Natural Phenomena and Human Economic Behavioral …

Natural Phenomena and HumanEconomic Behavioral Influence inMulti-Factor Predictive Modeling

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Natural Phenomena and Human Economic Behavioral Influence in Multi-Factor

Predictive Modeling

Shawn J. Mushtaq

A Thesis in the Field of International Relations

for the Master of Liberal Arts Degree

Harvard University

November 2017

Abstract

This research investigates the impact of human economic behavioral activity and

the Earth’s magnetic field in the area of financial economics using the Fama-French 3-

Factor Model as a test subject. The research objective is to test whether human economic

and geomagnetic activity could improve quantifiable estimated outputs in the Fama-

French Model—and to discover if there are any relationships with these variables that

could have a profound influence in predicting financial market or economic activity.

After reviewing all data and research approaches, the concluding analysis

indicates that geomagnetic activity does not have strong enough influence to reasonably

predict equity and fund returns. For human economic behavior, the absolute change in

Money Velocity and U-3 Unemployment improves the original Fama-French 3-Factor

Model by nearly 3% and outpaces the 5-Factor model under an array of tests. Keywords

for this research are: (i) Financial Economics, (ii) Quantitative Methodology, (iii)

Investment Portfolio Management, (iv) Geophysics, and (v) Machine Learning. Research

supervision was directed under Muhammet Bas, Ph.D. at the Department of Government,

Harvard University Graduate School of Arts and Sciences.

iv

Table of Contents

I. Introduction….……………………………………………….…………………………1

Research Questions………………………………….…...………………………..2

Research Hypothesis……………………………………………...……….…...….2

Research Significance……………………………………….……...…………..…3

II. Definition of Terms…..…...............................................................................................4

III. Literature Review – Background of the Problem…..…................................................8

IV. Research Methodology……………………………………………..………………..16

V. Data Transformations…………………………………...…………………………….23

VI. Limitations…………………………………………………………………...………26

VII. Quantitative Modeling with Returns………..…………………………..………..…27

Original Approach: State Street Corporation Stock Returns……….....................27

Original Approach: Vanguard S&P 500 Fund Returns.…….…………….……..34

EMA Approach: State Street Corporation Stock Returns….……………..……...43

EMA Approach: Vanguard S&P 500 Fund Returns….…………....……...……..46

Concluding Analysis for Chapter VII…………………………………...…...…..50

VIII. Model Validation & Estimation ………………………………………...…………53

List of Qualifying Models………………………………………………..………53

Model Fitness Test: STT Observed verses Predicted Values…..……………..…54

Model Fitness Test: Vanguard Observed verses Predicted Values ………..……56

v

Robustness Analysis on Modeled Vanguard Returns: 2008-2009 Financial

Crisis..........................................................................................................58

Alternative 5-Factor Model verses the Fama-French 5-Factor Model…………..59

Concluding Analysis for Chapter VIII…………………………….......................62

IX. Research Conclusion………………………………………………...........................64

Appendix A: Experiential Modeling with Adjusted Closed Prices…………...…………67

Section A-1: Modeling with STT Stock Prices ………………….....…...………68

Section A-2: Modeling with Vanguard Fund Prices……………....……...……...69

Section A-3: STT Robustness Analysis & Model Fitness…………..…...…...….72

Section A-4: Vanguard S&P 500 Robustness Analysis & Model Fitness…….…75

Appendix B: Data Transformation Approach for Returns………………...……………..78

Section B-1: State Street Corporation Stock Returns…………………….…..….79

Section B-2: Vanguard S&P 500 Fund Returns……………………………..…..82

Appendix C: Causality of Earth’s Magnetic Field and Human Economic Behavior……85

Appendix D: Correlation Matrix for STT Prices & Returns……………………….….…87

Appendix E: Correlation Matrix for Vanguard S&P 500 Fund Prices & Returns….…....91

X. References…………………………………………………………………...…..……95

vi

List of Tables

Table 5-1: Data Transformations………………………………………………………...23

Table 7-1: STT Original Model Regression Results, Part 1…………………………..…28

Table 7-2: STT Original Model Regression Results, Part 2…...……….………………..29

Table 7-3: STT Original Model Regression Results, Part 3.……...……………………..30

Table 7-4: STT Money Velocity Relationship Test...........................................................31

Table 7-5: STT Adjusted FFModel v. Original.................................................................32

Table 7-6: STT Original Model Regression Results, Part 4…..…………………………33

Table 7-7: Van500 Original Model Regression Results, Part 1……………………….…35

Table 7-8: Van500 SumKp Relationship Test……………………………………...……36

Table 7-9: Van500 Ap Relationship Test…………..………………………………..…..36

Table 7-10: Van500 Cp Relationship Test…………………………………………….…36

Table 7-11: Van500 Adjusted DirectModelEcon v. FFModel…………..…………....…37

Table 7-12: Van500 Original Model Regression Results, Part 2……………...…………38

Table 7-13: Van500 Adjusted Model 2 v. FFModel ……………..…………………...…39

Table 7-14: Van500 Original Model Regression Results, Part 3………………...………40

Table 7-15: Van500 Original Model Regression Results, Part 4……..……………….…41

Table 7-16: STT EMA Approach, Part 1…………...……………………………………44

Table 7-17: STT EMA Kp Index Relationship Test…………………………………..…45

Table 7-18: STT EMA Approach, Part 2...………………………………………………45

Table 7-19: Van500 EMA Approach, Part 1…...……………………………..…………47

vii

Table 7-20: Van500 PerSavRateEMA Relationship Test...………………………...……48

Table 7-21: Van500 EMA Approach, Part 2………………………………………….…49

Table 7-22: STT Short-Listed Models for Chapter VII……………………………….…51

Table 7-23: Van500 Short-Listed Models for Chapter VII…………………………...…53

Table 8-1: All Qualifying Models…………………………………………………..……54

Table 8-2: 2008-2009 Financial Crisis (Vanguard) Predicted vs. Observed Returns……59

Table 8-3: Alternative 5-Factor v. Fama-French 5-Factor on STT Returns ………….…60

Table 8-4: Alternative 5-Factor v. Fama-French 5-Factor on Vanguard Returns ………61

Table A-1.1: STT Model Regression Results ………………………………………...…68

Table A-2.1: Van500 Regression Results……………………………………………..…69

Table A-3.1: 2008-2009 Financial Crisis (STT) Predicted vs. Observed Prices…...……74

Table A-4.1: 2008-2009 Financial Crisis (Vanguard) Predicted vs. Observed Prices…..77

Table B-1.1: STT Transformed Data Approach, Part 1……………………………..…...79

Table B-1.2: STT Transformed Data Approach, Part 2…………………………….....…80

Table B-2.1: Van500 Transformed Data Approach, Part 1……………………..…….…82

Table B-2.2: Van500 Transformed Data Approach, Part 2…………………………..….83

Table C-1: Results for Causality of Earth’s Magnetic Field and Human Economic

Behavior………………………………………………………………...…..……86

1

Chapter I

Introduction

The epic Sci-fi drama of George Lucas’s first Star Wars movie in May 1977 (Los

Angeles Times 2011) made headlines for decades with its subsequent releases thereafter.

The Star Wars story influenced ideas in science and technology—so much so, in fact, the

United States Government’s ballistic missile space defense system was nicknamed “Star

Wars” (Kreig 2008-2009: 1). What makes Star Wars an interesting topic in academia,

specifically within econometric modeling, is this quote from the 1977 movie by Obi-Wan

(Ben) Kenobi: “The Force is what gives a Jedi his power. It’s an energy field created by

all living things. It surrounds us and penetrates us. It binds the galaxy together” (IMDb

2016). Here, old Ben is describing natural phenomena influencing life—he is essentially

describing galactic magnetic fields (Han 2003: 3-12). Interestingly enough, the use of

natural phenomena in academic research has been investigated since the late nineteenth

century.

A multitude of researchers, from a variety of academic disciplines, researched (to

a limited extent) the influence of natural phenomena on the human body. In early

economic literature, scholars studied the interconnection between sunspot activity and

commercial collapses in addition to price fluctuations. Other studies have noted the

connection with sunspot activity, market behavior, and its use in equilibrium models.

Only recently, however, has some research investigated another natural phenomena

called the “Earth’s magnetic field” and its connection with political behavior that

2

potentially influences the outcome of market behavior in quantitative modeling (East

2014: 193-195). With such a colorful array of literature spanning physics to psychology,

however, this thesis will not continue to investigate how sunspot activity impacts

quantifiable societal outcomes, but use the natural phenomena of Earth’s magnetic field

to understand its influence and predictive power.

Research Questions

Since there is a research gap associating the Earth’s magnetic field with market

activity, this research will attempt to answer the following questions:

1. Although research has revealed the potential interconnection of geomagnetic

activity with market behavior, could this natural phenomena actually increase the

prediction power of quantitative models?

2. What about the human behavioral element—does that play a role in econometric

modeling?

Research Hypotheses

This research hypothesizes that, based on existing literature, the Earth’s magnetic

field might have a minute influence on improving quantifiable estimated outputs.

Although it can be hypothesized that magnetic activity could influence human economic

behavior, the use of the human behavioral element in econometric modeling might also

reveal some changes in predicted outputs. Despite the possibility of these variables

having some influence in quantitative estimation, the purpose of the thesis is to provide

grounded analysis for a better understanding of this research area—and contribute

3

meaningful findings that could give rise to new research areas outside the scope of

financial economics.

The thesis uses quantitative techniques to determine the variables’ possible impact

in estimated outputs. Additionally, this analysis relies on historical time-series data used

by an array of academic disciplines and institutions: such as geophysics, the social

sciences, and governmental agencies.

Research Significance

The significance of the final outcome in this research should reveal (a) the

relationships between or among the variables used in this research; (b) the influence of

geomagnetic activity in econometric outputs; (c) lastly, the impact of human economic

behavior, with and without geomagnetic activity, in quantitative estimation.

4

Chapter II

Definition of Terms

Chapter II defines all data used in this research. Applications, such as RStudio

(including packages) and Microsoft Excel, was utilized for data transformations,

adjustments, analysis, and storage:

Kp Index (abbreviation:“SumKp”): an independent variable of the Earth’s Magnetic

Field activity derived from the K Planetary Index which is transformed from its 3-

hourly range to a monthly average (NOAA 2016). Due to the lack of data quality from

the United States National Oceanic and Atmospheric Administration (NOAA), this data

was retrieved from the British Geological Survey in the United Kingdom. Chapter V

discusses additional transformations for this variable.

Ap Index (abbreviation:“Ap”): an independent variable measuring geomagnetic storm

events in a 24-hour time period derived from the Kp Index which aligns, to some

degree, with sunspot activity (NOAA 2016). For this research, the Index was

transformed to a monthly average. Due to the lack of data quality from the United

States National Oceanic and Atmospheric Administration (NOAA), this data was

retrieved from the British Geological Survey in the United Kingdom. The data is also

transformed using a variety of mathematical techniques to test its impact on market

activity—this is discussed later in Chapter V.

Cp & C9 Index (abbreviation:“Cp” & “C9”): both Cp and C9 are independent variables

measuring overall magnetic activity. The C9 Index, however, converts the Cp Index to

5

a single digit from 0 to 9 (Ivory 2016: 1). These variables were converted to a monthly

average for this research. Since this data is not provided by the United States National

Oceanic and Atmospheric Administration (NOAA) at the time of retrieval, the British

Geological Survey in the United Kingdom served as an access-point for this

information. Chapter V discusses additional transformations for these variable.

