“Doing the Numbers” — What Nuclear Physics Can Teach Us About the Stock Market

“The trouble with the profit system has always been that it was highly unprofitable to most people.” —E. B. White

“We’ll have the details when we do the numbers” is one of the ritualized comments of the hosts of the popular NPR radio show Marketplace. The same ritual can be found every day in countless newspapers and websites. Interestingly, the song that NPR plays if the market’s outcome that day is mixed is “It Don’t Mean A Thing (If It Ain’t Got That Swing)”. The show’s hosts, I suspect, have no idea how apt that song is regardless of what the market does.

I am not an economist. However, as a nuclear physicist, I have been examining the disintegration of radioactive nuclei for years. It’s an innocuous pursuit; no bombs or anything sinister comes from this research. But, unlikely as it may seem, the results can tell us a lot about the stock market.

Quantum mechanics, the most fundamental theory of matter that physicists have developed so far, predicts that radioactive nuclei decay independently and randomly. That means there is no information whatever in a time series of disintegrations to allow us to determine how many nuclei will decay at any subsequent moment in the future. Nuclear decay, to adapt a phrase, is the Mother of All Randomness. Nothing in the universe is supposed to be more random than that.

No experimental test can actually prove that radioactive nuclei decay randomly, but it is possible to test whether they decay nonrandomly. Several particularly sensitive means to do this are to look for correlations, periodicities, and runs.

If at some moment a greater (or lesser) number of nuclei than average for the series decay, and one finds that fluctuations of this kind recur after certain intervals of time, then the decays are not independent, but correlated—and this correlation can provide useful predictive information. The correlation function quantifies the correlations for all intervals within the duration of the time series.

If the mean number of disintegrating nuclei varies periodically, then the process causing the nuclear disintegrations is again not random. The Fourier transform finds all such periods within a time series.

Finally, if the record of disintegrations were to contain some long sequences of counts in which each count was greater (or lesser) than the preceding one, you might think the decay process was not random because such “runs” of increasing (or decreasing) numbers would signify a certain degree of order or organization, whereas a series of random numbers must be...well, random, i.e. without any order. You would be wrong. A long list of random numbers contains a predictable number of long runs, otherwise the series could not be random. Humans who see patterns in data frequently deceive themselves into thinking the data contain information.

Having tested various kinds of nuclear decay by these and other measures, I was able to conclude in every investigation that there was no reproducible evidence to suggest nonrandom behavior. The results did not overthrow quantum mechanics, but they were published1 because in science it is always important to test one’s beliefs carefully and thoroughly.

The daily closing prices of stocks in a stock market provide another time series of numbers. For a while the series may rise; shareholders are happy and economists will tell you that the market is doing well. Then things change; the series may fall; shareholders are unhappy and economists will now tell you that the market is doing poorly. Economists will always have reasons for why the market is not doing well and solutions to fix the problem.

But maybe there isn’t a problem.

I have examined the change in daily closing prices of numerous stocks with the same tests I used to search for nonrandom behavior in the disintegration of radioactive nuclei. I looked at the records of a broad range of companies from before the financial meltdown as well as afterward. And here are the results: In no instance did I find evidence of predictably useful nonrandom behavior. Correlations, periodicities, runs, and other statistical indices showed that for all practical purposes of prediction, each company or fund could well have been some kind of radioactive nucleus. Physicists call this kind of randomness “white noise”, a name that refers to a broad, flat spectrum of frequencies, rather than to the preponderance of Caucasian traders in the New York Stock Exchange. Moreover, the “white-noise” character of these track records seemed to be independent of economic, political, or social perturbations. The implications of these results, if they accurately characterize stock price fluctuations, are consequential.

First, you have undoubtedly read or been told whenever you invest that “Past performance is no guarantee of future results.” Believe it! If your experience is like mine, however, you can sense the prospectus winking at you as it offers this warning (usually in small font size) because the company executives really don’t want you to believe it. In one flyer I received from TIAA-CREF, the warning was followed by another sentence (in larger font size) that claimed to offer me “a track record of competitive investment performance.” Competitive in regard to what—other random processes? If the prospectus were completely truthful, the warning would read more strongly: “Our past performance—i.e. track record—is no more correlated with future results than is the decay of radioactive nuclei.” Of course that might not mean much unless the reader were a physicist.

