John Yang

Well, Monte Carlo, what it was simply doing is creating many possible future paths instead of pretending there's only one future.

If you're only looking at summary statistics, you're

essentially assuming there's only one possibilities.

And that is what I think is going to happen.

But Monte Carlo generate many possible path.

And on average, they match the expected volatility and expected return that you specify.

One analogy that I really like when I'm explaining this is that expected return and expected volatility is the destination that you set.

And Monte Carlo simulation tells you many different passes that you can get there.

The next part is going to be very useful, especially for wealth planning when the market condition is changing all the time.

I mentioned earlier that we're learning the shape of distribution from history, but we're not necessarily assuming the historical return is going to be the same as what it is now.

Instead, we can impose a forward-looking assumption on our simulation model.

And up to this point, the model has learned the pattern of risk, the pattern of return from the history, but we do not want to simply replay history.

So the model first creates standardized shocks, but now you can re-standardize everything into a standard space, and then you

impose the target return and target volatility on the shock sizes.

Think about the simulation as a generator that's generating shocks, but it only tells you how bad is the shock relative to normal, but you haven't defined what normal is.

And by imposing those mean volatility, you're defining what normal is.

It's actually a lot of fun doing that in the process.

When we were trying to model it in the first place, we kind of assumed the historical meaning is going to be the same as the future because we didn't think that would be an issue.

But when we're doing testing, we realize it is completely off because let's say you take a set of data from the 1990s and then you compare it to today's market scenario.

The distribution of the return can even look very different.