Personal Consumption Expenditure (abbreviation:“PerConsumEx”): an independent

human economic behavior variable representing spending on goods and services within

the United States. This data frequency is monthly and seasonally adjusted with

additional data transformations discussed in Chapter V. The information was retrieved

from the Federal Reserve Bank of St. Louis.

Velocity of M2 Money Stock (abbreviation:“ M2Money”): an independent human

economic behavior variable representing all U.S. currency in circulation which includes

investment, savings, and deposit accounts. The data frequency is monthly in billions of

U.S. Dollars and seasonally adjusted. This information was retrieved from the Federal

Reserve Bank of St. Louis. Additional data transformations were conducted for this

research study (See Chapter V).

Personal Savings Rate (abbreviation:“PerSavRate”): an independent human economic

behavior variable describing the percentage rate at which U.S. citizens save their

money from disposable income. This data has a monthly frequency, is seasonally

adjusted, and in billions of U.S. Dollars. The data was provided by the Federal Reserve

Bank of St. Louis. Additional data transformations were conducted for this research

study (See Chapter V).

6

Unemployment (abbreviation:“U3Unemploy”): an independent human economic

behavior variable that represents seasonally adjusted U-3 unemployment rate in the

United States. The data frequency is monthly and retrieved from the United States

Bureau of Labor of Statistics. Additional data transformations were conducted for this

research study (See Chapter V).

MktRF, SMB, HML, RMW, and CMA: independent variables representing factors used

in Fama-French’s model: such as MktRF, also abbreviated as (Rmt – Rft), which

represents the return for the New York Stock Exchange (NYSE), NASDAQ, and the

American Stock Exchange (AMEX) minus the U.S. Treasury Bill rate (at one month);

SMB reflects the mean return from a small portfolio minus large portfolios; HML is

calculated by subtracting the high book-to-market to the Small B/M value on value

portfolios and growth portfolios; RMW is calculated by subtracting two robust

portfolios from two weak operating portfolios in term of their mean return; lastly,

CMA’s calculation is similar to RMW, but considers the level of risk tolerance by

subtracting high and low risk portfolios (French 2016: 1). These variables were

retrieved from Kenneth French’s website at the Tuck School of Business, Dartmouth

College.

STT: a dependent variable representing State Street Corporation’s monthly closed-

adjusted stock price to incorporate dividends and splits (NYSE: STT). The data was

retrieved from Yahoo Finance.

Van500: a dependent variable representing Vanguard’s S&P 500 Index fund

(NASDAQ: VFINX) that closely tracks the S&P 500 Index. The fund consists of the

largest American corporations which accounts for 75% of the U.S. stock market’s value

7

(Vanguard 2016). The data frequency is monthly and incorporates adjusted closed

domestic stock price to account for dividends and splits. This data was retrieved from

Yahoo Finance.

8

Chapter III

Literature Review − Background of the Problem

The first academic literature documenting the Earth’s Magnetic Field was

published by William Gilbert in De Magnete. Gilbert (1600/1958) discussed the Earth’s

magnetic field as a force controlling the North and South Pole. In addition, Gilbert

(1600/1958) also explained how the geomagnetic field dictates the behavior of a

compass’s needle in terms of the true North, South, East, and West that is dependent on

the geographical location of the measurement being observed or recorded.

Lanza & Meloni (2006) has noted that the Earth’s magnetic field is divided into

three parts: (1) the internal field, also known as the Main Field; (2) the magnetosphere,

which is the external field; and (3) the ionosphere, which is responsible for global

variation in magnetism on Earth. Although the origins of the geomagnetic field are still

being studied, the Main Field is produced by the Earth’s fluid core; in addition, the

external field (i.e., magnetosphere) is produced by electric currents protecting Earth from

solar wind dictated by the Sun’s behavior (Lanza & Meloni 2006: 1). According to the

National Oceanic and Atmospheric Administration (NOAA), the Earth’s magnetic field is

measured by the following:

declination (D), inclination (I), horizontal intensity (H), the north (X) and

east (Y) components of the horizontal intensity, vertical intensity (Z), and

total intensity (F). The parameters describing the direction of the magnetic

field are declination (D) and inclination (I). D and I are measured in units

of degrees, positive east for D and positive down for I. The intensity of the

total field (F) is described by the horizontal component (H), vertical

component (Z), and the north (X) and east (Y) components of the

9

horizontal intensity. These components may be measured in units of gauss

but are generally reported in nanoTesla (1nT * 100,000 = 1 gauss). The

Earth’s magnetic field intensity is roughly between 25,000 - 65,000 nT (.25

- .65 gauss). Magnetic declination is the angle between magnetic north and

true north. D is considered positive when the angle measured is east of true

north and negative when west. Magnetic inclination is the angle between

the horizontal plane and the total field vector, measured positive into Earth.

In older literature, the term “magnetic elements” often referred to D, I, and

H (NOAA 2016).

NOAA (2016) also measures the magnetic field with indices: such as [K], [KP], and

[AP]; the [K] Index represents a 3 hour range of magnetic activity; the [KP] Index is a

planetary mean measurement of the [K] Index; the [AP] Index is similar to the [KP]

Index in that it measures the earliest maximum value in a 24-hour time period. Lastly, the

[Cp] Index is a qualitative estimate of overall magnetic activity, which aggregates daily

[AP] measurements—this index also has a counterpart called the [C9] Index that converts

the [Cp] Index to one digit ranging from 0 to 9 (Ivory 2016: 1). With this knowledge, the

question is: how influential could magnetic activity be in quantitative modeling? Since

there is limited information on the subject, history has shown that researchers have used

natural phenomena in a variety of studies.

Hyde Clarke’s “A Preliminary Inquiry into the Physical Laws Governing the

Periods of Famines and Panics” was one of the first publications describing how a natural

phenomenon could be interconnected with economic activity. After Clarke (1847)

introduced the concept of “physical economy,” he compared cycles of crops including

price fluctuations, famine periods, the influence of solar and lunar winds on Earth’s

weather, and harvest periods. The result was that speculation, famine, and panic can

occur in roughly ten or eleven year intervals (Clarke 1847: 157). Outside factors, such as

10

solar and lunar winds influencing weather trends on Earth leading to economic

fluctuations, prompted an investigation into the physical laws of sunspot behavior.

In “Commercial Crisis and Sun-Spots,” Jevons referenced Hyde Clarke’s

exploration on how nature can influence economic outcomes. Jevons (1878) focused his

research on sunspot activity and commercial collapses; the end result from his study

revealed a 10.8 year interval in the commercial collapse timeline of 1825, 1836-9, 1847,

1857, and 1866; when comparing that interval with the duration of sunspot activity, the

results revealed a difference of 0.3.1 The discovery of business cycles linking with

sunspot activity led to a quantitative standard in the twentieth century.

“Do Sunspots Matter?” introduced the sunspot equilibrium formulated by Karl

Shell and David Cass in response to the 1878 study by Jevons. The purpose of this

equilibrium model was to deviate away from the traditional models that yielded certainty

equilibria to a broader and more non-traditional approach (Shell and Cass 1983: 195).

Shell and Cass’s final overall result was that sunspots are an extrinsic random variable

that do not influence general economic principles; the equilibrium, however, can offer an

explanation of excess volatility.

Bizer et al. (2014) produced one of the first and most recent experimental studies

which explored strategic coordination and sunspot activity in economic forecasting. The

final result was that accurate predictions were finite with low payoffs under this model.

1 The commercial collapse interval (10.8) was deducted by the sunspot interval

(10.5). This calculation was intended to show the difference between actual verses

predicted results.

11

Bizer et al. (2014) suggested that more research should be conducted to reduce herding

for forecasters to support anti-herding.

“Sunspots, GDP, and the Stock Market” used raw data from the National

Aeronautics and Space Administration (NASA) that recorded the number of sunspots

over time. They analyzed the moving average of sunspot behavior, the Dow Jones

Industrial Average (DJIA), and the U.S. gross domestic product. The concluding results

were that the correlation between these variables is insignificant. Modis (2007), however,

noted that sunspot activity and its unusual similarity with the DJIA and U.S. GDP

warrants further investigation by scholars.

Russian academics Belkin & Poluyakhtov investigated the relationship between

solar activity cycles (i.e., sunspots), real U.S. GDP, and interest rates in “Unconventional

Cyclical Theory: Cyclical Solar Activity and the Cyclical Development of the Economy.”

Data used in their research was the annual indexes of real U.S. GDP and the number of

Wolf W—an indicator of solar activity. Belkin & Poluyakhtov (2011) analyzed extreme

deviations from the mean solar cycle activity including maximums and minimums in

correlation with GDP and interest rate growth. Belkin & Poluyakhtov (2011) concluded

that solar activity and interest rates appear to be correlated with a coefficient of 79%. In

addition, the authors (2011) also noted a possible economic decline from 2013-2015.

“Unemployment, and Recessions, or Can the Solar Activity Cycle Shape the Business

Cycle?” revisited solar activity maximums and their correlation with U.S. recessions—

roughly seven solar maximums revealed eight out of thirteen recessions plus low U.S

unemployment being preceded by six solar maximums with a rapid increase of

unemployment following a two to three year lag. Gorbanev (2012) methodology used

12

monthly data of sunspot numbers from the National Aeronautics and Space

Administration (NASA) and the U.S. National Oceanic and Atmospheric Administration

(NOAA).

In 2014, Jakie R. East published the first political science dissertation on how

natural phenomena, such as the Sun and Earth, could not only have a connection with

economics, but human behavior entitled “Natural Phenomena as Potential Influence on

Social and Political Behavior: The Earth’s Magnetic Field.” East’s ( 2014) dissertation

analyzed the baseline relationship between geomagnetic frequencies and an array of

societal outcomes within several social science disciplines.

For Political Science and Criminology, East (2014) illustrated that one area of the

natural phenomena effect on human behavior was expressed by the “opportunity and

motivation theory” under SAD (Seasonal Affective Disorder), where higher temperatures

correlates with less crime and the lack of sunlight is associated with depression and

suicide that influences the melatonin and serotonin areas of the brain (East 2014: 14-15).

Sociology, Psychology, and Biology has predominantly used a number of natural

phenomena variables to explain human behavior derived from Charles Darwin’s idea of

natural selection (East 2014: 16-17). For example, East (2014) noted that the New

Ecological Paradigm (NEP) uses natural phenomena variables to explain how human

behavior might be influenced by this environment (East 2014: 17). In addition, subfields

of psychology, such as environmental and evolutionary, examines how human behavior

and the environment interact with each other (East 2014: 17-18).

Although Economics has not heavily researched how geophysical variables are

interconnected with human behavior, which in turn, to some degree, could influence

13

market fluctuations, East (2014) analyzed how the Earth’s magnetic field could explain

swings in market prices. More specifically, for daily low & high numbers in the stock

market, an escalation in the [y] and [h] component of the magnetic field tends to increase

the distance between high and low numbers (East 2014: 193). In addition, East (2014)

also used the AP Index of the magnetic field to refine a model that analyzes U.S.

