Tail risks

What is a left tail and right tail risk? Can anyone explain please?

In short: left tail events are losses and right tail events are gains.

If you look at a return distribution, you have gains on the right and losses on the left-hand side. The “deeper” you are in the tail (i.e. the further you go right or left), the less likely the event but also the more extreme the outcome. How risky these events are depend on the shape of the return distribution: the same outcome will be more likely under fat-tail assumptions compared to the assumption of normal distributions.

I hope this makes it a bit clearer…

in general, left tail and right tail risks refer to the probability that a random variable X with a given probability distribution is below a certain threshold value (left tail risk) or above some threshold value (right tail risk). for example, the probability that X is below the 5th percentile (or some other small percentile) of the distribution is the left tail risk, while X above, say, the 95th percentile (or some high percentile value) is the right tail risk.

the actual meaning of “risk” will depend largely on the context - what the distribution represents. for example, if the distribution represent capital gains, then the left tail would represent capital gains that are far below average, while right tail “risk” would represent capital gains that are far above the average. if, on the other hand, the distribution represent insurance losses, then the left tail would represent losses that are much lower than the expected amount, while the right tail would represent losses that far exceed the expected amount of losses.

Thanks for your response. I understand downside- left tail risk. But why right tail? making money is never a problem?

for insurance losses, higher values are detrimental, so the insurance companies are more concerned with the right tail risk.