Extreme Value Theory in Your Portfolio – Explained

By Hudson Cooper

 

The traditional 60/40 portfolio is a good example of a portfolio that has been constructed to manage volatility. Because fluctuations in the value of equities and fixed income securities are largely uncorrelated, they are able to offset each other’s volatility without sacrificing too much in terms of expected returns. 50/50 or 40/60 portfolios work in the same basic way, but they are tuned for slightly different overall volatility tolerance levels.

 

Let’s look at a concrete example and compare SPY to a 60/40 portfolio of SPY and TLT, an ETF tracking the value of  20+ year treasury bonds. To put the two on equal footing, the 60/40 portfolio has been scaled up to have the same realized ROI as SPY since 2003.

 

Looking at their largest drawdowns over this period, we can actually see that the 60/40 portfolio has done a decent job of reducing the impact of these events. The magnitude of the 2008 financial crisis was reduced by almost 44%, and its duration was reduced by about 43%. Several of the other large drawdowns were similarly abated.

 

 

So if 60/40 has worked so well in the past, why am I harping on about the ineffectiveness of traditional portfolios? What’s really crucial here is that we cannot take historical data at face value. The most extreme event in history is a really poor estimate of the most extreme event we should expect to see in the future, because in a real sense, “the worst has yet to come”. We need to be able to mitigate the risk of the next big “unprecedented” event, and that means we need to move beyond looking at raw historical data.

 

By looking at how the rarity of drawdowns changes as they get rarer and rarer, we can infer how frequently to expect the unprecedented drawdowns, even if we don’t necessarily have explicit models of the mechanisms that will cause them. Let me show you visually what I mean.

 

This graph shows the frequency of drawdowns on the Y-axis plotted against their magnitudes on the X-axis. The frequency here is expressed as the probability that any drawdown lasting at least a week meets or exceeds the magnitude expressed on the X-axis.

 

The scattered points correspond to the historical data (3-month time horizon), while the dotted lines correspond to statistical models that let us make inferences about behavior far into the upper tail. The shaded regions are confidence intervals that let us express the uncertainty in our models due to variability in the historical data.

 

Here we are just looking at the smallest and most frequent drawdowns, the ones that occur in 90% of the cases and that are less than around 10% in magnitude. We can see a really clear separation between SPY and the 60/40 portfolio here, meaning that 60/40 is able to effectively reduce the frequency of these drawdowns. This is exactly as we should expect since the 60/40 portfolio is designed to mitigate these small, volatility-driven risks.  

 

 

Now let’s zoom out and look at the rarer and larger drawdowns. The separation that we saw before really breaks down. Particularly as we look at drawdowns occurring with probability less than 1% and with losses of 20, 40, 60%, and above, the model uncertainty is simply too high to conclude that the 60/40 portfolio effectively manages these risks. Quantifying this uncertainty is a really important step because we would otherwise feel unjustifiably safe in the 60/40 portfolio and make ill-informed investment decisions. 

 

This means that we really can’t trust that these kinds of portfolios that are often sold as “safe” actually protect our assets from the extreme events that are rare but catastrophic and may occur relatively frequently over longer time horizons like those that are preparing for retirement might be facing.

 

It is important that we manage the risks that actually threaten our goals, and that means we need to move away from volatility-based approaches to approaches that model and manage long-term tail risks directly. 

 

Thankfully, there is a whole field of statistics called “Extreme Value Theory” that has been built to estimate, model, and reason about the magnitudes and frequencies of extreme and unprecedented events. It has its roots in meteorology and the climate sciences and is used to estimate the size of one-in-100-year floods and to detect systematic changes in the occurrence rates of extreme weather events due to climate change. Combining this statistical framework with the flexibility, adaptability, and efficacy of modern AI and Machine Learning has really opened the door to building portfolios that can extract profit while being far more robust to these risks that we care about.