Presidential messages and its influence on the Dow Jones Industrial Average (DJIA) and

the National Association of Securities Dealers Automated Quotations (NASDAQ) index;

in East’s (2014) analysis, the magnetic variable did, in fact, slightly refine Martin’s (2008)

model (East 2014: 197-200).

Other literature, authored by Babayev & Allahverdiyeva (2007), noted that severe

magnetic disturbances can cause negative human emotional responses. Palmer, Rycroft,

and Cermack (2006) revealed that extreme low or high geomagnetic activity could affect

melatonin levels and cardiovascular health. Karasek et al. (1998) also published a study

revealing the effect of magnetic fields on melatonin levels within the human brain. East

(2014) also cited the interconnection between magnetic activity and the human brain’s

melatonin and serotonin levels. To better understand how both natural phenomena (i.e.,

magnetic activity) and human behavior could potentially influence outputs in quantitative

modeling, the Fama-French model is reviewed.

William F. Sharpe introduced the theory of the Capital Pricing Asset Model

(CAPM) in 1964 entitled “Capital Asset Prices: A Theory of Market Equilibrium under

Conditions of Risk,” with later contributions by John Linter (1965a, b), Jack Treynor

(1962), and Jan Mossin (1966); the CAPM model is described as:

Er= rf + βi(Em – rf) (1)

14

where:

Es = Expected return,

Rf = Risk free rate,

βi = Sensitive of a security,

Em = Expected market return,

(Em – rf) = Risk premium.

This model calculates the expected (predicted) return of a security or portfolio. In

equilibrium, the total risk is not priced—instead, it is market risk (systematic); in addition

the model also takes on specific risk (i.e., β)—meaning risk of the asset being estimated.

CAPM eventually became a benchmark for later quantitative equations to estimate

(predict) possible returns.

Following the contribution from Sharpe (1964), Linter (1965a, b), Treynor

(1962), and Mossin (1966) was the introduction of the three-factor model by Eugene

Fama and Kenneth French (1992, 1993) extending the CAPM model; the Fama-French

(1992, 1993) regression model is represented by the following equation:

Rit – Rft = αi + βi(Rmt – Rft) + siSMB +hiHMLt +ϵit ;

t = 1, 2..T for each i = 1, 2…N (2)

where:

αi = Intercept of the regression line;

Rit = For period t, return on security or portfolio i;

Rft = Risk free return;

Rmt = Return on the value-weighted market portfolio;

βi = Sensitive of a security;

siSMB = Small minus big;

hiHMLt = High minus low B/M;

ϵit = Standard error of the estimate.

The extension of the CAPM model by Fama and French (1992, 1993) added two more

betas (β) to the equation: SMB and HML. HML (β2) is calculated by subtracting the high

15

book-to-market to the Small B/M value. The theory behind this Fama and French’s

(1992, 1993) beta allows the model to recognize additional risk exposure between growth

and valued stocks. For SMB (β3), this is calculated by the difference between small and

large stocks—Fama and French’s (1992, 1993) calculation is essentially trying to explain

excess returns on a portfolio by market capitalization making this beta a measure of size

risk—meaning that smaller firms are exposed to more risk due to their lack of

diversification.

Overall, these models are designed to predict an outcome based on market

behavior. Since there is literature suggesting the interconnection with geomagnetic

activity and its influence on human behavior, could this natural phenomena actually

increase the prediction power of this model? What about the human element—does that

play a role in econometric modeling? This research will attempt to answer these

questions and provide grounded analysis for real-world model owners.

16

Chapter IV

Research Methodology

The research design will use a scenario analysis with differing categories: such as

a direct, indirect, and alternative quantitative modeling approach for the Fama-French 3-

factor model—this analyzes any improvement of the original model’s prediction

capabilities—and investigates the possible impact of the added variables on expected

returns without the Fama-French’s 3-Factor Model. The output of expected (predicated)

returns also incorporates a two-fold comparative analysis for model performance—this

includes single stock returns (i.e., State Street Corporation) and fund returns representing

500 of America’s largest corporations closely tracking the S&P 500 Index (i.e., Vanguard

S&P 500 Index Fund). The reason for using the Vanguard S&P 500 Fund is because the

Fama-French model typically performs much stronger compared to the use of a single

stock due to most of the 3-factors being constructed on a microeconomic level—the Fund

is also used to better understand how added variables behave in a larger market

environment. These assets are analyzed to determine if the modeling approaches

mentioned below increase estimation performance of the original Fama-French output.

The following is the direct approach equation:

Rit = αi + βi(Rmt – Rft) + siSMB +hiHMLt + β4it + β5it + β6it + ϵit ;

t = 1, 2..T for each i = 1, 2…N (3)

where:




17





β4it = SumKp activity for period t;

β5it = AP activity for period t;

β6it = Cp activity for period t;


The direct approach equation with human economic behavior variables is as follows:

Rit = αi + βi(Rmt – Rft) + siSMB +hiHMLt + β4it + β5it + β6it + β7it + β8it + β9it +

β10it + ϵit ; t = 1, 2..T for each i = 1, 2…N (4)

where:











β7it = Personal Consumption Expenditure for period t;

β8it = Velocity of M2 Money Stock for period t;

β9it = Personal Savings Rate for period t;

β10it = U-3 Unemployment for period t;


Alternative Model 1 Equation:

Rit = αi + βi(Rmt – Rft) + siSMB +hiHMLt + ∆β4it + ∆β5it + ∆β6it + ϵit ;

t = 1, 2..T for each i = 1, 2…N (5)

where:




18





∆β4it = SumKp activity for period t;

∆β5it = AP activity for period t;

∆β6it = Cp activity for period t;



Rit = αi + βi(Rmt – Rft) + siSMB +hiHMLt + ∆β4it + ∆β5it + ∆β6it + ∆β7it + ∆β8it

+ ∆β9it + ∆β10it + ϵit ; t = 1, 2..T for each i = 1, 2…N (6)

where:











∆β7it = Personal Consumption Expenditure for period t;

∆β8it = Velocity of M2 Money Stock for period t;

∆β9it = Personal Savings Rate for period t;

∆β10it = U-3 Unemployment for period t;



Rit = αi + βi(Rmt – Rft) + siSMB +hiHMLt + ∆β4it + ∆β5it + ∆β6it + ∆β7it + ϵit ; t =

1, 2..T for each i = 1, 2…N (7)

where:



19












Rit = αi + ∆β1it + ∆β2it + ∆β3it + ∆β4it + ∆β5it + ∆β6it + ∆β7it + ϵit ; t = 1, 2..T for

each i = 1, 2…N (8)

where:












Rit = αi + ∆β1it + ∆β2it + ∆β3it + ϵit ; t = 1, 2..T for each i = 1, 2…N (9)

where:







20


Rit = αi + ∆β1it + ∆β2it + ∆β3it + ∆β4it + ϵit ; t = 1, 2..T for each i = 1, 2…N (10)

where:









Rit = αi + β1it + β2it + β3it + β4it + β5it + β6it + β7it + ϵit ; t = 1, 2..T for each i = 1,

2…N (11) where:












Rit = αi + β1it + β2it + β3it + ϵit ; t = 1, 2..T for each i = 1, 2…N (12)

where:





21




Rit = αi + β1it + β2it + β3it + β4it + ϵit ; t = 1, 2..T for each i = 1, 2…N (13)

where:








In addition to the original modeling approach noted above, the research also utilizes two

other frameworks: such as the data transformation and exponential moving average

(EMA) approach. The transformation approach (see Appendix B) uses existing data to

better understand if any real impact may be viable for quantitative estimation; the data

transformation approach, however, will not use models located in the original approach.

Moreover, since geomagnetic data tends to be noisy, added betas are re-calculated to their

EMA form—human economic behavioral data is also transformed to understand their

impact in quantitative estimation. In addition, since both Cp and C9 are measurements of

the same geomagnetic frequency (with differing approaches), only Cp is utilized due to a

slight positive correlation increase with State Street stock returns—the same approach is

also applied to the Vanguard S&P 500 Fund. Lastly, data is correlated, using Pearson’s

correlation, to determine if any relationships exists between or among independent and

dependent variables (see Appendix D & E).

22

The variable selection process will have a p-value cap of 5%; a variance inflation

factor (VIF) analysis is also conducted to ensure that the selected variables are not

inflating model fitness metrics and to reduce multicollinearity; if a VIF analysis reveals

severe inflation, the removal of the variable will likely occur. Autocorrelation will be

addressed on a case-by-case basis—if severity is detected, generalized least square

regression or dependent variable differencing might occur. Data with the strongest

dependent variable relationship and model fit is tested against the Fama-French’s original

model (see Chapter VIII) to determine if there is any quantitative estimation

improvement—this includes conducting an analysis comparing actual verses estimated

outcomes to determine the model’s true reliability of predicted returns. Additionally, a

robustness analysis, during the 2008-2009 Financial Crisis, is used to test whether the

selected models can predict swings in the market. Lastly, human economic behavioral

and geomagnetic variables are tested for causality using the Granger test (see Appendix

C)—this is to determine if there are any underlying relationships among human

behavioral economic and geomagnetic variables (Granger 1988: 199-211). Although it is

not known if these variables reveal a relationship with each other for a predicted

outcome, it could be hypothesized that the unknown and known measurement error for

the time-series regression models should not reveal a significance of - 0 -.

23

Chapter V

Data Transformations

All variables used in Chapter II have undergone data transformations outside the

scope of absolute delta to better understand their impact in predicting returns; although a

select number of variables have already undergone a seasonality transformation from

their original source, this research did not adjust for seasonality. Table 5-1 below

illustrates the equation used to transform each independent variable including its name

and variable description ranging from September 1986 to November 2014.

Table 5-1: Data Transformations

Variable Name Variable

Equation Variable Description

PerConsumExDelta X2t - X1t

Personal Consumptions Expenditure transformed to express

the change (∆) from the current rate in time X2t minus the

previous rate X1t.

M2MoneyDelta X2t - X1t Velocity of Money transformed to express the change (∆)

from the current rate in time X2t minus the previous rate X1t.

PerSavDelta X2t - X1t Personal Savings Rate transformed to express the change (∆)

from the current rate in time X2t minus the previous rate X1t.

U3UnemployDelta X2t - X1t

U-3 unemployment rate transformed to express the change

(∆) from the current rate in time X2t minus the previous rate

X1t.

Kppwhalf √Xt The KP Index datum is square-rooted .

KPLN Ln(Xt) The KP Index datum transformed to its natural-logarithm.

SumKPDelta X2t - X1t The KP Index transformed to express the change (∆) from the

current rate in time X2t minus the previous rate X1t.

SumKPInv 1 ÷ Xt 1 divides the KP Index datum.

SumKPInvDelta X2t - X1t The derivative of SumKPInv transformed to express the

change (∆) from the current rate in time X2t minus the

24

previous rate X1t.

Appw8 Xt(1/0.8) The AP Index datum is squared by 1/0.8.

ApLn Ln(Xt) The AP Index datum transformed to its natural-logarithm.

APSqrt √ Xt The AP Index datum square-rooted for the data series.

APDelta X2t - X1t

The AP Index data series transformed to express the change


X1t.

APInv 1 ÷ Xt 1 divides the AP Index datum.

APInvDelta X2t - X1t

The derivative of APInv transformed to express the change


X1t.

Cppwnine Xt(1/9) The CP Index datum is squared by 1/9.

