By Jamal Mecklai
Classic risk management models assume that currency pairs follow (or closely follow) a normal distribution, where daily returns are evenly distributed around the mean, which in the “normal” world is zero. This allows for an easy calculation of risk – the value at risk (VaR) at a 95% confidence level calculates up to 2 standard deviations – which can then be used to set benchmarks based on the risk appetite of the ‘user. Likewise, the classic Black-Scholes option pricing model assumes a normal distribution. Of course, the truth is that there is nothing “normal”. 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) in a box to simplify analysis is akin to using “efficient markets theory” to explain market phenomena. market, which have led to financial regulation in recent decades; few would disagree that regulatory failure was one of the main causes of the multiple financial crises the world experienced during the period. It is particularly ironic, as economist Mariana Mazzucato explained, that this attempt by economists to build deterministic models began around 80/90 years ago, just as physicists and other “hard” scientists ‘moved away from determinism.
To show the error of “normal”, we have studied the behavior of EURUSD between 2010 and 2021. EURUSD is by far the most liquid asset, and we compared the actual behavior of the market with what would be. predicted by the normal distribution assumptions. On a point-to-point basis, the euro weakened against the USD by 17.5%, with an average return of –0.0001, which is reasonably acceptable for normalcy. However, the skewness of the distribution was –6%, indicating some deviation from “normal”. Again, the kurtosis, which measures the sum of the value of the points of the distribution closest to the edges (“tails”) relative to the points in the middle of the distribution, was 2.12, compared to 3 for a distribution. normal. This means that the tails were thinner than what would be predicted by a normal distribution, indicating that the extreme movements were less frequent than in a normal distribution. Due to these deviations, the VaR of the normal distribution at a 95% confidence level (calculated as 2 X STDEV), which corresponds to 1.04%, was significantly higher than the historically achieved overnight VaR. (To find the historical VaR, we first calculated the overnight returns over the period, ranked them from highest to lowest, and then found the return such as number of entries greater / less than that made up of 5% of the total sample.) This The actual realized VaR was 0.80% for a short exposure in USD and 0.82% for a long exposure in USD, both well below the 1.04 Theoretically calculated%. Incidentally, the fact that long and short exposures carried different risks reflects another deviation from normal.
The final nail in the coffin of “normal” distribution theory is how risk varies with grade. For a normal distribution, the theoretical risk up to, say, 3 months is simply the overnight risk multiplied by the square root of the duration (say, 63 trading days). The attached graph shows the difference between the risk realized at different tenors (defined as the threshold of 5% of the distribution of the 1-month return, 3-month return, etc.) and that predicted by the theoretical approach – again once the variations are substantial and different for short and long exposures.
While all of these numbers can be mind-boggling, what is important is that the implications of “bad” risk numbers can be quite severe. For EURUSD, normal distribution risk figures over the period were higher than realized. This means that using the theoretical model overestimates the risk, indicating that (a) the prices of options, which are largely calculated using the Black-Scholes model, are higher than they should be. , which implies that you can make more money by selling rather than buying and (b) the capital requirements for intraday traders are higher than they should be, reducing the efficiency of the capital up to 25%.
For companies, the higher risk figures imply an additional buffer of caution, which is good in principle. Having said that, it is important to understand that risk management is not just about eliminating risk; on the contrary, a well-designed program carries a predetermined level of risk in trying to improve financial performance. Using too much of a risk buffer, especially for short-term USD long exposures, would, on average, lead to significant lost opportunities over time and reduced efficiency in asset management. risks.
Writer is the CEO of Mecklai Financial (www.mecklai.com)