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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