202 Frequently Asked Questions In Quantitative Finance
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Scaled return
SPX Returns PDF
Normal
Figure 2-11:The standardized probability density functions for SPX
returns and the Normal distribution.
Over that period it was 0.0106, equivalent to an average
volatility of 16.9%. What is the probability of a 20% or
more fall when the standard deviation is 0.0106? This is
a staggeringly small 1.8 10−^79. That is just once every
21076 years. Empirical answer: Once every 20 years.
Theoretical answer: Once every 2 10^76 years. That’s how
bad the normal-distribution assumption is in the tails.
Long Answer
Asset returns are not normally distributed according to
empirical evidence. Statistical studies show that there
is significant kurtosis (fat tails) and some skewness
