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THE MODERN THEORY

IN OPTIMIZING RISKY-ASSET PORTFOLIO

A Project Presented to the Faculty of California State Polytechnic University, Pomona

In Partial Fulfllment Of the Requirements for the Degree Master of Science In Economics

By Musaad A. Abalkhail 2017 SIGNATURE PAGE

PROJECT: THE IN OPTIMIZING RISKY-ASSET PORTFOLIO

AUTHOR: Musaad A. Abalkhail

DATE SUBMITTED: Fall 2017

Economics Department

Dr. Carsten Lange Project Committee Chair Economics

Dr. Kellie Forrester Economics

Dr. Bruce Brown Economics

ii ACKNOWLEDGMENTS

I would like to express my sincere gratitude to my project and academic advisor Dr.

Carsten Lange for his valuable inputs in preparing my research and for his continuous support throughout the Masters program. His open doors for me and all of my fellow students is what made this program an enduring and worthwhile experience.

I also would like to express my deepest appreciation to my professors: Dr. Moham- mad Safarzadeh, Dr. Kellie Forrester, Dr. Craig Kerr, and to the Economics Department

Chair Dr. Bruce Brown, whom I attribute my invaluable knowledge I gained from their classes and for their insightful discussions and guidance that extended beyond their offce hours.

I also thank the staff in the Economics Department and the Library at California

Polytechnic University of Pomona who have contributed directly or indirectly in accom- plishing my research paper and making it a piece that I feel proud of.

Words cannot express my very special thanks to my family whom I love dearly. My father Ahmed and my lovely mom Wafa who are my life source of wisdom and pas- sion, and my beautiful wife Sarah and my two-year-old son Salman who are my source of joy and happiness, made fnishing this journey possible. Their endless support and encouragement through my tough times in the program and their joy and pride in my achievements means everything to me. I owe them all greatly.

iii ABSTRACT

This paper aimed to fnd if a fund or a portfolio constructed based on a market index of risky-assets is an optimum portfolio. This was tested by creating a hypothetical opti- mum portfolio for four sectors in the US market (consumer discretionary, energy, fnancials, and ), then examining its weights (investment allocations) with those in Vanguard and SPDR sector-index funds. Additionally, the paper tested if the actively managed sector-based funds by Fidelity are optimum portfolio choices. The study showed that those funds (sector-index and sector-based funds) are not optimum portfolios, therefore, the paper conducted a performance analysis between the optimum portfolios and the funds. The result for the analysis varies but, generally speaking, the optimum portfolios have better performances than those funds, especially if the asset al- location is set for a -term investment. Additionally, the literature review in the paper explains the Modern Portfolio Theory (MPT), the effcient frontier and how it is formed, and how to fnd an optimum portfolio value.

iv Contents

1 Introduction 1

2 Literature Review 3

2.1 What is Modern Portfolio Theory? ...... 3

2.2 The Effcient Frontier ...... 4

2.2.1 Case 1: Perfect Positive Correlation (ρAB = +1) ...... 7

2.2.2 Case 2: Perfect Negative Correlation (ρAB = −1) ...... 9

2.2.3 Case 3: None Perfect Correlation (−1 < ρAB < +1) ...... 9 2.3 The Optimum Portfolio Value ...... 11

3 Empirical Study 14

3.1 Study Terminology & Characteristics ...... 15

3.2 Methodology ...... 16

4 Conclusion: Study Findings and Analysis 20

Appendix 25

A Allocation For ovportA & ovportB 25

v B Stocks Allocation For Vanguard, Fidelity, and SPDR 30

C Annual Portfolio Performance 43

vi List of Tables

3.1 Sectors, Fund Managers, Ticker Symbols, and Fund Type ...... 18

4.1 Portfolio Performance For The Whole Period (Consumer Discretionary) 22

4.2 Portfolio Performance For The Whole Period (Energy) ...... 22

4.3 Portfolio Performance For The Whole Period (Financial) ...... 22

4.4 Portfolio Performance For The Whole Period (Utility) ...... 22

A.1 Allocation for Optimum Portfolio ovportA & ovportB (Consumer Dis-

cretion) ...... 26

A.2 Allocation for Optimum Portfolio ovportA & ovportB (Energy) . . . . . 27

A.3 Allocation for Optimum Portfolio ovportA & ovportB (Financial) . . . 28

A.4 Allocation for Optimum Portfolio ovportA & ovportB (Utility) . . . . . 29

B.1 Consumer Discretionary Allocation for Vanguard Fund (VCR) . . . . . 31

B.2 Consumer Discretionary Allocation for Fidelity Fund (FSCPX) . . . . . 32

B.3 Consumer Discretionary Allocation for SPDR Fund (XLY) ...... 33

B.4 Energy Sector Allocation for Vanguard Fund (VDE) ...... 34

B.5 Energy Sector Allocation for Fidelity Fund (FSENX) ...... 35

B.6 Energy Sector Allocation for SPDR Fund (XLE) ...... 36

B.7 Financial Sector Allocation for Vanguard Fund (VFH) ...... 37

vii B.8 Financial Sector Allocation for Fidelity Fund (FIDSX) ...... 38

B.9 Financial Sector Allocation for SPDR Fund (XLF) ...... 39

B.10 Utility Sector Allocation for Vanguard Fund (VPU) ...... 40

B.11 Utility Sector Allocation for Fidelity Fund (FSUTX) ...... 41

B.12 Utility Sector Allocation for SPDR Fund (XLU) ...... 42

C.1 Annual Portfolio Performance (Consumer Discretionary) ...... 44

C.2 Annual Portfolio Performance (Energy) ...... 44

C.3 Annual Portfolio Performance (Financial) ...... 44

C.4 Annual Portfolio Performance (Utility) ...... 44

viii List of Figures

2.1 The relationship between RP and σP if correlation is +1 ...... 8

2.2 The relationship between RP and σP if correlation is - 1 ...... 10

2.3 The relationship between RP and σP if correlation is - 0.5, 0.5, and +1 . 11 2.4 and its Line with Effcient Frontier 13

3.1 Consumer Discretionary Sector M-Portfolio Allocation for ovportA . . 19

ix Chapter 1

Introduction

“A good portfolio is more than a long list of good stocks and bonds. It is a balanced whole, providing the with protection and opportunities with respect to a wide range of contingencies” – [8].

Markowitz is considered to be the one who set the foundation of the Modern Portfolio

Theory (MPT) we know and use today to construct and select a proper portfolio. After making deep analysis on companies listed in the US , many good companies can be found that show promising future performance. The following step when making investment decisions needs to address two major questions. First, which of those com- panies should we invest in? Second, what is the weight of each investment (how much money should we invest in the company)? Although there could be several conventional and creative ways to answer the questions, the Modern Portfolio Theory (MPT) sug- gests applying Markowitz’s portfolio theory to select a portfolio that is suitable for the investor’s needs. The theory states that we can fnd a number of possible combinations of assets that are described as effcient portfolios. Each portfolio yields the best possible return at a given level (or the lowest possible risk at a given return). Investment

1 strategies vary based on ’ needs. Some would argue that buying the index is a good , but if the investor was looking to maximize their risk-adjusted return, then the investor should select an effcient portfolio with the optimum value of

Sharpe ratio.

Therefore, this paper provides an empirical study to examine if buying the index is the optimum portfolio choice to maximize . If it is not, a follow up question would be to fnd if an optimum portfolio can/would outperform an . Also, in the same follow up question, the paper will test if an optimum portfolio choice can outperform actively managed funds. The literature review of this paper will expand more on explaining the MPT and how it helps investors to select an optimum portfolio from a number of effcient portfolios.

2 Chapter 2

Literature Review

2.1 What is Modern Portfolio Theory?

The Modern Portfolio Theory is considered a framework that infuences the decision of portfolio managers when constructing a portfolio based on its and its risk-level [5]. MPT involves a number of theories but it is largely based on Harry

Markowitz’s article, “Portfolio Selection” in The Journal of Financial in March 1952, and later his book, “Portfolio Selection Effcient Diversifcation” published in 1959. In his article, Markowitz explains that the portfolio selection process consists of two stages:

1. “Starts with observation and experience and ends with beliefs about the future per-

formances of available securities” [7].

