With the price of oil down 50% over the last six months, there seems to be a resurgence of pundits predicting the possibility of tail events — on the downside and/or the upside — for 2015. This may lead people to ask their financial adviser how these potential tail events would impact their portfolios.
Before answering this important question, we first need to discuss what constitutes a tail event.
A tail event is far away from the average. How far? Well, far enough that its theoretical probability is very small. This is still not saying much, and that's the crux of the problem.
Since there are many different ways of assigning probabilities to events (a.k.a., probability models), then our definition of what constitutes a tail event depends crucially on the probability model being used.
For example, using a basic bell-curve model, a six-month tail event in the S&P 500 index starts around a -28% decline. But using a more advanced 'heavy-tail' model, a six-month tail event starts around the -42% mark. Moreover, a drop of 42% in six months of the S&P 500 index has a probability of 0.06% if one uses the traditional bell-curve model, and a probability of 0.50% using a heavy-tail model.
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So tail events don't exist in a vacuum, they depend entirely on the quality of the probability model in use, and different models will give different answers.
Finally, tail events also depend of the time period being considered. The longer the time period considered, the larger the tail event, since more can happen in a year than, say, in a week.
So here are tail event values for the S&P 500 and the 10-year U.S. Treasury rate for different time horizons, computed using our heavy-tailed distribution model. These represent levels at which bona fide tail events would begin (These are not 'max loss' numbers).
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It is worth repeating that the values above are not to be interpreted as the maximum change possible in their respective time periods. Instead, these are the limits at which we could start talking about legitimate 'tail events', according to our particular model.
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Your model may come up with different values, and do the pundits' models. Also, there could be tail events in many other instruments and asset classes.
What to do with this information?
As financial experts, we earn our clients' trust by keeping them well informed and by setting proper expectations. Can you clearly articulate and demonstrate what a tail event means in terms of gains and losses for you clients' portfolios?
We hope to have shed some light on what constitutes tail events. Tail events levels depend on the probability model used, the distance away from the mean, and the time horizon.
Saying that a tail event may be on the horizon is akin to saying that we saw a 'non-elephant' on our way to work. It is certainly true but doesn't really help us.
More importantly, clients won't understand it.
Ron Piccinini is co-founder and managing partner of Prairie Smarts.
