The following is a screen capture of a comment exchange between BG (the same BG who comments on posts here at AFM) and Pamela Yellen:

Ms. Yellen doesn’t understand that compound annual growth rate (CAGR) is the same as the average annual return.

The calculation is very simple. Using the VFINX adjusted closing price of $95.51 on 12/19/2005 and the closing price of $188.21 on 12/18/2015, we can calculate the CAGR or average annual return like this:

**[(188.21 ÷ 95.51)**

^{1 ÷ 10}] – 1**[1.970545**

^{.1}] – 1**1.070184 – 1**

**.070184 or 7.02%**

THIS is the return that investors should be concerned with.

The average return (also known as the arithmetic mean), which is simply adding up all the one-year returns and dividing them by the number of years, would have been a much higher, but misleading, 8.92%.

Be wary of anyone who calls themselves an expert.

She doesn’t seem to grasp that you can not invest in the S&P500, except via an Index Mutual Fund. VFINX is Vanguard’s index mutual fund that tracks the S&P500, and VFINX has a ‘beta’ of 1.00 — meaning that it tracks the S&P500 perfectly. The fund has a slightly negative ‘alpha’, which is caused by that indeed funds fees.

So her first remark against using VFINX as a proxy for the S&P500 index is without merit.

Then she discusses CAGR (which is good), but fails to realize that she did not use CAGR when coming up with her 2.15% claim of S&P500 returns. Of course, the numbers I gave her were the actual CAGR annualized returns (which I had copied from the morningstar.com website).

Merry Christmas!