Tail risk is a type of portfolio risk that emerges when the probability of an investment dramatically deviating more than three standard deviations from its mean is considerably higher than what is implied by a normal distribution. These infrequent yet significant movements, occurring at both ends of a distribution curve, can have profound impacts on your investment strategy.
Key Takeaways
- Tail risk represents the chance of experiencing a loss due to an unusual market event as forecasted by a probability distribution.
- Short-term movements exceeding three standard deviations often exemplify tail risk.
- Although tail risk encompasses both ends of the distribution curve, investors are typically more concerned with losses (the left tail).
- Experts are challenging the assumed probability distribution of returns for investable assets due to historical tail events.
Understanding Tail Risk
Conventional portfolio strategies rely on the belief that market returns follow a normal distribution. Tail risk challenges this by proposing that the distribution of returns is actually skewed with fatter tails. This means there’s a higher-than-expected probability of investments moving beyond three standard deviations.
For instance, distributions with fat tails are common when examining hedge fund returns. These fat tails indicate a larger likelihood of extreme variations. Below is a chart showing three curves with increasing right-skewness and prominent fat tails:
Right skewness.
Normal Distributions and Asset Returns
A typical investment portfolio assumes that returns will follow a normal distribution. Under this paradigm, the probability that returns will shift within three standard deviations, positively or negatively, from the mean is approximately 99.7%. This implies only a 0.3% chance of returns deviating beyond this range.
This assumption is fundamental to many financial models, such as Harry Markowitz’s modern portfolio theory (MPT) and the Black-Scholes-Merton option pricing model. However, the frequency and impact of tail events suggest that these models may not adequately capture market returns, evidenced by landmark market disruptions discussed by Nassim Taleb in The Black Swan.
Other Distributions and Their Tails
Market returns tend to resemble a normal distribution with excess kurtosis—a statistical measure indicating whether observed data have heavy or light tails compared to the normal distribution. Unlike normal distributions with a kurtosis of three, distributions exceeding this often exhibit fat tails.
Leptokurtic distributions, characterized by fat tails, indicate more frequent extreme outcomes than those predicted by a normal distribution. Securities following this type of distribution see returns surpassing three standard deviations more often than the anticipated 0.3% probability. Below, a graph contrasts normal distribution (in green) with increasingly leptokurtic curves (in red and blue), showcasing fat tails:
Kurtosis and distribution peaks.
Hedging Against Tail Risk
While tail events that negatively affect portfolios are rare, their impacts can be devastating with substantial negative returns. As a result, it’s imperative for investors to hedge against such risks. Hedging strategies intend to enhance long-term returns, though they may incur short-term costs.
For example, if an investor is long on exchange-traded funds (ETFs) tracking the S&P 500 Index, they could mitigate tail risk by acquiring derivatives on the Cboe Volatility Index, which exhibits an inverse relationship to the S&P 500. Diversifying investment portfolios is another effective approach to managing tail risk.
Tail risk management is crucial for not only shielding portfolios from rare yet significant losses but also for potentially bolstering returns through meticulous and well-informed investment strategies.
Related Terms: Standard Deviation, Kurtosis, Hedging, Investment Risk, Fat Tails.
References
- Markowitz, Harry. “Portfolio Selection”. *The Journal of Finance,*Vol. 7, No. 1, March 1952, pp. 77-91.
- Black, Fischer and Myron Scholes. “The Pricing of Options and Corporate Liabilities”. The Journal of Political Economy, Vol. 81, No. 3, May-June 1973, pp. 637-654.
- Nassim Nicholas Taleb. “The Black Swan: The Impact of the Highly Improbable”. Random House Publishing Group, 2007.
- Cboe. “Vix Volatility Products”.
