John Yang

So we are looking at the shape of the return pattern rather than the absolute return level.

And then we use that standardized historical pattern as the empirical distribution.

We're basically replicating the historical probability of each return level happening in the simulated data.

That works for the majority of the distribution because we have enough observation there, like in the top 90%.

But in the bottom 10%, that's like when this asset class is doing the worst, that becomes a problem.

This is because these events are rare and bad outcomes.

Think about 2020 when COVID happens.

U.S.

equity was down, I believe, 34% in a month when it was like the worst.

So those are sort of outliers if you purely look at it from a data science perspective.

However, from a wealth planning perspective, it is a completely different story because those crises are actually the most important challenges to your wealth plan if you're trying to conserve wealth.

For the bottom part of the distribution, we use extreme value theory.

More specifically, we're using a generalized Pareto distribution.

What it does is it is a specific distribution that is designed to fit those extreme events.

So by combining those two methods together, when we're estimating the marginal distribution of the return of each asset class, we're essentially using historical data where we have enough data.

And then we are using like tail specific model where data is sparse.

Yeah, exactly.

And I wouldn't say manufacturer because it is still based on historical instead of forcing it into a specific bell shape or forcing it to look like historical exactly, which has a lot of zigzags because the frequency those events happen, we fit it with a more appropriate distribution.

And that's how we model the individual asset classes return.

And once the individual return distribution and the cult movement structure are defined, we now use Monte Carlo simulation to generate scenarios.