation changes the values of most of the correlation parameters used in the calculation of the ES of the risk bearing capital (RBC) – in some cases the cross‐asset correlation parameters double. Once the presence of smoothing is accounted for, the ES increases by 1 per cent in relative value.

Other asset classes may also feature smoothed time‐series requiring thus an account of their autocorrelation structure and their interaction with the property asset. An analysis of the time stability of the cross‐asset correlations may also improve the estimation of the optimal RBC.

The proposed method focuses on the proper calculation of the RBC through the judicious estimation of the relevant risk measure for an investor who, while not having access to the underlying data pool from which the property index is computed, cannot adjust the index for the potential presence of temporal aggregation and market illiquidity.