Traditional portfolio strategies and many financial models like Harry Markowitz’s modern portfolio theory, the Black-Scholes Merton option pricing model typically follow the idea that market returns follow a normal distribution.
Under this assumption, the probability that returns will move between the mean and three standard deviations, either positive or negative, is approximately 99.97%. This means that the probability of returns moving more than three standard deviations beyond the mean is 0.03%.
Tail risk is a form of portfolio risk that arises when the possibility that an investment will move more than three standard deviations.
But Stock market returns tend to follow a normal distribution that has excess kurtosis. So tail risk happens certainly more or less than 0.03%.
Although it is rare, it may generate huge negative returns. The tail risk may happen on major fundamental news like Brexit. That’s why we always hedge properly and it is called hedging against the tail risk.
Huge Gap downs and gap ups also fall under tail risk. If one has a position on BANKNIFTY (let’s say), it is always good to have hedged against respective CEs and PEs or other hedging methods.
Stock markets returns are defined by Log (T/P) and hence follow a log-normal distribution.
It’s more realistic than normal distribution hence but we assume a normal distribution in our models to make our life easier.