Tracker Portfolio Construction: Analysis, Methods, and Performance

This report investigates various methods for constructing a tracking portfolio using 12 stocks and the ASX200 index. It transforms stock prices into weekly returns and analyzes annualized returns, variance-covariance matrix, and beta. Three portfolios are constructed using different methods to track the ASX200, and their performance is compared. The analysis includes variance minimization and RMSE optimization. The report also evaluates the tracker portfolio's performance over 12 months, assessing how closely it follows the index, and discusses the expected return, variance, beta, and R-squared for each portfolio. It concludes by recommending the tracker portfolio that minimizes RMSE for tracking the index due to its higher R-squared value.

Report

TABLE OF CONTENTS
CHAPTER 1 : INTRODUCTION.......................................................................................................................1
CHAPTER 2 : ANALYSIS OF 12 STOCKS AND INDEX......................................................................................2
CHAPTER 3 : PORTFOLIO CONSTRUCTION...................................................................................................6
CHAPTER 4 : PERFORMANCE OF THE TRACKER PORTFOLIO........................................................................9

CHAPTER 1: INTRODUCTION
The purpose of this report is to investigate the different methods of constructing a
tracking portfolio using the 12 stocks below and the ASX200 index.
Code Company
CBA Commonwealth Bank
BHP BHP Billiton Limited
CSL CSL Limited
WBC Westpac Banking Corp
ANZ ANZ Banking Group Limited
NAB National Aust. Bank
WES Wesfarmers Limited
MQG Macquarie Group Limited
WOW Woolworths Group Limited
TLS Telstra Corporation
WPL Woodside Petroleum
RIO RIO Tinto Limited
In Chapter 2, the 12 stock prices and index from the sample data are transformed into
weekly returns. The data is then analyzed to determine the annualized returns, variance
covariance matrix and beta.
In Chapter 3, three portfolios out of the 12 stocks that track the ASX200 index are
constructed and compared using three different methods.
In Chapter 4, the performance of the tracker portfolio is analyzed after 12 months to
determine how close it follows the index.
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CHAPTER 2: ANALYSIS OF 12 STOCKS AND INDEX
The table below shows the weekly returns annualized expected returns, variance and
standard deviation for the 12 stocks and ASX200.
Weekly Returns Annual Returns Annual Variance
Annual Standard
Deviation
CBA 0.0002% 0.0103% 3.7387% 19.3357%
BHP -0.0477% -2.4797% 11.2708% 33.5721%
CSL 0.4376% 22.7564% 3.9468% 19.8665%
WBC 0.0015% 0.0755% 4.8913% 22.1163%
ANZ -0.0189% -0.9828% 5.2796% 22.9774%
NAB 0.0384% 1.9977% 4.9629% 22.2777%
WES 0.0238% 1.2355% 3.0230% 17.3866%
MQG 0.2725% 14.1695% 5.4349% 23.3128%
WOW -0.1589% -8.2626% 4.4082% 20.9957%
TLS -0.1882% -9.7869% 2.9918% 17.2969%
WPL -0.1701% -8.8427% 5.4856% 23.4215%
RIO 0.1457% 7.5770% 8.6946% 29.4866%
ASX200 0.0443% 2.3019% 1.8244% 13.5072%
The table below shows the covariance variance matrix for the 12 stocks
CBA BHP CSL
WB
C ANZ NAB WES
MQ
G WOW TLS WPL RIO
ASX
CBA 3.74% 2.95% 1.12% 3.41% 3.50% 3.26% 1.23% 2.67% 1.75% 1.03% 2.06% 1.97% 2.11%
BHP 2.95% 11.27% 0.82% 3.97% 4.09% 3.91% 2.23% 3.06% 2.82% 0.68% 4.66% 8.35% 3.15%
CSL 1.12% 0.82% 3.95% 1.28% 0.91% 1.15% 1.29% 1.44% 0.91% 0.73% 0.86% 0.54% 1.16%
WBC 3.41% 3.97% 1.28% 4.89% 4.31% 4.02% 1.73% 2.92% 2.19% 0.92% 2.57% 2.76% 2.52%
ANZ 3.50% 4.09% 0.91% 4.31% 5.28% 4.29% 1.39% 3.02% 2.19% 0.65% 2.64% 2.98% 2.52%
NAB 3.26% 3.91% 1.15% 4.02% 4.29% 4.96% 1.79% 3.38% 2.66% 0.97% 2.54% 2.68% 2.52%
WES 1.23% 2.23% 1.29% 1.73% 1.39% 1.79% 3.02% 1.15% 2.32% 1.09% 1.85% 1.50% 1.47%
MQG 2.67% 3.06% 1.44% 2.92% 3.02% 3.38% 1.15% 5.43% 1.92% 0.55% 1.92% 1.54% 2.10%
WOW 1.75% 2.82% 0.91% 2.19% 2.19% 2.66% 2.32% 1.92% 4.41% 1.09% 2.33% 1.70% 1.78%
TLS 1.03% 0.68% 0.73% 0.92% 0.65% 0.97% 1.09% 0.55% 1.09% 2.99% 0.92% 0.60% 0.94%
WPL 2.06% 4.66% 0.86% 2.57% 2.64% 2.54% 1.85% 1.92% 2.33% 0.92% 5.49% 3.11% 2.08%
RIO 1.97% 8.35% 0.54% 2.76% 2.98% 2.68% 1.50% 1.54% 1.70% 0.60% 3.11% 8.69% 2.28%
ASX20
0 2.11% 3.15% 1.16% 2.52% 2.52% 2.52% 1.47% 2.10% 1.78% 0.94% 2.08% 2.28% 1.82%
2

