Braden Warwick

So that is the need for the geometric mean.

From that example, it should be clear that if you're doing a multi-year projection, multi-year financial planning projection with a constant rate of return, you need to use the geometric mean.

But if there's volatility included,

If you're able to use a varying rate of return year over year, then you can use the arithmetic mean and sample from that distribution accordingly.

They should match, exactly.

So if you sample from that distribution of arithmetic means, and then you use that data in your financial planning projection, then the geometric mean will kind of come out as the end result.

That's right.

If you have access to the higher order moments of distribution, which we'll get to with our interview with John.

But simply speaking, the difference between the geometric mean and the arithmetic mean is just the volatility drag.

That's what it's called.

And it's nothing crazy.

It's just half of the variance or half of the standard deviation squared.

You can easily calculate that based on the data that we publish in our expected returns paper.

There's nothing really more to it than that.

But it is important.

There's a really important implication when you're calculating the portfolio expected return, because that volatility drag of the portfolio is different than the volatility drag of those asset classes in isolation.

We hear all the time that diversification is the only free lunch in investing.

So I think it's really important that you include those diversification benefits in calculating the expected return of the portfolio.

Let me walk through how to do that.

In our expected return paper, we publish the geometric return of the asset classes in isolation.