The random walk hypothesis holds that stock price changes are unpredictable from past prices, meaning returns cannot be forecast from historical data. Lo and MacKinlay (1987) tested this hypothesis in Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test. Using 1,216 weekly returns of the CRSP NYSE-AMEX equal-weighted index from September 6, 1962 to December 26, 1985, they found a 30 percent weekly autocorrelation. The rejection held across the full sample and was strongest among small-capitalization stocks.
What the Study Found
The variance ratio for the equal-weighted CRSP index at aggregation value q=2 was 1.30 for the full sample period. That ratio implies a weekly autocorrelation of approximately 30 percent for the equal-weighted index. Portfolios of the smallest NYSE-AMEX market-value quintile showed a 42 percent weekly autocorrelation over the full sample period. The largest-quintile portfolio showed a smaller but still significant 14 percent weekly autocorrelation over the same period. Variance ratios for the smallest-quintile portfolio at q=8 with a four-week base interval reached 1.41, with a z-statistic of 2.04.
Methodology
The study uses weekly returns derived from the CRSP daily returns file for NYSE-AMEX common stocks. The full sample includes 1,216 weekly observations, with five size-sorted portfolios containing between 2,036 and 2,720 stocks. The test period spans September 6, 1962 to December 26, 1985, and is also examined in 608-week and 304-week sub-periods. The variance ratio test controls for heteroscedasticity using a robust z* statistic and rules out infrequent trading using a separate non-trading simulation model.
Key Statistics
| Metric | Finding | Context |
|---|---|---|
| Weekly autocorrelation, equal-weighted CRSP index | ~30 percent | Full sample, September 6, 1962–December 26, 1985 |
| Variance ratio (q=2), equal-weighted CRSP index | 1.30 | Full sample period |
| Weekly autocorrelation, smallest-quintile portfolio | 42 percent | Full sample period |
| Weekly autocorrelation, largest-quintile portfolio | 14 percent | Full sample period |
| Variance ratio (q=8, h=4 weeks), smallest-quintile portfolio | 1.41 (z = 2.04) | Full sample period |
| Variance ratio test statistic M(q) | M(q) = σ²c(q) / σ²a − 1 | Compares variance estimators across sampling frequencies q |
| Non-trading-induced autocorrelation | ρ(j) = p·(1−p)^j | Theoretical spurious autocorrelation from infrequent trading |
Why This Matters
The findings challenge the efficient markets hypothesis as commonly tested through linear forecastability of returns. Because the predictability persists in small-capitalization stocks after controlling for thin trading and changing volatility, it is unlikely to be a microstructure artifact. The pattern fits short-term positive return momentum rather than a mean-reverting fads story, a distinction relevant to option pricing models that assume a random walk. Quantitative researchers building short-horizon signals should treat weekly-frequency predictability as a feature of price dynamics rather than evidence of guaranteed, cost-adjusted trading profits.