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The random walk hypothesis is a
financial theory Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of fi ...
stating that
stock market A stock market, equity market, or share market is the aggregation of buyers and sellers of stocks (also called shares), which represent ownership claims on businesses; these may include ''securities'' listed on a public stock exchange, ...
prices A price is the (usually not negative) quantity of payment or compensation given by one party to another in return for goods or services. In some situations, the price of production has a different name. If the product is a "good" in t ...
evolve according to a
random walk In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb Z ...
(so price changes are
random In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual ran ...
) and thus cannot be predicted.


History

The concept can be traced to French broker
Jules Regnault Jules Augustin Frédéric Regnault (; 1 February 1834, Béthencourt – 9 December 1894, Paris) was a French stock broker's assistant who first suggested a modern theory of stock price changes i''Calcul des Chances et Philosophie de la Bourse' ...
who published a book in 1863, and then to French mathematician
Louis Bachelier Louis Jean-Baptiste Alphonse Bachelier (; 11 March 1870 – 28 April 1946) was a French mathematician at the turn of the 20th century. He is credited with being the first person to model the stochastic process now called Brownian motion, as part ...
whose Ph.D. dissertation titled "The Theory of Speculation" (1900) included some remarkable insights and commentary. The same ideas were later developed by
MIT Sloan School of Management The MIT Sloan School of Management (MIT Sloan or Sloan) is the business school of the Massachusetts Institute of Technology, a private university in Cambridge, Massachusetts. MIT Sloan offers bachelor's, master's, and doctoral degree programs ...
professor Paul Cootner in his 1964 book ''The Random Character of Stock Market Prices''. The term was popularized by the 1973 book '' A Random Walk Down Wall Street'' by Burton Malkiel, a professor of economics at
Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...
, and was used earlier in
Eugene Fama Eugene Francis "Gene" Fama (; born February 14, 1939) is an American economist, best known for his empirical work on portfolio theory, asset pricing, and the efficient-market hypothesis. He is currently Robert R. McCormick Distinguished Servic ...
's 1965 article "Random Walks In Stock Market Prices", which was a less technical version of his Ph.D. thesis. The theory that stock prices move randomly was earlier proposed by
Maurice Kendall Sir Maurice George Kendall, FBA (6 September 1907 – 29 March 1983) was a prominent British statistician. The Kendall tau rank correlation is named after him. Education and early life Maurice Kendall was born in Kettering, Northampton ...
in his 1953 paper, ''The Analysis of Economic Time Series, Part 1: Prices''.


Testing the hypothesis

Whether financial data are a random walk is a venerable and challenging question. One of two possible results are obtained, data are random walk or the data are not. To investigate whether observed data follow a random walk, some methods or approaches have been proposed, for example, the variance ratio (VR) tests, the
Hurst exponent The Hurst exponent is used as a measure of long-term memory of time series. It relates to the autocorrelations of the time series, and the rate at which these decrease as the lag between pairs of values increases. Studies involving the Hurst expone ...
and
surrogate data testing Surrogate data testing (or the ''method of surrogate data'') is a statistical proof by contradiction technique and similar to permutation tests and as a resampling technique related (but different) to parametric bootstrapping. It is used to detec ...
. Burton G. Malkiel, an economics professor at Princeton University and writer of ''A Random Walk Down Wall Street'', performed a test where his students were given a hypothetical
stock In finance, stock (also capital stock) consists of all the shares by which ownership of a corporation or company is divided.Longman Business English Dictionary: "stock - ''especially AmE'' one of the shares into which ownership of a compan ...
that was initially worth fifty dollars. The closing stock price for each day was determined by a coin flip. If the result was heads, the price would close a half point higher, but if the result was tails, it would close a half point lower. Thus, each time, the price had a fifty-fifty chance of closing higher or lower than the previous day. Cycles or trends were determined from the tests. Malkiel then took the results in chart and graph form to a chartist, a person who "seeks to predict future movements by seeking to interpret past patterns on the assumption that 'history tends to repeat itself'." The chartist told Malkiel that they needed to immediately buy the stock. Since the coin flips were random, the fictitious stock had no overall trend. Malkiel argued that this indicates that the market and stocks could be just as random as flipping a coin.


