Why you think Arith mean – 0.5xSD^2 is bad approximation for the geometric mean. I understand that its not 100% perfect for investment returns (which are nearly normal but not normal) but you do know how small the error on that formula is right? If I say the geo return is 1.05% and it truly is 1.0495%, it’s not going to change the portfolio composition.Uncorrelated wrote: ↑Wed Feb 19, 2020 3:37 pmThe academic approach is to use the arithmetic excess return, the return above the t-bill rate. This figure stays stable during periods of inflation/deflation.

I think the idea of calculating the arithmetic return based on anything less than the full sample is an extremely bad idea. There is a wide array of research that suggests that the monthly return of stocks has a correlation of zero with the return of the preceding month. Some academics claim it's impossible to create a better estimate than the average over the full sample.

What is the rationale for using gold, given that gold has a return and correlation with stocks/bonds that are statistically indistinguishable from zero. And that factors (for example, the value factor) have statistically significant positive return? How do you avoid survivorship bias with gold?

I don't think the graphs showing the rebalanced interval can be interpreted with any statistical confidence. The best resource I know about rebalancing is this page: https://www.aacalc.com/docs/when_to_rebalance. Don't forget transaction costs either, 0.5% per transaction seems to be a common figure.

His formula for calculating geometric from arithmetic assumes that the underlying distribution is normal and independently distributed. But if you are using a market timing algorithm, then chances are that you don't believe that returns are normal and independently distributed...jimbomahoney wrote: ↑Wed Feb 19, 2020 1:16 pmYes, I totally get that the arithmetic mean return is 7.6% (take the average of each year's returns).

I also totally get the geometric mean return is 3.1% (take the total period return and raise to one over the total period etc.)

If your risk tolerance is so low you are unwilling to use 2-3x leverage, CAGR is unsuited as a performance metric.jimbomahoney wrote: ↑Wed Feb 19, 2020 11:30 am6) No leverage, or possibly slightly small leverage using the remnants of a low-cost loan if I borrow to get the bathroom done or some such, or remortgage.

I absolutely think investment returns are i.i.d. and I think markets are efficient.