CpLn Ln(Xt) The CP Index datum transformed to its natural-logarithm.

CpSqrt √ Xt The CP Index datum square-rooted for the data series.

CPDelta X2t - X1t

The CP Index data series transformed to express the change


X1t.

CpInv 1 ÷ Xt 1 divides the CP index datum.

CpInvDelta X2t - X1t

The derivative of CpInv transformed to express the change


X1t.

C9pwsqurt Xt(2) The C9 Index datum is squared.

C9Ln Ln(Xt) The C9 Index datum transformed to its natural-logarithm.

C9Squrt √ Xt The C9 Index datum square-rooted for the data series.

C9Delta X2t - X1t

The C9 Index data series transformed to express the change


X1t.

C9Inv 1 ÷ Xt 1 divides the C9 Index datum.

C9InvDelta X2t - X1t

The derivative of C9Inv transformed to express the change


X1t.

25

In addition to the independent variable transformations above, this research also used one

of the most widely accepted formulas for technical traders to reduce noise, variance

modeling, and forecasting—Exponential Moving Average (EMA). Using a slightly

modified expression of Hutson’s (1984) equation, EMA is defined by the following:

EMA = Rt + α + µ (1-2) (14)

where:

Rt = Rate for period t;

α = 2 ÷ (n+1);

µ = (1 ÷ N) x ∑(xi).

For this research, EMA is applied to all geomagnetic and human economic behavior

variables. The mean (µ) data ranges from December 2004 to November 2009, or 60

monthly periods. EMA is calculated from December 2009 to November 2014, or 60

monthly periods—this totals 120 monthly periods for the entire EMA calculation per

variable. The filtered data is then applied to selected time-series regression equations

located in Chapter IV.

26

Chapter VI

Limitations

This research design is limited by advanced knowledge of geophysics. Since there

are multiple variables involved outside the scope of this design, it would be improbable

to identity every aspect and element influencing the research outcome. Moreover, the use

of more advanced quantitative techniques, such as vector autoregression (VAR)

modeling, is limited. Research limitations may also extends to medical and psychology

research used to evaluate and explain human behavior. In addition, this research is

limited to the 13 observatories measuring magnetic activity worldwide. Human economic

behavior data is limited to the United States. Data quality is limited to selected sources

mentioned in this research and cannot guarantee 100% accuracy of the raw data used.

The processing component is limited to least squares regression due to Fama and

French’s methodology choice; moreover, time-series data is not adjusted for lag. Models

that use Fama-French factors may only be applied to the equities market, or funds

constructed with stocks due to the research approach used. If the model(s) does not

include Fama-French factors, this research may only be applied to asset classes being

bought or sold in economies comparable with the United States—this is due to the nature

of the data being used in the analysis.

27

Chapter VII

Quantitative Modeling with Returns

Chapter VII is comprised of all time-series regression model approaches using

data in the original approach illustrated on Chapter IV and EMA filtered data for both

State Street Corporation’s stock and the Vanguard S&P 500 Index Fund percent-returns;

correlation matrices are located in Appendix D to E.

Original Approach: State Street Corporation Stock Returns

This section uses all equations (3 – 13) located in Chapter IV. After all regression

outputs have been calculated with the selected data, the model’s parameters maybe

modified (if applicable) to meet the cut-off p-value of any measurement over 5%. The

monthly time-series range is from October 1986 to November 2014. The first table

reveals regression results for the Direct Model Equation 3 (“DirectModel”) and the

direct model with human economic behavior variables, Equation 4 (“DirectModelEcon”)

compared with the Fama-French model (“FFModel”) using State Street Corporation

adjusted stock returns. For variable elimination, the focus of the regression output

includes the following: (i) Adj. R2, (ii) RMSE (root-mean-squared-error), and (iii) p-

values (0.1%, 1%, or 5%). A variance inflation factor (VIF) analysis will typically occur

after the model’s parameters have been adjusted.

28

Table 7-1: STT Original Model Regression Results, Part 1

In both the DirectModel and DirectModelEcon, added variables have reduced the

models’ goodness-of-fit compared the FFModel by the decrease in Adj. R2. In addition,

RMSE has increased compared to the FFModel which suggests that these models have

less predictability. All added variables compared to the original FFModel have a p-value

above 5% regardless if they were tested separately or together—this suggests a weak

relationship with State Street Corporation’s stock return. In the DirectModel equation,

aggregating all geomagnetic indices creates multicollinearity with variance inflation

factors (VIF) ranging from 14 (min) to 502 (max). DirectModelEcon, which includes

both geomagnetic and human economic variables, revealed that the economic parameters

DirectModel DirectModelEcon FFModel

===============================================

(Intercept) 0.23272 0.97533 -0.06705

(0.86118) (1.29853) (0.13014)

MktRF 0.36905 *** 0.37291 *** 0.36832 ***

(0.02981) (0.02994) (0.02967)

SMB -0.09371 * -0.09492 * -0.09350 *

(0.04258) (0.04299) (0.04236)

HML 0.21288 *** 0.21666 *** 0.21147 ***

(0.04670) (0.04671) (0.04613)

SumKp -0.01097 -0.00385

(0.01889) (0.01983)

Ap 0.00214 -0.00456

(0.06268) (0.06380)

Cp 2.75657 1.81069

(4.86835) (5.10027)

PerConsumEx -0.00029

(0.00031)

M2Money 0.0004

(0.00031)

PerSavRate -0.11966

(0.14328)

U3Unemploy -0.13806

(0.12954)

-------------------------------------------------------------------------------

R^2 0.32797 0.33967 0.32647

Adj. R^2 0.31579 0.31948 0.32042

Num. obs. 338 338 338

RMSE 2.3617 2.35532 2.3537

===============================================

*** p < 0.001, ** p < 0.01, * p < 0.05

29

have inflation factors at 49 and 40 for personal consumption expeditors (PerConsumEx)

including money velocity (M2Money)—the results suggest that severe multicollinearity

exists when these parameters are used. The Fama-French model is the best model for

predicting State Street stock returns under this scenario based on Adj. R2, RMSE, and

probability values. Table 7-2 displays results for models 1 to 3 which includes the

absolute change (delta) in both geomagnetic and human economic behavior.


Model 1 Model 2 Model 3 FFModel

==========================================================

(Intercept) -0.06662 -0.05318 0.15167 -0.06705

(0.13064) (0.21847) (0.59268) (0.13014)

MktRF 0.36615 *** 0.36058 *** 0.36019 *** 0.36832 ***

(0.02995) (0.03035) (0.08190) (0.02967)

SMB -0.09061 * -0.10563 * 0.04623 -0.09350 *

(0.04272) (0.04336) (0.11671) (0.04236)

HML 0.21403 *** 0.20961 *** 0.31496 * 0.21147 ***

(0.04669) (0.04716) (0.12686) (0.04613)

SumKPDelta -0.00727 -0.00953

(0.02919) (0.02930)

APDelta -0.01159 -0.00677

(0.05243) (0.05248)

CPDelta 1.38283 1.73015

(6.10560) (6.12231)

PerConsumExDelta 0.00619 -0.01094

(0.00446) (0.01206)

M2MoneyDelta -0.00652 0.01342

(0.00471) (0.01270)

PerSavDelta 0.00559 -0.17342

(0.16921) (0.45808)

U3UnemployDelta 0.68023 -2.66238

(0.84619) (2.28092)

--------------------------------------------------------------------------------------------------

R^2 0.32746 0.33676 0.07174 0.32647

Adj. R^2 0.31527 0.31648 0.05211 0.32042

Num. obs. 338 338 339 338

RMSE 2.3626 2.36052 6.40795 2.3537

==========================================================

*** p < 0.001, **p < 0.01, * p < 0.05

Both models 1 and 2 has decreased performance compared to the Fama-French

model. Multicollinearity exists when geomagnetic indices are used in Model 1: such as

30

SumKPDelta (VIF: 55.62), CPDelta (VIF: 55.12), and APDelta (VIF: 5.107). For Model

2, SumKPDelta (VIF: 56.17), CPDelta (VIF: 55.52), and APDelta (VIF: 5.12). When

these variables are removed, the only geomantic index that does not have a high inflation

factor is APDelta—however, even though ApDelta’s VIF results are relatively low

compared to other geomagnetic parameters, its p-value with the dependent variable

exceeds alpha significance at 15%—this suggests that APDelta is not a good predictor

for State Street stock returns. As for the absolute change in human economic behavioral

variables in Models 2 & 3, moderate-to-severe multicollinearity does not exist for

PerConsumExDelta, M2MoneyDelta, PerSavDelta, and U3UnemployDelta—regardless

of these results, however, neither variable can be used due to p-values exceeding alpha

with the dependent variable. Overall, the Fama-French model is the best predictor of

State Street stock returns under the scenario in Table 7-2. The next table displays model

results that does not include Fama and French’s 3-factors.


Model4 Model5 Model6 FFModel

=====================================================

(Intercept) 0.26108 0.21087 0.49135 -0.06705

(0.25956) (0.15545) (0.60308) (0.13014)

SumKPDelta -0.01645 -0.00906

(0.03509) (0.03519)

APDelta -0.00339 -0.01255

(0.06269) (0.06311)

CPDelta 2.07186 0.80039

(7.32018) (7.34871)

PerConsumExDelta 0.00983 -0.00519

(0.00526) (0.01219)

M2MoneyDelta -0.01200 * 0.00629

(0.00560) (0.01295)

PerSavDelta 0.12217 -0.01871

(0.20266) (0.47011)

U3UnemployDelta -0.49959 -3.69542

(1.00363) (2.31913)

MktRF 0.36832 ***

(0.02967)

SMB -0.09350 *

31

The absolute change (delta) in geomagnetic activity, defined by SumKPDelta,

APDelta, CPDelta, and C9Delta under Model 5, does not have a deterministic

relationship with State Street Corporation’s stock returns based on probability values.

The change in human economic behavior variables, defined under Model 4 and 6 by

PerConsumExDelta (Personal Consumptions Rate), M2MoneyDelta (Money Velocity),

PerSavDelta (Personal Savings Rate), and U3UnemployDelta (U-3 Unemployment), does

not have probability significance with the dependent variable except M2MoneyDelta

(Money Velocity); this parameter, as illustrated on Table 7-4, has a p-value of 2.1% with

the dependent variable making the relationship significant.

Table 7-4: STT Money Velocity Relationship Test

The table below displays a comparison of the adjusted Fama-French Model

(AdjFFModel), which includes M2MoneyDelta and the original model (FFModel).

