Do Stock Prices Have Memory?

Felix Salmon recently had a post about a bet between Justin Wolfers and Barry Ritholtz on the stock market and trends. Barry took the pro-trend view while Justin stood for random walks. (For the record, Justin won $20 from Barry.)

There’s an emerging amount of literature on this topic and it’s starting to point toward the trend camp. As strange as this may sound, stock prices seem to have a bit of “memory.” One day’s move has an impact on the next day’s move. It’s not big, but it’s there. If the market followed a random walk, this shouldn’t happen. In my mind, this is another chink in the armor of EMH that can’t be easily dismissed.

Here’s a good example of what I mean. Plus, I guarantee you that this is one of freakiest charts you’ll see all day:

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Ok, some explanation is needed. I took every daily change of the S&P 500 from 1950 to today and ranked them, left to right, going from worst to best. The blue line shows the cumulative gain of the next day’s market.

As you can see, if you stayed in after bad days, the market kept going down. After flat days, the market remained somewhat flattish. And after good days, the market continued to rally. Whatever one day’s trend was, it followed through to the next day.

The blue crosses 1.0 at a point that corresponds with a daily gain of 0.64%. This means that the market’s entire gain has come on days following a 0.64% up move. The rest of the time (over 80%), the market is net flat. Half the market’s gain came on day’s following 3.2% up moves. On average, that happens slightly less than once a year.

The black line shows the market’s behavior two days later and it’s much closer to what we would expect, a growing line without any strong discernable trend. Actually, to the extent there is a trend, it seems to be a small reversal from what the market did two days before (notice the strong rise early on followed by a weaker rally). Roughly speaking, two days after the market drops more than 0.8%, the market rises at an annualized rate of nearly 28%.

If the market is trend sensitive, then these reversals are crucial. They appear to happen after extreme moves.

Posted by on February 11th, 2008 at 1:44 pm


The information in this blog post represents my own opinions and does not contain a recommendation for any particular security or investment. I or my affiliates may hold positions or other interests in securities mentioned in the Blog, please see my Disclaimer page for my full disclaimer.