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

Abstract

Purpose - The failure of the Efficient Market Hypothesis has a direct bearing on the Geometric Brownian Motion model of asset returns. The current paper investigates the effect that the autocorrelation in the time series of returns has on the calculation of Expected Shortfall for an asset-liability investor.

Design/methodology/approach - To uncover the appropriate autocorrelation structure an autoregressive model is estimated. The model selection is guided by the Akaike and the Schwarz Information Criterion. The AR model is estimated using a rolling window and a series of tests are used to check the stability of the autocorrelation parameters. Autocorrelation-adjusted formulas for volatility and cross-asset correlations are then employed to compute the risk bearing capital.

Findings - The presence of autocorrelation changes the values of most of the correlation parameters used in the calculation of the Expected Shortfall (ES) of the Risk Bearing Capital - in some cases the cross-asset correlation parameters double. Once the presence of smoothing is accounted for, the ES increases by 1% in relative value.

Research limitations/implications - The present study focuses on the effect of smoothing in the time series of transaction-based property returns. Other asset classes may also feature smoothed time series requiring thus a further analysis of their autocorrelation structure and the way these interact with the real estate asset class. Furthermore, an analysis of the time stability of the cross-asset correlations may further improve the estimation of the optimal risk bearing capital.

Practical implications - The paper provides a routine to check if the assumption of independent and identically distributed asset returns is fulfilled. The failure of this assumption leads to the failure of the Geometric Brownian Motion model and in sequence to a miscalculation of the optimal risk capital of an asset-liability investor. If the former occurs the paper indicates a procedure one may adopt to account for this failure in the calculation of the volatility and cross-asset correlations needed to compute the optimal risk capital.

Originality/value - The proposed method focuses on the proper calculation of the risk bearing capital through the judicious estimation of the cross-asset correlation parameters and the asset volatility 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.