Monday, January 6, 2020

The 20th Century Equity Sine Wave

A while back, probably even before I started blogging, I noticed that US equities in the 20th century seem to follow a fairly steady sine wave.  This is data that Robert Shiller makes available on historical S&P 500 or equivalent values dating to 1871.  Equity returns were fairly linear before 1900, according to this data.  Here, I use total real returns, which includes dividends and is adjusted for inflation.  That's really the only way you should look at long term index returns.  (The values on the y-axis don't match the current value of the S&P 500 because this is in inflation-adjusted dollars, with re-invested dividends.  The trend is important.  The values are somewhat arbitrary.)

Here is a chart of the fitted wave.  This only uses 1900-1999 data, so the last 20 years are out of sample, yet still seem to be following the trend.  Of course there are lots of technical theories about predictable movements in asset prices, most of which are questionable.  There could be a reasonable explanation here, though, having to due with baby boomer types of generational fluctuations, for instance, which might create long-term shifts in real growth rates that are difficult to arbitrage because they literally cross generations.

Anyway, for what it's worth, the sine curve fluctuates from annual total real gains of about zero to about 10%, and we are currently right at the peak, where expected annual returns would be about 10%.  Make of that what you will, if anything.

There is still a standard deviation of close to 30% in the difference between market prices and the fitted curve, but if that means that in, say, 5 years, equity holdings after reinvested dividends would be expected to be worth around 15% to 75% more than they are today, that seems reasonably better than if (using a linear trend line instead) they were only expected to be worth 0% to 60% more.  With equities, it is still the holding period that should dominate one's allocation, because short term noise is the key risk factor.  But, this seems like something to consider on the margins.


  1. Fascinating...and makes intuitive sense.

    In general, I agree with Scott Sumner that there is no such thing as a bubble or a reverse bubble. But that is not totally satisfying. There are times when there is optimism and times when there is pessimism, influenced by recent history. Hyman Minsky had some interesting observations along these lines.

    Of course, the real-world is messy, with demographics and wars and technological advances and even restricted access cities.

    As my late great Uncle Jerry used to say, "If you are not confused, then you probably do not understand the situation."

    1. Great last line, although I don't think Minsky is a helpful corrective.