Unexpectedly Intriguing!
21 January 2005

Update: Political Calculations has mapped the extremes in market performance for the S&P 500 too!

Compared to determining the effective return that an average "investor" can expect to earn from their "investment" in Social Security, working out the best and worst case investment returns from investing in the stock market turned out to be a breeze!

It turns out that there are whole bodies of scholarly work that have been done in this area with results that have been posted on the Internet. There are two sources I recommend. The first is an excerpt from mutual fund pioneer John Bogle's book, Bogle on Mutual Funds that shows the general trend between investment holding period and the best and worst case performance of the stock market between 1926 and 1992.

The second source, an interactive example provided by the Foundation for Investor Education, takes inflation-adjusted stock market performance data for a variety of holding periods from work done by Wharton School professor Jeremy Siegel, whose book, Stocks for the Long Run covers his research into the history of U.S. stock market returns since 1802. The following table shows Siegel's best and worst case historical stock market returns, which have been adjusted for inflation:

Inflation Adjusted Stock Market Annual Rates of Return
Holding Period (years) Worst Case (%) Best Case (%)
1 -38.6 +66.6
5 -11.0 +26.7
10 - 4.1 +16.9
20 + 1.0 +12.6
30 + 2.6 +10.6

I used Siegel's data to create the best and worst case, inflation-adjusted, stock market performance formulas below, using various regression techniques available in Microsoft Excel (and some other mathematical manipulation) to come up with the equations:

Best Case Stock Market Return = 62.212 * (Holding Period)-0.5167
Worst Case Stock Market Return = -49.742 * (Holding Period)-0.5587 + 10

In these equations, "Holding Period" represents the number of years that the stock market investment is held. Investors should note that Siegel's work is based on the performance of the entire U.S. stock market, which today may be best be tracked through the performance of the diversified Wilshire 5000 stock index. I've provided a simple calculator that performs this math below for reference:

Stock Holding Period
Input Data Values
Holding Period (Years)

Annualized Stock Market Rates of Return
Calculated Results Values
Best Case (%)
Worst Case (%)

Additional Note: Since the formulas are based on a limited number of data points, the results calculated will only approximate historical inflation-adjusted rates of return over time, with greater differences between historical and calculated results at very short holding periods, a result of the regression method. For long term results, the formulas also deviate from what would be expected due to the limited number of data points used to create the formulas (after 93 years, the worst case calculated return is higher than the best case calculated return!) As a result of this long term conflict with reality, I arbitrarily placed the effective long-term useful limit of the formulas at a holding period of 75 years for the Social Security versus Private Retirement Accounts comparison calculator, which should provide reasonably good approximations of returns without too great a discrepancy with what would actually occur in real market performance.

Update: Want to see what the future value of a fully diversified stock market investment might look like if you consecutively kept having the best or worst market performance over time? Take the Lemony Snicket vs. King Midas challenge today!

Update 30 July 2007: We've gone way beyond this tool! For the most recent analysis we've done, see our following posts:

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About Political Calculations

Welcome to the blogosphere's toolchest! Here, unlike other blogs dedicated to analyzing current events, we create easy-to-use, simple tools to do the math related to them so you can get in on the action too! If you would like to learn more about these tools, or if you would like to contribute ideas to develop for this blog, please e-mail us at:

ironman at politicalcalculations

Thanks in advance!

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