The degree of correlation between risk indicators varies depending on certain factors. Two possibilities were analyzed: the time interval from the moment of portfolio creation until the expiration date and the market volatility at the moment of portfolio creation.
Within one trading day, the interrelationship between risk indicators can be measured by the variance of returns of the four portfolios selected by these indicators on that day. The higher the variance, the lower the correlation of risk indicators. If the indicators are perfectly correlated, each of them chooses the same portfolio; in this case the variance is zero.
“Time effect” (page 47) shows the inverse non-linear relationship between variance and the time interval left until the expiration. It means that close to the expiration risk indicators are weakly correlated and, hence, all of them (or, at least, some of them) carry a considerable load of additional information. On the other hand, the variance of returns of the portfolios created long before the expiration is rather low, which means that risk indicators are strongly interrelated during this period.
Market volatility also influences the interdependence of risk indicators, though this effect is stronger shortly before expiration. Thus, for portfolios created two days before expiration, the correlation coefficient between variance and volatility was r = 0.62 for historical volatility and r = 0.68 for implied volatility (see “Volatility effect,” page 47). Yet, for portfolios created 60 days before the expiration correlation coefficients were much lower (r = 0.24 and r = 0.28, correspondingly).
The risk indicators discussed in this series represent the type of evaluation tools that can be used to develop a multi-criteria risk management system. These indicators by no means exhaust the list of potential opportunities for creating additional risk forecasting algorithms.
At the same time, risk management systems should not involve too many indicators. This would overburden calculations and lower the efficiency of evaluation procedures. While considering new indicators, their uniqueness should be thoroughly measured. All potential candidates must provide new information not contained in other gauges. Two of the four indicators analyzed in this article duplicated each other — VaR and loss probability. Hence, we should use only one of them in a multi-criteria risk management system.
Our investigation shows that the multi-criteria approach to risk evaluation may be most appropriate when portfolios are formed close to expiration date and when the market volatility is relatively high. Under these conditions, evaluation tools are less correlated. Further research should reveal additional factors influencing the correlation of risk indicators and determine the necessity for additional gauges.
Sergey Izraylevich has a Ph.D. from Hebrew University of Jerusalem. He is chief investment officer of Horton SARL and chairman of High Technology Inc. Vadim Tsudikman is a director at Horton and develops trading systems based on genetic optimization algorithms. Contact the authors at firstname.lastname@example.org