Random walk hypothesis
Encyclopedia
The random walk hypothesis is a financial theory stating that stock market
prices
evolve according to a random walk
and thus the prices of the stock market cannot be predicted. It is consistent with the efficient-market hypothesis.
The concept can be traced to French broker Jules Regnault
who published a book in 1863, and then to French mathematician Louis Bachelier
whose Ph.D. dissertation titled "The Theory of Speculation" (1900) included some remarkable insights and commentary. Same ideas were later developed by MIT Sloan School of Management
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
, and was used earlier in Eugene Fama
'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
in his 1953 paper, The Analytics of Economic Time Series, Part 1: Prices.
Burton G. Malkiel
, an economist professor at Princeton University and writer of A Random Walk Down Wall Street, performed a test where his students were given a hypothetical stock
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 a 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. When Malkiel told him it was based purely on flipping a coin, the chartist was very unhappy. Malkiel argued that this indicates that the market and stocks could be just as random as flipping a coin.
The random walk hypothesis was also applied to NBA basketball
. Psychologist
s made a detailed study of every shot the Philadelphia 76ers
made over one and a half seasons of basketball. The psychologists found no positive correlation
between the previous shots and the outcomes of the shots afterwards. Economists and believers in the random walk hypothesis apply this to the stock market. The actual lack of correlation of past and present can be easily seen. If a stock goes up one day, no stock market participant can accurately predict that it will rise again the next. Just as a basketball player with the “hot hand” can miss the next shot, the stock that seems to be on the rise can fall at any time, making it completely random.
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 behavioral 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
outperform other stocks in the forthcoming 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 and the University of Pennsylvania, respectively, have also tried to prove the random walk theory wrong. They wrote the book A Non-Random Walk Down Wall Street, which goes through a number of tests and studies that try to prove there are trends in the stock market and that they are somewhat predictable.
They prove it with what is called the simple volatility-based specification test, which is an equation that states:
where
is the price of the stock at time t
is an arbitrary drift parameter
is a random disturbance term.
With this equation, they have been able to put in stock prices over the last number of years, and figure out the trends that have unfolded. They have found small incremental changes in the stocks throughout the years. Through these changes, Lo and MacKinlay believe that the stock market is predictable, thus contradicting the random walk hypothesis. Lo and MacKinlay have authored a paper, the Adaptive Market Hypothesis
, which puts forth another way of looking at predictability of price changes.
Stock market
A stock market or equity market is a public entity for the trading of company stock and derivatives at an agreed price; these are securities listed on a stock exchange as well as those only traded privately.The size of the world stock market was estimated at about $36.6 trillion...
prices
Market price
In economics, market price is the economic price for which a good or service is offered in the marketplace. It is of interest mainly in the study of microeconomics...
evolve according to a random walk
Random walk
A random walk, sometimes denoted RW, is a mathematical formalisation of a trajectory that consists of taking successive random steps. For example, the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the...
and thus the prices of the stock market cannot be predicted. It is consistent with the efficient-market hypothesis.
The concept can be traced to French broker Jules Regnault
Jules Regnault
Jules Augustin Frédéric Regnault was a French economist who first suggested a modern theory of stock price changes in Calcul des Chances et Philosophie de la Bourse and used a random walk model...
who published a book in 1863, and then to French mathematician Louis Bachelier
Louis Bachelier
-External links:** Louis Bachelier webpage at the Université de Franche-Comté, Besançon / France. Text in French.** also from Index Funds Advisors, this discussion of...
whose Ph.D. dissertation titled "The Theory of Speculation" (1900) included some remarkable insights and commentary. Same ideas were later developed by MIT Sloan School of Management
MIT Sloan School of Management
The MIT Sloan School of Management is the business school of the Massachusetts Institute of Technology, in Cambridge, Massachusetts....
professor Paul Cootner
Paul Cootner
Paul H. Cootner was a financial economist noted for his book The Random Character of Stock Market Prices....
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
A Random Walk Down Wall Street
A Random Walk Down Wall Street, written by Burton Malkiel, a Princeton economist, is an influential book on the subject of stock markets which introduced the random walk hypothesis. Malkiel argues that asset prices typically exhibit signs of random walk and that one cannot consistently outperform...
, by Burton Malkiel
Burton Malkiel
Burton Gordon Malkiel is an American economist and writer, most famous for his classic finance book A Random Walk Down Wall Street...
