**Long-Term Equity Returns, the Power of Compounding,and the Indians**

It has been estimated in various studies that the long-term average expected return from equity investments is 10%. If this is so, then the mathematically inclined might amuse themselves with the following circumstance.In 1626, Peter Minuit purchased Manhattan from the Indians for the equivalent of $24worth of merchandise. Had the Indians received $24 in cash, they might have invested this money in an index fund tied to the performance of the S&P 500 (were it then available). Given these marvelous possibilities, had the Indians received a 10% compound annual return, they would possess today a sum equal to 45.09 X 10 16 dollars. This is in excess of 45 quadrillion dollars.

Since such sums are beyond the daily experience of most individuals, the magnitudes become rather difficult to comprehend. It is therefore necessary to place this number into proper context. The current GNP of the United States is approximately 6 trillion dollars.The Indians would therefore possess 7,515 times the GNP of the U.S.

The reader may come to a variety of conclusions from a study of such absurdities. One can conclude that the Indians were extraordinarily poor investors. However, one can also conclude that an expected return of 10% per annum leads to ultimately ludicrous conclusions.

A reasonable means of estimating future equity returns would be to forecast the growth rate of nominal GNP. The nominal numbers are important in this connection since they include the effects of inflation on equity returns. In the long run, the equity market cannot grow faster than nominal GNP, since its value is ultimately derived from the value of goods and services produced.

If the future inflation rate were 3% per annum, then nominal GNP could be 10% per year only if the real GNP growth rate per annum were 7%. Of course, no creditable forecaster would predict such robust growth in the future. Indeed, even if this growth were achievable, it would be unlikely to be achieved with merely 3% inflation.

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