This stage is mostly based on fnancial fundamentals. It starts with fnancial ana-

lysts, accountants, and microeconomists performing a deep analysis on the com-

panies’ valuations, expected performance, and on the markets they fall into. Then

it ends when they fnd the companies that are believed to have a promising future.

2. “Starts with the relevant belief about future performance and ends with the choice

3 of portfolio” [7].

This stage starts with the results found in stage one (the promising future of a

number of stocks), and ends with fnding a number of possible effcient portfolios

that are estimated to have the maximum expected return at a given risk-level, or

the minimum risk-level at a given expected return. This stage leads to what is now

called the Modern Portfolio Theory.

Markowitz’s work gave us the approach to select the optimum portfolio of risky-assets from a set of effcient portfolios. In 1958, [11] introduced the idea that the process of investment choice goes through two phases. The frst phase is using

Markowitz’s approach to choose the optimum portfolio of risky-assets. The second phase is the investor’s choice to allocate funds between the optimum portfolio and single risk- free asset [9, p. 426]. Now, Modern Portfolio Theory (also known as the mean- analysis [or approach]), says, “given estimates of the returns, volatilities, and correlations of a set of and constraints on investment choices [for example, the portfolio expected return to be greater that the return of risk-free asset], it is possible to perform an optimization that results in the risk/return or mean-variance effcient frontier” [5].

In the following sections of this paper, the formation of the effcient frontier and the

Capital Market Line will be explained and will illustrate their importance in MPT.

2.2 The Effcient Frontier

In Markowitz’s paper, he described the effect of risky-asset diversifcation (combining

two or more assets in a portfolio) on the expected return and the variance (risk) of the

investment. He explained that diversifcation gives investors a set of effcient portfolio

choices that maximizes expected return at a given risk-level the investor is willing to

4 accept (or that minimizes risk-level at a given expected return the investor is planning to

get), and adding that diversifcation cannot eliminate risk [7, p. 79]. Such an effcient

set of asset combinations ( also called portfolios) in MPT is now more commonly called

the effcient frontier.

The formation of the effcient frontier is based on the two parameters that determine

investors’ portfolio choice. Those parameters are expected return and risk. Risk is typi-

cally measured by the of the mean return of the investment (which is

the square root of the variance). The expected return of a portfolio of many risky-assets

is the sum of the weighted average of the expected returns of all assets in the portfolio.

It is expressed is in the following formula [4, p. 51]:

n RP = ∑ wiRi i=1 where n ∑wi = 1 i=1

RP is the expected return of the portfolio; E(RP)

wi is the weight invested in asset i ; where 0 ≤ w ≤ 1

Ri is the expected return on asset i; E(Ri)

The variance of a portfolio of many risky-assets is the deviation from its mean return, which can be represented by the following formula [10, p. 331]:

n 2 σP = ∑ wiw jCov(Ri, j) i, j=1,i6= j

5 So in a case of investing in two assets, asset A and asset B, the expected return of the

portfolio becomes [4, p. 65-66]:

RP = wARA + wBRB

Assuming that investors are fully invested in both assets:

wA + wB = 1

so

wB = 1 − wA (2.1)

The standard deviation of a portfolio is the square-root of its variance, and in the case of a two-security portfolio, the variance is expressed in the following formula [4, p. 66]:

2 2 2 σP = E(RP − RP) = E[wARA + wBRB − (wARA + wBRB)]

hence

� 2 2 2 2 1/2 σP = wAσA + wBσB + 2wAwBσAB

Since

σAB = ρABσAσB

so

� 2 2 2 2 1/2 σP = wAσA + wBσB + 2wAwBρABσAσB (2.2)

6 σP is the standard deviation of the return of a two-asset portfolio

2 2 σA, σB are the variance of the return for asset A and B respectively

σAB is the of assets A and B

ρAB is the correlation between asset A and B ; where −1 ≤ ρ ≤ +1

σA, σB are the standard deviation of the return for asset A and B

Given equation (2.1), we can rewrite equation (2.2) to be [4]:

 2 2 2 2 1/2 σP = wAσA + (1 − wA) σB + 2wA(1 − wA)ρABσAσB (2.3)

What determines the shape of the effcient frontier is the correlation between the assets that investors are able to and willing to buy. Given that −1 ≤ ρ ≤ +1 , we can examine equation (2.3) and fnd how the relationship between the expected return and risk are affected when changing the value of ρAB , hence, how the shape of the effcient frontier is affected as well.

2.2.1 Case 1: Perfect Positive Correlation (ρAB = +1)

In this case, equation (2.3) will be:

 2 2 2 2 1/2 σP = wAσA + (1 − wA) σB + 2wA(1 − wA)σAσB

We can observe that the term inside the squared brackets is similar to the form x2 +

2xy + y2 which equals x2 + y2. Thus, we can rewrite it to [4, p. 67]:

7 Expected Return

B

A

Standard Deviation

Figure 2.1: The relationship between RP and σP if correlation is +1

1/2 h 2 2i σP = (wAσA) + 2(wAσA)((1 − wA)σB) + ((1 − wA)σB)

so

1/2 h 2 2 i σP = (wAσA) + ((1 − wA)σB)

Thus

σP = wAσA + (1 − wA)σB (2.4)

From equation (2.4) and from Figure 2.1, we can see that when ρAB = +1 , σP be- comes a straight line equation, hence, a linear relationship between expected return and the standard deviation of the portfolio, and based on weights of assets invested in A and

B, the of the portfolio is σA ≤ σP ≤ σB .

8 2.2.2 Case 2: Perfect Negative Correlation (ρAB = −1)

In this case, equation (2.3) will be [4]:

 2 2 2 2 1/2 σP = wAσA + (1 − wA) σB − 2wA(1 − wA)σAσB

We can observe that the term inside the squared brackets is similar to the form x2 −

2xy + y2 which equals x2 − y2. Thus, we can rewrite it to be:

1/2 h 2 2 i σP = (wAσA) − 2(wAσA)((1 − wA)σB) + ((1 − wA)σB)

1/2 h 2 2 i σP = (wAσA) − ((1 − wA)σB)

thus, volatility will be:

σP = wAσA − (1 − wA)σB (2.5)

or

σP = −wAσA + (1 − wA)σB (2.6)

Theoretically, from equations (2.5) and (2.6), and from Figure 2.2, if the right weights are found, we can eliminate risk. Realistically, this kink relationship cannot happen be- cause an extreme case of a -1 correlation between different stocks cannot be found.

2.2.3 Case 3: None Perfect Correlation (−1 < ρAB < +1)

Finally, in this case, the correlation of the two assets is anywhere between -1 and 1,

and this keeps equation (2.3) as it is. If, for example, the correlation is equal to -0.5

9 Expected Return

B

Standard Deviation

Figure 2.2: The relationship between RP and σP if correlation is - 1 or 0.5, the curve would be something similar to what is illustrated in Figure 2.3 by the blue and red curves. As we can see, it represents a nonlinear relationship between the expected return and risk. Based on the weights invested in asset A and B, the portfolio falls on any point along the curve (hyperbola). Point “G” in the fgure is refers to the global minimum variance portfolio, which represents the portfolio with the lowest risk.

Therefore, we can defne the effcient frontier as “the effcient set consists of the envelope curve of all portfolios that lie between the global minimum variance portfolio [(G)] and the maximum return portfolio” [4, p. 77], which is point B in Figure 2.3. Typically, the maximum return portfolio is a portfolio of one asset with the highest return possible at the maximum risk-level of the frontier.

