Paul Samuelson

Paul Samuelson was an American economist, born in Gary, Indiana in 1915. He took his first degree at the University of Chicago and his doctorate at Harvard, where Joseph Schumpeter and Wassily Leontief were among his teachers, and joined the Massachusetts Institute of Technology in 1940, building its economics department into one of the strongest in the world.

His Foundations of Economic Analysis, published in 1947, rewrote economics in mathematical form and is largely responsible for the field looking the way it does. The following year he published Economics, an introductory textbook that went through nineteen editions and taught the subject to several generations. In 1970 he became the first American to receive the Nobel Memorial Prize in Economic Sciences.

Two pieces of his work reach investors directly. The first is a 1965 paper, Proof That Properly Anticipated Prices Fluctuate Randomly, which shows that if a price already incorporates expectations about the future, then changes in it must be unpredictable. The randomness is a consequence of anticipation rather than evidence of disorder, and this is one of the foundations the efficient-market literature was built on.

The second is more direct. In 1974, in the first issue of the Journal of Portfolio Management, he published a short article called Challenge to Judgment arguing that most active managers did not beat the market and that somebody should therefore establish a fund that simply tracked an index. Jack Bogle launched the first index fund available to ordinary investors two years later and repeatedly credited that article as a spur.

He also spent years arguing against the Kelly criterion as a general objective, on the grounds that maximising the long-run growth rate of wealth does not follow from expected utility for investors whose preferences differ. He made the point in 1979 in a paper written almost entirely in words of one syllable, apparently to remove any excuse for misunderstanding it. He wrote a Newsweek column from 1966, alternating with Milton Friedman, and passed away in 2009.

Samuelson's 1965 result is more careful than the way it is usually reported. He did not prove that markets are efficient or that prices are correct. He proved something narrower and more durable: that if a price already reflects expectations about future events, then the change in that price must be unforecastable, because any forecastable part would already have been incorporated. Randomness is therefore what a well-anticipated price should look like, and observing it tells you about anticipation rather than about wisdom.

The 1974 article turns that into a practical position, and it is unusual for an academic argument in that it names a product that did not exist. His claim was that the evidence on active management did not support its cost, that a fund tracking an index would serve most investors better, and that since no such fund existed for ordinary people, someone ought to build one. He wrote that if nobody would do it, a university endowment should. Bogle did it two years later.

His disagreement about the Kelly criterion runs the other way and is worth understanding alongside the indexing argument, because both are about not overclaiming. Maximising the expected logarithm of wealth produces the highest long-run growth rate, which is a real mathematical result. Samuelson's objection was that this is only the correct objective for an investor whose preferences happen to match that formula, and that presenting it as universally optimal smuggles in an assumption about risk tolerance that most people do not share.

The thread across all three is a refusal to let a correct narrow result be reported as a broader one. He established what randomness in prices does and does not imply, what the evidence on active management supported, and what growth-optimal sizing does and does not prove. In each case the popular version claims more than he did.

The index fund industry traces part of its intellectual origin to a four-page article by an economist with nothing to sell. Bogle repeatedly cited Challenge to Judgment, and the argument it makes is still the one indexing rests on.

His 1965 randomness result gave the efficient-market literature its formal footing, though he was more careful than most of what followed about what it actually implied.

His long objection to growth-optimal position sizing remains the standard citation for anyone arguing that a mathematically attractive betting rule is not automatically the right objective for a real investor.