A Non-Random Walk Down Wall Street
Summary
Lo and MacKinlay collected their research papers challenging the random walk hypothesis, with connecting commentary. The title responds directly to Malkiel's A Random Walk Down Wall Street.
The central technical contribution is the variance ratio test. If prices follow a random walk, the variance of returns measured over a long interval should equal the sum of the variances over the shorter intervals composing it, so the ratio should be one. Lo and MacKinlay showed that for American stock indices over the postwar period the ratio exceeds one at weekly horizons, meaning returns are positively autocorrelated and the random walk is rejected. The rejection is stronger for small capitalisation stocks and for portfolios than for individual securities.
They are careful about what this does and does not mean. Rejecting the random walk does not establish that markets are inefficient, because efficiency permits predictable variation in expected returns arising from time-varying risk premia. Nor does it establish that the predictability is exploitable after transaction costs, which for the small-cap effects they document is doubtful.
Other papers in the collection address data snooping bias, meaning the distortion produced when many researchers test many hypotheses on the same data set and only the significant results are published; the statistical properties of long-horizon return regressions; the nonsynchronous trading effect that generates spurious autocorrelation in index returns; and a paper applying pattern recognition methods to technical analysis, which found that some chart patterns carry information.
The papers are technical and require econometrics. Lo's later work developed the adaptive markets hypothesis, which frames these findings within an evolutionary account of market efficiency. The specific predictabilities documented have weakened since publication, which is consistent with the argument that identified inefficiencies get traded away.
Key takeaways 7
- Variance ratio tests reject the random walk hypothesis for American stock index returns at weekly horizons.
- Rejecting the random walk does not establish inefficiency, because efficient markets permit time-varying expected returns.
- Predictability documented in small capitalisation stocks is unlikely to survive transaction costs.
- Nonsynchronous trading across securities generates autocorrelation in index returns that is a measurement artefact rather than a market property.
- Data snooping bias distorts published results because many researchers test the same data and only significant findings appear.
- Pattern recognition applied to technical chart formations found that some patterns carry statistically detectable information.
- Documented predictabilities weaken after publication, which is consistent with the market absorbing identified inefficiencies.
Who should read it
Quantitatively trained investors and researchers who want the primary evidence against the random walk and the careful statement of what it implies.
About Andrew W. Lo
Charles E. and Susan T. Harris Professor, MIT Sloan School of Management; Director, MIT Laboratory for Financial Engineering; founder of AlphaSimplex Group
The Econometrics of Financial Markets and the variance-ratio work with MacKinlay are primary sources the field builds on, and the Adaptive Markets Hypothesis is a named framework in its own right.
MIT Sloan School of Management, MIT Laboratory for Financial Engineering, AlphaSimplex Group
Similar books 6
Chosen by shared topics, the entries that hold them, and the people who recommended both.
The statistical tools of empirical finance and the questions they test.
The cross-sectional testing methods behind every factor claim.
A formal model of markets whose efficiency shifts as participants adapt.
How physicists and mathematicians came to run money; useful context for Simons.
Recommended by: Eric Weinstein
Where it sits in the reference 2
Topics