Understanding tail risk

July 22, 20225 min read
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Key takeaways:

  • Tail risk is the probability that the asset performs far below or far above its average past performance. Investors are most concerned with “left” tail risk, or the likelihood that observations fall three standard deviations below the average expected return.

     
  • All else being equal, volatile assets have higher standard deviations because there’s greater variability in their observed returns. In the event of a left tail market movement, returns for these assets could derail even more significantly. 

  • Strategies adopted by investors to curb the losses predicted by left tail risk, such as different hedging positions can provide significant value in the long run, not only to individuals but to the market as whole.

Return on investments are by definition, not guaranteed. Portfolio managers tend  to prepare and account for periods of extreme market volatility by gauging the probabilities of extremely negative returns, which can occur after a market shock triggered by events like a war, a sector wide crisis or most relevant to our current time –  a global pandemic.

Tail risk is a key concept in these considerations. It measures the probability of an asset performing significantly below or above its average performance.

Because it’s technically in anticipation of rare events,  tail risk is inherently the probability of a very unlikely event, though it happens more often than many investors might think, and at an increasingly global scale. By some estimates, over the past three decades market shocks have occurred about every three to five years, resulting in “fatter” tails than a normal distribution curve would predict. 

Strategies to mitigate tail risk, such as different hedging positions, can provide investors with significant value in the long run, while history shows that preemptive analysis of tail risks in the wider markets can potentially curtail the effects of systemic shock on a spectrum of investments.

No discussion of tail risk can take place without first looking at normal distribution, or the bell shaped curve that demonstrates the relationship between observed returns (observations) and  their likelihood of occurring (their probability).

The bell curve, shown below, gets its name from its shape – a symmetrical bulge in the center tapers out toward two “tail” ends, and the resulting curve resembles the silhouette of a bell.

The above graph tells investors that given past performance, some events are more likely than others. The observations concentrated near the end sections of the bell (the tails) have the least probability of happening, while those that are concentrated in the middle have the highest. 

Standard deviation, an important concept demonstrated in the bell curve, measures how far observations at either end are from the center, which represent the mean, or the average of all data points. Again, the observations closest to the center of the graph are the investor’s most probable returns, given the instrument’s historical performance.  

Standard deviation is really looking at the average variability in the data, and so higher the volatility in the asset performance, the higher the standard deviation. For a normal distribution, 68% of the observations are within +/- one standard deviation of the mean, while 95% are within +/- two standard deviations, and 99.7% are within +/- three standard deviations. 

Tail risk is defined as the possibility that return will be more than three standard deviations from the mean, which means it’s targeting observations with 0.3% (=100-99.7) odds of happening. While a probability of 0.3% seems extremely low, left tail events have historically decimated portfolios, especially if the impact of the triggering event lasts for some time.

In the aftermath of the housing bubble for example, that led to the global financial crisis in 2008, even broadly diversified, multi-asset class portfolios suffered losses that ranged anywhere from 20% to 30% in the course of just a few months. Highly sophisticated institutions such as American university endowments and long-established sovereign wealth funds weren’t exempt either: all of them also experienced large double digit percentage drops in value. 

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Many important financial models, such as Harry Markowitz’s modern portfolio theory (MPT) which advocates for portfolio diversification for maximum profit, assume that returns follow a normal distribution. But real market returns don’t align perfectly with a normal distribution and tail events can have a lasting impact on what investors really earn, which is why supplementing these models with tail risk analysis is a more thorough way of analyzing potential income.

The process of applying tail risk when evaluating portfolios is pretty straightforward. Though the exact formula to calculate is a daunting one, it’s still based around an intuitive concept.

When the equation below is stripped to its most basic concept, it’s really measuring the average deviation of any given observation from the average observation. When it comes to financial assets, standard deviation is really the average volatility in the instrument’s returns, or how much its performance fluctuates in general. 

But tail risk can be approximated just by using its definition (three standard deviations below the average.) If the average equity market performance in any given month is +2% for example, and the standard deviation of past observations is 5%, the expected return in the event of a left leaning tail event would be about – 13% (=2-(5*3)). Going from an average return of 2% to a loss of 13% is a huge jump, but preparing for such drastic moves in the market can make a significant difference. 

Take historical market downturns for example. Due to trade wars and economic slowdown beginning in autumn of 2018, the whole US market suffered. The Dow Index at the time was made up of primarily healthcare names and experienced a massive fall in response to each tail event, trading down close to 19℅ within a few months. The tail risk in the Dow Index was the 24k mark in October 2018 but when it neared that, many market analysts dismissed it as a behavioral movement. When the Dow continued to fall, it was clear that the index was suffering from a tail event and that the losses stood to be massive.

While most discussions of tail risk surround left tail events, one can argue that the art of strategic investing is being able to protect against left‐hand events while aiming to participate in the events on the right, which are profit making. But the latter requires more complicated analyses and is a risky venture in itself, so the primary focus for many investors is to hedge against the left tail risk.