The Random Walk Hypothesis first emerged in the 1800s and was popularized in 1973 by Burton Malkiel in his book titled, “A Random Walk Down Wall Street”. This theory asserts that stock prices move randomly and can not be predicted by market participants; any observed cycles are purely due to chance.

It is closely linked to the Efficient Markets hypothesis, which argues that all available information is fully reflected in the price of a security, making its price a good estimate of its intrinsic value. In an efficient market, no analyst should perform better than an appropriate benchmark.

The Random Walk Hypothesis has been compared to coin flips, baseball batting streaks, and basketball shooting streaks. Proponents agree that among the thousands of money managers, a certain number are sure to stand out and outperform; however, the belief is this is purely due to chance- just like batting streaks.

But let’s focus on basketball. Cornell academic Thomas Gilovich studied the Philadelphia 76ers in 1985, releasing a paper called, “The Hot Hand in Basketball: On the Misperception in Random Sequences.” Gilovich analyzed each player’s probability of making a field goal after having previously made, or missed a shot; he calculated the results following up to three consecutive made or missed field goals.

Of the nine players analyzed, none appeared to show a “hot-streak” or “cold-streak”. Players did not score any better after making a shot or any worse after missing one. In fact, the correlations were mostly slightly negative, signalling a reversion to the mean as players’ shooting worsened after a made basket or improved after a miss.

Gilovich also looked at the New York Knicks and New York Jets, observing 23 players all together. The data was not broken out for these teams. He noted that Bill Cartwright of the Knicks was the only one of these 23 to show proof of hot-streaks. Daryl Dawkins of the Sixers on the other hand, had a terrific negative correlation when it came to missed shots – with each additional consecutive miss, his odds of scoring a field goal increased.

The study has been highly cited as an example of the public mistakenly seeing patterns in random events, buttressing the argument that stock prices, which seemingly form recognizable patterns, are unpredictable.

A Second Look:

Here is an updated look at some basketball statistics with analysis from 82games.com, a basketball statistics website, which gives a good look at the relationship between the probability of making a shot based on the outcome of a previous shot. It comes as no surprise that on average, the results agree with Gilovich; but things get a bit more interesting upon closer examination.

The following is a look at field goal percentages made by players with at least 800 streak shots. These are big name players who have taken lots of shots (the data is compiled from the 2005-2006 season):

After 1 Make FG%
.539 – Yao
.520 – Garnett
.504 – West
.498 – Wade
.496 – Brand
.494 – Bosh
.492 – Marion
.491 – Nash
.485 – Tony Parker
.482 – LeBron James

Nothing unusual here- if anything, most percentages drop slightly after the first made FG.

Narrowing down to shots made after at least two previous scored field goals, the data changes quite suddenly. Below are 10 players whose shooting improved when shooting after two made field goals:

After 2+ Makes FG%
.637 – Shaq
.635 – Childress
.578 – Curry
.567 – Nelson
.562 – Diaw
.553 – PJ Brown
.542 – Yao
.538 – McDyess
.534 – Garnett
.527 – Gerald Wallace

The site does not provide p-values so I don’t know if the increases are statistically significant, but each of these players saw their shooting percentage after two made field goals improve from their 2005 season average.

Why no 3+ shots? The author deemed this category too difficult, with only Kobe Bryant and Lebron James accumulating over 160 such streaks. Gilovich calls these “runs”, which may not be captured in the broader statistic of improvement over previous shots. Interesting both players are missing from the 2+ list. Statisticians don’t believe there is such a thing as “being in the zone.” If they’ve ever watched these two athletes play, they may think differently. It’s not a matter of shots simply going in- everything goes in; three pointers, fade-aways, contested lay-ups. These guys can be falling to the ground as the ball drops into the basket.

The same goes for missed shots. For some players, misses simply beget more misses:

After 1 Miss FG%
.416 – McGrady
.414 – Hinrich
.404 – Peterson
.397 – Stephen Jackson
.389 – Baron Davis

After 3+ Misses
.389 – Kidd
.382 – Murphy
.375 – Turkoglu
.369 – Alston
.330 – Bobby Jackson

In summary, by looking at a broader pool of players,  we see a good number of players who show streaky performance either in makes or misses. 82games.com does some other interesting shot analysis showing the predictability of some players’ field goal percentages based on prior results, but I think this is enough for basketball.

Bringing things back to the world of investing. Ever since the Random Walk theory had been proposed, many have attempted to disprove it. Lo and MacKinlay of MIT Sloan contributed substantially to this effort, beginning with a series of papers starting with the seminal piece, “Stock Market Prices Do Not Follow Random Walks: Evidence From a Simple Specification Test” in 1988, and culminating with the well-known 1999 book, “A Non-Random Walk Down Wall Street.”

Lo and Mackinlay showed in their studies that stock prices could indeed be predicted, rejecting the Random Walk hypothesis. The 1988 paper analyzed samples from 1962 to 1985, found that for longer holding periods, significant positive serial correlations existed for weekly and monthly returns. The investigators also noted that rejection of the Random Walk hypothesis was possible largely because of the behavior of small cap stocks.

These two men’s findings have practical implications, particularly in biotech investing. The vast majority of biotech stocks are small cap, even micro cap. Because such securities often move in a non-random fashion, their prices are predictable to some degree. Biotech is a sector of relatively inefficient information flow, where products are not always well understood by all market participants, taking it another step further from random behavior.

This leaves an opening for certain analysts to outperform the market indices – and not by sheer luck.