Geometric mean vs. CAGR

This is Challenge Problem 1C from Schweser’s “Structural Concepts and Market Returns” section in Study Session 2.

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Table

Year / Year-End Share Price / Year-End Dividend / Holding Period Return

2004 / $28.50 / $0.14 / N/A

2005 / $26.80 / $0.15 / -5.44%

2006 / $29.60 / $0.17 / 11.08%

2007 / $31.40 / $0.17 / 6.66%

2008 / $34.50 / $0.19 / 10.48%

2009 / $37.25 / $0.22 / 8.61%

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I understand that geometric mean and CAGR are supposed to be equivalent. When I calculate:

Geometric mean: ((0.9456)(1.1108)*(1.0666)*(1.1048)*(1.0861))^(1/5)-1 = 6.10%

CAGR: ((37.25+0.22+0.19+0.17+0.17+0.15)/28.50)^(1/5)-1 = 6.01%

Can somebody explain the fallacy of comparing these two calculations?

Thanks!

The second ignores the time value of the dividends.

Thanks, that was my gut instinct, but I couldn’t validate the logic in my head because I always viewed CAGR as a computation of total return — since you’re not earning any interest on the dividends.

Playing around with it, I think it has less to do with time-value, as opposed to where you’re money-weighting the dividends. For example, if I take the sum of the dividends received ($0.90) and applied to any single-year, theoretically, receiving the dividend in the earlier years should be worth more than receiving them in the later years, due to TVM. Using this concept, I would also expect the CAGR formula presented above to yield the same result as back-weighting all dividends to year 5 and calculating the geometric mean (which it does).

If, however, the stock price showed a loss as opposed to a gain, the TVM of the dividends should still be worth more in the earlier years than the later years. I changed the stock price to start at $37.00 in year 0 and fall by $1.00 every year, while keeping the dividend the same. The return of the stock is the same regardless of when you receive the dividend, however, if I weight all $0.90 of the dividend in year 1, I get a geometric mean of -2.38%, whereas if I weight it all in year 5, I get a higher geometric mean of -2.32%. Under TVM, I would expect receiving a positive cash inflow earlier on would raise the rate of return (unless, of course, there’s a negative discount rate).

I think I answered my own question as I was typing this out…