Tail risk is the additional risk of an asset or portfolio of assets moving more than 3 standard deviations from its current price, above the risk of a normal distribution. Prudent asset managers are typically cautious with tail risk involving losses which could damage or ruin portfolios, and not the beneficial tail risk of outsized gains.

Tail risk is a form of portfolio risk that arises when the possibility that an investment will move more than three standard deviations from the mean is greater than what is shown by a normal distribution. Tail risks include events that have a small probability of occurring and occur at the ends of a normal distribution curve.

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 probability that returns will move between the mean and three standard deviations, either positive or negative, is approximately 99.97%. This means that the probability of returns moving more than three standard deviations beyond the mean is 0.03%. The assumption that market returns follow a normal distribution is key to many financial models, such as Harry Markowitz's modern portfolio theory and the Black-Scholes Merton option pricing model. However, this assumption does not properly reflect market returns and tail events have a large effect on market returns.

Stock market returns tend to follow a normal distribution that has excess kurtosis. Kurtosis is a statistical measure that indicates whether observed data follow a heavy or light tailed distribution in relation to the normal distribution. The normal distribution curve has a kurtosis equal to three, and therefore, if a security follows a distribution with kurtosis greater than three, it is said to have fat tails. A leptokurtic distribution, or heavy tailed distribution, depicts situations in which extreme outcomes have occurred more than expected. Therefore, securities that follow this distribution have experienced returns that have exceeded three standard deviations beyond the mean more than 0.03% of the observed outcomes.

Although tail events that negatively impact portfolios are rare, they may have large negative returns. Therefore, investors should hedge against these events. Hedging against tail risk aims to enhance returns over the long-term, but investors must assume short-term costs. Investors may look to diversify their portfolios to hedge against tail risk. For example, if an investor is long exchange-traded funds (ETFs) that track the Standard & Poor's 500 Index (S&P 500), the investor could hedge against tail risk by purchasing derivatives on the Chicago Board Options Exchange (CBOE) Volatility Index, which is inversely correlated to the S&P 500.

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The probability of returns moving more than three standard deviations beyond the mean is .3.

Because stock market returns tend to follow a normal distribution with excess kurtosis. Kurtosis indicates whether observed data follows heavy or light tailed distributions in relation to the normal distribution curve. The normal distribution curve has a kurtosis equal to 3, and therefore securities following this type of distribution have experienced extreme outcomes exceeding 3 standard deviation more than .3 of the time.

No , but many are

Returns moving beyond three standard deviations means that returns are moving in either direction, positive or negative, beyond the mean.

Tail risk is a form of portfolio risk that arises when the possibility that an investment will move more than three standard deviations from the mean is greater than what is shown by a normal distribution.

Yes , you can use statistical tests such as Jarque-Bera test ( JB )

You can reduce your exposure by reducing position size or increasing stop loss limits .

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