Moreover, in the case of a zero correlation, the curve will be somewhere between the red and the blue curves in Figure 2.3. From this note and from the three cases above, we can conclude that the closer the correlation to -1, the more bowed inwards the curve will become. Furthermore, a perfect negative or positive correlation is not realistic, and any

10 Expected Return

B

Standard Deviation

Figure 2.3: The relationship between RP and σP if correlation is - 0.5, 0.5, and +1

effcient portfolio must fall on any point along the envelope curve between the G portfolio

(which is referred to as the global minimum variance portfolio) and the maximum return

portfolio (which has the higher risk-level).

2.3 The Optimum Portfolio Value

The effcient frontier represents many effcient portfolios that only contain risky-assets.

In 1964, William Sharpe expanded on portfolio theory and explained the effects of com-

bining the portfolio of risky-assets with a risk-free asset [9]. A risk-free asset (R f ) lies on the y-axis with zero risk. Any combination of an effcient portfolio and a risk-free as-

set creates a line that is referred to the Capital Allocation Line (CAL). Figure 2.4 shows

CAL intercepts at R f on the y-axis and at point A (one of many possible effcient risky- asset portfolios) on the effcient frontier. Any point along the CAL and between A and

R f expresses a combination of buying the risky-asset portfolio and the risk-free asset

11 (lending at R f ). Any point along the CAL beyond point A expresses a combination of buying the risky-asset portfolio and borrowing (leveraging) for that risky portfolio.

A special case of CAL where the line is tangent with the effcient frontier and inter- cepts at R f is called the (CML) [10]. That tangency point is referred to as the (M), which represents the optimum value of a risky-asset port-

folio given the risk-free . If borrowing and lending activities are allowed

for the to facilitate, the CML becomes the effcient frontier. The slope R −R of the CML (or any CAL) is P f [9, 438], which is now know as the Sharpe ratio. σP The Sharpe ratio is typically used to compare the performance of different investments by measuring the return per one-unit of risk [6, p. 72]. Therefore, we can optimize our risky-asset investment by estimating the market portfolio (M). This can be done by fnding the maximum value of Sharpe ratio given risk-free rate (R f ). This optimization problem can be expressed as [3, p. 15]:

0 we .Re− R f Maximize p (2.7) 0 we .CgOV.we

0 Subject to we .1 = 1

we is the vector of weights Re is the vector of expected returns COVg is the variance-

The following part of this paper will implement the MPT framework by fnding the market portfolio (M) for each sector in the US stock market and comparing its perfor- mance with sector-index funds managed by Vanguard and SPDR. The actively managed

12 Expected Return CML

Standard Deviation

Figure 2.4: Capital Allocation Line and its Capital Market Line with Effcient Frontier sector-based funds from Fidelity were include to the comparison. The process of fnding the optimum portfolio (market portfolio) will be performed by using STATA software, which solves for the maximum value of Sharpe ratio by using the Lagrange multipliers

–the previously stated optimization problem in equation (2.7).

13 Chapter 3

Empirical Study

In this part we will test if a sector-index fund is the optimum value choice for investors given a risk-free rate. If the sector-index fund is not the optimum portfolio choice for investors, the study will compare the performance of those sector-index funds against hypothetical market portfolios that only apply the optimum value methodology. In addition, the study will include sector-based funds that are actively managed and seek to outperform indices that are considered the funds’ benchmark. The reason to include sector-based funds is to fnd if the MPT framework can also outperform funds that are actively managed but are not applying the optimum portfolio value methodology.

The study is based on the following assumptions:

• Investors have no specifc preference for a specifc risk-level or return – only seek-

ing to optimize their investments.

• Capital Market theory is applied by investors – which states that investors must

assume higher risk to get higher returns.

• No -selling is allowed (no combinations of lending or borrowing when con-

structing a portfolio).

14 • The investor has a choice between investing in a portfolio of risk-assets or in a

risk-free asset.

• Transaction costs are minimal and do not affect returns.

• Buying and selling stocks (either buying at the beginning of the investment or when

re-positioning) happens at the price stated for that month.

3.1 Study Terminology & Characteristics

The following is a list of defnitions for terms and characteristics that the paper is basing its study on:

• Investment period is three years

• Investment starting and ending period is from April 1, 2014 to March 30, 2017

– Year 1 is from April 2014 to March 2015; (Yr. 1)

– Year 2 is from April 2015 to March 2016; (Yr. 2)

– Year 3 is from April 2016 to March 2017; (Yr. 3)

• Data frequency is monthly

• Risk-free rate is 0.88% – which is the US 3-year Constant Maturity Rate, Not

Seasonally adjusted T-Bill (GS3) of April 1st, 2014 [1]. This rate suits our invest-

ment starting date and it matures in three years which accommodates our invest-

ment period. At the investment staring date, the investor would choose to invest in

this risk-free rate or to buy the optimum risky-asset portfolio (the market portfolio).

15 • r_XYZ is the continuously compounded returns, which is the percentage re-

turns for the stock with the ticker XYZ. The way it is calculated in time t is

ln( Ad justed Price f or XYZt ). The adjusted prices are taken from Yahoo Finance database. Ad justed Price f or XYZt−1

• A Sector presents a group of companies listed in the US stock market that are

involved in similar activities.

• Sector-index fund is a fund that is passively managed where its assets are con-

structed based on tracking the weights of each stock in a specifc index such as the

MSCI or the S&P 500 index.

• Sector-based fund is a fund that is actively managed and seeks to outperform a

specifc benchmark such as the MSCI or the S&P 500 benchmark.

• Optimum portfolio value (or optimum portfolio) is the market portfolio (M),

and was explained previously in section 2.3.

• ovportA is a hypothetical portfolio that only uses the optimum portfolio methodol-

ogy to construct the portfolio, and carries out same weights allocated for the stock

throughout the whole investment period (no weight re-balancing).

• ovportB is also a hypothetical portfolio that only uses the optimum portfolio

methodology to construct the portfolio, but it changes the weights allocated ev-

ery year (an annual weight re-balancing).

3.2 Methodology

Our frst empirical question is to examine if sector-index funds are the optimum choice for investors given a risk-free rate of return. Vanguard and SPDR sector-index fund

16 were used to perform the study in the following sectors: consumer discretionary, energy,

fnancial services, and the sector. Vanguard sector-index funds are tracking the

MSCI-US Investable Market Index for each sector, which includes large, mid, and small cap segments of the US market. SPDR sector-index funds are tracking the S&P 500 index for each sector (a market cap index), and weights are estimated based on the index components. Fidelity sector-based funds are actively managed and seek to outperform certain benchmarks (mostly they use S&P 500, and MSCI IMI as their benchmark).

Additional information on the funds picked for this study are listed in Table 3.1. To fnd our answer, we need to form the effcient frontier for each sector and fnd our market portfolio for each sector, then compare the weights of our portfolios with the percentage holdings of those funds in Table 3.1. Weights in those funds do not have to be exactly equal to our market portfolio, but what we look for is some similarity.

In order to form the effcient frontier, we will pick stock that represents at least 60% of the holdings of each sector fund, then use the stocks’ continuous returns as the base to form the frontier. Those returns are based on the monthly stock adjusted prices from

January of 1995 to March of 2017 (a maximum of 267 continuously compounded returns data point for each stock). Some companies were listed in the market after that date and this is fne. Tables in Appendix A show the list of ticker symbols for companies used to form the effcient frontier for each sector. The tables also show the weights for the optimum portfolios (market portfolios) – ovportA and ovportB– for each sector. To estimate the market portfolio, we use equation (2.7). We can use the command “ovport” in STATA that uses equation (2.7) to construct our market portfolio.

