What Goes Up Must Come Down?

LinearRegression-S&P500INDEX-0%Percentile

Relationship between one year’s returns and the next. Essentially, there’s not much of a relationship except in cases of extreme losses, which are often followed by a better year.

Investor Analytics just published the fifth in a series of articles in a new column I have in Risk Magazine’s Hedge Fund Review, which you can find here. The topic for this article is both simple and profound: since 2013 was a great year for stocks, chances are that 2014 will be bad so that the stock market maintains its long-term average. The phenomenon is call “reversion to the mean” and is the underlying logic behind thinking that a sports player is “due” (a fallacy) and for the notion that a tall parent is more likely to have a shorter child (a truth).

We looked at the returns of the S&P 500 over the past 86 years and constructed rolling 1-year windows to generate over 20,000 data points to examine in our hunt for signs that if you have a “good year” that the next year has an increased likelihood of being a “bad year”. It turns out that it’s just not so. You can read the article for the details, but it’s very clear that having a good year really doesn’t change the odds of the next year being good or bad. The average return of the next year is slightly lower than usual, but the range of returns is tremendously wide. Specifically, the overall average for the S&P500 is 7.5%, with a volatility of 20%. That means that for any given year, at the 95% confidence interval, the stock market gives a return somewhere between -25% and +40%. But following a year like 2013 (up 30%), the market returns on average 4.7% with a volatility of 17.5% which translates to a 95% confidence interval between -24% and 33.6%. See the big difference? Neither do I.

The plot in this post shows the overall relationship between two subsequent years: the first year on the horizontal axis, the second on the vertical. The large blob in the middle represents about 98% of the data, which essentially shows that one year tells you next to nothing about the next year.

The graphs we published showed a striking lack of relationship between one year’s returns and the next, except in the most extreme cases. Our conclusion is simple: your risk is not really changed from last year, and this year is has just a good chance of being good as it does of being bad. It’s up to you to make the most of it.