Using the classic models tended to overstate the risk for EURUSD
By Jamal Mecklai
Classic risk-management models assume currency pairs follow (or closely follow) a normal distribution, where the daily returns are evenly distributed about the mean, which, in the “normal” world is zero. This enables ready calculation of risk—the value at risk (VaR) to a 95% confidence level calculates out to 2 standard deviations—which can then be used to set benchmarks based on the user’s risk appetite. So, too, the classic Black-Scholes option pricing model assumes a normal distribution. Of course, the truth is that there is no “normal” anything. No currency follows a normal distribution even closely and the risk measures generated using this assumption can be quite dangerous. This attempt to put economic forces (ultimately related to how people behave) into a box to simplify analysis is akin to using the “efficient markets theory” to explain market phenomena, which has driven financial regulation over the past several decades; few would disagree that regulatory failure is a prime cause of the multiple financial crises the world has seen over the period. It is particularly ironic, as articulated by the economist Mariana Mazzucato, that this attempt by economists to build deterministic models began some 80/90 years ago, just as physicists and other “hard” scientists were moving away from determinism.
To show the fallacy of “normal”, we studied the behaviour of EURUSD between 2010 and 2021. EURUSD is by far the most liquid asset, and we compared real market behaviour with what would be predicted by normal distribution assumptions. On a point-to-point basis, EUR weakened against USD by 17.5%, with a mean return of –0.0001, which is reasonably acceptable for normalcy. However, the distribution skewness was –6%, signaling some deviation from “normal”. Again, the kurtosis, which measures the sum of the value of the points in the distribution closer to the edges (“tails”) as compared to points in the middle of the distribution, was 2.12, as compared to 3 for a normal distribution. This means that the tails were thinner than what would be predicted by a normal distribution, indicating extreme moves were less frequent than would be in a normal distribution. As a result of these deviations, the normal distribution VaR to a 95% confidence level (calculated as 2 X STDEV), which worked out to 1.04%, was substantially higher than the historically-realised overnight VaR. (To find the historic VaR, we first calculated the overnight returns over the period, ordered them from highest to lowest, and then found the return such that the number of entries higher/lower than that comprised 5% of the total sample.) This actually realised VaR was 0.80% for a short USD exposure and 0.82% for a long USD exposure, both substantially lower than the theoretically-calculated 1.04%. Incidentally, the fact that long and short exposures carried different risks reflects another divergence from normal.
The final nail in the coffin of the “normal” distribution theory is the way the risk varies with tenor. For a normal distribution, the theoretical risk to, say, 3 months is simply the overnight risk multiplied by the square root of the tenor (say, 63 trading days). The accompanying graphic shows the difference between the realised risk to different tenors (defined as the 5% cutoff of the distribution of the 1-month return, 3-month return, etc.) and that forecast by the theoretical approach—again, the variations are substantial and different for short and long exposures.
While all these numbers can be mind-numbing, what is important is that the implications of “wrong” risk numbers can be quite serious. For EURUSD, the normal distribution risk numbers over the period were higher than those realised. This means that using the theoretical model overstates the risk, which indicates that (a) option prices, which are widely calculated using the Black-Scholes model, are higher than they should be, which implies you can make more money by selling rather than buying options, and (b) capital requirements for intra-day traders are higher than they should be, reducing capital efficiency by as much as 25%.
For corporates, the higher risk numbers imply an extra buffer of conservatism, which is good in principle. Having said that, it is important to understand that risk management is not simply about eliminating risk; rather, a well-designed programme carries a pre-determined amount of risk to try and improve financial performance. Using an excessively large risk buffer, particularly for long USD exposures in the near term, would, on average over time, result in considerable opportunity loss and reduced risk management effectiveness.
Writer is the CEO of Mecklai Financial (www.mecklai.com)