BE314 – Spring 2018 – Coursework
In this coursework, our goal is to explore whether past dividend yields and past stock returns can predict stock returns. The data sets are all on Moodle, under Week 19.
- Download the Excel file that corresponds to your assignment. The file has the name “Shiller data – coursework dataset.xlsx”.
- You are asked to answer the four questions below. Fill in this Word document and submit it as your coursework. Keep the margins of this document and the templates given underneath each question as they are and use a 11 pt. font or larger when writing up your answers. Keep in mind that illegible or badly formatted answers will cost marks.
COURSEWORK QUESTIONS
- [20 marks] In your Excel file, column B contains the end-month value of a stock market index and column C contains the monthly aggregate dividend payment from all stocks in the index, both in nominal dollars. The starting month differs from data set to data set, but the ending month is December 2016 in all cases.
The monthly price return of the index, rt, without continuous compounding is given by
where Pt is month t’s closing index value and Pt-1 is the closing index value from month t-1. The monthly dividend yield, dt, is given by
and the monthly total return, Rt, is given by
Determine rt, dt and Rt for the entire time period and produce their sample statistics (mean, median, standard deviation, skewness, kurtosis) in a table in the box below. Then, answer the following questions, again in the same box:
Which series is more variable, the price return or the dividend yield? What is your interpretation of the skewness statistics for the price return series? Does investing in the stock market index in this period appear to be a good investment decision? Justify your answer.
| Insert Descriptive Statistics table here and then your answers to the questions above right beneath the table. |
- [30 marks] Estimate the following model using your dataset and OLS in Excel:
where is an error term. Note that your independent variables are the total return and dividend yield from the previous month. Copy and paste your Excel regression output in the box provided below:
| Insert your Excel regression output here. Format it in Excel first if necessary, make sure that it fits and is readable. |
Is the model able to explain index returns with some success? Comment using the r-square from the OLS output. Comment on this outcome in the context of market efficiency, i.e. would you expect stock returns to be predictable when one uses past data that is easily obtainable?
| Type your answer here. |
Predict the total return for the index when the previous month’s total return is +0.03 and the previous month’s dividend yield is 0.005.
| Type your answer here. Show your work. |
3) [15 marks] Test the null hypothesis that using a two-tailed test. Show your calculation of the test statistic. Make sure that you state the null and alternative hypotheses, the degrees of freedom used and the critical value from the Student’s t-distribution.
| Type your answer here. |
4) [35 marks] We will now examine if adding one more lag of returns and dividend yields to the model above will improve its explanatory power. Run the following model in Excel:
| Insert your Excel regression output here. Format it in Excel first if necessary, make sure that it fits and is readable.
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Perform an F-test to see if we should pick the shorter model from Q2 or the longer model given in this question. Carefully state your null and alternative hypotheses, the numerator and denominator degrees of freedom you are using to determine the critical value from the F-table, and the 5% critical value from the F-distribution. Which model is better to use according to the result of your F-test?
| Type your answer here. |
How could we proceed, along the lines of the modification to the model in Q2 that we made above in this question, in our search for better explanatory power? Briefly explain.
| Type your answer here. |