Understanding Tail Risk: Investing's Wild Card

Tail risk is a financial concept that refers to the probability of an asset's performance deviating significantly from its average past performance, moving more than three standard deviations from the mean. This can occur at both ends of a normal distribution curve but typically focuses on the left tail, where losses can damage or ruin portfolios. Tail risk is challenging to measure as these events are rare and have varying impacts. However, they can have disastrous effects on portfolio returns in a short span of time, and strategies such as diversification and hedging can help mitigate this risk.

How to calculate tail risk

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

Calculating tail risk is challenging because tail events are rare and their impacts vary. The most popular measures are conditional value-at-risk (CVaR) and value-at-risk (VaR). These are used in finance and insurance industries, as well as in highly reliable, safety-critical uncertain environments with heavy-tailed underlying probability distributions.

Value-at-risk (VaR) is a statistical measure that assesses the financial risk associated with a portfolio or firm over a specified period. VaR measures the probability that a portfolio will not exceed a threshold loss value. It is based on potential losses and determines the loss distribution. VaR can be calculated by using historical returns and plotting the distribution of profits and losses.

Expected Tail Loss (ETL) is another measure used to understand the effect of tail events. ETL is an extension of VaR and is calculated by averaging the losses beyond a certain threshold of a portfolio return distribution.

To implement an effective tail risk hedging program, it is important to carefully define tail risk by identifying the elements of a tail event that investors are hedging against. A true tail event should exhibit three properties: falling asset prices, increasing risk premia, and increasing correlations between asset classes.

Strategies to mitigate tail risk

Tail risk is the financial risk of an asset or portfolio of assets moving more than three standard deviations from its current price, above the risk of a normal distribution. While tail risk cannot be eliminated, there are strategies that can be employed to mitigate its impact. Here are some strategies that investors can use to protect their portfolios:

• Diversification: Diversification across assets, sectors, and strategies is a crucial way to reduce tail risk. By spreading investments across various areas, the potential impact of a negative event is lessened. This is because the chances of all assets being affected simultaneously are lower.
• Asymmetric Hedge: Using an asymmetric hedge means that the potential losses from a negative event are reduced. This strategy involves taking on less risk in certain areas of the portfolio to balance out the overall risk.
• Long Puts: Also known as buying portfolio insurance, this strategy involves purchasing put options to protect against sudden and severe sell-offs. While this can be an effective hedge, it can also be costly, especially during prolonged bear markets.
• Credit Default Swaps: A credit put strategy involves using credit default swaps as a hedge. While this strategy may be cheaper than long puts, it may not provide as reliable protection.
• Gold as a Safe Haven: Gold has traditionally been viewed as a safe-haven asset, expected to maintain or increase its value during equity and bond drawdowns. However, gold has provided mixed results, with negative returns outside of equity drawdown periods.
• Treasury Bonds: Treasury bonds have also been considered safe-haven investments, particularly in periods of low inflation and interest rates. However, research suggests that they are unreliable hedges during periods of rising inflation.
• Trend Following: This strategy involves buying assets that have recently performed well and selling or shorting assets that have done poorly. Trend following can provide protection against tail risk, especially during severe market downturns.
• Volatility Targeting: This strategy aims to counter fluctuations in volatility by targeting a constant level of volatility. It is based on the negative correlation between volatility and returns, with high volatility leading to negative equity returns.
• Strategic Rebalancing: Mechanical rebalancing can exacerbate drawdowns in severe bear markets. Using trend signals to determine when to rebalance can help reduce the drawdown.
• Tail Risk Hedging: This strategy enables investors to pursue their objectives without significantly adjusting their risk and return expectations after a market crisis. It can involve weighting asset allocation towards less volatile sectors or complementing existing allocations with strategies like equity puts and currency options.

It is important to note that each crisis is unique, and different strategies may be more or less effective in different situations. As such, diversifying across multiple promising strategies may be the most prudent approach.

Tail risk and normal distribution

Tail risk is a financial risk that arises when an asset or portfolio of assets moves more than three standard deviations from its current price, above the risk of a normal distribution. It is the chance of portfolio losses caused by rare events, as shown by a normal distribution curve. Tail risk is usually associated with the left tail, as investors are more concerned with unexpected losses than gains.

Traditional portfolio strategies assume that market returns follow a normal distribution, often represented by a bell curve. This curve illustrates that, given enough observations, all values in a sample will be distributed symmetrically with respect to the mean. In a normal bell curve, the most probable returns are concentrated in the centre, with more extreme returns tapering off at the ends as tails. The empirical rule states that about 99.7% of all variations following a normal distribution lie within three standard deviations of the mean, meaning there is only a 0.3% chance of an extreme event occurring.

