In this, the fourth and final post in our Math Matters series, we discuss the distribution of returns and how investors react to “tail” events.
Everything we discussed previously in this series, “Compound Growth”, “The Importance of Avoiding Large Losses”, and “Volatility is a Drag”, culminates with this post on the shape of the distribution of returns.
In the image below we see the textbook definition of a normal Gaussian distribution. Most of the occurrences fall near the mean value, while a few data points occur far from the mean. If a set of data over a long period of time falls into this pattern, then we can make assumptions about future occurrences with a high degree of accuracy.
However, in the real world two unfortunate facts collide with this theory and are impediments to an investor’s long-term success:
When these tail events do occur, investors tend to make poor choices.
Actual market returns do not fit the nice, clean, symmetric layout of the normal distribution.
It is often said that two things drive the market: fear and greed. That might not be true all of the time, but it does appear to be true when markets are at their extremes.
A recent study by DALBAR found that the average investor did much worse than the broad market. Moreover, the biggest gaps in underperformance tended to happen when markets were experiencing “tail” events.
Anyone with market experience will recognize the culprits: panic selling in a bear market, chasing after “hot” stories in a bull market, selling low and buying high…all of these are quantified in the above table. And in the previous posts on the mathematics of investing, we’ve seen how hard it is to overcome these mistakes once they happen. Sadly, investors are often their own worst enemy.
Another issue is that actual market returns don’t fit the idealized normal distribution.