To answer our follow-up empirical question if a market portfolio can outperform sector-index funds managed by Vanguard and SPDR, and the actively managed sector- based funds by Fidelity, two hypothetical portfolios (ovportA and ovportB) were con-

17 Table 3.1: Sectors, Fund Managers, Ticker Symbols, and Fund Type Sector Fund Manager Fund Symbol Fund Type Vanguard VCR Sector-Index Fund Consumer Fidelity FSCPX Sector-Based Fund Discretionary SPDR XLV Sector-Index Fund Vanguard VDE Sector-Index Fund Energy Fidelity FSENX Sector-Based Fund SPDR XLE Sector-Index Fund Vanguard VFH Sector-Index Fund Financials Fidelity FIDSX Sector-Based Fund SPDR XLF Sector-Index Fund Vanguard VPU Sector-Index Fund Utility Fidelity FSUTX Sector-Based Fund SPDR XLU Sector-Index Fund structed by only using the methodology. The frst portfolio, ov- portA, allocates assets at the investment starting date (April 2014) and holds on to the same until the end of the investment period (March 2017). Figure 3.1 is one example of how the optimized portfolio for ovportA looks for companies in the consumer discretionary sector. The second portfolio, ovportB, allocates the same as- sets as ovportA for the frst year only. In the following year, it re-balances the weights by including the pricings of the frst year in the frontier and adjusts the asset allocation accordingly, and repeats the same process for year three.

The prices of the funds shown in Table 3.1 represents the performance of those funds, thus, we can use the continuously compounded returns of those funds to compute and compare their performances against the optimum portfolios ovportA and ovportB. We will pay more attention to the risk-adjusted return measure when making the per- R −R formance analysis. The risk-adjusted return that will be used is Sharpe ratio, P f σP .

18 '""-:

qCX)

(!) q

""'0

qN

0 0 .05 .1 .15 Portfolio Risk

• Port. Returns in EFrontier (Without short sales)--- Capital Market Lin

Figure 3.1: Consumer Discretionary Sector M-Portfolio Allocation for ovportA

19 Chapter 4

Conclusion: Study Findings and

Analysis

Addressing the frst question, we can compare the tables in Appendix A with the tables in

Appendix B– the top 25 holding for the funds manged by Vanguard, Fidelity and SPDR.

The weights for our optimized portfolios (ovportA & ovportB) in Appendix A are very

different to those in Appendix B. Therefore, neither the sector-index funds nor the sector-based fund in this study are the investor’s optimum portfolio choice.

Addressing the second question, we will examine and compare the performances of the funds with the optimum portfolio choice (ovprotA, and ovportB). Tables 4.1, 4.2,

4.3, and 4.4 show the arithmetic mean return, the standard deviation (which represent the volatility or the risk level), and Sharpe ratio (risk-adjusted return) of the all three funds and optimum portfolios created for each sector for the whole period (3 years).

By paying more attention to Sharpe ratio, we can observe that both optimum portfolios did better in most cases (in those tables, the green font highlights high performances in

Sharpe ratio). However, ovpostA outperformed the funds in all four sectors, especially

20 in energy, fnancial, and utility. See tables in Appendix C for the annual performance of all portfolios and funds.

From those fndings we can conclude this chapter by sharing the following points:

1. Generally, both hypothetical portfolios have better performances than the sector-

index funds. Also, the optimum portfolios outperformed the actively managed

sector-based funds by Fidelity.

2. The ovportA approach shows more consistency on having at least as good perfor-

mance as the others. This may indicate that this approach is better for long-term

investments.

3. The ovportB approach may have unsatisfactory performance if the portfolio was

constructed (or re-balanced) after a short term “disturbance” in the market sector

(e.g. performance in Financial sector).

21 Table 4.1: Portfolio Performance For The Whole Period (Consumer Discretionary) Portfolio Mean Return Std. Deviation Sharpe Ratio ovportA (no rebalancing) 0.01053 0.05296 0.03261 ovportB (annual rebalance) 0.01209 0.05068 0.06486 VCR - Vanguard ConsDiscr 0.00838 0.03444 -0.01217 FSCPX - Fidelity ConsDiscr 0.00723 0.03396 -0.04619 XLV - SPDR ConsDiscr 0.00978 0.03456 0.02840

Table 4.2: Portfolio Performance For The Whole Period (Energy) Portfolio Mean Return Std. Deviation Sharpe Ratio ovportA (no rebalancing) -0.00058 0.07795 -0.12034 ovportB (annual rebalance) -0.00168 0.06658 -0.15734 VDE - Vanguard Energy -0.00615 0.05784 -0.25850 FSENX - Fidelity Energy -0.00453 0.06344 -0.21021 XLE - SPDR Energy -0.00460 0.05443 -0.24619

Table 4.3: Portfolio Performance For The Whole Period (Financial) Portfolio Mean Return Std. Deviation Sharpe Ratio ovportA (no rebalancing) 0.01288 0.03947 0.10329 ovportB (annual rebalance) 0.00825 0.04014 -0.01368 VFH - Vanguard Financial 0.00951 0.04116 0.01716 FIDSX - Fidelity Financial 0.00664 0.03895 -0.05556 XLF - SPDR Financial 0.00928 0.04321 0.01110

Table 4.4: Portfolio Performance For The Whole Period (Utility) Portfolio Mean Return Std. Deviation Sharpe Ratio ovportA (no rebalancing) 0.01655 0.04440 0.17456 ovportB (annual rebalance) 0.01521 0.05091 0.12593 VPU - Vanguard Utility 0.00865 0.03983 -0.00389 FSUTX - Fidelity Utility 0.00535 0.03572 -0.09664 XLU - SPDR Utility 0.00882 0.04060 0.00043

22 Bibliography

[1] Economic Research at the St. Louis Fed, FRED. Retrieved in March 22, 2017 from

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of Business, Queretaro Campus.

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Finance, pages 69–76, 2014.

23 [7] Harry Markowitz. Portfolio selection. The Journal of Finance, Vol. 7(No. 1):77–91,

March 1952.

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Cowles Foundation for Research in Economics at Yale University, 1959.

[9] William F. Sharpe. Capital asset prices: A theory of market equilibrium under

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[10] Vijay Singal. Corporate Finance and Portfolio Management, volume Volume 4

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24 Appendix A

Stocks Allocation For ovportA & ovportB

A list of tables that presents the ticker symbols for all companies used to form the frontier in each sector. The weights stated presents the weights needed for the market portfolio for ovportA and ovportB.

25 Table A.1: Allocation for Optimum Portfolio ovportA & ovportB (Consumer Discretion) ovportA ovportA # Symbol ovportB Weights for Each Year # Symbol ovportB Weights for Each Year Weights Weights 3-Yr. Period Before Yr. 1 Before Yr. 2 Before Yr. 3 3-Yr. Period Before Yr. 1 Before Yr. 2 Before Yr. 3 1 r_AMZN 0 0 0.02625486 0 27 r_AZO 0 0 0 0 2 r_CCV 0 0 0 0 28 r_DLPH 0.50862808 0.50862808 0.40539687 0.20445737 3 r_HD 0 0 0 0 29 r_RCL 0 0 0 0 4 r_ DIS 0 0 0 0 30 r_EXPE 0 0 0 0 5 r_MCD 0 0 0 0 31 r_ BBY 0 0 0 0 6 r_PCLN 0 0 0 0 32 r KMX 0 0 0 0 7 r_SBUX 0 0 0 0 33 r_CMG 0.0292 1142 0.029 21142 0.1096659 0.077 05748 8 r_NKE 0 0 0 0 34 r_TI F 0 0 0 0 9 r_TWX 0 0 0 0 35 r_ DLTR 0 0 0 0.0 171439 10 r_CHTR 0.21563107 0.2156311 0.2990 1239 0.38375957 36 r_HLT 0 0 0 0