The variance of the ASX200 is 1.8244%. Using the ASX200 index as a proxy for the
market portfolio, the betas for the 12 stocks can be determined as:
Beta = covariance (stock, ASX200)/Variance (ASX200)
The table below shows the Beta for the 12 stocks
Beta
CBA 1.1552
BHP 1.7251
CSL 0.6333
WBC 1.3791
ANZ 1.3793
NAB 1.3806
WES 0.8081
MQG 1.1518
WOW 0.9740
TLS 0.5179
WPL 1.1411
RIO 1.2494
The table below shows the variance of each stock decomposed into its systematic and
unsystematic components. Furthermore, it also shows the diversification ratio (R2) for all
12 stocks and ASX200.
Variance Systematic Risk Unsystematic Risk R2
CBA 0.0374 0.0243 0.0130 0.6512
BHP 0.1127 0.0543 0.0584 0.4817
CSL 0.0395 0.0073 0.0322 0.1854
WBC 0.0489 0.0347 0.0142 0.7094
ANZ 0.0528 0.0347 0.0181 0.6574
NAB 0.0496 0.0348 0.0149 0.7007
WES 0.0302 0.0119 0.0183 0.3941
MQG 0.0543 0.0242 0.0301 0.4453
WOW 0.0441 0.0173 0.0268 0.3926
TLS 0.0299 0.0049 0.0250 0.1635
WPL 0.0549 0.0238 0.0311 0.4331
RIO 0.0869 0.0285 0.0585 0.3275
3

Assuming the risk free rate is 2%, the graph below shows the capital market line with
positions of the 12 stocks and index.
The graph below shows the security market line with positions of the 12 stocks and
ASX200 index.
4

From the graph above, we observe the following:
 The CSL, RIO and MQG stocks are undervalued as they appear above the SML.
 TLS, WES, WOW, WPL, CBA, NAB, WBC, ANZ and BHP stocks are overvalued
as they appear below the SML.
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Chapter 3 : PORTFOLIO CONSTRUCTION
In this section, three portfolios that track the ASX200 index were constructed out of the
12 stocks using 3 methods as defined below.
Portfolio a- A portfolio of 12 stocks whose variance is minimized but exposure to
index is exactly one
In this method, excel solver in the data analysis tool pack was used to determine the
weights that satisfy the following conditions:
 Minimizes the portfolio variance (the portfolio variance is determined as the
product of the weights and covariance variance matrix for the 12 stocks).
 Sum of weights equals must equal one i.e. ∑ W = 1
 Exposure to Beta is one i.e. ∑ β∗W = 1
The table below shows the weights which satisfy the conditions above. Based on these
weights, the portfolio’s minimized variance is 1.94%.
Weights
CBA 11.92%
BHP 1.03%
CSL 11.16%
WBC 5.52%
ANZ 11.23%
NAB 1.22%
WES 13.59%
MQG 10.24%
WOW 4.33%
TLS 14.82%
WPL 6.77%
RIO 8.17%
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Portfolio b - A portfolio of 12 stocks that minimizes the RMSE of the difference in
weekly returns between the ASX200 and portfolio
In this method, excel solver in the data analysis tool pack was used to determine the
weights that satisfy the following conditions.
 Minimizes the portfolio variance which is the difference between the portfolio
return and the index.
 Sum of weights equals must equal one
The table below shows the weights which satisfy the conditions above. Based on these
weights, the portfolio’s minimized variance is 2.08%.
Weights
CBA 11.97%
BHP 3.74%
CSL 10.82%
WBC 7.36%
ANZ 10.54%
NAB 3.37%
WES 12.67%
MQG 9.70%
WOW 3.92%
TLS 12.85%
WPL 6.50%
RIO 6.55%
Portfolio c - A portfolio of 6 out of 12 stocks that minimizes the RMSE of the
difference in weekly returns between the ASX200 and portfolio
In this method, the top 6 stocks from method 2 are chosen to construct the portfolio.
Based on these stocks, the portfolio’s minimized RMSE is 0.857%. Hence removal of
less risky assets from portfolio reduces the portfolio’s variance.
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Weights
CBA 11.97%
CSL 10.82%
ANZ 10.54%
WES 12.67%
MQG 9.70%
TLS 12.85%
The table below summarizes the expected return, variance, beta and R2 for the three
portfolios above.
Portfolio a Portfolio b Portfolio c
Expected
Return 0.0227 0.0221 0.0263
Portfolio
Variance 1.94% 2.08% 0.86%
R2 0.9406 0.9493 0.8524
Beta 1.0000 1.0398 0.6329
Based on the above, we recommend that the tracker portfolio that mininmizes the
RMSE should be used to track the index because it has the highest R2.
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Chapter 4 : PERFORMANCE OF THE TRACKER PORTFOLIO
The graph below plots the tracker portfolio and index from September 22, 2017 to
September 14 2018. The values have been normalized to base 100 for comparison.
The simple annualized returns for the tracker portfolio and ASX200 index are 9.4085%
and 7.7145% respectively.
The table below summarizes the beta, R2 and RMSE for the tracker portfolio over the
investment period.
Variance 1.059%
RMSE 0.00213%
R2 0.90308
Beta 1.08502
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In summary, the tracker portfolio did not perfectly track the index, because it is
impossible to achieve this objective unless the portfolio is rebalanced regularly.
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