*The Business Professor*, updated December 11, 2018, last accessed August 14, 2020, https://thebusinessprofessor.com/lesson/random-walk-theory-stock-market-explained/.

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### Random Walk Theory Explained

The Random Walk Theory or Random Walk Hypothesis is a financial theory that states the prices of securities in a stock market are random and not influenced by past events. It suggests the price movement of the stocks cannot be predicted on the basis of its past movements or trend.

### A Little More on the Random Walk Theory

The theory is named after the book “A Random Walk Down Wall Street” written by American economist Burton Malkiel. The theory argues the stock price movements are independent of one another and have the same probability distribution. It says the stocks prices take an unpredictable random path. According to this theory, it is impossible to outperform the market without taking an additional risk as the chances of a stock’s future price going up is the same as the chances of it going down. This fluctuation cannot be predicted by looking into its past movement. The theory discards all the methods of predicting stock prices as a futile effort.

However, the critics of this theory believe stocks maintain a price trend over time and one can outperform the market by carefully planning entry and exit points without assuming the risk.

In his book Malkei argued it is a common misconception that the events are correlated as they come in “cluster and streaks” but the streaks occur in random data such as coin tosses. Malkei’s theory argues the intrinsic value is undependable as it depends on subjective estimates of future earnings using different factors including expected growth rates, estimated risk, and interest rate.

In his book Malkei stated, “a blindfolded monkey throwing darts at a newspaper’s financial pages could select a portfolio that would do just as well as one carefully selected by experts.” This comment attracted a lot of criticism from the finance experts in the U.S and outside. In 1988, the Wall Street Journal created the annual Wall Street Journal Dartboard contest to test this theory propagated by Malkei. In the contest, the staffs of the Wall Street Journal played the role of the dart-throwing monkeys and experts were invited to participate in the contest against the dart-throwing monkeys. The Wall Street Journal published the result of the contest after 100 rounds. It was seen the experts won in 61 round and the dart-throwers won 39 times. In the reaction, Malkei said when experts make a recommendation the stock enjoys publicity jump and that helped the experts to win the contest.

Malkei and other proponents of this theory advocates for a long-term buy and hold strategy. According to them, it is the best practice for the investors to invest in a passively managed, well-diversified fund. That reduces the risk and involves much lower management fees.

Although many investors still hold that Malkei’s ideas were partially or completely true the investing experts argue the theory is redundant in present context. They are of the view that as now all the relevant news and up to date stocks quotes are available to every investor it is quite possible to plan a well-devised investment strategy without taking much risks.

### References for Random Walk

https://www.investopedia.com/terms/r/randomwalktheory.asp

https://en.wikipedia.org/wiki/Random_walk

https://whatis.techtarget.com/definition/random-walk

http://www.businessdictionary.com/definition/random-walk-theory.html

**Academic Research on Random Walk**

· Portfolio returns and the **random walk theory**, Cheng, P. L., & Deets, M. K. (1971). *The journal of finance*, *26*(1), 11-30. This study explains the random work theory and the correlation between this theory and the finance of a government. This research thesis also explains the interaction between the portfolio and the random work theory and how they have helped to improve the situation of finance of an economy.

· The application of continuous-time **random walks **in **finance **and economics, Scalas, E. (2006). *Physica A: Statistical Mechanics and its Applications*, *362*(2), 225-239. This study primarily explains the main application of the continuous time random walks (CTRWs) to economics and finance of a company, firm or a government. The CTRW is subdivided into two categories. The first categories explain the connection between the anomalous diffusion and the CTRW while the second category helps to study the way the CTRW can be applied to the ruin theory of most insurance companies. This second process helps to improve the inequality process and the growth as well as the change in prices of the financial market as they are well explained and outlined in this research paper.

· Random walks and technical theories: Some additional evidence, Jensen, M. C., & Benington, G. A. (1970). *The Journal of Finance*, *25*(2), 469-482. This study explains the technical theories and random walks. The correlation between these two variables is well explained in this research thesis. This research was supported by the security trust company (STC) in New York. This paper acknowledges the assistance of David Besenfelder for his help on the success of this study.

· Random walks in stock market prices, Fama, E. F. (1995). *Financial analysts journal*, *51*(1), 75-80. This paper simply explains the theory of random works and some of the crucial issues concerning the works of market analysts. According to this paper, two main approached was studied regarding the stock prices and this approach include the chartist theory and the intrinsic/fundamental theory. This study explains the theory of the market as efficient and was also characterized as a random walk states that successive price changes in the individual securities are independent of changes in the stock price. This paper gave empirical evidence which indicates that although the changes in price may not be totally independent.