However, financial markets are largely shaped by unpredictable human behaviour, and evidence suggests that the distribution of returns is skewed rather than normal. Observed tails are fatter than traditionally predicted, indicating a significantly higher probability that an investment will move beyond three standard deviations. This is known as a fat tail or leptokurtic distribution, where extreme outcomes occur more frequently than expected. In these cases, the likelihood of extreme events is greater than that predicted by traditional strategies, which underestimate the volatility and risk of the asset.

The importance of considering tail risk is not just theoretical. From the late 1980s to the early 2010s, there were at least seven episodes that can be considered tail events, including the 2008 financial crisis. These events led to a significant increase in awareness of tail risks, as even sophisticated institutions suffered large double-digit percentage drops in value.

While tail risk cannot be eliminated, its impact can be mitigated through robust diversification across assets and strategies, as well as the use of an asymmetric hedge. Investors can also adopt hedging strategies to curb the losses predicted by left-tail risk, providing value to both individuals and the market as a whole.

Tail risk vs. tail value at risk (TVaR)

Tail risk is a form of portfolio risk that arises when there is a significant chance of an investment moving more than three standard deviations from the mean. These are rare events that can result in substantial losses. Tail risk is often defined as the risk of rare events, with the potential to cause large negative impacts on portfolios.

On the other hand, Tail Value at Risk (TVaR), also known as Conditional Value at Risk (CVaR), is a risk measure used to assess the expected loss of an investment portfolio beyond a specified Value at Risk (VaR) level. VaR, a statistical measure, assesses the probability that a portfolio will not exceed a certain loss value. However, it does not thoroughly evaluate the tail loss of the distribution.

TVaR addresses this limitation by focusing on the tail end of the loss distribution. It provides insights into the severity of losses in extreme scenarios beyond the VaR threshold. For instance, if an investment has a 95% VaR of $10,000, TVaR might reveal that the expected loss, if it exceeds $10,000, is $15,000. Thus, TVaR offers a more comprehensive understanding of potential extreme losses.

While tail risk focuses on the likelihood of rare events causing losses, TVaR quantifies the expected value of those losses, providing a more detailed analysis of the potential financial impact. TVaR is always greater than or equal to VaR for the same confidence level as it considers more extreme loss events.

In summary, tail risk refers to the probability of rare events impacting a portfolio, while TVaR quantifies the expected loss given that those rare events occur, offering a more nuanced view of potential losses beyond the VaR threshold.

Tail risk and portfolio management

Tail risk is a financial risk that arises when an asset or portfolio of assets moves more than three standard deviations from its current price, above the risk of a normal distribution. It is a form of portfolio risk that includes low-probability events at both ends of a normal distribution curve. Investors are generally more concerned with the "left tail risk", which indicates the possibility of losses.

Traditional portfolio strategies assume that market returns follow a normal distribution, or a bell curve, where 99.7% of all variations are within three standard deviations of the mean, and there is only a 0.3% chance of an extreme event occurring. However, financial markets are largely shaped by unpredictable human behaviour, and evidence suggests that the distribution of returns is skewed, with fatter tails. This indicates a higher probability of an investment moving beyond three standard deviations, resulting in significant fluctuations in the value of the stock.

The importance of considering tail risk in portfolio management is underscored by several episodes in recent decades that can be viewed as tail events, including the 1987 equity market crash, the 1994 bond market crisis, and the 2007-2008 financial crisis. These events had dramatic impacts on investment portfolios, even affecting highly sophisticated institutions.

Managing Tail Risk

While tail risk cannot be eliminated, its impact can be mitigated through robust diversification across assets and strategies, as well as the use of an asymmetric hedge. Actively managed tail hedge strategies, employing macroeconomic forecasting and quantitative modelling techniques, are crucial for devising effective hedging strategies in complex markets.

Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) are commonly used measures to assess tail risk. VaR is a statistical measure that assesses the financial risk associated with a portfolio over a specified period, providing a single value for the downside risk. However, it does not provide information about the severity of losses beyond the threshold. CVaR, on the other hand, addresses this limitation by measuring the expected loss if the worst-case threshold is crossed.

In summary, tail risk is an important consideration in portfolio management, and investors should employ appropriate strategies and tools to mitigate its impact and protect their portfolios from significant losses.

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