Second, if the fluctuations in share price of a stock fund contain no useful information, then it evidently matters little what the fund manager does. You might want to think about that if you are paying management fees. Moreover, if your financial advisor selects investments for you on the basis of a company’s track record—i.e. past performance—you are paying for advice of no greater predictive value than if you selected funds yourself by dartboard, coin toss...or nuclear decay. You might want to think about that too if you are paying for the financial advice.

Third, if the change in closing price represents “white noise”, then it follows mathematically that the record over time of the closing price itself exhibits a different statistical pattern known as “Brownian noise”, one characteristic feature of which is “persistence”. Brownian noise has long correlation times. Brownian sequences show long upward trends that inexorably reverse to long downward trends and vice versa, not as a result of any specific cause, but simply because that is what Brownian noise does2. Bear that in mind the next time you are told to “buy and hold” or when some economist either gushes about a market upswing or grieves over a market downswing.

When all is said and done, there are basically three ways to do well in the stock market:

  • The first is by luck. In any game of chance— and investing in the stock market is the equivalent of a crapshoot—there will be some people who win although most usually don’t.
  • The second is to have information that other investors do not have. This is known as insider trading and is ordinarily illegal—except, apparently, in the case of members of Congress. A recent statistical study3 of the annual average stock performance of US senators in relation to the market has shown that US senators beat the stock market by 12.3% during a period when the average American household had a (negative) return of -1.5%.
  • The third is to be very wealthy. Mathematical analyses of games of chance (e.g. “gambler’s ruin”) show that the greater the initial capitalization, the lower is a gambler’s probability of ultimate loss. With regard to the stock market, the more capital you have, the better you can absorb losses from high-risk ventures that promise—and with an estimable probability deliver— exceptionally high returns. When, following the financial meltdown, Warren Buffett wrote a New York Times op-ed piece4 “Buy American. I am”, he expressed the irrationally optimistic view that “Over the long term, the stock market news will be good.” That expectation may or may not be true; if stocks are like radioactive nuclei, then there is little reason to believe it. (If the term is long enough, the investor is dead and his interest in the stock market is considerably diminished.) What Buffett neglected to mention, however, is that his wealth enabled him to undertake risks that would be unwise for the average investor, so that irrespective of the outcome, he will still end up wealthy whereas those of modest means who follow his advice may lose most of their savings.

There is actually a fourth way to do well in the market—at least for a short while—if you have access to super-fast computers, a steady stream of market data, your own brokerage firm, and clever programmers. With these resources you can search for and take advantage of transient market disequilibria on the time scale of seconds, while the rest of “ordinary” investors—even including members of Congress—can, at best, access market data from the internet.

In short, the result of “doing the numbers” with nuclear physics is to realize with near mathematical certainty that investing in the stock market is no different from gambling in a casino—but for one important distinction. The latter is done by choice for amusement with money people can afford to lose (if they gamble responsibly). However, for the increasing number of workers who are required to secure their retirement income from some kind of defined contribution plan, the gambling is done out of necessity with money they will need to live on.

  • 1. M P Silverman and W Strange, “Search for correlated fluctuations in the decay of Na-22”, Europhysics Letters 87 (2009) 32001.
  • 2. M P Silverman, “Computers, Coins, and Quanta: Unexpected Outcomes of Random Events”, A Universe of Atoms, An Atom in the Universe (Springer, 2002) 279-324.
  • 3. A J Ziobrowski, P Cheng, J W Boyd, and B J Ziobrowski, “Abnormal Returns from the Common Stock Investments of the U.S. Senate”, Journal of Financial and Quantitative Analysis 39 (2004) 661-676.
  • 4. W Buffett, “Buy American. I am”. The New York Times, October 17, 2008

This paper was originally submitted to the Wall Street Journal in 2009.

About the author

Mark P. Silverman is Jarvis Professor of Physics at Trinity College. He wrote of his investigations of light, electrons, nuclei, and atoms in his books Waves and Grains: Reflections on Light and Learning (Princeton, 1998), Probing the Atom (Princeton, 2000), and A Universe of Atoms, An Atom in the Universe (Springer, 2002). His latest book Quantum Superposition (Springer, 2008) elucidates principles underlying the strange, counterintuitive behaviour of quantum systems.