Benjamin Felix

For sure.

And then the geometric mean of that distribution, well, would be the geometric mean, I guess.

If you've run a bunch of simulations using the arithmetic mean and the other moments of the distribution that you have, the geometric mean of those distributions will be same as the calculated distribution.

If you're sitting down using Excel or whatever to do a projection and you're just using a constant rate of return, you want to use the geometric mean.

But if you're sitting down and simulating a whole bunch of possible returns, you need to use the arithmetic mean and the other moments of the distribution.

Yeah, it's really interesting.

If you're not doing that, if you're not going through those steps to calculate the portfolio level expected return, you're underestimating your expected returns and you're ignoring the effects of the positive effects of diversification.

constantly nerding out, looking for little things like that.

It matters.

As you mentioned, it does increase the expected return that we're using as an assumption, which changes the advice on like, how much can you spend in retirement?

How much do you need to save like this stuff?

Now the future is super uncertain, but I would still say that this stuff matters.

Definitely.

So real quick, right now, when we do our simulations, returns are modeled as random.

We're defining the mean, the standard deviation, the correlations, and then we're just pumping out a thousand simulations.

It's a pretty basic simulation process.

John Yang, we're going to go to our interview with him in a second.

He's going to talk about what him and his student group did for their industry project and how it changed

how they came up with an improved way to do the simulations.

And then once we've talked with John Braden, you've got some really interesting analysis on how using their simulation process instead of ours changes, long-term projections and what they specifically change and why it's anyway, super interesting.