26 11 r_ LOW 0 0 0 0 37 r_LB 0 0 0 0 12 r_NFLX 0 0 0 0.02186575 38 r_OMC 0 0 0 0 13 r_TJX 0.00263908 0.0026391 0.0025 10 1 0.082 18867 39 r_VFC 0 0 0 0 14 r_GM 0 0 0 0 40 r_ DG 0.221243 9 1 0.22 12439 1 0.1435189 0.1303442 1 15 r F 0 0 0 0 4 1 r_CCL 0 0 0 0 16 r_TSLA 0.01623679 0.0162368 0.01364097 0.05893892 42 r_ RCL 0 0 0 0 17 r_FOXA 0 0 0 0 43 r_ EXPE 0 0 0 0 18 r_TGT 0 0 0 0 44 r_DISH 0 0 0 0 19 r_MAR 0 0 0 0 45 r_AA P 0 0 0 0 20 r_ROST 0.00640964 0.0064096 0 0 46 r_WHR 0 0 0 0 21 r_CBS 0 0 0 0 47 r_U LTA 0 0 0 0 22 r_ORLY 0 0 0 0.02424413 48 r_ DHI 0 0 0 0 23 r_ LVS 0 0 0 0 49 r_ RL 0 0 0 0 24 r_YUM 0 0 0 0 50 r_AN 0 0 0 0 25 r_LBTYA 0 0 0 0 51 r_DISCA 0 0 0 0 26 r NW L 0 0 0 0 Table A.2: Allocation for Optimum Portfolio ovportA & ovportB (Energy) ovportA ovportA # Symbol ovportB Weights for Each Year # Symbol ovportB Weights for Each Year Weights Weights 3-Yr. Period Before Yr. 1 Before Yr. 2 Before Yr. 3 3-Yr. Period Before Yr. 1 Before Yr. 2 Before Yr. 3 1 r_XOM 0 0 0 0 21 r_HES 0 0 0 0 2 r CVX 0 0 0 0 22 r FTI 0 0 0 0 3 r_SLB 0 0 0 0 23 r_MRO 0 0 0 0 4 r_COP 0 0 0 0 24 r_XEC 0 0 0 0 5 r EOG 0 0 0 0 25 r OKE 0 0 0 0 6 r_OXY 0 0 0 0 26 r_EQT 0 0 0 0 7 r_HAL 0 0 0 0 27 r_TRGP 0 0 0.07997384 0

27 8 r KMI 0 0 0.06584 14 0 28 r COG 0.3683071 0.368307 1 0.09265771 0 9 r_PSX 0 0 0 0.19739863 29 r_TSO 0 0 0 0 10 r APC 0 0 0 0 30 r LNG 0 0 0 0 11 r_PXD 0 0 0 0 31 r_FANG 0 0 0.704649 12 0.80260137 12 r_VLO 0 0 0 0 32 r_RICE 0 0 0 0 13 r M PC 0.12961276 0.1296128 0 .05687793 0 33 r PDCE 0 0 0 0 14 r_BHI 0 0 0 0 34 r_NFX 0 0 0 0 15 r_WM B 0 0 0 0 35 r_RSPP 0.42794801 0.4279480 1 0 0 16 r DVN 0 0 0 0 36 r_CPE 0 0 0 0 17 r_APA 0 0 0 0 37 r_SM 0.074132 14 0.07413214 0 0 18 r CXO 0 0 0 0 38 r BP 0 0 0 0 19 r_NBL 0 0 0 0 39 r_PE 0 0 20 r_ NOV 0 0 0 0 Table A.3: Allocation for Optimum Portfolio ovportA & ovportB (Financial) ovportA ovportA # Symbol ovportB Weights for Each Year # Symbol ovportB Weights for Each Year Weights Weights 3-Yr. Period Before Yr. 1 Before Yr. 2 Before Yr. 3 3-Yr. Period Before Yr. 1 Before Yr. 2 Before Yr. 3 1 r_JPM 0 0 0 0 24 r_SPGI 0 0 0 0 2 r W FC 0 0 0 0 25 r STT 0 0 0 0 3 r_BAC 0 0 0 0 26 r_AON 0 0 0 0 4 r_BRK_B 0 0 0 0 27 r_ALL 0 0 0 0 5 r C 0 0 0 0 28 r AFL 0 0 0 0 6 r_USB 0 .13137388 0.13 137388 0 0.13060443 29 r_STI 0 0 0 0 7 r_GS 0 0 0 0 30 r_MTB 0 0 0.052182 1 0 8 r AIG 0 0 0 0 31 r PGR 0 0 0 0 9 r_CB 0 0 0 0 32 r_FITB 0 0 0 0 28 10 r MS 0 0 0 0 33 r MCO 0 0 0 0 11 r AXP 0 0 0 0 34 r_NTRS 0 0 0 0 12 r_PNC 0 0 0 0 35 r_BEN 0 0 0 0 13 r BK 0 0 0 0 36 r HBAN 0 0 0 0 14 r_M ET 0 0 0 0 37 r_DFS 0 0 0 0 15 r_SCHW 0 0 0 0 38 r_TMK 0 0 0 0 16 r PRU 0 0 0 0 39 r FNF 0 0 0 0 17 r_BLK 0 0 0 0 40 r_FRC 0.3210682 0.32106822 0 0.16222242 18 r COF 0 0 0 0 41 r ETFC 0 0 0 0 19 r_CME 0 .0437 107 1 0.0437107 1 0.0938024 0.12769862 42 r V 0 0 0 0 20 r_BBT 0 0 0 0 43 r_MA 0.5038472 0.503847 19 0 0.57947453 21 r MMC 0 0 0 0 44 r BX 0 0 0 0 22 r_TRV 0 0 0 0 45 r_SYF 0 .8540 155 0 23 r ICE 0 0 0 0 46 r CFG 0 0 Table A.4: Allocation for Optimum Portfolio ovportA & ovportB (Utility) ovportA ovportA # Symbol ovportB Weights for Each Vear # Symbol ovportB Weights for Each Vear Weights Weights 3-Yr. Period Before Yr. 1 Before Yr. 2 Before Yr. 3 3-Yr. Period Before Yr. 1 Before Yr. 2 Before Yr. 3 1 r NEE 0 0 0 0.01307884 16 r DTE 0 0 0 0 2 r_DUK 0 0 0 0 17 r_AWK 0.76970649 0.76970649 0.88765251 0.09132692 3 r SO 0 0 0 0 18 r ETR 0 0 0 0 4 r_D 0 0 0 0 19 r_FE 0 0 0 0 5 r_EXC 0 0 0 0 20 r_AEE 0 0 0 0 29 6 r PCG 0 0 0 0 21 r CMS 0 0 0 0 7 r_AEP 0 0 0 0 22 r_CNP 0 0 0 0 8 r_SRE 0 0 0 0 23 r_SCG 0 0 0 0 9 r EIX 0 0 0 0 24 r PNW 0 0 0 0 10 r_PPL 0 0 0 0 25 r_LNT 0 0 0 0 11 r ED 0 0 0 0 26 r UGI 0.23029351 0.23029351 0.11234749 0 12 r_PEG 0 0 0 0 27 r_ATO 0 0 0 0 13 r_XEL 0 0 0 0 28 r_NI 0 0 0 0 14 r W EC 0 0 0 0 29 r GXP 0 0 0 0 15 r ES 0 0 0 0 30 r AGR 0.89559424 Appendix B

Stocks Allocation For Vanguard,

Fidelity, and SPDR

A list of tables that presents the top 25 Holdings in the Sector-Index Funds Managed by

Vanguard and SPDR, and in the actively managed Sector-based Funds by Fidelity: [2]

30 Table B.1: Consumer Discretionary Allocation for Vanguard Fund (VCR) % Portfolio Shares Shares Top 25 Holdings Weight... Owned Change