Asset pricing with a random walk

Modelling asset prices with a random walk takes the form: S_=S_+\mu\DeltaS_+\sigma\sqrtS_Y_ where \mu is a drift constant \sigma is the
standard deviation In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, whil ...
of the returns \Delta is the change in time Y_i is an
i.i.d. In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent. This property is us ...
random variable satisfying Y_i\sim N(0,1).


A non-random walk hypothesis

There are other economists, professors, and investors who believe that the market is predictable to some degree. These people believe that prices may move in trends and that the study of past prices can be used to forecast future price direction. There have been some economic studies that support this view, and a book has been written by two professors of economics that tries to prove the random walk hypothesis wrong. Martin Weber, a leading researcher in behavioural finance, has performed many tests and studies on finding trends in the stock market. In one of his key studies, he observed the stock market for ten years. Throughout that period, he looked at the market prices for noticeable trends and found that stocks with high price increases in the first five years tended to become under-performers in the following five years. Weber and other believers in the non-random walk hypothesis cite this as a key contributor and contradictor to the random walk hypothesis. Another test that Weber ran that contradicts the random walk hypothesis, was finding stocks that have had an upward revision for
earnings Earnings are the net benefits of a corporation's operation. Earnings is also the amount on which corporate tax is due. For an analysis of specific aspects of corporate operations several more specific terms are used as EBIT (earnings before intere ...
outperform other stocks in the following six months. With this knowledge, investors can have an edge in predicting what stocks to pull out of the market and which stocks — the stocks with the upward revision — to leave in. Martin Weber’s studies detract from the random walk hypothesis, because according to Weber, there are trends and other tips to predicting the stock market. Professors Andrew W. Lo and Archie Craig MacKinlay, professors of Finance at the
MIT Sloan School of Management The MIT Sloan School of Management (MIT Sloan or Sloan) is the business school of the Massachusetts Institute of Technology, a private university in Cambridge, Massachusetts. MIT Sloan offers bachelor's, master's, and doctoral degree programs ...
and the University of Pennsylvania, respectively, have also presented evidence that they believe shows the random walk hypothesis to be wrong. Their book ''A Non-Random Walk Down Wall Street'', presents a number of tests and studies that reportedly support the view that there are trends in the stock market and that the stock market is somewhat predictable. One element of their evidence is the simple volatility-based specification test, which has a null hypothesis that states: :X_t = \mu + X_ + \epsilon_t\, where :X_t is the log of the price of the asset at time t :\mu is a drift constant :\epsilon_t is a random disturbance term where \mathbb epsilon_t0 and \mathbb epsilon_t \epsilon_\tau0 for \tau \neq t (this implies that \tau and t are independent since \mathbb epsilon_t \epsilon_\tau\mathbb epsilon_t\mathbb epsilon_/math>). To refute the hypothesis, they compare the variance of (X_t-X_) for different \tau and compare the results to what would be expected for uncorrelated \epsilon_t. Lo and MacKinlay have authored a paper, the
adaptive market hypothesis The adaptive market hypothesis, as proposed by Andrew Lo,Lo, 2004. is an attempt to reconcile economic theories based on the efficient market hypothesis (which implies that markets are efficient) with behavioral economics, by applying the princi ...
, which puts forth another way of looking at the predictability of price changes.
Peter Lynch Peter Lynch (born January 19, 1944) is an American investor, mutual fund manager, and philanthropist. As the manager of the Magellan Fund at Fidelity Investments between 1977 and 1990, Lynch averaged a 29.2% annual return, consistently more ...
, a mutual fund manager at
Fidelity Investments Fidelity Investments, commonly referred to as Fidelity, earlier as Fidelity Management & Research or FMR, is an American multinational financial services corporation based in Boston, Massachusetts. The company was established in 1946 and is o ...
, has argued that the random walk hypothesis is contradictory to the
efficient market hypothesis The efficient-market hypothesis (EMH) is a hypothesis in financial economics that states that asset prices reflect all available information. A direct implication is that it is impossible to "beat the market" consistently on a risk-adjusted bas ...
-- though both concepts are widely taught in business schools without seeming awareness of a contradiction. If asset prices are rational and based on all available data as the efficient market hypothesis proposes, then fluctuations in asset price are ''not'' random. But if the random walk hypothesis is valid then asset prices are not rational as the efficient market hypothesis proposes.


References

{{DEFAULTSORT:Random Walk Hypothesis 1964 introductions Finance theories Stochastic processes