问一道题：NO.PZ2020011101000030 [ FRM I ]

问题如下：

If returns are fat-tailed, and we instead assume that they are normally distributed, is the probability of a large loss over-or under-estimated?

解释：

We will underestimate the probability of a large loss because the normal has thin tails. For example, the probability of a $4\sigma$ loss from a normal is .003% (3 in 100,000). The probability of a $4\sigma$ loss from a standardized Student’s $t_4$ is .24% or 80 times more likely.