(0.04236)

HML 0.21147 ***

(0.04613)

-----------------------------------------------------------------------------------------

R^2 0.03463 0.00698 0.00816 0.32647

Adj. R^2 0.01415 -0.00194 -0.00372 0.32042

Num. obs. 338 338 339 338

RMSE 2.83488 2.85793 6.59396 2.3537

=====================================================

*** p < 0.001, ** p < 0.01, * p < 0.05

===============================================

Residuals:

Min 1Q Median 3Q Max

-13.8415 -0.8245 -0.2493 1.1647 11.1416

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 0.549933 0.212255 2.591 0.00999 **

M2MoneyDelta -0.012830 0.005529 -2.320 0.02093 *

===============================================

*** p < 0.001, ** p < 0.01, * p < 0.05

32

Table 7-5: STT Adjusted FFModel v. Original

AdjFFModel FFModel

=================================

(Intercept) 0.11346 -0.06705

(0.18044) (0.13014)

MktRF 0.36421 *** 0.36832 ***

(0.02975) (0.02967)

SMB -0.09746 * -0.09350 *

(0.04238) (0.04236)

HML 0.20425 *** 0.21147 ***

(0.04633) (0.04613)

M2MoneyDelta -0.00667

(0.00463)

--------------------------------------------------------

R^2 0.33065 0.32647

Adj. R^2 0.32261 0.32042

Num. obs. 338 338

RMSE 2.34991 2.3537

=================================

*** p < 0.001, ** p < 0.01, * p < 0.05

Although the p-value for M2MoneyDelta is no longer significant due to inflation

from other parameters, the Adj. R2 and RMSE appears to have slightly improved model

performance at 32.26% (AdjFFModel) verses 32.04% (FFModel)—RMSE at 2.35

(AdjFFModel) verses 2.353 (FFModel). For all variables in the alternative model,

variance inflation factors are within reasonability at 1.09 (MktRF), 1.13 (SMB), 1.14

(HML), and 1.03 (M2MoneyDelta). The intercept of AdjFFModel suggests that the

expected State Street single stock return rate is 11% per month; the slope can be viewed

as the expected one-unit per share stock increase results in an escalation of MktRF’s

coefficient by 0.36, SMB by -0.097, and HML by 0.20 with the change in money velocity

by -0.006, respectively. The Fama-French model reveals that the expected State Street

single stock return rate decreases 7% per month; the slope can be viewed as the expected

one-unit per share stock return decrease results in an increase of MktRF’s coefficient by

33

0.37, SMB by -0.093, and HML by 0.21, respectively. To further study the model

performance between these models, AdjFFModel is back-tested against the Fama-French

model in Chapter VIII. Table 7-6 compares models 7, 8, and 9 to the FFModel.


Model7 Model8 Model9 FFModel

=================================================

(Intercept) 2.40213 0.52296 0.94714 -0.06705

(2.80791) (1.66798) (0.89970) (0.13014)

PerConsumEx -0.00054 -0.0003

(0.00040) (0.00028)

M2Money 0.0006 0.0004

(0.00039) (0.00032)

U3Unemploy -0.08371 -0.14236

(0.15862) (0.13432)

PerSavRate -0.15773

(0.17836)

SumKp -0.0092 -0.00658

(0.03800) (0.03535)

Ap 0.02239 0.02421

(0.07765) (0.07569)

Cp 1.68505 0.88542

(8.61664) (8.31994)

MktRF 0.36832 ***

(0.02967)

SMB -0.09350 *

(0.04236)

HML 0.21147 ***

(0.04613)

-----------------------------------------------------------------------------------

R^2 0.00921 0.00049 0.00596 0.32647

Adj. R^2 -0.01181 -0.00849 -0.00297 0.32042

Num. obs. 338 338 338 338

RMSE 2.87196 2.86725 2.85939 2.3537

=================================================

*** p < 0.001, ** p < 0.01, * p < 0.05

Models 7, 8, and 9 all have insignificant performance results compared to the

FFModel in predicating single stock returns for the State Street Corporation in terms of p-

values, RMSE, and Adj. R2. Raw data, without any transformations for human economic

behavior and geomagnetic activity, has generally shown worse results compared to their

delta counterparts.

34

To conclude, neither model presented in this section has shown promising results

against the Fama-French model with the exception of AdjFFModel—this model slightly

exceeds model performance of the Fama-French model which qualifies for backtesting in

Chapter VIII. Lastly, the absolute change (delta) in money velocity appears to have

influence and significance, but that variable alone cannot accurately predict stock returns

for the Company. In the next section, the same scenario analysis is applied, but to a group

of equities that closely tracks the Standard & Poor’s Index (i.e., S&P 500)—this is to see

if the proposed parameters have any meaningful impact in quantitative estimation within

a larger market environment.

Original Approach: Vanguard S&P 500 Fund Returns

The Vanguard S&P 500 Index fund is used as the dependent variable in this

section. The rationale for the use of such a diversified mutual fund is due to the fact that

Fama and French’s three-factor model performs stronger since their equation contains

mostly microeconomic parameters: such as MktRF, SMB, and HML. This section uses

all equations (3 – 13) located in Chapter IV to analyze if alternative methods could

improve the original model. The monthly time-series range is from October 1986 to

November 2014. Table 7-7 displays regression results for the Direct Model Equation 3

(“DirectModel”) and the direct model with human economic behavior variables, Equation

4 (“DirectModelEcon”) compared with the Fama-French model (“FFModel”). For

variable elimination, the focus of the regression output includes the following: (i) Adj.

R2, (ii) RMSE (root-mean-squared-error), and (iii) p-values (0.1%, 1%, or 5%). A

35

variance inflation factor (VIF) analysis will typically occur after the model’s parameters

have been adjusted.

Table 7-7: Van500 Original Model Regression Results, Part 1

The DirectModel produces model performance results that is similar to the

FFModel by Adj. R2 and RMSE; however, after testing for significance at 5% or below

(Tables 7-8 to 7-10) with geomagnetic variables located below, these variables produce

inflated model performance metrics.

DirectModel DirectModelEcon FFModel

===============================================

(Intercept) -0.00290 0.00718 0.00257 ***

(0.00330) (0.00538) (0.00032)

MktRF 0.01005 *** 0.01006 *** 0.01004 ***

(0.00007) (0.00007) (0.00007)

SMB -0.00196 *** -0.00192 *** -0.00195 ***

(0.00010) (0.00010) (0.00010)

HML 0.00026 * 0.00024 * 0.00027 *

(0.00011) (0.00011) (0.00011)

SumKp 0.00008 -0.00002

(0.00007) (0.00007)

Ap -0.00001 0.00014

(0.00015) (0.00015)

Cp -0.01374 0.00075

(0.01649) (0.01650)

PerConsumEx 0.00000

0.00000

M2Money 0.00000

0.00000

PerSavRate 0.00052

(0.00034)

U3Unemploy -0.00087 **

(0.00030)

-------------------------------------------------------------------------------

R^2 0.98399 0.98521 0.98361

Adj. R^2 0.9837 0.98476 0.98347

Num. obs. 338 338 338

RMSE 0.00566 0.00547 0.0057

===============================================

*** p < 0.001, ** p < 0.01, * p < 0.05

36

Table 7-8: Van500 SumKp Relationship Test

==================================================

Residuals:


-0.226434 -0.024655 0.005276 0.027916 0.124208

Coefficients:


(Intercept) 1.38E-02 8.01E-03 1.726 0.0853

SumKp -2.94E-05 4.67E-05 -0.631 0.5288

=================================================

*** p < 0.001, ** p < 0.01, * p < 0.05

Table 7-9: Van500 Ap Relationship Test

Table 7-10: Van500 Cp Relationship Test ==================================================

Residuals:


-0.226527 -0.024633 0.005289 0.027911 0.124023

Coefficients:


(Intercept) 1.24E-02 6.01E-03 2.063 0.0399 *

Cp -6.37E-03 1.03E-02 -0.615 0.5386

==================================================

*** p < 0.001, ** p < 0.01, * p < 0.05

These results suggests that geomagnetic activity, with market factors, does not improve

model performance compared to the Fama-French model. DirectModelEcon, however,

==================================================

Residuals:


-0.226976 0.024691 0.005151 0.027895 0.123805

Coefficients:


(Intercept) 1.19E-02 5.16E-03 2.3 0.0221 *

Ap -2.34E-04 3.74E-04 -0.627 0.5314

==================================================

*** p < 0.001, ** p < 0.01, * p < 0.05

37

has an improved Adj. R2, decrease in RMSE, and only one variable (i.e., U3Unemploy)

with a p-value below 5%. Despite one variable being significant, the cause for majority of

the increase in model performance is due to the variance being inflated by additional

parameters having p-values exceeding alpha. The table below is the adjusted

DirectModelEcon model compared to the FFModel:

Table 7-11: Van500 Adjusted DirectModelEcon v. FFModel

RMSE has shown a noticeable decrease compared to the FFModel which suggest

stronger model predictability (i.e., -0.0016). In addition, Adj. R2 has increased by 0.095%

compared to the Fama-French model. The U3Unemploy (i.e., unemployment) variable

has significance with the Vanguard S&P 500 Fund returns where p < 0.001. Severe

multicollinearity does not exist with this particular model with variance inflation factors

at 1.08 (MktRF), 1.13 (SMB), 1.13 (HML), and 1.009 (U3Unemploy). The intercept of

AdjDirectModelEcon suggests that the expected Vanguard S&P 500 Fund return rate is

AdjDirectModelEcon FFModel

=======================================

(Intercept) 0.00823 *** 0.00257 ***

(0.00126) (0.00032)

MktRF 0.01006 *** 0.01004 ***

(0.00007) (0.00007)

SMB -0.00193 *** -0.00195 ***

(0.00010) (0.00010)

HML 0.00027 * 0.00027 *

(0.00011) (0.00011)

U3Unemploy -0.00093 ***

(0.00020)

-----------------------------------------------------------------

R^2 0.98461 0.98361

Adj. R^2 0.98442 0.98347

Num. obs. 3 38 338

RMSE 0.00554 0.0057

=======================================

*** p < 0.001, ** p < 0.01, * p < 0.05

38

0.82% (USD) per month; the slope can be viewed as the expected one-unit fund return

increase, per month, results in an escalation of MktRF’s coefficient by 0.01, SMB by -

0.001, and HML by 0.0002 with U-3 unemployment by -0.006, respectively. The Fama-

French model reveals that the expected Vanguard fund return rate is an increase of 0.26%

(USD) per month; the slope can be viewed as the expected one-unit Fund return increase,

per month, results in an escalation of MktRF’s coefficient by 0.01, SMB by -0.002, and

HML by 0.0002, respectively. To further study model performance between these

models, AdjDirectModelEcon is back-tested against the Fama-French model in Chapter

VIII. Table 7-12 compares models 1 through 3 against the FFModel.



============================================================

(Intercept) 0.00257 *** 0.00393 *** 0.00393 *** 0.00257 ***

(0.00032) (0.00051) (0.00051) (0.00032)

MktRF 0.01004 *** 0.01004 *** 0.01004 *** 0.01004 ***

(0.00007) (0.00007) (0.00007) (0.00007)

SMB -0.00196 *** -0.00198 *** -0.00196 *** -0.00195 ***

(0.00010) (0.00010) (0.00010) (0.00010)

HML 0.00026 * 0.00024 * 0.00025 * 0.00027 *

(0.00011) (0.00011) (0.00011) (0.00011)

SumKPDelta -0.00004 -0.00003

(0.00007) (0.00007)

APDelta 0.00011 0.00011

(0.00013) (0.00012)

CPDelta 0.00603 0.0056

(0.01476) (0.01443)

PerConsumExDelta -0.00001 -0.00001

(0.00001) (0.00001)

M2MoneyDelta -0.00004 *** -0.00004 ***

(0.00001) (0.00001)

PerSavDelta 0.00069 0.00066

(0.00040) (0.00040)

U3UnemployDelta 0.00454 * 0.00447 *

(0.00199) (0.00199)

------------------------------------------------------------------------------------------------ -----

R^2 0.98371 0.98474 0.98462 0.98361

Adj. R^2 0.98341 0.98427 0.98429 0.98347

39

The change in geomagnetic activity (i.e., SumKPDelta, APDelta, and CPDelta),

as shown in Model 1, has decreased model performance in RMSE, p-values, and Adj. R2.

