Anyone Who Understands Financial Math Will Get This

December 23, 2015

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:

Yellen Comment

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.

One response to Anyone Who Understands Financial Math Will Get This

  1. 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!