Unexpectedly Intriguing!
May 16, 2006

Building on our previous post, here is the tool we promised for estimating the best, worst and average annualized nominal rates of return for investments made in the S&P 500 since 1871! The tool below will approximate these rates for any holding period you enter between 1 month and 130 years:

S&P 500 Investment Horizon
Input Data Values
Holding Period for Investment (Years)


Annualized Nominal Rates of Return
Calculated Results Values
Modeled Best Case Return (%)
Modeled Average Return (%)
Modeled Worst Case Return (%)
Code created with assistance from Political Calculations

Note: Given the difficulties in fitting curves around sharp corners, the error between actual and modeled rates of return are greatest for the shortest investment holding periods.

For example, the actual best case one-year rate of return is nearly 140% (recorded between July 1932 and July 1933), while this tool conservatively estimates it to be less than half that value at 60.5%. A similar error occurs in the short time period portion of the worst-case modeled curve, where the calculator will return values far lower than the actual worst case return for these shorter periods of time. The errors may be seen in the vertical spread between the actual data and the modeled curves in the graph presenting the basic data and formulation.

The error comes about as a trade-off for getting accurate estimates of the rates of return for longer investment horizons while limiting the number of very short-holding period calculations that would have to be done to capture the corresponding rates of return for these periods. It can be done, and I leave it as an exercise for an enterprising analyst with more time than myself....

Previously on Political Calculations

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