In this update, I want to explain why typical bank FX forecasts are uninformative and why it is extreme events (and their impact on your business) that we should be concerned about.
Let's Talk Statistics
To do this, we steer the conversation towards a branch of statistics called Extreme Value Theory (EVT) which deals with the study of extreme deviations from the median of a probability distribution. It is used to model the risk of extreme and rare events such as natural disasters, insurance, pandemics, pipeline failures, and of course the movement of financial markets – including foreign exchange!
Hopefully you are still with me…
A famous type of distribution widely used to model extreme events is known as the Pareto Distribution. The famous Pareto Principle (aka “the 80/20 rule”) is a specific case of the Pareto Distribution. It implies that you get the majority of effects from a minority of the samples. For example, 80% of the wealth of a nation is held by 20% of the population. In financial markets, 20% of the moves in FX markets account for 80% of the impact on your business (as it relates to FX).
Still with me? Read on…
Let's Talk "Fat Tails"
Please read this section carefully. This is a subtlety in risk management that – in my opinion – few truly understand.
Loosely speaking, a fat-tailed distribution (like Pareto) is one that exhibits larger asymmetry and “tailedness” when compared to the normal distribution (aka “the bell curve”). More specifically, fat tails describe the contribution of events away from the “center” of the distribution to the total properties of the distribution.
Confused? The following example will help clarify:
Let’s suppose you have 1000 humans. The heaviest person would only contribute ~0.2% to the total weight of the 1000 humans. But, if you look at the wealth distribution of those same 1000 humans which also included someone like Bill Gates, his percentage of the total would be close to 100%. His wealth contributes to almost all of the total (this is fat tails). And more importantly, the other 999 humans contribute almost nothing!
So, what does this mean in practice?
The point of risk management techniques, derivative products, and overall strategy is to minimize the impact of fat tails because it is fat-tailed events that have the largest economic impact on your business!
Consensus bank forecasts are akin to the 999 other humans (i.e. they contribute nothing). Rather, one should focus on managing the potential impact of a “Bill Gates” event. I cannot overstate this principle enough. If you are visual like me, the diagram below will almost surely help.
Fat-Tailed Distribution vs. Normal Distribution (bell curve)
Let's Do a Simulation
Imagine for a moment you expect a certain outcome (e.g. a bank forecast) which is the average of a distribution represented by the dotted red line in the diagram below. When you simulate events that follow a Pareto Distribution (e.g. Foreign Exchange returns), on the surface one would initially expect that after several trials the average of those events would ‘converge’ to the red line (the average of the distribution, or the bank’s forecast).
What is interesting is that the ‘spike’ events that appear push the average of simulations away from the true average (i.e. away from the bank’s forecast, red line), and often after several thousands of simulations the convergence to the average is never actually realized. This is what makes forecasts in general dangerous. They rely on the center of the distribution (or the 999 humans from above). They offer no practical information because it is the fat-tailed events that have the biggest impact, and are the ones businesses should be hedging.
Pareto Distribution Simulation
As we head into 2021/2022 it will be incredibly important to implement a sound risk management strategy. That is, one that genuinely removes risk from your business. The volatility we will see will be truly historical – levels not seen perhaps in centuries.
Until next time…
Alexander Grant, FRM is Olympia Trust CGP’s Head of FX Options Trading. He can be reached at email@example.com if you have questions.