# Compounding Outcomes

Suppose the following example, taken from the book Fooled by Randomness by Nicholas Taleb.

As of writing this, the World Bank life expectancy for the US is 79 years. That is to say, the average person at age 0 has an expected lifespan of 79 years. But what does this mean for the person at 30 years? What about 80?

As Taleb points out, each year you survive, your personal life expectancy increases from 79 as others your age and younger have died, taking your spot in the statistics. An 80-year-old is not implicitly dead because they lived beyond the life expectancy, nor is their life expectancy ever below 80.

The probability an 80-year-old will live to 90 is higher than that of a 20-year-old. This is because they have already beat the average.

## What does this mean for trading?

Suppose the excepted value for RTH ES ranges is 40 pts. If we go beyond 1 sigma of range, the probability we go to 2 sigmas is now much higher than any ordinary day. The probabilities compound. As it turns out, each day in the market is not independent of the prior, making the 'normal distribution' a foolish tool to use without a tablespoon of salt.

This is why we see 2/3 sigma events cluster. When there is elevated volatility it tends to cluster.

One should look into their own forward tested statistics, do they have a similar compounding probability? How often do your winners (could be defined in R-value instead of just +/- outcome) cluster? Do probabilities of you hitting your target compound? That is to say, if we go 3 pts in your favor, the probability we will now trade to your potential destination has increased substantially?

These questions are vitally important for a trader to understand about their own trading, it impacts expectations and risk management. Never discount probabilities compounding, this is, after all, what helps materialize the notion of 'fat-tailed' distributions.