Human economic behavior variables M2MoneyDelta (i.e., the change in money velocity)

and U3UnemployDelta (i.e., the change in unemployment) all have promising results and

statistically significant. Table 7-13 represents the adjusted version of Model 2 compared

to the FFModel.

Table 7-13: Van500 Adjusted Model 2 v. FFModel

AdjModel 2 FFModel

====================================

(Intercept) 0.00354 *** 0.00257 ***

(0.00043) (0.00032)

MktRF 0.01003 *** 0.01004 ***

(0.00007) (0.00007)

SMB -0.00199 *** -0.00195 ***

(0.00010) (0.00010)

HML 0.00026 * 0.00027 *

(0.00011) (0.00011)

M2MoneyDelta -0.00004 **

(0.00001)

U3UnemployDelta 0.00489 *

(0.00198)

-------------------------------------------------------------

R^2 0.98434 0.98361

Adj. R^2 0.9841 0.98347

Num. obs. 338 338

RMSE 0.00559 0.0057

====================================

*** p < 0.001, ** p < 0.01, * p < 0.05

Model performance of AdjModel 2 has shown an increase in Adj. R2 by 0.063%.

In addition, RMSE has decreased by 0.0011 which indicates stronger estimation

performance (and absolute fit) compared to the FFModel when the absolute change

(delta) in both Money Velocity and U-3 unemployment is used in the model. Severe

Num. obs. 338 338 338 338

RMSE 0.00571 0.00556 0.00556 0.0057

============================================================

*** p < 0.001, ** p < 0.01, * p < 0.05

40

multicollinearity does not exist with this particular model with variance inflation factors

at 1.10 (MktRF), 1.14 (SMB), 1.15 (HML), 1.027 (M2MoneyDelta), and 1.0031

(U3UnemployDelta). The intercept of AdjModel 2 suggests that the expected Vanguard

S&P 500 Fund return rate is 0.35% (USD) per month; the slope can be viewed as the

expected one-unit fund return increase, per month, results in an escalation of MktRF’s

coefficient by 0.01, SMB by -0.002, HML by 0.0003, and the change in money velocity

by -0.00004 with U-3 unemployment (delta) by 0.005, respectively. To further study the

model performance between these models, AdjDirectModelEcon is back-tested against

the Fama-French model in Chapter VIII. Table 7-14 compares models 4 to 6 against the

FFModel.



========================================================

(Intercept) 0.00940 * 0.00900 *** 0.00933 * 0.00257 ***

(0.00403) (0.00241) (0.00403) (0.00032)

SumKPDelta -0.00048 -0.00037

(0.00054) (0.00055)

APDelta -0.00037 -0.00051

(0.00097) (0.00098)

CPDelta 0.08572 0.06691

(0.11366) (0.11393)

PerConsumExDelta 0.00014 0.00014

(0.00008) (0.00008)

M2MoneyDelta -0.00016 -0.00016

(0.00009) (0.00009)

PerSavDelta 0.00325 0.00368

(0.00315) (0.00314)

U3UnemployDelta -0.01553 -0.01367

(0.01558) (0.01555)

MktRF 0.01004 ***

(0.00007)

SMB -0.00195 ***

(0.00010)

HML 0.00027 *

(0.00011)

----------------------------------------------------------------------------------------------- -

41

Models 4 to 6 do not contain any Fama-French factors (i.e., MktRF, SMB, and

HML). These models use absolute change (delta) in either geomagnetic activity, human

economic behavior, or both. Based on performance results, neither of these models would

be a candidate for backtesting against the FFModel. In addition, no statistical significance

was revealed in this scenario between each additional variable (aside from the Fama-

French factors) and the dependent variable. Table 7-15 includes results for models 7 to 9

against the Fama-French model.


R^2 0.03533 0.01072 0.02445 0.98361

Adj. R^2 0.01487 0.00184 0.01273 0.98347

Num. obs. 338 338 338 338

RMSE 0.04402 0.04431 0.04406 0.0057

========================================================

*** p < 0.001, ** p < 0.01, * p < 0.05


==================================================

(Intercept) 0.05952 0.01761 0.02433 0.00257 ***

(0.04347) (0.02590) (0.02393) (0.00032)

PerConsumEx -0.00001 -0.00001

(0.00001) (0.00001)

M2Money 0.00001 0.00001

(0.00001) (0.00001)

U3Unemploy 0.00107 0.00166

(0.00246) (0.00237)

PerSavRate -0.00165 -0.00168

(0.00276) (0.00276)

SumKp -0.00038 -0.00012

(0.00059) (0.00055)

Ap -0.00001 -0.00019

(0.00120) (0.00118)

Cp 0.0678 0.02516

(0.13340) (0.12917)

MktRF 0.01004 ***

(0.00007)

SMB -0.00195 ***

(0.00010)

HML 0.00027 *

(0.00011)

42

Models 7 to 9 do not have any Fama-French factors (i.e., MktRF, SMB, and

HML). These models contain raw monthly-averaged data for either geomagnetic activity,

human economic behavior, or both. Based on the performance results, neither of these

models would be a candidate for backtesting against the FFModel due to model fitness

and statistical significance. As illustrated above, the Fama-French factors provide

stronger model performance metrics with the additional parameters having a minute

influence.

Overall, nearly every model presented in this section has not shown promising

results against the Fama-French model with the exception of three models: (1)

AdjDirectModelEcon, (2) AdjModel 2, and (3) AdjFFModel. In regards to statistical

significance of individual variables, the absolute change (delta) in the U-3 unemployment

rate and money velocity has an interconnection with fund returns under this scenario; it

should be important to note that with single stock returns (i.e., State Street Corporation)

and Fund returns (i.e., Vanguard S&P 500), the change in money velocity has statistical

significance under both dependent variables. In any event, the selected models have met

the minimum standard to be back-tested against the original Fama-French model. The

next section analyzes the impact of using the EMA approach for predicting both single

stock and fund returns.

-------------------------------------------------------------------------------------

R^2 0.01563 0.00132 0.01066 0.98361

Adj. R^2 -0.00525 -0.00765 -0.00123 0.98347

Num. obs. 338 338 338 338

RMSE 0.04446 0.04452 0.04437 0.0057

==================================================

*** p < 0.001, ** p < 0.01, * p < 0.05

43

EMA Approach: State Street Corporation Stock Returns

In this section, the Exponential Moving Average (EMA) calculation is applied to

all geomagnetic and human economic behavior variables. The mean (µ) data ranges from

December 2004 to November 2009, or 60 monthly periods. EMA is calculated from

December 2009 to November 2014, or 60 monthly periods—this totals 120 monthly

periods for the entire EMA calculation per variable. The filtered data is then applied to

selected time-series regression equations without absolute delta (i.e., models 7, 8, and 9)

located in Chapter IV. After the time-series regression outputs have been calculated with

the selected data, the model’s parameters are later modified (if applicable) to meet the

cut-off p-value of any measurement over 5%. To meet this requirement, the focus of the

regression output includes the following: (i) Adj. R2, (ii) RMSE (root-mean-squared-

error), and (iii) p-values (0.1%, 1%, or 5%). A variance inflation factor (VIF) analysis

will typically occur after the model’s parameters have been adjusted (or removed). Table

7-16 includes the DirectModelEMA, where geomagnetic variables are included with the

Fama-French factors—and DirectModelEconEMA, which includes all variables from

DirectModelEMA, but with human economic behavior—these models are then compared

to the original Fama-French model (FFModel).

44

Table 7-16: STT EMA Approach, Part 1

DirectModelEMA DirectModelEconEMA FFModel

==========================================================

(Intercept) -145.83535 * -446.40157 -0.03378

(59.42577) (254.28985) (0.29873)

MktRF 0.49109 *** 0.51782 *** 0.51092 ***

(0.08590) (0.08977) (0.08534)

SMB -0.0117 -0.03624 -0.05085

(0.14966) (0.15563) (0.14276)

HML 0.41218 * 0.29543 0.34808 *

(0.16210) (0.17854) (0.15638)

SumKPEMA 3.02710 * 2.66491

(1.23583) (1.38704)

APEMA 18.87762 32.51185

(10.93672) (19.66680)

CPEMA -1061.32479 * -1286.97534 *

(476.66508) (606.47685)

PerConsumExEMA 0.05901

(0.04160)

PerSavRateEMA 1.63146

(3.48629)

U3UnemployEMA -1.96478

(1.99826)

M2MoneyEMA -0.03292

(0.02227)

---------------------------------------------------------------------------------------------------

R^2 0.58268 0.60854 0.53096

Adj. R^2 0.53544 0.52865 0.50583

Num. obs. 60 60 60

RMSE 2.08313 2.09828 2.14849

==========================================================

*** p < 0.001, ** p < 0.01, * p < 0.05

With the FFModel at an Adj. R2 of 50.58%, a RMSE of 2.1484, and an

insignificant p-value of Fama and French’s market parameter (SMB), a leaner

DirectModelEMA equation may prove more viable since the geomagnetic variable

(SumKPEMA) appears to have a statistical significance with its dependent variable. In

regards to DirectModelEconEMA, the model appears to not provide any significant

factors other than its inflated Adj. R2 and RMSE including insignificant p-values, with the

exception of Fama and French’s market parameter (MktRF). Below is a relationship test,

45

to determine if DirectModelEMA should be re-fitted, of the geomagnetic parameter

SumKPEMA with the dependent variable (i.e., STT).

Table 7-17: STT EMA Kp Index Relationship Test

Based on a p-value for SumKPEMA of 51.4%, this variable is insignificant and deflated

by other parameters in the DirectModelEMA equation. Table 7-18 below displays a

comparison of models 7, 8, and 9 to the FFModel:

Table 7-18: STT EMA Approach, Part 2

Model7EMA Model8EMA Model9EMA FFModel

===========================================================

(Intercept) -262.68058 -132.11973 17.09298 -0.03378

(358.02382) (87.03036) (187.22814) (0.29873)

PerConsumExEMA 0.03922 -0.00194

(0.05749) (0.03552)

PerSavRateEMA 5.83306 4.5926

(5.01775) (2.87692)

U3UnemployEMA -3.51136 -2.26238

(2.86517) (2.05875)

M2MoneyEMA -0.02315 -0.00042

(0.03069) (0.01976)

SumKPEMA 1.38665 2.62064

(1.96201) (1.79145)

APEMA 25.65702 19.95769

(27.99070) (15.91724)

CPEMA -902.60629 -981.66054

(881.36444) (697.82388)

MktRF 0.51092 ***

(0.08534)

===========================================

Residuals:


-6.7003 -1.6085 0.2185 1.7968 7.3115

Coefficients:


(Intercept) -1.12E+01 1.79E+01 -0.622 0.536

SumKPEMA 9.91E-02 1.51E-01 0.656 0.514

===========================================

*** p < 0.001, ** p < 0.01, * p < 0.05

46

SMB -0.05085

(0.14276)

HML 0.34808 *

(0.15638)

----------------------------------------------------------------------------------------------------

R^2 0.11598 0.0419 0.06518 0.53096

Adj. R^2 -0.00302 -0.00942 -0.00281 0.50583

Num. obs. 60 60 60 60

RMSE 3.0609 3.07066 3.06057 2.14849

===========================================================

*** p < 0.001, ** p < 0.01, * p < 0.05

Overall, the Exponential Moving Average (EMA) data filter approach for both

geomagnetic and human economic behavioral activity appears to not have meaningful

significance for predicting single stock returns by p-values, Adj. R2, and RSME. In the

end, the best performer for quantitative estimation, in this exercise, is the Fama-French

model (i.e., FFModel). The next section will use the same approach with the

Corporation’s stock returns, but at the fund level exposing the proposed variables to a

larger market environment.

