Power Law of Returns

Definition & Origins

The power law of returns is the empirical observation that equity market returns are not normally distributed: the overwhelming majority of aggregate stock market wealth is generated by an extremely small number of companies. Instead of a bell curve in which most stocks cluster around an average outcome, the distribution of long-run stock returns is radically skewed — a tiny cohort of exceptional companies accounts for essentially all net wealth creation, while the median stock historically underperforms even Treasury bills over its lifetime.

The concept entered Anderson's work through academic research, above all Hendrik Bessembinder's paper "Do Stocks Outperform Treasury Bills?" — work Anderson has called "the most important research paper published for many a year." Bessembinder examined all U.S. common stocks from 1926 to 2016 and found that the entire net wealth creation of the American stock market over ninety years was attributable to a mere 4% of listed companies. Just 90 companies — out of roughly 24,000 — created half of nearly $35 trillion of value above Treasury bills. In the Masters in Business interview (2022), Anderson distilled it for a general audience: "What the academic data shows is that most stocks over long time periods underperform cash. The whole game is finding the few that don't."

Anderson's own portfolio data confirmed the academic finding. In Aberration or Premonition? (2018) he disclosed that for the Long Term Global Growth mandates, approximately 5% of annual outperformance of the MSCI ACWI over ten years had been generated by just two stocks. The power law is not, in his telling, a curiosity of market history — it is the operating reality of any honestly examined investment record, "however they invest, wherever they invest, whether they embrace it or not."

Core Ideas

The return distribution is radically skewed, not normal. The foundational claim. If 4% of companies create all net wealth, then the mean return is meaningless for portfolio construction: it describes a world that no individual stock actually inhabits. As Anderson put it in Graham or Growth (2018), the great growth companies have "altered the patterns of stock market return sufficiently that the very utility of the 'mean' has been undermined. The mean is now so far above the median stock that our entire notion of the distribution of returns has to be reviewed."

Missing the outliers is the catastrophic error; owning some failures is tolerable. In a normal world, risk management means avoiding losers. In a power-law world, the asymmetry inverts: the cost of not owning the tiny number of extreme winners dwarfs the cost of holding many mediocre performers. Anderson quotes Jeff Bezos's 2015 shareholder letter with approval: "Given a ten percent chance of a 100 times payoff, you should take that bet every time. But you're still going to be wrong nine times out of ten." The mathematics of the skew make the hunt for outliers the whole game — "one success matters more than one failure" (Graham or Growth).

Public equity returns now resemble venture capital returns. A direct consequence. The skewed distribution that defines venture outcomes — a few home runs paying for many write-offs — increasingly describes quoted equities too. In the 2022 interview Anderson noted that a chart of where public market returns come from leads observers to assume "it's a return structure of the venture capital industry rather than the public equity markets." This is why he rejected the traditional rule "Rule 1: don't lose money" as portfolio-level folly: it optimizes for a distribution that no longer exists.

Concentration is the rational response to the skew. If returns are top-heavy, diversification across the whole index guarantees owning the vast dead mass of the distribution. The task becomes "to give ourselves the best possible chance of owning the outliers" — which is the intellectual basis for Scottish Mortgage's concentrated portfolio and for his critique of benchmark-driven construction.

Practical Application

Portfolio construction at Scottish Mortgage. The power law dictated the trust's entire shape: a concentrated portfolio of roughly 50–100 positions, holding sizes set by "the potential upside and its probability" rather than index weights, and a refusal to trim winners merely because they had grown large. In the 2017 Annual Report Anderson cited the figure directly: 33% of U.S. equity wealth created between 1926 and 2015 came from just 30 companies out of 26,000. Hence "our prime task lies in giving our shareholders the best possible opportunity to capture the extreme winners."

The top-five-percent selling test. The power law also governed exits. As he explained in the 2022 interview, the standing question for any holding was whether it retained "the possibility to be in the top five percent of outcomes over the next five years." Tesla was trimmed in early 2021 only when its market capitalization appeared to leave insufficient remaining upside to clear that bar — a decision he conceded was open to error, noting that selling Apple on similar reasoning years earlier had been a mistake. The test operationalizes the power law: you only sell when the extreme outcome is no longer available.

Scenario-weighting instead of price targets. In Graham or Growth, Anderson built the Tesla case explicitly on power-law logic: a roughly 20% probability of a scenario worth $400 billion, against a real possibility of a 75% drawdown — "isn't this the type of skewed, asymmetric and to many frightening sets of potential pay-offs that we should welcome?" For NIO the range ran from a 30% chance of worthlessness to a 5% chance of a 65-fold return. This is investment imagination deployed in the service of the skew: what matters is the shape of the outcome distribution, not its point estimate.

Common Misconceptions

Misconception 1: The power law justifies momentum chasing. Anderson's claim is not "buy what has gone up." The skew identifies where returns come from over decades, not which stocks will supply them next. The search is for companies with the characteristics — exponential growth, vast addressable markets, low capital intensity, deep moats — that might place them in the extreme tail. Buying recent winners indiscriminately is as unthinking as selling them.

Misconception 2: Concentration is reckless. The conventional reading of risk treats a concentrated portfolio as fragile. Anderson inverts this: in a power-law world, spreading capital across the whole distribution dilutes the only returns that matter while providing no real protection — most stocks underperform cash anyway. "We think over-diversification is a far more prevalent and insidious threat than excessive concentration in today's investment world" (2017 Annual Report). The honest acknowledgment is that concentration feels dangerous because it fails often and visibly; the power law says it succeeds through a few overwhelming outcomes.

Misconception 3: The outliers were obvious in advance. A related error is hindsight: Amazon, Tesla and Tencent look inevitable now, so the power law seems exploitable after the fact. Anderson is blunt that it was not so — "the most likely forecast a dozen years ago was clearly that Amazon would fail. That was rational analysis. But it wasn't a very good assessment of the probability adjusted pay-offs." The power law is exploited not by prediction but by constructing a portfolio that can survive being wrong about which specific companies reach the tail, while guaranteeing exposure to the tail itself.

Anderson's Own Words

Thought Evolution

Key Letters / Related Concepts

Key letters: Aberration or Premonition? (2018) · Graham or Growth (2018) · Scottish Mortgage Annual Report 2017 · Stay on the Road Less Travelled (2021) · Masters in Business Interview (2022)

Related concepts: Transformative Companies · Long-Termism · Imagination in Investing · Benchmark Irrelevance · Patient Capital

Source: Chian.io — James Anderson Knowledge Base