, a Professor of Economics at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
, and was used earlier in Eugene Fama
Eugene Fama
Eugene Francis "Gene" Fama is an American economist, known for his work on portfolio theory and asset pricing, both theoretical and empirical. He is currently Robert R...
'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
Maurice Kendall
Sir Maurice George Kendall, FBA was a British statistician, widely known for his contribution to statistics. The Kendall tau rank correlation is named after him.-Education and early life:...
in his 1953 paper, The Analytics of Economic Time Series, Part 1: Prices.
Testing the hypothesis
Burton Malkiel
Burton Gordon Malkiel is an American economist and writer, most famous for his classic finance book A Random Walk Down Wall Street...
, an economist professor at Princeton University and writer of A Random Walk Down Wall Street, performed a test where his students were given a hypothetical stock
Stock
The capital stock of a business entity represents the original capital paid into or invested in the business by its founders. It serves as a security for the creditors of a business since it cannot be withdrawn to the detriment of the creditors...
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 a chart and graph form to a chartist
Technical analysis
In finance, technical analysis is security analysis discipline for forecasting the direction of prices through the study of past market data, primarily price and volume. Behavioral economics and quantitative analysis incorporate technical analysis, which being an aspect of active management stands...
, 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. When Malkiel told him it was based purely on flipping a coin, the chartist was very unhappy. Malkiel argued that this indicates that the market and stocks could be just as random as flipping a coin.
The random walk hypothesis was also applied to NBA basketball
National Basketball Association
The National Basketball Association is the pre-eminent men's professional basketball league in North America. It consists of thirty franchised member clubs, of which twenty-nine are located in the United States and one in Canada...
. Psychologist
Psychologist
Psychologist is a professional or academic title used by individuals who are either:* Clinical professionals who work with patients in a variety of therapeutic contexts .* Scientists conducting psychological research or teaching psychology in a college...
s made a detailed study of every shot the Philadelphia 76ers
Philadelphia 76ers
The Philadelphia 76ers are a professional basketball team based in Philadelphia, Pennsylvania. They play in the Atlantic Division of the Eastern Conference of the National Basketball Association . Originally known as the Syracuse Nationals, they are one of the oldest franchises in the NBA...
made over one and a half seasons of basketball. The psychologists found no positive correlation
Correlation
In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....
between the previous shots and the outcomes of the shots afterwards. Economists and believers in the random walk hypothesis apply this to the stock market. The actual lack of correlation of past and present can be easily seen. If a stock goes up one day, no stock market participant can accurately predict that it will rise again the next. Just as a basketball player with the “hot hand” can miss the next shot, the stock that seems to be on the rise can fall at any time, making it completely random.
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 trendsMarket trend
A market trend is a putative tendency of a financial market to move in a particular direction over time. These trends are classified as secular for long time frames, primary for medium time frames, and secondary for short time frames...
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 behavioral 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
Rate of return
In finance, rate of return , also known as return on investment , rate of profit or sometimes just return, is the ratio of money gained or lost on an investment relative to the amount of money invested. The amount of money gained or lost may be referred to as interest, profit/loss, gain/loss, or...
outperform other stocks in the forthcoming 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
Andrew Lo
Andrew W. Lo is the Harris & Harris Group Professor of Finance at the MIT Sloan School of Management. He is a leading authority on hedge funds and financial engineering; he proposed the Adaptive market hypothesis...
and Archie Craig MacKinlay, professors of Finance at the MIT Sloan School of Management and the University of Pennsylvania, respectively, have also tried to prove the random walk theory wrong. They wrote the book A Non-Random Walk Down Wall Street, which goes through a number of tests and studies that try to prove there are trends in the stock market and that they are somewhat predictable.
They prove it with what is called the simple volatility-based specification test, which is an equation that states:
where
is the price of the stock at time t is an arbitrary drift parameter is a random disturbance term.With this equation, they have been able to put in stock prices over the last number of years, and figure out the trends that have unfolded. They have found small incremental changes in the stocks throughout the years. Through these changes, Lo and MacKinlay believe that the stock market is predictable, thus contradicting the random walk hypothesis. Lo and MacKinlay have authored a paper, the Adaptive Market Hypothesis
Adaptive market hypothesis
The adaptive market hypothesis, as proposed by Andrew Lo, is an attempt to reconcile economic theories based on the efficient market hypothesis with behavioral economics, by applying the principles of evolution to financial interactions: competition, adaptation and natural selection.Under this...
, which puts forth another way of looking at predictability of price changes.