Amazon.com I nc 11.43 303,979 4,044

The Home Depot Inc 5.82 9 16,841 12,142

Comcast Corp Class A 5.71 3,587,601 47,668

Walt Disney Co 5.35 1,137,956 15,182

McDonald's Corp 3.55 625,102 8,382

The Priceline Group I nc 2.79 37,146 494

Starbucks Corp 2.67 1,095,424 14,608

Time Warner Inc 2.34 580,381 7,690

Charter Communicat ions Inc 2.29 162,971 2,168 A

Nike Inc B 2.26 1,005,716 13,420

Lowe's Companies Inc 2.26 654 ,667 8,642

Netflix Inc 2.00 323,023 4,332

TJX Companies I nc 1.57 490,633 6,502

General Motors Co 1.4 6 1,034 ,473 13,873

Ford Motor Co 1.30 2,791,780 38,376

Tesla Inc 1.24 96,864 1,272

Twenty-First Century Fox I nc 0.99 795,446 10,376 Class A

Marriott I nternational Inc 0.96 249,679 2,990 Class A

Target Corp 0.91 401,906 5,422

CBS Corp Class B 0.80 294 ,965 3,586

Las Vegas Sands Corp 0.79 329,069 4,086

Ross Stores Inc 0.79 298,381 3,616

O'Reilly Automotive I nc 0.72 71,069 864

Yum Brands Inc 0.70 262,485 3,302

Delphi Aut omotive PLC 0.67 203,765 2,788

31 Table B.2: Consumer Discretionary Allocation for Fidelity Fund (FSCPX) % Portfolio Shares Shares Top 25 Holdings Weight... Owned Change

Amazon.com Inc 14.56 127,800 -16,700

The Home Depot Inc 10.21 530,800 0 Walt Disney Co =i= 10.12 7 10,647 -13,900 Charter Communications Inc 7.10 167,069 -9,700 A

Nike Inc B 6 .27 919,050 -10,200

Dollar Tree Inc 4 .74 464,721 -17,800

TJX Companies I nc 4 .04 416,895 0

L Brands Inc 3.50 537,625 0

The Interpublic Group of 2 .72 937,057 0 Companies Inc

Comcast Corp Class A 2.10 435,200 0

Time Warner Inc 2.00 163,400 -21,500

Ross Stores Inc 1.83 228,759 0

O'Reilly Automotive Inc 1.75 57,098 16,740

Starbucks Corp 1.72 232,600 0

Spectrum Brands Holdings I nc 1.58 89,402 -22,200

QVC Group Class A 1.41 541,510 0

Las Vegas Sands Corp 1.35 185,770 0

Marriott International Inc 1.26 108,044 11,600 Class A

The Priceline Group I nc 1.23 5,400 5,400

Monster Beverage Corp 1.21 216,420 0

Wyndham Worldwide Corp 1.14 96,700 49,400

Mattel I nc 1.06 384,200 0

Tenneco Inc 1.04 134,116 0

Ocacio Group PLC 1.04 2,599,056 0

Hilton Worldwide Holdings Inc 1.03 142,186 -22,800

32 Table B.3: Consumer Discretionary Allocation for SPDR Fund (XLY) % Portfolio Shares Shares Top 25 Holdings Weight Owned Change ....

Amazon.com I nc 15.27 1,951,915 0

Comcast Corp Class A 7.50 23,345,669 0

The Home Depot I nc 7.30 6,003,354 0

Walt Disney Co 6.11 7,170,539 0

McDonald's Corp 4.75 4,035,839 0

Starbucks Corp 3.57 7,182,568 0

The Priceline Group Inc 3.55 242,367 0

Time Warner Inc 2.97 3,816,228 0

Charter Communications Inc 2.81 1,059,893 0 A

Lowe's Companies Inc 2.71 4,267,770 0

Netflix I nc 2.71 2,121,197 0

Nike Inc B 2.70 6,540,952 0

TJX Companies I nc 1.9 1 3,212,755 0

General Motors Co 1.74 6,717,061 0

Ford Motor Co 1.65 19,237,282 0

Marriott International Inc 1.30 1,549,848 0 Class A

Ta rget Corp 1.17 2,740,717 0

Twenty-First Century Fox Inc 1.10 5,201,071 0 Class A

Carnival Corp 1.03 2,062,286 0

Newell Brands I nc 0.99 2,377,362 0

Ross Stores I nc 0.97 1,939,008 0

Yum Brands I nc 0.94 1,656,297 0

Delphi Automotive PLC 0.92 1,333,133 0

CBS Corp Class B 0.88 1,828,965 0

O'Reilly Automotive Inc 0.88 451,563 0

33 Table B.4: Energy Sector Allocation for Vanguard Fund (VDE) % Portfolio Shares Shares Top 25 Holdings Weight Owned Change ..,.

Exxon Mobil Corp 22.94 13,734,789 -38,601

Chevron Corp 13.65 6,252,723 -17,613

Schlumberger Ltd 6.84 4,608,294 -12,931

ConocoPhillips 4.02 4,103,880 -11,547

EOG Resources Inc 3.61 1,909,363 -5,336 +--- Occidental Petroleum Corp 3.19 2,531,118 -7, 133

Halliburton Co 2.69 2,863,249 -8,045

Kinder Morgan Inc P 2.65 6,284,975 -17,638

Phillips 66 2.53 1,552,650 -4,287

Anadarko Petroleum Corp 2.16 1,851,188 -5, 180

Pioneer Natural Resources Co 1.99 562,083 -1,540

Valero Energy Corp 1.98 1,499,282 -4,142

Marathon Petroleum Corp 1.82 1,748,149 -4,781

Williams Companies I nc 1.69 2,702,815 -7,200

Baker Hughes I nc 1.62 1,330,234 -3,571

Devon Energy Corp 1.26 1,560,396 -4,302

Concho Resources Inc 1.25 483,638 -1,566

Apache Corp 1.25 1,256,483 -3,408

Noble Energy Inc 0.99 1,498,086 5,648

Hess Corp 0.94 943,271 -3,208

TechnipFMC PLC 0.90 1,467,953 -4,211

Nat ional Oilwell Va rco Inc 0.90 1,251,652 -2, 704

Marathon Oil Corp 0.85 2,807,558 -6,100

Cimarex Energy Co 0.75 314,322 -1,202

ON EOK Inc 0.75 696,987 -1,770

34 Table B.5: Energy Sector Allocation for Fidelity Fund (FSENX) % Portfolio Shares Shares Top 25 Holdings Weight... Owned Change

Exxon Mobil Corp 8.65 2,174,148 13,900

Chevron Corp 7.78 1,496,523 0

EOG Resources Inc 6.52 1,446,864 -13,700

Baker Hughes I nc 5.54 1,915,800 -35,400

Pioneer Natural Resources Co 4.67 554,299 7,800

Halliburton Co 4.16 1,863,200 92,700

Anadarko Petroleum Corp 4.07 1,466,015 -62,700

Diamondback Energy Inc 3.94 810,900 41,200

Schlumberger Ltd 3.18 900,358 0

Kinder Morgan I nc P 2.60 2,590,700 0

Pa rsley Energy I nc A 1.96 1,352,500 -14,000

Rice Energy I nc 1.94 1,867,529 7,000

Cimarex Energy Co 1.93 340,245 0

RSP Permian Inc 1.83 988,800 -30,600

Phillips 66 1.71 440,773 -33,300

Marathon Petroleum Corp 1.68 675,700 -43,400

Newfield Exploration Co 1.56 927,200 -60,400

Williams Companies I nc 1.55 1,041,500 73,900

PDC Energy Inc 1.51 560,751 0

Continental Resources Inc 1.47 709,800 36,700

LyondellBasell I ndustries NV 1.43 347,600 108,900

Callon Petroleum Co 1.40 2,420,500 0

Delek US Holdings Inc 1.31 1,117,900 -26,300

Encana Corp 1.30 2,497,000 -58,900

Noble Energy Inc 1.28 813,688 -186,100

35 Table B.6: Energy Sector Allocation for SPDR Fund (XLE) % Portfolio Shares Shares Top 25 Holdings Weight... Owned Change

