When the likelihood that an investment will deviate by more than three standard deviations from the mean is higher than what a normal distribution indicates, tail risk, a type of portfolio risk, arises. This article explores the concept of tail risk, its implications, and how investors can hedge against it.
What is tail risk?
Tail risk is a unique form of portfolio risk that defies the expectations of a normal distribution in investment returns. It occurs when the likelihood of an investment moving more than three standard deviations from the mean is greater than what a typical bell-shaped curve would suggest.
Understanding tail risk
Traditional investment strategies often rely on the assumption that market returns follow a normal distribution. This means that returns are expected to fall within three standard deviations from the mean, with a probability of around 99.7%. However, tail risk challenges this assumption by revealing that the distribution of returns is not normal. Instead, it is skewed with fatter tails.
The “fat tails” indicate a higher probability of an investment moving beyond three standard deviations from the mean. This phenomenon is frequently observed in hedge fund returns, among others, and indicates that rare, extreme events are more likely than expected. As depicted in the chart below, these fat tails disrupt the symmetrical bell curve shape of the normal distribution.
When constructing an investment portfolio, the conventional approach assumes that returns will follow a normal distribution. This is a fundamental assumption underlying many financial models, including Harry Markowitz’s modern portfolio theory (MPT) and the Black-Scholes-Merton option pricing model. However, market returns are not always normal, and the occurrence of tail events significantly affects investment performance. Nassim Taleb’s bestselling book, “The Black Swan,” highlights the concept of tail risk.
Other distributions and their tails
In the world of finance, stock market returns are often assumed to follow a normal distribution with excess kurtosis. Kurtosis is a statistical measure that assesses whether observed data deviate from the normal distribution’s tail behavior. The normal distribution has a kurtosis value of three. When a security exhibits kurtosis greater than three, it is considered to have fat tails.
A leptokurtic distribution, or a heavy/fat-tailed distribution, represents scenarios in which extreme outcomes occur more frequently than expected. These distributions exhibit excess kurtosis, and securities following them have experienced returns exceeding three standard deviations from the mean more than 0.3% of the time. The graph below shows a normal distribution in green and fat-tailed distributions, which are shown by curves that get flatter in red and blue.
Hedging against tail risk
While tail events that negatively impact investment portfolios are infrequent, they can result in significant losses. To safeguard against these events, investors may employ hedging strategies. Hedging against tail risk seeks to enhance long-term returns but may involve short-term costs.
Investors can diversify their portfolios as a means of hedging against tail risk. For example, an investor holding exchange-traded funds (ETFs) tracking the Standard & Poor’s 500 Index (S&P 500) could hedge against tail risk by purchasing derivatives linked to the Cboe Volatility Index, which tends to move inversely to the S&P 500.
Here is a list of the benefits and the drawbacks to consider.
- Enhanced understanding of tail risk and its implications.
- Potential for more robust risk management.
- Protection against rare, extreme market events.
- Short-term costs associated with hedging strategies.
- Complexity in implementing some hedging techniques.
- Potential for reduced returns in non-tail risk scenarios.
Frequently asked questions
1. What is tail risk?
Tail risk refers to the possibility of incurring losses due to rare and extreme events that deviate from the expected normal distribution of investment returns. It challenges the assumption of traditional portfolio strategies.
2. How can investors hedge against tail risk?
Investors can hedge against tail risk by diversifying their portfolios and using various hedging techniques. One common approach is to purchase derivatives that move inversely to the assets in their portfolio, providing protection in times of extreme market volatility.
3. Are tail events common in financial markets?
Tail events are relatively rare in financial markets, but when they occur, they can have a substantial impact on investment portfolios. It’s essential for investors to be prepared for such events and consider risk management strategies.
- Tail risk challenges the assumption of normal distribution in investment returns, emphasizing the likelihood of rare, extreme events.
- Fat-tailed distributions have a higher probability of returns moving beyond three standard deviations from the mean.
- Hedging against tail risk can enhance long-term portfolio performance, but it may involve short-term costs and complexity.
- Diversification and the use of inverse derivatives are common strategies for mitigating tail risk.
View article sources
- The Effect of Tail Risk on Government Bond Liquidity – St. Louis Fed
- Effect of Tail Risk on Asset Prices – National Bureau of Economic Research (NBER)
- Understanding Tail Risk in Financial Markets – North Dakota State University Library
- Distribution – Supermoney