# QUANTITATIVE ELEMENT

QUANTITATIVE ELEMENT

The Research Methods course assessment for the Quantitative element is based on 60% on an individual empirical project. This empirical project consists of two parts: ? Part I requires estimation of Ordinary Least Squares (OLS) regression models and interpretation of the results; ? Part II is a set of tests for Weak Form Efficiency and their interpretations.

These two empirical topics require understanding of material covered in the Research Methods lectures and computer labs. You will also need to use SPSS for the tasks required for this project. Further details about the writing up and presentation of this individual project are at the end of this document.

You are required to submit your report on Monday 24th Feb, 2013 at 15.00PM.

Part I: Regression Analysis

The main objective of this component of the individual project is to 1) run the regression using OLS and 2) to write up a concise report, discussing and analyzing your results, based on suitable results Tables and Graphs.

Step 1: Obtain the Data In the excel file “RM_Data” you will find a dataset for 758 young men from the US in 1969.

Step 2: Run the Regression You are required to run the following regression model using OLS:

ii6i5i4i3i2i1i UrbanMarIQAgeExprEduY ?? ?? ?? ?? ????????

where: i Y is the log hourly wage in US dollars for i i Edu is the number of years of education for i i Expr is the years of work experience for i i IQ is the IQ score for i i Mar is a dummy variable, = 1 if married, = 0 if single i Urban is a dummy variable, = 1 if lives in a city, = 0 if not

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Step 3: Empirical Discussions

1) Report the results1 in a simple table – which should include the estimated coefficients, their standard errors, the value of 2 R , adj- 2 R , and any other statistics you think are appropriate. 2) Discuss your findings, for example, what this wage equation means and how it can be justified? What are the interpretations of the estimated coefficients? What are the confidence intervals for the estimated coefficients on the independent variables? Are the estimated coefficients statistically significant? How well does the model describe the relationship between the variables? 3) Do the assumptions underlying the model hold? 4) Any possible implications for public policy?

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 stocks (quoted in major stock exchange) or market indices over a span of at least two years up until 24 January 2014.

You can obtain the data from Yahoo Finance: http://uk.finance.yahoo.com/, and here are the main steps:

a) Search for company or index you want in the “Get quotes” box. b) After you find the company or the market index, you should use an option on the left labeled “Historical Prices”. Set the dates you are interested in (for example, 1 Jan 2012 to 24 January 2014) and the select the frequency of the data. c) At the bottom of the page you will find “Download to Spreadsheet”, which will allow you to save the data in a file in “.csv” format.

The data include the date of the quote and some other information. The variable you are interested is called “Adj close”. It is the closing share price adjusted for dividends and splits. Note that the data arrive in reverse chronological order, with the most recent quote at the top of the spreadsheet. You should sort the data so that they are in chronological order, so that the first (earliest) quote is at the top and the last (most recent) is at the bottom. 1 When reporting numerical results round up the numbers to three or four decimal places. You should check how published papers report numerical results and follow a consistent and clear style. You should not report numbers like 0.00001243; this is not very useful to a reader.

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You can compute the simple return as:

100

1

1 ? ?

? ? ?

t

tt t Y YY R

where t R is return at time t, t Y is the Adjusted close price at time t and 1 ?tY is the Adjusted close price at time t-1.

You should printout the FIRST PAGE ONLY of the spreadsheet with all the data and included it in the Appendix.

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. You should report these results of the “stylized facts” of your data using suitably designed Tables. 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:

ttt uRR ????? ?1

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where the dependent variable t R is the return for the time t, and the independent variable 1 ?tR 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:

tt,Frit,Thut,Wedt,Tuet,Mont uDDDDDR ??????????? 54321

where: t R = return at time t

? ? ?

?

Otherwise Monday

D t , 0 1 1 t,D 2 , t ,D 3 , t ,D 4 and t ,D 5 are dummy variables for Tuesdays, Wednesdays, Thursdays and Fridays, respectively.

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.

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Guidelines for the writing the Project Report

a) The marking criteria are as follows:

? 40%: For neat and logical presentation, crisp and precise language and adherence to the academic journal style (e.g., Journal of Finance, Journal of Financial Economics etc). You will lose marks for providing only raw computer output, untidy presentation and sketchy discussion of the results and non-compliance with the style guidelines.

? 40%: For the Empirical Analysis – especially the discussion of the test results and importantly any “economic” interpretation of the results. For tips on how to describe and discuss the empirical results you get look at the template papers accompanying the Exercises.

? 10%: For overall conciseness, cogent and careful analysis of results and logical flow of the entire Report.

? 10%: For work that shows initiative and understanding of the material “on your own” that will add value to your work and demonstrating that you have an appreciation of the topic. However this is all subject to the allocated word limit!

b) The length for the Report should be around 2,000 words.

The following items are excluding from the word count: ? Tables, Figures and Graphs ? Reference ? Appendix

You must use at least 1.5 spacing and a font not smaller than 12 pts. It is your decision as to how to balance the word count between Parts I and II of the Exercise.

REPEAT AGAIN – Your report must not contain any raw output from Excel, SPSS or any other package.

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**Category**: Essay Writing