4  The random walk hypothesis

The Random Walk Hypothesis is closely related to the Efficient Markets Hypothesis. It states that stock price changes are independent of each other and have the same probability distribution, making future movements unpredictable based on past movements. Technical analysis (analysing chart patterns and past trading data) should not provide any advantage in predicting future prices

This aligns with the weak form of the Efficient Markets Hypothesis, which states that prices already reflect all information contained in the history of past trading.

4.1 Statistical foundations

In a true random walk, the best predictor of tomorrow’s price is today’s price plus a random error term:

P_{t+1} = P_t + \mu + \epsilon_t

Where:

  • P_{t+1} is the price at time t+1
  • P_t is the price at time t
  • \mu is the drift term (expected return)
  • \epsilon_t is a random error term with mean zero

The drift term is included due to the historical observation that equity markets tend to have positive expected returns over long periods. The drift term represents factors like economic growth, inflation, and the risk premium demanded by investors.

4.2 Early empirical evidence

One of the most influential early studies supporting the Random Walk Hypothesis was conducted by Maurice Kendall and Hill (1953). Examining UK stock and commodity prices, Kendall expected to find regular price cycles but instead discovered that price changes appeared random. He found almost zero correlation between price movements on consecutive days.

In his famous work, Burton Malkiel (2020) popularised this concept through a thought experiment: a blindfolded monkey throwing darts at the financial pages could select a portfolio that would do just as well as one carefully selected by experts.

4.3 Tests of randomness

Several statistical tests can determine if a series of price changes follows a random walk:

  1. Serial correlation tests: Measure correlation between consecutive price changes
  2. Runs tests: Analyse sequences of consecutive price increases or decreases
  3. Variance ratio tests: Compare variances of returns across different time intervals

4.4 Implications for investors

If markets truly follow a random walk:

  • Technical analysis should not outperform simple buy-and-hold strategies
  • Timing the market is impossible
  • Passive investment strategies should perform as well as active management (although the costs of active management strategies often make active strategies underperform)

This does not mean investors cannot earn positive returns. Rather, it suggests that finding consistent ways to beat the market through analysis of past price movements alone is unlikely.