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Fun with Compounded Annual Growth Rates (CAGR).

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Fun with Compounded Annual Growth Rates (CAGR).


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This article was posted on June 1, 2001.

One frequent complaint often heard from financial professionals is that "you can't rely on constant average returns -- they don't reflect reality." Obviously, that's true with respect to withdrawal rates from a retirement portfolio. (While the stock market has returned about 10% per annum over tha past 130 years, the "100% safe" withdrawal rate is only about 4% per year, adjusted for inflation, see link.) However, during the accumulation phase, while you are building your retirement nest egg, using compounded average growth rate (CAGR) to estimate your investment returns comes very close to real life experience.

The first table below shows the maximum, median, and minimum compounded annual growth rates for holding periods from 10 to 60 years using Shiller's 1871-2000 S&P500 database. The second table lists the portfolio balance at the end of the holding period for an investor contributing $2,000 per year at the CAGR indicated with investment expenses of 0.17% per annum. The third table assumes the same $2,000 per year investment, but with ACTUAL annual investment returns year-by-year from Shiller's database. Finally, the fourth table shows which method yielded the highest portfolio balance at the end of the holding period. In 10 out of the 18 cases examined, CAGR underestimated the actual ending portfolio balance. In other words, CAGR errs on the conservative side.

Don't let an insurance or investment salesman tell you that CAGR "doesn't work", and use that as an excuse to sell you a product with a low "guaranteed" investment return -- and a high commission for the salesman.


Returns for the S&P500 (Shiller 1871-2000 database), dividends reinvested

Holding Period
. 10 Years 20 Years 30 Years 40 Years 50 Years 60 Years
Number of
Periods
Examined
120 110 100 90 80 70
Distribution of the Componded Annual Growth Rates (CAGR) for the holding periods examined, S&P500 index, exp. ratio = 0.00%
Max 19.08% 17.14% 13.40% 12.03% 13.23% 12.53%
Median 8.33% 7.81% 9.37% 9.14% 8.98% 9.18%
Min -1.23% 3.30% 5.13% 5.44% 5.65% 5.91%
Value at end of holding period for $2,000 per year invested at CAGRs in table above, S&P500 index fund, exp. ratio = 0.17%
Max $58,502 $303,107 $694,550 $1,650,738 $7,996,603 $19,766,410
Median $31,576 $94,625 $309,031 $730,487 $1,658,606 $4,258,840
Min $18,523 $56,162 $138,514 $271,729 $516,034 $1,012,013
Value at end of holding period for $2,000 per year invested, ACTUAL returns from Shillers' 1871-2000 database, S&P500 index fund, exp. ratio = 0.17%
Max $60,932 $279,517 $909,843 $1,998,073 $5,724,833 $21,279,008
Median $30,233 $95,996 $250,368 $842,441 $2,060,251 $4,807,616
Min $15,484 $54,083 $122,071 $277,117 $534,981 $1,010,311
Which provides a larger value at the end of the holding period, CAGR or ACTUAL historical returns?
Max ACTUAL CAGR ACTUAL ACTUAL CAGR ACTUAL
Median CAGR ACTUAL CAGR ACTUAL ACTUAL ACTUAL
Min CAGR CAGR CAGR ACTUAL ACTUAL CAGR

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Copyright 2001 John P. Greaney, All rights reserved.

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