Are Recent Stock Market Returns Normal?
Some market analysts and traders think the stock market is a bubble especially after the rally since the start of the year.
Specifically, the S&P 500 index has risen 4.21% in nine trading days since the start of this year. The fact that these gains have occurred at new all-time highs makes them appear not normal to anyone who is not familiar with the longer-term statistical distribution of S&P 500 returns and fuels speculation about a bubble market.
Below is a daily S&P 500 chart since 1960 that includes two return charts. The top return chart hows positive 9-day returns at new all-time highs. The second return chart shows only those positive 9-day returns that are greater than 4.20%.
From the first return chart it is shown that there have been 990 positive 9-day returns at new all-time highs.
From the second return chart it is shown that 139 positive 9-day returns at new all-time highs were greater than 4.20%.
About 14% of all positive 9-day returns at new all-time highs have been greater than 4.20%. This result does not suggest anything out of the ordinary. In fact, in July 2016 the index rose 6.83% in nine days to new all-time highs.
Someone could argue that the whole 9-day sequence started from a new all-time high. The occurrences of positive 9-day returns that start from a new all-time high and those that are in addition greater than 4.2% are shown in the chart below.
There are 232 9-day positive returns starting from a new all-time high and 27 of those are greater than 4.20%.
The proportion of the events under consideration, i.e., returns greater than 4.20% starting from new all-time highs is 10.8% % and that is greater than the usual 5% used for the rare event rule. Therefore, the 9-day return of 4.2% starting from new all-time highs is still well within normal bounds.
If the index returns after the next trading day next week increase to let us say 5% in 10 days, then this will be close to a rare event with 5% rate as shown in the chart below.
There are 12 of the 10-day returns greater than 5% in a total of 235 positive returns starting from an all-time high. This can be called nearly rare and in some loose sense an indication of an over-extended market. Calling a market a bubble requires much more than just looking at returns and this is outside the scope of this article but the author’s short answer is that the U.S. stock market is not a bubble but has developed conditions that may lead to one.
Related articles can be found here.
If you have any questions or comments, happy to connect on Twitter:@mikeharrisNY
About the author: Michael Harris is a trader and best selling author. He is also the developer of the first commercial software for identifying parameter-less patterns in price action 17 years ago. In the last seven years he has worked on the development of DLPAL, a software program that can be used to identify short-term anomalies in market data for use with fixed and machine learning models. Click here for more.
