Random Walk Hypothesis
Also written Random walk theory · Random walk model
The early form of the efficient market model: security price changes occur randomly, so successive one-period returns are independent and identically distributed.
In plain language
Suppose today's price already reflects everything that is known. Then tomorrow's price change can only come from news nobody knows yet. And news arrives at random. So price changes should look random too.
The workbook says early thinking on efficient markets was based on the Random Walk hypothesis. This held that security prices change randomly.
The idea went like this. The current price fully reflects all known information. So each period's return is independent of the last, and all follow the same pattern. Put another way, returns are independent and identically distributed. This is the random walk model.
Early academic work mostly tested this against data. Then, in 1970, Eugene Fama built the theory into a clear form and sorted the evidence. He presented the efficient market hypothesis as a fair game model.
How it works
Independent means yesterday's return tells you nothing about today's. Identically distributed means each period's return is drawn from the same distribution.
Link to the weak form (Chapter 13, section 13.2.1). Weak-form EMH says current prices fully reflect all historical information — past prices, returns and trading volume. So current prices are independent of past prices, and the workbook concludes that under the weak form, market prices do follow a random walk. Chapter 13's sample question 2 asks what the weak form states — the independence of successive price changes is the idea at stake.
What follows for strategy:
| Implication | Where in the workbook |
|---|---|
| Little to gain from technical analysis | Section 13.5.1 |
| "From the random walk theory, we understand that it is impossible to consistently outperform the market" — an argument for indexing | Chapter 18, section 18.4 |
| Standard finance: the EMH describes random movement in prices | Chapter 14, Table 14.1 |
The counter-view. Momentum investors believe that even though the market is random, there are upward or downward trends for brief periods — minutes to months (Chapter 18, section 18.7). Behavioural finance attributes such patterns to biases such as the disposition effect.
A worked example
Illustrative figures. A trader notices that a Nifty stock rose on each of the last four days and buys 500 shares at ₹1,200 (₹6 lakh), expecting a fifth up day.
Under the random walk hypothesis, the four up days are history already reflected in ₹1,200. Tomorrow's move is independent of them. If up and down days are equally likely, the probability of a fifth up day is still 50% — not higher because of the streak.
Now consider a simple check the trader could run. Over 200 trading days, she records whether each day's move matched the previous day's direction.
| Days | |
|---|---|
| Same direction as the day before | 101 |
| Opposite direction | 99 |
| Total | 200 |
101 ÷ 200 = 50.5% — essentially a coin toss. That is what a random walk predicts. If instead she found, say, 140 of 200 (70%) days continuing the previous direction, successive returns would not be independent, and the weak form would be in doubt.
Why NISM asks about it
Chapter 13 (Concept of Informational Efficiency), section 13.2, introduces the random walk hypothesis as the early basis of the efficient market model, before Fama's 1970 fair game formulation; section 13.2.1 ties it to weak-form efficiency. Chapter 18 (section 18.4) uses random walk theory to justify indexing. Expect questions on independence of successive price changes and on what the hypothesis implies for technical analysis.
Common exam traps
- Successive returns are independent and identically distributed — not dependent, not biased, not driven by trading volume.
- Random walk came first; Fama (1970) formalised the EMH as a fair game model. Do not attribute the random walk hypothesis to Fama's 1970 article.
- The weak form is the one tied to random walks in the workbook's text.
- Random does not mean irrational. Prices move randomly because new information arrives randomly.
- A random walk makes technical analysis futile, not fundamental analysis. Fundamental analysis is challenged by the semi-strong form.
Where this is taught
Free preparation for NISM Series XXI-BRelated terms
- Efficient Market HypothesisThe proposition that share prices already incorporate and reflect all relevant information — which, if true, leaves nothing for an analyst to find by studying that information.
- Technical analysisForecasting price direction from past price and volume alone, on the assumption that everything worth knowing about a company is already in its price.
- Fair Game ModelEugene Fama's 1970 framing of the efficient market hypothesis: current price fully reflects available information, so no investment strategy can consistently earn above-average risk-adjusted returns.
- Informational EfficiencyHow fully and quickly security prices reflect available information. It is what "market efficiency" usually means, as against operational efficiency, which is about transaction costs.
- Weak-form EfficiencyThe hypothesis that current prices already reflect all historical market information — past prices, returns and volumes — so technical analysis cannot earn above-average risk-adjusted returns.
- Momentum investingAn active strategy that rides an ongoing price trend — long in a rising trend, short in a falling one — worked from price and volume data rather than a company's fundamentals.
- Wash SaleA US tax rule, cited by the workbook to explain the January Effect: it disallows a loss deduction when an investor sells a security at a loss and buys back a substantially identical one within 30 days before or after.
- Internal contradiction of efficiencyThe paradox that a market can only become informationally efficient if enough participants believe it is not — because it is their search for mispricing that drives prices to fair value.
- Unbiased EstimateThe technical definition of an efficient market price: the market price is an unbiased estimate of a security's true value, so deviations are random rather than one-sided.