ECMT 2130: Financial Econometrics
1 Part 1: Basic computation questions on empirical CAPM
Data
The dataset “empirical-capm.csv" contains variables for the empirical analysis of CAPM. The orig- inal source of this dataset is Chris Brooks’ textbook. We consider the time series variables observed from January 2002 to February 2018.
Variable description:
• SANDP : Monthly S&P 500 (first-day-of-month) indices
• FORD, GE, MICROSOFT and ORACLE : monthly (first-day-of-month) prices of four stocks
• USTB3M : Annualized yield of three-month US treasury bills.
Instruction
• Use log-returns for the analysis.
• It is recommended to begin this computing assignment after Week 7.
• Provide numerical answers first, followed by interpretations of the results.
We consider the empirical CAPM:
rp,t - rf,t = α + β(rm,t - rf,t) + ut , (1)
where
— rm,t - rf,t: market excess return.
— rp,t - rf,t: excess return on an asset.
Q1. Let rp,t be the return on GE. Report the sample mean of x t, the sample variance of xt , and the sample correlation between xt and xt-k for k = 1, 2, and 3.
Q2. Let rp,t be the return on GE. Report the OLS estimates α and β . Interpret the results.
Q3. Consider the setup of Q2. Test whether there is no abnormal return. Report two t- statistics assuming that (i) there is neither heteroskedasticity nor autocorrelation, and (ii) there is heteroskedasticity and autocorrelation. Report the test results and interpret them.
Q4. Consider the setup of Q2. Test whether β = 1. Report two t-statistics assuming that (i) there is neither heteroskedasticity nor autocorrelation, and (ii) there is heteroskedasticity and autocorrelation. Report the test results (rejection or non-rejection) and interpret them.
Q5. Summarize the results given in Q2–Q4. How can you summarize all these results related to the CAPM?
Q6. Repeat the same analysis in Q1-Q5 using “ORACLE" data.
2 Part 2: How CAPM predicts NVIDIA?
Instruction
• The dataset we considered in Part 1 (hereafter referred to as "DATA1" for shorthand) spans from January 2002 to February 2018. We will reuse this dataset.
• Find the prices of NVIDIA (I assume you know what "NVIDIA" refers to, without further explanation) for the full sample period (from January 2002 to February 2018) or for a sub- sample period. It is best to obtain NVIDIA prices for the full sample period to ensure more accurate results. If you can only find data for a sub-period, you may use it, but you must clarify this. There are various types of prices, but use "close prices" if possible. Other types of prices may be allowed, but in any case, clearly state which type of price is used in your analysis.
• In the subsequent analysis, you are required to implement an empirical analysis using the prices of NVIDIA and DATA1 (particularly the variables SANDP and USTB3M). Merge the NVIDIA data with DATA1. If you obtain NVIDIA prices for only a sub-sample period, ensure that you match the observed time of the variables.
• How to find appropriate data in practice is part of this assignment. Please refrain from asking the instructor or tutors for guidance on where to find data or requesting the dataset.
- If you cannot find the NVIDIA data, you may consider using an alternative stock that you wish to analyze. However, in this case, the work may be regarded as less valuable than that using the NVIDIA data.
Q. Analyze NVIDIA using the empirical CAPM model. It is important to include the following results, in the order:
(1) Details of the dataset you find (data span, source, and any other relevant information).
(2) The basic sample statistics, including the sample mean and variance of xt (where x t is the log-return of NVIDIA), as well as the sample correlation between xt and xt-k for k = 1, 2 and 3.
(3) Estimation results (OLS estimates and their interpretation).
(4) Test results for the hypothesis that there is no abnormal return, along with an interpre- tation of the findings.
(5) Interpretation of the results based on the CAPM.