# Random Walk Theory

## History of Random Walk Theory

The term ‘Random Walk’ was popularized by the 1973 book, “A Random Walk Down Wall Street”, by Burton Malkiel, Professor of Economics and Finance at Princeton University.

Burton G. Malkiel, did 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, and subsequently if the result was tails, it would close a half point lower. Each time there was a fifty-fifty chance of the price closing higher or lower than the previous day. There were cycles or trends 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. This indicates that the market and stocks could be just as random as flipping a coin.

## Random Walk Hypothesis

The first specification of efficient markets and their relationship to the randomness of prices for things traded in the market goes to Samuelson and Mandelbrot. Samuelson has proved in 1965 that if a market has zero transaction costs, if all available information is free to all interested parties, and if all market participants and potential participants have the same horizons and expectations about prices, the market will be efficient and prices will fluctuate randomly.

According to the Random Walk Theory, the changes in prices of stock show independent behavior and are dependent on the new pieces of information that are received but within themselves are independent of each other. Whenever a new price of information is received in the stock market, the market independently receives this information and it is independent and separate from all the other prices of information. For example, a stock is selling at Rs. 40 based on existing information known to all investors. Afterwards, the news of a strike in that company will bring down the stock price to Rs. 30 the next day. The stock price further goes down to Rs. 25. Thus, the first fall in stock price from Rs. 40 to Rs. 30 is caused because of some information about the strike. But the second fall in the price of a stock from Rs. 30 to Rs. 25 is due to additional information on the type of strike. Therefore, each price change is independent of the other because each information has been taken in, by the stock market and separately disseminated. However, independent pieces of information, when they come together immediately after each other show that the price is falling but each price fall is independent of the other price fall.

The basic essential fact of the Random Walk Theory is that the information on stock prices is immediately and fully spread over that other investors have full knowledge of the information. The response makes the movement of prices independent of each other. Thus, it may be said that the prices have an independent nature and therefore, the price of each day is different. The theory further states that the financial markets are so competitive that there is immediate price adjustment. It is due to the effective communication system through which information can be disturbed almost anywhere in the country. This speed of information determines the efficiency of the market.

### Difference Between Random Walk Theory and the Efficient Market Hypothesis (EMH)

According the Efficient Market Hypothesis (EMH) the market is a “fair game” where prices are set fairly and there are no market inefficiencies for investors to exploit. The efficient market model says nothing about stability in the process generating returns. The random walk model is a special and more restrictive case of the efficient market model which carries the added assumptions that successive returns be independent and identically distributed.

### Implications of Random Walk Theory in Portfolio Management

The common practice of forecasting returns and portfolio volatility based on historical mean returns and standard deviations requires the belief that the return generating process is stable and the assumptions of the random walk model are valid. If the return generating process is not stable or does not conform to the random walk model assumptions, then the practice of forecasting future returns from historical returns is unreliable because investment opportunities vary from period to period, and thus the appropriate investment solution is subject to change.