EMA Approach: Vanguard S&P 500 Fund Returns

The reason for using Vanguard S&P 500 is because the Fama-French model

typically performs much stronger compared to the use of a single stock due to its

parameter construction. In this section, the Exponential Moving Average (EMA)

calculation is applied to all geomagnetic and human economic behavior variables. The

mean (µ) data ranges from December 2004 to November 2009, or 60 monthly periods.

EMA is calculated from December 2009 to November 2014, or 60 monthly periods—this

totals 120 monthly periods for the entire EMA calculation per variable. The filtered data

is then applied to selected time-series regression equations without absolute delta (i.e.,

models 7, 8, and 9) located in Chapter IV. After the time-series regression outputs have

47

been calculated with the selected data, the model’s parameters could be modified (if

applicable) to meet the cut-off p-value of any measurement over 5%. To meet this

requirement, the focus of the regression output includes the following: (i) Adj. R2, (ii)

RMSE (root-mean-squared-error), and (iii) p-values (0.1%, 1%, or 5%). A variance

inflation factor (VIF) analysis will typically occur after the model’s parameters have been

adjusted (or removed). Table 7-19 contains the DirectModelEMA, where geomagnetic

variables are included with the Fama-French factors—and DirectModelEconEMA, which

uses all variables from DirectModelEMA, but with human economic behavior—these

models are then compared to the original Fama-French model (FFModel) for Vanguard

S&P 500 Fund returns.

Table 7-19: Van500 EMA Approach, Part 1

DirectModelEMA DirectModelEconEMA FFModel

===========================================================

(Intercept) 0.01426 -0.2371 -0.0001

(0.05186) (0.21621) (0.00025)

MktRF 0.00990 *** 0.00992 *** 0.00993 ***

(0.00007) (0.00008) (0.00007)

SMB -0.00133 *** -0.00135 *** -0.00140 ***

(0.00013) (0.00013) (0.00012)

HML 0.00012 0.00017 0.00005

(0.00014) (0.00015) (0.00013)

SumKPEMA 0.00005 0.00106

(0.00108) (0.00118)

APEMA -0.00677 0.01156

(0.00954) (0.01672)

CPEMA 0.0923 -0.45197

(0.41594) (0.51565)

PerConsumExEMA 0.00003

(0.00004)

PerSavRateEMA -0.00666 *

(0.00296)

U3UnemployEMA 0.00272

(0.00170)

M2MoneyEMA -0.00001

(0.00002)

----------------------------------------------------------------------------------------------------

48

The FFModel has a near-perfect fit with an Adj. R2 of 99.76%, a RMSE of

0.00182, and an insignificant p-value of Fama and French’s market parameter (HML). A

leaner DirectModelEconEMA equation may prove more viable since the human

economic behavior variable PerSavRateEMA (Personal Savings Rate) appears to have a

statistical significance with its dependent variable. With regards to DirectModelEMA, the

model appears to not provide significant factors other than its inflated Adj. R2 and RMSE

including insignificant p-values, with the exception of Fama and French’s market

parameter MktRF and SMB. Below is a relationship test of the geomagnetic variable

PerSavRateEMA with Van500 to determine if DirectModelEconEMA should be re-fitted:

Table 7-20: Van500 PerSavRateEMA Relationship Test

Based on a p-value for PerSavRateEMA of 56%, this variable is insignificant and

deflated by other parameters in the DirectModelEconEMA equation. The table below

illustrates a comparison of models 7, 8, and 9 to the FFModel.

R^2 0.99789 0.99812 0.99777

Adj. R^2 0.99765 0.99773 0.99765

Num. obs. 60 60 60

RMSE 0.00182 0.00178 0.00182

===========================================================

*** p < 0.001, ** p < 0.01, * p < 0.05

=================================================

Residuals:


-0.088367 -0.023917 0.007454 0.023316 0.097167

Coefficients:


(Intercept) -1.30E-02 4.45E-02 -0.293 0.771

PerSavRateEMA 5.04E-03 8.58E-03 0.588 0.559

=================================================

*** p < 0.001, ** p < 0.01, * p < 0.05

49

Table 7-21: Van500 EMA Approach, Part 2

Model7EMA Model8EMA Model9EMA FFModel

===========================================================

(Intercept) 4.52898 -0.04043 2.30615 -0.0001

(4.56418) (1.08908) (2.34629) (0.00025)

PerConsumExEMA -0.00066 -0.00044

(0.00073) (0.00045)

PerSavRateEMA 0.05978 0.00697

(0.06397) (0.03605)

U3UnemployEMA -0.01716 0.00952

(0.03653) (0.02580)

M2MoneyEMA 0.00034 0.00024

(0.00039) (0.00025)

SumKPEMA -0.01219 0.00232

(0.02501) (0.02242)

APEMA -0.2175 0.00681

(0.35683) (0.19919)

CPEMA 6.46832 -0.81379

(11.23586) (8.73245)

MktRF 0.00993 ***

(0.00007)

SMB -0.00140 ***

(0.00012)

HML 0.00005

(0.00013)

------------------------------------------------------------------------------------------------------

R^2 0.04441 0.00207 0.02354 0.99777

Adj. R^2 -0.08423 -0.05139 -0.04748 0.99765

Num. obs. 60 60 60 60

RMSE 0.03902 0.03843 0.03835 0.00182

============================================================

*** p < 0.001, ** p < 0.01, * p < 0.05

Models 7-EMA to 9-EMA all have an insignificant relationship with the dependent

variable—even tested separately. Overall, using the Exponential Moving Average (EMA)

data filter approach for both geomagnetic and human economic behavioral activity

appears to not have any meaningful use for predicting Vanguard S&P 500 Fund returns

by p-values, Adj. R2, and RSME. In the end, however, the best performer for quantitative

50

estimation in this exercise is the Fama-French model (i.e., FFModel). The last section

concludes the analysis for Chapter VII.

Concluding Analysis for Chapter VII

Chapter VII analyzed how geomagnetic and human economic behavioral

parameters could impact fund and stock returns against the Fama-French model. This

Chapter used the original approach, which includes regression equations in Chapter IV

and the EMA approach located in Chapter V. The original approach in State Street

Corporation’s stock returns concluded that the absolute change (delta) in the velocity of

money (M2MoneyDelta) is statistically significant at 2.1%; by adding that parameter to

the original Fama-French model (i.e., AdjFFModel), it slightly improved model

performance compared to the original despite the p-value being inflated above the 5%

significance level. Model output for the Vanguard S&P 500 Fund experienced promising

results with AdjDirectModelEcon and AdjModel 2. For AdjDirectModelEcon, the U-3

unemployment rate has statistical significance at p < 0.001 with improved Adj. R2 and

RMSE when compared to the original Fama-French model. AdjModel 2 revealed that not

only the absolute change in the U-3 unemployment rate has statistical significance with

fund returns, but also the velocity of money at p < 0.001 and p < 0.01, respectively; the

overall model performance revealed a slight improvement in both Adj. R2 and RMSE

when compared to the original Fama-French model. Since these models have challenging

metrics against the benchmark, they are back-tested in Chapter VIII. The tables below

represent short-listed models for this Chapter.

51

Table 7-22: STT Short-Listed Models for Chapter VII

AdjFFModel FFModel

=================================

(Intercept) 0.11346 -0.06705

(0.18044) (0.13014)

MktRF 0.36421 *** 0.36832 ***

(0.02975) (0.02967)

SMB -0.09746 * -0.09350 *

(0.04238) (0.04236)

HML 0.20425 *** 0.21147 ***

(0.04633) (0.04613)


(0.00463)

--------------------------------------------------------

R^2 0.33065 0.32647

Adj. R^2 0.32261 0.32042

Num. obs. 338 338

RMSE 2.34991 2.3537

=================================

*** p < 0.001, ** p < 0.01, * p < 0.05

52

Table 7-23: Van500 Short-Listed Models for Chapter VII

AdjDirectModelEcon AdjModel2 FFModel

=====================================================

(Intercept) 0.00823 *** 0.00354 *** 0.00257 ***

(0.00126) (0.00043) (0.00032)

MktRF 0.01006 *** 0.01003 *** 0.01004 ***

(0.00007) (0.00007) (0.00007)

SMB -0.00193 *** -0.00199 *** -0.00195 ***

(0.00010) (0.00010) (0.00010)

HML 0.00027 * 0.00026 * 0.00027 *

(0.00011) (0.00011) (0.00011)

U3Unemploy -0.00093 ***

(0.00020)


(0.00001)


(0.00198)

-------------------------------------------------------------------------------------------

R^2 0.98461 0.98434 0.98361

Adj. R^2 0.98442 0.9841 0.98347

Num. obs. 338 338 338

RMSE 0.00554 0.00559 0.0057

=====================================================

*** p < 0.001, ** p < 0.01, * p < 0.05

53

Chapter VIII

Model Validation & Estimation

This chapter uses validation techniques to analyze model performance against the

Fama-French model: such as observed verses predicted values for model fit and a

comparative Mean Absolute Percentage Error (MAPE) of predicted values (Myttenaere et

al. 2015: 1-7). Models with strong performance metrics are compared to Fama-French’s

5-factor model. Below is a table of all short-listed models ready for backtesting.

Table 8-1: All Qualifying Models

Model Name Research Approach Dependent Variable Adj. R2 RMSE

AdjFFModel Original State Street Stock Returns 32.26% 2.34991

AdjDirectModelEcon Original Vanguard S&P 500 Returns 98.44% 0.00554

AdjModel2 Original Vanguard S&P 500 Returns 98.41% 0.00559

54

Model Fitness Test: STT Observed verses Predicted Values

This section will use the selected models above and predict values, compare those

predicted values to observed (actual) values, then analyze those quantities to the

corresponding Fama-French model for State Street Corporation’s stock returns. This

section uses 338 known periods (months) in this exercise for both dependent and

independent variables using returns. For a model(s) to meet or exceed performance

metrics against the benchmark, their average predication accuracy, calculated by the

Mean Absolute Percentage Error (MAPE), has to outperform the Fama-French model;

any model with a percentage error over 100 is absolutely inaccurate. Figure 8-1 compares

observed (actual) stock returns to the model’s predicted results (AdjFFModel) including

the Fama-French model (FFModel).

55

This figure displays only 6-months (out of 338 months) of State Street stock returns from June 2014 to November

2014. The MAPE calculation ranges from October 1986 to November 2014. Despite the AdjFFModel outpacing the Fama-

French model by a MAPE of 18%, both models are terribly inaccurate since they exceed the 100% threshold and cannot

accurately predict stock returns (i.e., STT Observed Returns). Results from the alternative model, however, are interesting; by

adding the absolute change in Money Velocity (M2MoneyDelta) to the original Fama-French model, this variable decreases

the percentage error by 18%.

