Tail Risk

What Is Tail Risk?

Tail risk is a form of portfolio risk that emerges when the possibility that an investment will move multiple standard deviations from the mean is greater than whatever is shown by a normal distribution.

Tail risks incorporate events that have a small likelihood of happening and happen at the two finishes of a normal distribution curve.

Understanding Tail Risk

Customary portfolio strategies regularly follow the possibility that market returns follow a normal distribution. Nonetheless, the concept of tail risk recommends that the distribution of returns isn't normal, yet skewed, and has fatter tails.

The fat tails show that there is a likelihood, which might be larger than in any case anticipated, that an investment will move past three standard deviations. Distributions that are described by fat tails are in many cases seen while taking a gander at hedge fund returns, for instance.

The chart below portrays three curves of expanding right-skewness, with fat tails to the disadvantage — and which vary from the symmetrical bell curve state of the normal distribution.

Normal Distributions and Asset Returns

At the point when a portfolio of investments is put together, it is assumed that the distribution of returns will follow a normal distribution. Under this assumption, the likelihood that returns will move between the mean and three standard deviations, either positive or negative, is around 99.7%. This means that the likelihood of returns moving multiple standard deviations past the mean is 0.3%.

The assumption that market returns follow a normal distribution is key to numerous financial models, for example, Harry Markowitz's modern portfolio theory (MPT) and the Black-Scholes-Merton option pricing model. In any case, this assumption doesn't as expected reflect market returns, and tail events generally affect market returns.

Tail risk is featured in Nassim Taleb's top rated financial book The Black Swan.

Different Distributions and Their Tails

Securities exchange returns will more often than not follow a normal distribution that has excess kurtosis. Kurtosis is a statistical measure that shows whether noticed data follow a weighty or light-tailed distribution comparable to the normal distribution. The normal distribution curve has a kurtosis equivalent to three and, consequently, in the event that a security follows a distribution with kurtosis greater than three, having fat tails is said.

A leptokurtic distribution, or weighty/fat-tailed distribution, portrays circumstances in which extreme results have occurred more than expected. Compared to the normal distribution, these curves have excess kurtosis. Consequently, securities that follow this distribution have encountered returns that have surpassed three standard deviations past the mean over 0.3% of the noticed results.

The graph below portrays the normal distribution (in green) as well as progressively leptokurtic curves (in red and blue), which display fat tails.

Hedging Against Tail Risk

In spite of the fact that tail events that negatively impact portfolios are rare, they might have large negative returns. In this way, investors ought to hedge against these events. Hedging against tail risk means to upgrade returns over the long term, however investors must expect short-term costs. Investors might hope to differentiate their portfolios to hedge against tail risk.

For instance, assuming an investor is long exchange-traded funds (ETFs) that track the Standard and Poor's 500 Index (S&P 500), the investor could hedge against tail risk by purchasing derivatives on the Cboe Volatility Index, which is [inversely correlated](/reverse connection) to the S&P 500.

Features

• Tail risk is the chance of a loss happening due to a rare event, as predicted by a likelihood distribution.
• Informally, a short-term move of multiple standard deviations is considered to launch tail risk.
• While tail risk technically alludes to both the left and right tails, individuals are generally worried about losses (the left tail).
• Tail events have had specialists questions the true likelihood distribution of returns for investable assets.