Random Walk Hypothesis

Abstract

This chapter covers history, definition, assumptions, and implications of the Random walk hypothesis. The basic idea is that stock prices take a random and unpredictable path. Discussion includes why the random walk hypothesis is still relevant in finance in spite of several criticisms? Detailed discussion made on random walk hypothesis and market efficiency. Fama’s joint hypothesis problem and its implication is covered in detail. In addition to it martingales and its features are conversed in detail. Illustrations are shown for different random walk models using R-Programming namely Random Walk with Fixed Moves and Random Walk with Random Moves. Critical issues related to the various Random Walk models in practice are discussed in detail. At the end testing of the various Random Walk models and Martingales using EViews are demonstrated.

Exercises

2.1.1 Multiple Choice Questions

• 1. EMH does not assume

  • (a) Security prices follow a random walk

  • (b) Security prices follow a martingale

  • (c) Security prices do not follow a random walk

  • (d) None

• 2. Which of the following statement(s) about martingales is/are false?

  • (a) Martingale and random walk are the same

  • (b) Martingale is not a stochastic process

  • (c) Martingales are the sequences of random variables

  • (d) All of the above

• 3. Which of the following version of EMH does not exists?

  • (a) Weak form

  • (b) Semi Weak form

  • (c) Semi Strong form

  • (d) Strong form

• 4. Dart Throwing Investment Contest initiated in which year?

  • (a) 1987

  • (b) 1988

  • (c) 1989

  • (d) 1991

• 5. Which of the following test is not associated with testing random walk?

  • (a) Variance ratio test

  • (b) Wald (Chi-Square) joint tests

  • (c) Chow-Denning maximum |z| joint tests

  • (d) BDS Independence test

• 6. The random walk hypothesis is mostly related to the

  • (a) Weak form of EMH

  • (b) Semi Weak form of EMH

  • (c) Semi Strong form of EMH

  • (d) Strong form of EMH

• 7. An investor notices a particular trend in a security price movements. This is a violation of the

  • (a) Weak form of EMH

  • (b) Semi Weak form of EMH

  • (c) Semi Strong form of EMH

  • (d) Strong form of EMH

• 8. Which of the following test is used for testing random walk?

  • (a) Variance ratio test

  • (b) Phillips-Perron test

  • (c) KPSS test

  • (d) BDS independence test

• 9. Which among the following test is used for autocorrelation analysis?

  • (a) Kendall’s tau

  • (b) Ljung-Box test

  • (c) Pearson correlation

  • (d) Shapiro–Wilk test

• 10. According to Eugene Fama test of the market efficiency is difficult due to

  • (a) Joint hypothesis problem

  • (b) Forward hypothesis problem

  • (c) Backward hypothesis problem

  • (d) None of the above

2.1.2 Fill in the Blanks

• 1. Market efficiency should be tested jointly with the __________ & __________.

• 2. Test of market efficiency seems to be impossible due to __________ problem.

• 3. ____________ test is used for autocorrelation analysis.

• 4. Dart Throwing Investment Contest initiated by _________ in the year ______.

• 5. EMH stands for ____________________.

• 6. $E({\mathrm{Price}}_{t+1}- {\mathrm{Price}}_{t}|{\Phi}_{t})=0$, represents a ______________.

• 7. In the following random walk model: ${Price}_{t}= {Price}_{t-1}\pm {\alpha }_{t}$, ${\alpha }_{t}$ represents ________________.

• 8. The arrival of relevant new information is a ___________ process.

• 9. Presence of the stock market anomalies evidence against the _________.

• 10. Martingale follows a ___________ process.

2.1.3 Long Answer Questions

• 1. Define Random walk hypothesis with suitable examples?

• 2. Define Efficient Market Hypothesis with suitable examples?

• 3. What are the three versions of EMH and its implications? Explain it in brief.

• 4. Develop a random walk model with random drifts using Poisson’s ratio and execute it with R programming to obtain the estimates?

• 5. Develop a random walk model with random drifts as the log returns and execute it with R programming to obtain the estimates?

• 6. Revisit Fig. 2.2 and replot it considering unequal probability of getting a head or tail?

• 7. Revisit Fig. 2.3 and replot it with the mean value equals to 0.02? Check the difference and comments on its implications.

• 8. Comment on the statement “Are markets really efficient during COVID-19 pandemic” with suitable examples.

• 9. Using different R operators define a martingale and execute it in R console?

• 10. What is your understanding on Joint Hypothesis Problem? Explain it in brief.

• 11. What are public and private information?

• 12. Discuss EMH with respect to the technical analysis and fundamental analysis?

• 13. A researcher wants to conduct a study to understand whether the security prices follow a random walk during the financial crisis 2008 and COVID-19 on the US and UK financial markets? But the researcher does not know from where to begin. So, help him/her to begin with the analysis.

• 14. A central banker want to examine whether the “USD_EUR” daily exchange rates for the past five years follow a martingale? Put yourself in the place of central banker and finish the task?

• 15. Define: what is a non-random walk?

2.1.4 Real-World Tasks

• 1. An instructor ask his/her student to test for the market efficiency during the COVID-19 first and second phase impact on the European stock markets? Assume yourself as the student and perform the task. Then prepare a detailed report of the analysis to be submitted to the instructor.

• 2. A senior researcher want to analyse whether the top seven cryptocurrencies returns follow a random walk during the noble Coronavirus pandemic. Assume yourself as the researcher: perform the mentioned task in details and develop the analysis report.

• 3. An investment analyst want to examine whether the world indices before, during, and after the subprime crisis follow a martingale. Help him/her to perform the said analysis and prepare the report.

• 4. A student need to test the weak form of EMH for the major three currency pairs daily exchange rate for the last three years as his/her project dissertation. Help the student to complete his/her project dissertation successfully and satisfactorily.

• 5. A senior manager of the Reserve bank of India (RBI) asked an intern working under him/her to conduct semi-strong form of EMH tests for all the technological securities traded in the BSE during the first phase of COVID-19 pandemic. Help the intern in analysing and developing the final report for timely submission to the senior RBI manager.

• 6. An individual investor is evaluating his/her investing option as the Herzfeld Caribbean Basin Fund (CUBA), a closed ended fund during early 2021. Help the investors to examine the CUBA fund with respect to the EMH and help him/her to make investment decision.

• 7. Conduct a simple empirical research to show that the security prices do react to the news announcements.

• 8. Conduct a simple empirical research that evidences against the EMH?

2.1.5 Case Studies

• 1. A researcher want to conduct a research to test whether stock market reacts to the government policy announcement. During the COVID-19 pandemic Indian government has taken several important policies to tackle the pandemic situation. In that aspect the researcher decided to test the Indian stock market efficiency with respect to the impact of Indian government important policies announcement between the period of January 2021 to September 2021.

  Consider yourself in place of the researcher conduct the research and prepare a detail report based on your analysis.

• 2. Below figures shows the Variance ratio test estimates and descriptive statistics for the GBP_USD currency pair daily exchange rates between the period 01/01/2021 to 31/03/2021. Based on these data comments on the market efficiency and distribution of the data. Then also comment on the relationship between the volatility and market efficiency if any.