An Empirical Investigation of the Rank Correlation between Different Risk Measures

The Value at Risk (VaR) is widely used to measure the risk of banks' trading books, but it also has been criticized in the previous academic literature due to some odd properties. Other risk measures have been suggested as potentially being superior from a theoretical perspective. This gives rise to the question whether or not it makes much difference in practical applications which index is being used. Certainly, the numbers indicating risk will be different. Whenever risk measures are ordinal, however, it only matters whether or not the ranking of risky alternatives (portfolios, say) coincides. Therefore, taking actual data from two trading books, we analyze the rank correlation of different measures. In most cases we observe high values of Spearman's rank correlation coefficient, indicating that the index choice might not be too important. But it also becomes apparent that the VaR could as well be replaced by indices with a more convincing theoretical basis which do not generate a very different ranking of risks and in fact seem to compromise better between competing risk judgements. On the basis of theoretical arguments, we modify the data in various ways and repeat the analysis. It turns out that the results do not vary much, i.e., they seem to be quite robust