Unit 4: Case Study: Sample Size and Portfolio Construction Sample Size and Tracking Error

 
Unit 4: 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
If you have multiple documents, create a ZIP file with all of them and upload that
as your assignment.
Make sure to use the following naming convention: Your_NameAssignment_Name-Date
Example:
Instructor-Final_Project-May_12_2016
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