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