Interpreting Left and Right Tail Risk in Return Distributions

Summary

The document explains that left and right tail risk refer to extreme outcomes on opposite sides of a return distribution. The left tail represents unusually poor returns, while the right tail represents unusually high returns. Analysts examine these outcomes to understand exposure to rare but consequential moves.

It connects tail behavior with skewness: strategies with negative skew may generate frequent small gains alongside occasional large losses, while option-like strategies can show positive skew. The discussion points to downside-focused performance measures, such as the Sortino ratio, as an alternative to the Sharpe ratio when an analyst wants to distinguish downside variability from upside variability. These are conceptual examples rather than a detailed estimation procedure. The document offers no empirical comparison or guidance on selecting thresholds, and its simplified reference to standard deviations should not be treated as a complete model of tail probabilities, especially when returns are not normally distributed.

Key ideas

• The left tail describes extreme negative returns, while the right tail describes extreme positive returns.
• Skewness helps characterize whether a return distribution has a longer or more influential loss or gain tail.
• Negative-skew strategies may pair frequent small gains with occasional large losses.
• The Sortino ratio focuses on downside risk, unlike the Sharpe ratio's broader volatility measure.
• Tail analysis can help assess the impact of rare, significant return events.

Tags

# How does left tail risk differ from right tail risk?


# How does left tail risk differ from right tail risk?












How does left tail risk differ from right tail risk? In what context would an analyst use these metrics?

## Answer by Shane (score 7)

https://quant.stackexchange.com/a/506

Here's a partial answer:

- This partly depends on the return characteristics. One way to look at this is to analyze the skewness and kurtosis of the returns. Most strategies have a negative skewness, which roughly means that they have mostly consistent small positive returns, with the occasional large negative return. Alternatively, some strategies have "option-like features", which results in the opposite distribution: positive skewness. See, for instance "The Risk in Hedge Fund Strategies" (Fung, Hsieh 2001).

- You might want to look at some of the work done on "post-modern portfolio theory" (PMPT) which attempted to differentiate between upside and downside risks. As an example, one simple adjustment based on this would be to use the Sortino ratio instead of the Sharpe ratio as a risk/reward metric.

## Answer by G__ (score 5)

https://quant.stackexchange.com/a/505

Tail risk represents the probability that the magnitude of returns on an asset/portfolio will exceed some threshold (usually three standard deviations) on the normal curve. If you visualize a normal curve on standard axes, the tail on the left side corresponds to an extreme low return and the tail on the right side corresponds to an extreme high return.

In other words, left vs right is a measurement of (the likelihood of) extreme low or high returns. An analyst might look at these in order to estimate the impact of rare but significant events.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.