Updated on Sun, 08 Nov 2020 03:01:01 GMT, tagged with ‘finance’.
2021 Feb 10 Update Earlier versions of this essay were, as many thought, plagued with a bug that severely underestimated long-term returns. A thousand apologies! The rest of this essay has been compressed to summarize the updated (and hopefully correct) findings.
Imagine. It's 1871. A promising young American has just entered the workforce and makes it a point to buy $100 of the S&P 500 index every month, with dividends reinvested, over a forty year career. It's now 1911. Our American, about to retire, stops these monthly purchases and asks, "What is the real return I achieved in excess of risk-free Treasuries over my forty-year investing horizon?" Answer: 3.6%.
Imagine now that every year after 1871, we can find one such promising young American to join the work force and to do the same thing: monthly-dollar-cost average into the S&P 500 index for forty years.
And similarly, for not just forty years, but for other time horizons.
The plot below shows the real excess return of the S&P 500 over risk-free Treasuries for a few time horizons, from ten to a hundred years. Thanks to Plotly, it's interactive so you can click, tap, zoom, pan, pinch, etc. You can turn off a line you don't want to see by clicking or tapping it in the legend.
Now, for each line above, you can imagine plotting a histogram of returns, showing the distribution of excess real returns you can expect over 10 year, 20 year, etc. horizons.
Finally we can convert each histogram above to a cumulative histogram below. This lets us answer questions like,
(Reminder, you can click on the legends above to turn off and on different lines and see just the horizons you want. You can also zoom, pan, etc.)
Some nerdy details: Robert Shiller's online dataset contains monthly numbers for the S&P 500 index's price (dollars per share), dividends (dollars per month), and 10-year Treasury yields, all starting in 1871. I assume you invested $1 at the beginning of each month, reinvesting the dividends that accrued over the previous month. After 480 such buying sessions (for forty year horizons), I calculate the internal rate of return (XIRR) by assuming the entire portfolio was liquidated, which is just an accounting choice to answer the question, "what real return did the S&P 500 yield over this forty year horizon after monthly dollar cost averaging".
I then do a similar exercise with Treasuries: every month I assume you put that $1 into a savings account-like vehicle that pays interest monthly at the same rate as the 10-year T-note's. XIRR again computes the internal rate of return, over the same time horizon. Excess return is just the S&P's real return minus the Treasuries' real return, and is expressed in a percentage just like any rate of return. Because inflation aflicts stocks and bonds equally, excess return is also the real excess return. (You can inspect the TypeScript code.)
Nota bene To those seeking to apply Dr Damodaran's Historic Returns dataset to check this analysis, please note that the annual returns on thirty-year Treasury bonds appear to be on the price of the bond itself, rather than the bond's yield over that year. For example, T-bonds in 2013 are shown to have -9.1% return but we see from DGS30 Fed time series that during 2013, the constant maturity rate for thirty-year bonds was between 2.8% and 3.9%. (Damodaran's annual returns for the three-month T-bills seems to jibe well with the Fed's DGS3MO numbers though, and might be an acceptable proxy for the ten-year T-note yields in Shiller's dataset.)
(Banner: a crop from "The Monitor and Merrimac: The First Fight Between Ironclads", chromolithograph by Louis Prang & Co., 1886. Wikimedia)
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