Part II is a set of tests for Weak Form Efficiency and their interpretations.

Part II: Tests for Weak Form Efficiency 

In this part of the project you will need to perform few tests for the weak form efficiency on the stocks and/or the market indices and discuss the empirical findings. 

Step 1: Obtain the Data 

 You need to obtain daily data for 2 - 3 commodity prices or stock prices over a span of at least two years up until the closet day of your last birthday1. You may obtain the data from DataStream, EIA, Worldbank, IMF, or Yahoo Finance2.

You can either compute the simple return as follows:

where Rt is return at time t, Yt is the price at time t and Yt-1 is the price at time t-1. Alternatively, you can make use of log returns.  

1 For example, if your birthday is 5th November, then you can have your data from 5th November 2016 to 5th November 2018.

2 Need to be care with Yahoo Finance, you need to sort the data from the earliest to latest order. They have data ordered from the latest to the earliest.  

Step 2: Tests of Weak Form Efficiency 

You should read one of the “overview” chapters detailed below and the research articles provided. These will give you guidance about how to interpret and comment on the results of the weak-form efficiency tests as applied to your data.  Textbook Overviews: ▪ Bodie, Zvi, Alex Kane and Alan Markus, Investments, Chapter 11 in the 8th Edition on “The Efficient Market Hypothesis” or same chapter in other Editions. ▪ Elton, Gruber, Brown, Goetzmann: Modern Portfolio Theory and Investment Analysis, 6th Edition Chapter 17 on Efficient Markets. ▪ Campbell, John, Andrew Lo and A Craig MacKinlay, The Econometrics of Financial Markets, Princeton University Press, 1997 (Chapters 1 and 2) Journal Articles: ▪ Cont, Rama, 2001, Empirical Properties of Asset Returns: Stylized Facts and Statistical Issues, Quantitative Finance, 1, 223–236. ▪ Jacobs, Bruce and Kenneth Levy, 1988, Calendar Anomalies: Abnormal Returns at Calendar Turning Points, Financial Analysts Journal, 28-39. 

1) Descriptive Statistics and return distributions 

 Begin by analyzing the data using the summary statistics (e.g., mean, median, max, min, skewness, kurtosis etc.) in a Table.  Provide a few (may be 1 or 2) plots of time series of returns of the data and a histogram of the return distribution for your stocks and indices. Using appropriate wording you should comment on the statistical and economic (if any) interpretation of your data.  

 2) Autoregressive (AR) Model 

You can test to see if the return data in your sample follow a random walk using the AR (1) model:  

Rt = alpha + betaRt-1 + epsilont 

where the dependent variable Rt is the return for the time t, and the independent variable Rt-1 is the return lagged one period for time t-1. 

You can create a one-period lag of return either manually in excel or you simply do that in SPSS, for instance, by using the LAG function under the Transform>Compute variables menu.  

You should report and discuss your results.  

3) Day of the Week Effect 

 In this part, you will test and see if the data show any seasonal effects over days of the week. Before you attempt this part, you should carefully read the relevant material, e.g.:  ▪ Koop, Gary, Analysis of Financial Data Chapter 7  ▪ Brooks, Chris, Introductory Econometrics for Finance, 2nd Edition; Chapter 9, Sections 9.2-9.3 pages 454-462. 

You should run the following regression: 

Note that there is no constant in the above regression; if you want to include a constant you can have only 4 dummy variables. Again, you should report and comment on your findings.  

4) Optional Opportunity for Individual Initiative 

 In this part of your Report you have the opportunity (if you wish to use it - not compulsory) to use the data on your sample stocks for either a) implementing a test for weak form efficiency that you have read about and can use on your own – different from the tests you have already done above; b) try and think of something that will add value to your report and reflect your understanding of the literature on weak form efficiency. For example, compute autocorrelation coefficients for your chosen stocks; use additional data to test “Month-of-the-Year” seasonal effect.   For ideas on what you could do you need to have a look at the references given and also search for further articles if necessary.