· Coupled continuous time **random walks **in **finance**, Meerschaert, M. M., & Scalas, E. (2006).. *Physica A: Statistical Mechanics and its Applications*, *370*(1), 114-118. This paper explains how the CTRW are adopted in physics to model the anomalous diffusion by merging a random waiting time between the particle jumps. The financial sector of an economy was taken into consideration and it was realized that the particle jumps are log-returns and the waiting times measure the delay between transactions. The waiting time and the log-return are mostly dependent on one another. According to this study, the probability density functions for the limit process were adopted to solve the fractional partial differential equations. This paper also reviewed the fundamental theory and gives two applications with a little by little stick and futures data.

· The coherence of the modern theories of finance, Hsia, C. C. (1981). *Financial Review*, *16*(1), 27-42. This paper studies the coherence of the modern theories of finance. This research thesis explains the compatibility of the financial developments and setbacks of an economy in relation to the modern theories and the relationship between them.

· Why might share prices follow a **random walk**, Dupernex, S. (2007)? *Student Economic Review*, *21*(1), 167-179. According to this paper, this study reveals the hypothesis of the Efficient Markets is no longer valid as it no longer holds the watertight position in finance as it used to. Thus, the assumption that claims that prices follow a random walk remains unclear. The definition of the random walk model by Samuel Dupernex explains the relationship between the efficiency of the markets. This paper uses empirical evidence to investigate the arguments against and for the model.

· Random walk and price trends: the live cattle futures market, Leuthold, R. M. (1972). *The Journal of Finance*, *27*(4), 879-889. According to this paper, the random walk and the price trends was explained in this research thesis. According to this paper, the live cattle futures market was taken into consideration and used as an example in explaining the random walks and the price trends.

· The cost of a central bank leaning against a **random walk**, Corrado, C. J., & Taylor, D. (1986). *Journal of International Money and Finance*, *5*(3), 303-314. This paper made use of a stochastic model which indicates that the central bank is expected to suffer a loss when it momentarily affects the exchange rate by a sterilized intervention against a random walk. This process was created primarily by only examining the periods where the total intervention adds up to zero and totally accounts for the apparently conflicting empirical results of several intervention profitability studies. Also, this process demonstrates the methodology used in most studies to explain the probability of the official central bank intervention towards finding a positive result.

· Note on the validity of the **random walk **for European stock prices, Solnik, B. H. (1973). *The Journal of Finance*, *28*(5), 1151-1159. According to this research paper, the validity of the random walk for the European stock prices was explained and appropriate examples that correlate this research was given in this study. Several models that help to justify this claim were also explained and a step by step guide was introduced in this research thesis.

· A variance ratio test of **random walks **in exchange rates: Evidence from Pacific Basin economies, Ajayi, R. A., & Karemera, D. (1996). *Pacific-Basin Finance Journal*, *4*(1), 77-91. According to the result obtained in this research thesis, the random walk model is defined as not consistent with the dynamics of weekly or daily exchange rate innovations in the majority of these markets. Modern methodological advances were studied in the light of testing the Random Walk Hypothesis (RWH) and the exchange rates have only been applied to only currencies of industrial economies. One of such advances was explained in this paper and it was used to explain the RHW for the currencies of eight economies of the Pacific Basin.

· Commodity futures: trends or **random walks**?, Stevenson, R. A., & Bear, R. M. (1970). *The Journal of Finance*, *25*(1), 65-81. This paper recognizes the Bureau of Business and Economic Research of The University of Iowa and Edith Ennis of the Bureau for assisting in the preparation of this study. According to the research analysts of this paper, commodity futures were explained and the random walks trends that help to define these commodity futures were explained and developed.

· Stock market prices do not follow **random walks**: Evidence from a simple specification test, Lo, A. W., & MacKinlay, A. C. (1988). *The review of financial studies*, *1*(1), 41-66. In this research paper, the random walk hypothesis for the weekly stock market returns was tested by comparing the variance estimators gotten from the data sampled at different frequencies. Although, this model was rejected for the whole sample period (1962-1985) and for all the sub-periods for a variety of aggregate size-sorted portfolios and return indexes. The rejection of this random walk cannot be explained by merely supporting a mean-reverting stationary model of asset prices. It is more consistent with a special non-stationary alternative guess.