Exxon Mobil Corp 24. 19 4 8,076,10 1 -88,452

Chevron Corp 15.80 24,446,993 -44,973

Schlumberger Ltd 7.82 18,077,434 -33,255

ConocoPhillips 4.52 16,156,972 -29,727

EOG Resources I nc 4.25 7,543,232 - 13,878

Occidental Petroleum Corp 3.77 10,020,110 - 18,432

Halliburton Co 3.22 11,397,669 -20,970

Kinder Morgan Inc P 3.00 25,262,571 -46,476

Ph illips 66 2.79 5,830,468 - 10,728

Pioneer Natural Resources Co 2.36 2,249,084 -4,140

Anadarko Petroleum Corp 2.36 7,385,582 - 13,590

Va lero Energy Corp 2.31 5,984 ,330 - 11,007

Marathon Petroleum Corp 2.29 7,032,102 - 12,942

Williams Companies I nc 2.02 11,042,486 -20,313

Baker Hughes I nc 1.94 5,676,010 - 10,440

Concho Resources Inc 1.62 2,001,656 -3,681

Devon Energy Corp 1.56 7,047,611 - 12,969

Apache Corp 1.52 5, 116,447 -9,414

TechnipFMC PLC 1.14 6,378,164 - 11,736

Noble Energy Inc 1.13 6,225,603 - 11,457

Hess Corp 1.10 3,709,524 -6,831

National Oilwell Va rco I nc 1.05 5, 179,375 -9,531

Marathon Oil Corp 0.97 11,682,308 -21,492

Cabot Oil & Gas Corp Class A 0.94 6,627,740 - 12,195

ONEOK I nc 0.94 2,938,653 -5,409

36 Table B.7: Financial Sector Allocation for Vanguard Fund (VFH) % Portfolio Shares Shares Top 25 Holdings Weight Owned Change

~ JPMorgan Chase & Co j 8.85 6,309,353 -4,549 Wells Fargo & Co 7.30 8,412,765 -6,118

Bank of Am erica Corporation 6.71 17,817,603 -12,980

Berkshire Hat haway Inc B 5.75 2,159,180 -1,696

Citigroup I nc 4.79 5,024 ,692 -3,805

US Bancorp 2.48 2,996,770 -2,442

Goldman Sachs Group Inc 2.28 631,010 -507

Chubb Ltd 1.82 820,397 -821

American International Group 1.78 1,811,014 -1,482 I nc

American Express Co 1.75 1,371,616 - 1,207

Morgan Stanley t 1.73 2,476,525 -2,079

PNC Financial Services Group 1.66 857,683 -832 I nc

Bank of New York Mellon Corp 1.41 1,864 ,195 -1,612

MetLife Inc 1.38 1,647,153 -1,500

BlackRock Inc 1.33 2 14,310 -188

Charles Schwab Corp 1.32 2,103,552 -1,871

Prudential Financial Inc 1.31 758,057 -836

CME Group I nc Class A 1.12 598,229 -755

Capital One Financial Corp 1.10 850,258 -874

Marsh & McLennan 1.09 908,982 -1,057 Companies Inc

I ntercontinental Exchange Inc 1.02 1,050,302 -1,245

BB&T Corp 1.00 1,430,576 -1,513

S&P Global Inc 0.99 456,727 -569

The Travelers Companies Inc 0.98 500,732 -429

State Street Corporation 0.92 680,068 -835

37 Table B.8: Financial Sector Allocation for Fidelity Fund (FIDSX) % Portfolio Shares Shares Top 25 Holdings Weight... Owned Change

Capital One Financial Corp 5.69 653,700 -6,300

Cit igroup I nc t 5.42 847,490 -20,000

Bank of America Corporation 5.27 2,087,300 -49,400

Berkshire Hathaway Inc B 5.04 282,000 -81,900

Wells Fargo & Co 4.84 830,300 -19,700

Huntington Bancshares Inc 4.66 3,350,000 0 Goldman Sachs Group I nc ~ 4.50 185,700 -4,300 The Travelers Companies I nc 3.65 276,800 1,800

Chubb Ltd 3.64 244,900 -100

JPMorgan Chase & Co t 3.50 371,700 -59,500

PNC Financial Services Group 3.29 253,600 -11,400 Inc

Intercontinental Exchange Inc 2 .85 436,800 -38,200

Allstate Corp 2 .56 291,000 -13,100

Synchrony Financial 2 .56 850,000 -100,000

Northern Trust Corp 2.48 254,100 -11,400

US Bancorp 2.47 444,900 -155,100

E*TRADE Financial Corp 2 .34 625,000 42,485

CBOE Holdings Inc 2 .24 250,900 -9,100

Torchmark Corp 2 .09 252,100 -37,000

BlackRock Inc 1.94 46,500 -3,500

Ameriprise Financial I nc 1.89 136,400 -3,600

Fidelity National Financial Inc 1.84 414,100 -10,900

TD Ameritrade Holding Corp 1.79 431,200 -6,300

CIT Group Inc 1.73 345,000 -5,000

Re Group of America 1.69 125,000 35,000 Inc

38 Table B.9: Financial Sector Allocation for SPDR Fund (XLF) % Portfolio Shares Shares Top 25 Holdings Weight... Owned Change

Berkshire Hat haway Inc B 10.89 14,648,624 77,500

JPMorgan Chase & Co 10.55 27,549,276 145,800

Wells Fargo & Co 8.17 34,730,270 183,800

Bank of America Corporation 8.06 77,320,162 409,200

Citigroup Inc 5.95 2 1,369,448 113,100

Goldman Sachs Group I nc 2.87 2,857,532 15,100

US Bancorp 2.84 12,281,804 65,000

Chubb Ltd 2.29 3,592,424 19,000

Morgan St anley 2.13 11,082,569 58,700

PNC Financial Services Group 2.04 3,749,635 19,800 I nc

American Express Co 2.03 5,838,962 30,900

American International Group 1.93 6,783,16 1 35,900 I nc

MetLife Inc 1.92 8,385,541 44,400

BlackRock Inc t 1.71 938,417 5,000

Bank of New York Mellon Corp 1.70 8,001,092 42,400

Charles Schwab Corp 1.66 9,369,478 49,600

Prudential Financial Inc 1.56 3,316,264 17,600

CME Group Inc Class A 1.39 2,619,441 13,900

Marsh & McLennan 1.36 3,972,105 21,000 Companies Inc

Capital One Financial Corp 1.33 3,707,072 19,600

S&P Global Inc 1.25 1,991,361 10,500

I ntercontinental Exchange Inc 1.24 4,594,251 24,300

The Travelers Companies I nc 1.20 2,157,185 11,400

BB&T Corp 1.19 6,235,713 33,000 Aon PLC t 1.18 2,023,231 10,700

39 Table B.10: Utility Sector Allocation for Vanguard Fund (VPU) % Portfolio Shares Shares Top 25 Holdings Weight... Owned Change

NextEra Energy I nc 7 .74 1,899,04 6 40,444

Duke Energy Corp 7 .0 5 2,800,144 59,540

Southern Co 6 .05 3,985,930 84 ,756

Dominion Energy I nc 6 .01 2,54 7,100 54 ,174

Xcel Energy Inc 5.67 4,128,854 87,872

PG&E Corp 4 .20 2,055,074 43,738

American Electric Power Co 4 .13 1,998,401 42,538 I nc

Exelon Corp 3.96 3,752,184 79,780

Sem pra Energy 3.33 965,442 20,498

Edison Internat ional 3.23 1,324,171 28,138

PPL Corp 3.21 2,762,100 58,798

Consolidated Edison Inc 2.99 1,238,422 26,444

Public Service Ent erprise 2.76 2,05 5,976 43,660 Group Inc

WEC Energy Group Inc 2.37 1,282,758 27,924

Eversource Energy 2.34 1,289,24 2 28,056

DTE Energy Co 2.33 729,277 15,878

American Water Works Co I nc 1.76 723,44 2 15,668

Entergy Corp 1.69 728,081 15,856

Ameren Corp 1.64 986,150 2 1,416

FirstEnergy Corp 1.58 1,730,288 37,580

CMS Energy Corp 1.58 1,137,628 24 ,786

CenterPoint Energy I nc 1.45 1,662,875 36,160

Pinnacle West Capital Corp 1.17 4 52,133 9,566

SCANA Corp 1.12 551,590 11,702

Alliant Energy Corp 1.11 924,099 19,506

40 Table B.11: Utility Sector Allocation for Fidelity Fund (FSUTX) % Portfolio Shares Shares Top 25 Holdings Weight Owned Change ..,.

