Assignment:
Case Study: Sample Size and Portfolio
Construction
Sample Size and Tracking Error
In this unit, you learned about population estimation, standard deviation and sample size. You will now put those concepts into practice in the following activities:
1. Download data for last 3 years for the DJIA (Dow Jones Industrial Average) and each of the 30 component stocks. Download data from an appropriate financial website such as Google Finance, Yahoo Finance, Quandl, CityFALCON, or another similar source. If you are using the R language, then there are videos in the "Supplemental Videos in R" located in the "Supplemental Materials" at the bottom of the course ware on how to import CSV files into your program.
2. Calculate Monthly returns of the DJIA index and the downloaded stocks over the period under study
3. Calculate mean and standard deviation of monthly returns for the DJIA index
4. Choose an equal weighted portfolio consisting of any 5 random stocks from the DJIA, calculate the mean monthly returns and its standard deviation. Do the same for portfolios of 10,15, 20 and 25 random stocks from the DJIA universe
5. Calculate tracking errors for each of the portfolios i.e. the margin by which the mean and standard deviation of the portfolio returns diverge from those of DJIA
6. Graphically represent the tracking error for returns and risk (standard deviation of returns used as a proxy for risk) on y-axis against the sample size of portfolio on the x-axis
Project Guidelines
The assignment below aims to expose students to applications of the theory learned in this Unit through hands on involvement in a case study. As such, the focus is on the correct application of the theory, and not on rigorous implementation of coding logic. We would prefer that this mini project be executed in R as it would enable the most graceful implementation of the said logic. Students are however free to execute the project in Microsoft Excel (or a corresponding free open-source spreadsheet tool) also. There are no technical limitations in either R or Excel that would force the students to choose one platform over another.
The submitted R code/Excel worksheet should constitute a fully workable version.
Students are encouraged to avoid usage of any special R/Excel packages for the assignment and stick to using standard R/Excel libraries. In case such a nonstandard package is anyway used, students should provide clear directions as to how to access and install the same.
Based on the results of your findings, complete the following analysis:
1. What all factors account for the tracking error of the constructed portfolios?
2. What is the relationship between tracking error and portfolio sample size?
3. What might be the most optimal way to decrease tracking error without having to construct a full portfolio matching the entire index