MIretired wrote: ↑Sat Sep 01, 2018 12:47 am
siamond wrote: ↑Fri Aug 31, 2018 11:48 pm
Yes, annual rebalancing is implicitly assumed. And yes, the portfolio return is weighted by the portfolio components. I am not sure to understand your formula in this case though. If Rs = stocks return, Rb=bonds return; Ws and Wb = respective portfolio weights, the portfolio return is Ws(1+Rs)+Wb(1+Rb)-1. Or more simply Ws*Es+Wb*Eb.

Well. Right about the not dividing the weighted returns. It's an addition of weights. Or called weighted return. But I've sensed something else: but in a sense you answered.

To get the 5 yr CAGR, you must have run the annual rebalancing returns of each AA independently.You just take the sets of 5 each annual returns. Then compound the desired weighting of each 5 times(or 4.)

Ok, let me take this step by step. Each cell of the table includes

annualized returns for time intervals of 5 (or 10) years, inflation-adjusted, for a given Asset Allocation made of US stocks and bonds. Annualized returns mean the (geometric) average return per year that would produce the same compound growth as the actual returns over this time interval.

First thing in a spreadsheet is to use the nominal annual returns of the individual asset classes (here US stocks and bonds) to infer the portfolio annual returns, as we just discussed. If Rs = stocks return (nominal), Rb=bonds return (nominal); Ws and Wb = respective portfolio weights; then NRp (nominal portfolio return for this year) is: NRp = Ws*Es+Wb*Eb.

Then we need to adjust for inflation, to get from a nominal number to a real number. To do this, we need to geometrically subtract the effect of inflation for this year. If Ius = inflation in the US, then the RRp (real portfolio return for this year) is: RRp = (1+NRp)/(1+Ius)-1.

Now let's take those numbers for 5 years in a row: RRp1, RRp2, RRp3, RRp4, RRp5. Now the question is, what the corresponding annualized (average) return, also known as Compound Annual Growth Rate (CAGR) for this time interval? You can look up the exact mathematical formula on

Wikipedia, but spreadsheet software like Excel provides a very handy function for this, and the way I do it is the following: GEOMEAN(1+RRp1, 1+RRp2, 1+RRp3, 1+RRp4, 1+RRp5)-1.

I hope this helps... Maybe some of us should create a few wiki entries about the math of investments with spreadsheets...