NextEra Energy I nc 17.59 918,485 0

Sempra Energy 13.00 802,327 3,100

PG&E Corp 8.74 909,204 0

Dominion Energy I nc 6.29 566,168 0

Avangrid I nc 4 .99 800,54 2 15,700

DTE Energy Co 4 .94 329,470 0

Great Plains Energy I nc 4 .82 1,136,268 64 ,200

Exelon Corp 4 .72 951,392 28,300

CenterPoint Energy I nc 4 .21 1,028,126 - 19,900

FirstEnergy Corp 3.87 902,200 4 ,900

SCANA Corp 3.05 320,500 -3,100

NextEra Energy Partners LP 2.77 558,286 0

Black Hills Corp 2.71 278,128 -5,100

NRG Energy I nc 2.34 966,002 0

PNM Resources I nc 2.18 4 07,266 -31,500

OG E Energy Corp 2.12 4 24,785 23,500

NRG I nc C 1.88 741,170 0

Pat tern Energy Group Inc 1.74 551,622 0 Class A

Cheniere Energy I nc 1.46 224,189 224 ,189

Charter Communications Inc 1.29 26,100 0 A

Cheniere Energy Partners LP 1.19 323,34 2 0 Holdings LLC f--- South Jersey Industries Inc 1.14 212,4 95 0 f--- Dynegy I nc 0.37 4 00,328 0

Kinder Morgan I nc P 0.27 89,700 89,700

InfraREIT I nc 0.10 37,800 37,800

41 Table B.12: Utility Sector Allocation for SPDR Fund (XLU) % Portfolio Shares Shares Top 25 Holdings Weight Owned Change ....

NextEra Energy I nc 9.82 5,054,688 276,842

Duke Energy Corp 8.19 6,971,4 52 382,036

Dominion Energy I nc 7.59 6,789,549 371,904

Southern Co 7 .46 10,708,111 586,762

American Electric Power Co 5.22 5,339,932 292,4 87 Inc

PG&E Corp 5.12 5,507,727 301,725

Exelon Corp 4 .95 10,015,208 548,618

Sempra Energy 4 .30 2,722,94 8 149,149

PPL Corp 4 .06 7,375,980 403,939

Edison Internat ional 3.90 3,537,821 193,700

Consolidat ed Edison Inc 3.76 3,320,462 18 1,929

Xcel Energy Inc 3.61 5,531,120 302,917

Public Service Ent erprise 3.36 5,472,131 299,639 Group Inc

DTE Energy Co 2 .95 1,960,243 107,429

WEC Energy Group Inc 2 .94 3,4 11,688 186,846

Eversource Energy 2 .90 3,4 25,838 187,591

Entergy Corp 2 .08 1,939,110 106,237

American Water Works Co I nc 2 .06 1,926,537 105,492

Ameren Corp 2 .05 2,64 5,083 144,828

CMS Energy Corp 2 .02 3,092,013 169,413

FirstEnergy Corp 1.91 4,774 ,954 261,942

Cent erPoint Energy I nc 1.85 4,722,135 258,664 Pinnacle West Capital Corp - 1.49 1,231,581 67,497 SCANA Corp 1.45 1,544,94 1 84 ,632

Alliant Energy Corp 1.40 2,4 61,204 134 ,845

42 Appendix C

Annual Portfolio Performance

43 Table C.1: Annual Portfolio Performance (Consumer Discretionary) Mean Return Std. Deviation Sharpe Ratio Portfolio Yr. 1 Yr. 2 Yr. 3 Yr. 1 Yr. 2 Yr. 3 Yr. 1 Yr. 2 Yr. 3 ovportA (no rebalancing) 0 .02161 0 .00104 0.00893 0.05890 0 .06177 0 .03750 0 .21746 -0.12566 0.00359 ovportB (annual rebalance) 0 .02161 -0.00039 0.01505 0.05890 0 .05660 0 .03495 0.21746 -0.16244 0.17874 VCR - Vanguard ConsDiscr 0 .01220 0 .00249 0.01045 0.03523 0 .04333 0 .02444 0 .0964 9 -0.14557 0.06754 FSCPX - Fidelity ConsDiscr 0 .01178 0.0013 1 0.00861 0.0348 7 0 .04367 0 .02200 0 .08532 -0.17157 -0.00859 XLY - SPDR ConsDiscr 0 .01384 0.0053 1 0.010 19 0.03426 0 .04484 0 .02399 0.14715 -0.07780 0.05800

Table C.2: Annual Portfolio Performance (Energy) Mean Return Std. Deviation Sharpe Ratio Portfolio Yr. 1 Yr. 2 Yr. 3 Yr. 1 Yr. 2 Yr. 3 Yr. 1 Yr. 2 Yr. 3 ovportA (no rebalancing) 0.0096 0 .0082 0.0208 0.0456 0.0430 0.0304 0 .0178 -0.0145 0.3964 ovportB (annual rebalance) 0 .009 6 -0.0040 0.0192 0.0456 0.043 1 0.0299 0 .0 178 -0.2976 0.3472 VFH - Vanguard Financial 0.008 1 -0.0033 0.0237 0.0304 0.0473 0.0428 -0.022 1 -0.2564 0 .3483 FIDSX - Fidelity Financial 0.0076 -0.0072 0.0195 0.0330 0.0469 0.0339 -0.0365 -0.3416 0 .3163 XLF - SPDR Financial 0 .008 1 -0.0037 0.0235 0.0337 0.0490 0.0447 -0.0211 -0.2553 0 .3281 44

Table C.3: Annual Portfolio Performance (Financial) Mea n Return Std. Deviation Sharpe Ratio Portfolio Yr. 1 Yr. 2 Yr. 3 Yr. 1 Yr. 2 Yr. 3 Yr. 1 Yr. 2 Yr. 3 ovportA (no rebalancing) 0 .0096 0.0082 0.0208 0.0456 0.0430 0.0304 0 .0 178 -0.0145 0.3964 ovportB (annual rebalance) 0 .0096 -0.0040 0.0192 0.0456 0.0431 0.0299 0 .0 178 -0.2976 0.3472 VFH -Vanguard Financial 0 .0081 -0.0033 0.0237 0.0304 0.0473 0.0428 -0.0221 -0.2564 0.3483 FIDSX - Fidelity Financial 0.0076 -0.0072 0.0195 0.0330 0.0469 0.0339 -0.0365 -0.3416 0.3163 XLF - SPDR Financial 0 .0081 -0.0037 0.0235 0.0337 0.0490 0.0447 -0.0211 -0.2553 0.328 1

Table C.4: Annual Portfolio Performance (Utility) Mean Return Std. Deviation Sharpe Ratio Portf olio Yr. 1 Yr. 2 Yr. 3 Yr. 1 Yr. 2 Yr. 3 Yr. 1 Yr. 2 Yr. 3 ovportA (no rebalancing) 0.01478 0.02153 0.01335 0.04636 0 .04282 0.04740 0.12888 0 .29720 0.09594 ovportB (annual rebalance) 0.0147 8 0.02178 0.00907 0.04636 0 .04386 0 .06391 0.12888 0 .29598 0.00428 VPU - Vanguard Utility 0.00772 0.01161 0.00661 0.04526 0 .03946 0.03779 -0.02394 0 .07116 -0.05792 FSUTX - Fidelity Utility 0 .0057 8 0.00269 0.00757 0.03510 0 .03814 0 .03687 -0.08594 -0.16006 -0 .03346 XLU - SPDR Utility 0 .00862 0.01223 0.005 61 0.0455 1 0 .03958 0 .03980 -0.00405 0 .086 54 -0.08011