Left-Tail Risk: What Is It, What Is the Impact, How to Manage It?

In finance, managing risks is essential for long-term success. One critical aspect of risk management is left-tail risk, which can often lead to unexpected financial losses. In this article, we’ll explore the concept of left tail risk, its impact on financial markets, and how you can manage it effectively.

What is Left-Tail Risk?

Simply put, left tail risk refers to the negative impact of rare and unexpected events, such as black swan events. These rare events are specifically related to harmful occurrences, like the 2008 financial crisis or the 2020 Covid-19 pandemic.

They are different from positive, rare occasions. For example, winning a large sum of money is rare, but it is a beneficial event. Thus, it falls under right tail risk rather than left tail risk.

Left-Tail Risk and Normal Distribution

In finance, we often assume that the distribution of events or asset returns follows a normal or Gaussian distribution. This assumption is crucial to many financial models, including Harry Markowitz’s modern portfolio theory (MPT) and the Black-Scholes-Merton option pricing model. Based on this assumption, the probability of returns fluctuating between the mean and three standard deviations (positive or negative) is approximately 99.7%. This means the likelihood of returns moving beyond three standard deviations from the mean is only 0.3%.

However, in reality, extreme negative events or significant losses occur more frequently than we expect. When illustrated on a probability distribution curve, this appears as a fatter tail.

Alternative Distributions

To tackle the challenge of normal distribution not fitting well with left-tail risk, people frequently use leptokurtic distributions to represent asset returns. Leptokurtic distributions, commonly known as fat-tailed distributions, suggest that extreme outcomes happen more often than anticipated. As a result, securities that follow these alternative fat-tailed distributions, like the Student’s t-distribution, have witnessed returns exceeding three standard deviations beyond the mean in over 0.3% of observed outcomes.

By considering these alternative distributions, you can craft more effective risk management strategies and evaluate the increased likelihood of extreme events.

Quantifying Left-Tail Risk

Skewness and Kurtosis

We can use two statistical measures to identify left tail risk: skewness and kurtosis. Skewness measures the asymmetry of a distribution. A perfectly symmetrical distribution has a skewness of 0, while a negatively skewed distribution has a value less than 0, indicating a higher probability of extreme negative returns.

Kurtosis evaluates the tail heaviness of a distribution. A normal distribution has a kurtosis value of 3. Suppose the kurtosis value is greater than 3. In that case, it suggests that the tails of the distribution are more extreme than those of a normal distribution, indicating a greater likelihood of extreme events.

Value-at-Risk (VaR) and its Limitations

Value-at-Risk (VaR) estimates the maximum potential loss for a portfolio over a specific time horizon at a given confidence level (e.g., 95% or 99%). For example, a 95% one-month VaR of $1 million means we have 95% confidence that the portfolio will not lose more than$1 million in a month. However, VaR has its drawbacks: it doesn’t capture tail risk beyond the specified confidence level. This limitation has led to the development of other risk measures like Expected Shortfall (ES).

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