RDP 1999-04: Value at Risk: On the Stability and Forecasting of the Variance-Covariance Matrix 5. Conclusion

There are two principal conclusions to be drawn from this paper. Firstly that there is considerable variation in variances and, to a lesser extent, correlations over time. This provides support for APRA's approach to market-risk measurement, which requires that banks update the parameters of the variance-covariance matrix at least quarterly. That said, moving from quarterly to daily updating of parameters only slightly improves forecast accuracy. Secondly, the cost, in terms of forecasting accuracy, of using simple models of the time-series evolution of variances and covariances does not appear to be high. Simple models such as equally-weighted moving averages and fixed-parameter exponentially-weighted moving averages appear to perform as well or often better than more complex GARCH models.

These findings provide some support for the practices prevalent in the Australian banking industry where comparatively simple models of variances and covariances are employed in formulating VaR models and the financial return data underlying the VaR models are periodically updated, often daily but at least quarterly.

There are a number of caveats to the application of the results of this forecasting exercise to the practical assessment of VaR models. Modelling variances and covariances is just one component of a VaR model, which must also address the overall distribution of financial returns, portfolio composition and measurement of the sensitivity of financial instruments to movements in underlying prices.

If it is assumed that financial returns follow a normal distribution the mean returns and the variance-covariance matrix are sufficient to describe the full distribution of financial returns. There is strong evidence to suggest, however, that financial returns are not normally distributed. In such a case a model that forecasts covariances well, will accurately forecast behaviour around the centre of the distribution but not necessarily in the distribution's tails. The focus of VaR models in measuring market-risk is on the extreme tails of the distribution (typically the first or fifth percentiles). Going beyond the variance-covariance VaR model, banks have developed a range of VaR models (such as historical simulation and Monte Carlo simulation) which place stronger emphasis on modelling the extremes of financial return distributions. Clearly more work remains to be done comparing the tail forecasting performance of various variance-covariance VaR formulations with that of other VaR models.

In this paper, equal weight has been given to each variable within the variance-covariance matrix. In practice, banks' portfolios tend to be concentrated in a small number of assets. For example, the bulk of banks foreign exchange exposure may derive from trading in major currencies such as the US dollar, German mark and Japanese yen. Accurate forecasting of the variability of these rates will be much more important than for other less actively traded currencies. The assessment of the forecasting performance of VaR models needs to be calibrated against the composition of banks' portfolios.

Accurate prediction of the variability of the value of a portfolio requires an accurate forecast of the probability of larger moves in market prices and precise measurement of the sensitivity of the value of various instruments to those larger price moves. For most simple instruments, such as spot and forward foreign exchange and bonds, measurement of price-sensitivity is a straightforward matter. In the case of complex instruments, such as options, however, there remains wide variation in the practices adopted to incorporate them into a VaR framework. Further research on these issues remains to be done.