56

Model Fitness Test: Vanguard Observed verses Predicted Values

This section uses selected models noted in this Chapter and predict values,

compare those predicted values to observed (actual) values, then analyze those predicted

quantities to the corresponding Fama-French model for the Vanguard S&P 500 Fund

returns—the fund represents 75% of the U.S stock market. This section uses 338 known

periods (months) in this exercise for both the dependent and independent variable using

returns. For a model(s) to meet or exceed expectations of model performance, their

average predication accuracy, calculated by the Mean Absolute Percentage Error

(MAPE), has to outperform the Fama-French model. Any model with a percentage error

over 100 is absolutely inaccurate. Figure 8-2 compares observed (actual) fund returns to

the models’ predicted results (i.e., AdjDirectModelEcon and AdjModel2) including the

Fama-French model (FFModel).

57

For the Vanguard S&P 500 Fund, the table displays only 6-months (out of 338 months) of percent returns, in USD (i.e.,

United States Dollars), from June 2014 to November 2014. The MAPE calculation ranges from November 1986 to November

2014. All models presented in this table has less than a 25% historical percentage error. AdjModel2, in this case, has the best

performance metrics—the equation incorporates all Fama-French factors, but with added variables: such as the absolute

change in both money velocity and U-3 unemployment. These added variables reduce the Fama-French forecasting error by

2.753% on a historical basis. AdjDirectModelEcon’s performance is slightly worse than AdjModel2 with only U-3

unemployment and Fama-French factors used.

58

Robustness Analysis on Modeled Vanguard Returns: 2008-2009 Financial Crisis

During the 2008-2009 Financial Crisis, all models have performed exceptionally

well compared to actual percent returns (i.e., Van500 Returns). As noted earlier,

historically, the alternative model (i.e., AdjModel2) had a mean absolute percentage error

of 2.753% less than the Fama-French model. Between September to November 2008,

AdjModel2 was slightly closer to actual returns by an average difference of 0.06%

compared to the Fama-French model at 0.12%. The alternative model does have stronger

performance metrics compared to the Fama-French model, but the results are so close

that some scholars may warrant this comparison immaterial. If these models were used on

actual portfolios, however, fund managers (or market participants) would choose the best

overall model by historical performance if it can increase their bottom-line. The

alternative model contains all Fama-French factors, plus the absolute change in both U-3

unemployment and velocity of money equating to a 5-factor model.

59

Table 8-2: 2008-2009 Financial Crisis (Vanguard) Predicted vs. Observed Returns

Aug-08 Sep-08 Oct-08 Nov-08 Dec-08 Jan-09

Van500 Returns (USD) 1.45% -8.90% -16.79% -7.17% 1.08% -8.41%

Predict.AdjModel2 (USD)

1.31% -8.78% -16.75% -7.15% 0.98% -8.14%

Predict.FFModel (USD) 1.13% -8.63% -16.67% -7.20% 1.29% -8.21%

Alternative 5-Factor Model verses the Fama-French 5-Factor Model

In 2015, Eugene Fama and Kenneth French published two additional factors for

the original 3-factor model entitled “A five-factor asset pricing model;” these two

parameters add the profitability and investment factor into the equation: such as RMW

and CMA. While RMW takes on 4 portfolios, two that are highly profitable and two that

are not, CMA considers risk tolerance from each of the 4 portfolios. The reason for two

additional factors is to capture low-averaged stock returns (Fama and French 2015: 1). In

this research, however, the one model that outperformed the Fama-French model was

AdjModel 2 which also uses two additional factors: such as the change in money velocity

and U-3 unemployment. To better understand if the alternative 5-factor model can

outperform Fama-French’s model, both models are compared to each other using State

Street Corporation’s stock return and the Vanguard S&P 500 Index Fund (500 stocks).

The time-series is from October 1986 to November 2014. Table 8-3 illustrates the model

performance output on State Street stock returns.

60

Table 8-3: Alternative 5-Factor v. Fama-French 5-Factor on STT Returns

The intercept of AdjModel2 suggests that the expected State Street stock return

rate is 12% (USD) per month; the slope can be viewed as the expected one-unit stock

return increase, per month, results in an escalation of MktRF’s coefficient by 0.366, SMB

by -0.095, HML by 0.20, M2MoneyDelta by -0.006, and U3UnemployDelta by 0.540,

respectively. For FFModel5, the model’s intercept suggests that the expected State Street

stock return rate is 2.1% (USD) per month; the slope can be viewed as the expected one-

unit stock return increase, per month, results in an escalation of MktRF’s coefficient by

0.34, SMB by -0.169, HML by 0.239, RMW by -0.20, and CMA by 0.015, respectively.

Lastly, FFModel’s output metrics resulted in an intercept that suggests expected State

AdjModel2 FFModel5 FFModel

==============================================

(Intercept) 0.12003 0.02099 -0.06705

(0.18088) (0.13438) (0.13014)

MktRF 0.36613 *** 0.34002 *** 0.36832 ***

(0.02993) (0.03293) (0.02967)

SMB -0.09938 * -0.16948 *** -0.09350 *

(0.04252) (0.04736) (0.04236)

HML 0.20703 *** 0.23944 *** 0.21147 ***

(0.04656) (0.06127) (0.04613)


(0.00465)

U3UnemployDelta 0.54042

(0.83120)

RMW -0.20639 ***

(0.06164)

CMA 0.01521

(0.08759)

------------------------------------------------------------------------------

R^2 0.3315 0.34925 0.32647

Adj. R^2 0.32143 0.33944 0.32042

Num. obs. 338 338 338

RMSE 2.35195 2.32052 2.3537

==============================================

*** p < 0.001, ** p < 0.01, * p < 0.05

61

Street stock return rate is at -7% (USD) per month; the slope can be viewed as the

expected one-unit stock return decrease, per month, results in an escalation of MktRF’s

coefficient by 0.368, SMB by -0.093, and HML by 0.211, respectively. Mean Average

Percentage Error (MAPE) for AdjModel2 is at 424.61%, Fama-French 5 Factor at

433.19%, and the original Fama-French Model (3-factor) at 408.92%. In this particular

scenario, with a single stock, the original Fama-French 3-factor model outpaces both

models by 15.7% less forecasting error. To better understand all performance results in

larger market environment, Table 8-4 displays model outputs for the Vanguard S&P 500

Index Fund.

Table 8-4: Alternative 5-Factor v. Fama-French 5-Factor on Vanguard Returns

AdjModel2 FFModel5 FFModel

===============================================

(Intercept) 0.00354 *** 0.00220 *** 0.00257 ***

(0.00043) (0.00032) (0.00032)

MktRF 0.01003 *** 0.01017 *** 0.01004 ***

(0.00007) (0.00008) (0.00007)

SMB -0.00199 *** -0.00182 *** -0.00195 ***

(0.00010) (0.00011) (0.00010)

HML 0.00026 * -0.00005 0.00027 *

(0.00011) (0.00015) (0.00011)


(0.00001)


(0.00198)

RMW 0.00045 **

(0.00015)

CMA 0.00056 **

(0.00021)

--------------------------------------------------------------------------------

R^2 0.98434 0.98429 0.98361

Adj. R^2 0.9841 0.98406 0.98347

Num. obs. 338 338 338

RMSE 0.00559 0.0056 0.0057

===============================================

*** p < 0.001, ** p < 0.01, * p < 0.05

62

The intercept of AdjModel2 suggests that the expected Vanguard S&P 500 Fund

return rate is 0.35% (USD) per month; the slope can be viewed as the expected one-unit

fund return increase, per month, results in an escalation of MktRF’s coefficient by 0.01,

SMB by -0.0019, HML by 0.00026, M2MoneyDelta by -0.00004, and U3UnemployDelta

by 0.0048, respectively. For FFModel5, the model’s intercept suggests that the expected

Fund return rate is 0.22% (USD) per month; the slope can be viewed as the expected one-

unit stock return increase, per month, results in an escalation of MktRF’s coefficient by

0.01, SMB by -0.182, HML by -0.00005, RMW by 0.00045, and CMA by 0.00056,

respectively. Lastly, FFModel’s output metrics resulted in an intercept that suggests

expected State Street stock return rate is at 0.257% (USD) per month; the slope can be

viewed as the expected one-unit stock return increase, per month, results in an escalation

of MktRF’s coefficient by 0.01, SMB by -0.0019, and HML by 0.00027, respectively. In

terms of MAPE, the AdjModel2 yields a 21.83% forecasting error, FFModel5 at 24.64%,

and the FFModel at 24.6%. Out of all the models, the alternative 5-factor construction

outpaces all Fama-French results, in this exercise, by at least 2.753% in forecasting error.

The next section concludes this chapter.

Concluding Analysis for Chapter VIII

This chapter back-tested selected models against both the Fama-French 3 and 5-

Factor model. With actual verses predicted values using State Street stock returns, the

alternative model (i.e., AdjFFModel) outperformed the Fama-French 3-factor model by

MAPE at 390.90% versus the FFModel at 408.923%.Vanguard S&P Index Fund’s top

performer in quantitative estimation, on returns, is AdjModel2 with proven metrics that

63

outpaces the Fama-French 3-Factor model by nearly 3% less in historical forecasting

error.

In the Fama-French 5 factor model comparison, AdjModel 2 had more forecasting

error compared to the 3-factor model, but less against the 5-factor equation for single

stock returns (i.e., State Street Corporation). In terms of larger market exposure (i.e.,

Vanguard S&P 500 Index Fund), AdjModel 2 captures less forecasting error compared to

both Fama-French models.

Overall, the model with best overall fit, the least mean absolute percentage error,

and able to recognize severe market fluctuations against the Fama-French model is

AdjModel2. Although, in most cases, equations containing human economic behavior has

stronger model performance metrics compared to geomagnetic parameters, the change in

human behavioral activity defined by unemployment and money velocity, in combination

with three Fama-French factors, has the strongest impact in quantitative estimation. Next,

Chapter IX will conclude the entire analysis for this research.

64

Chapter IX

Research Conclusion

This research attempted to shed light on natural phenomena and human economic

behavioral impact in quantitative estimation using the Fama-French 3-factor model as a

benchmark. Chapter VII analyzed how all three methodological approaches could impact

quantitative estimation of equity and fund returns. Chapter VIII validated, estimated, and

compared short-listed models in previous chapters to Fama-French’s three and five factor

model. Appendix B discussed modeling results from transformed data. Appendix C

analyzed causality between geomagnetic indices and human economic behavior.

Appendix D and E revealed correlation results for all variables used in the research. The

purpose of this analysis is to answer two questions listed below:

1. Although research has revealed the potential interconnection of geomagnetic

activity with market behavior, could this natural phenomena actually increase the

prediction power of quantitative models?

2. What about the human behavioral element—does that play a role in econometric

modeling?

In addition to the questions above, this research hypothesized that the Earth’s magnetic

field and human economic behavior might play a small role with improving quantifiable

estimated outputs. Moreover, it was also hypothesized that magnetic activity could have a

direct impact on the defined human economic behavioral variables. In essence, some

initial claims are true for the proposed research questions. To answer question one,

65

geomagnetic activity does not have a strong impact in improving quantitative estimation

on returns, as revealed earlier for both a single stock and the top 500 combined equity

shares traded on the U.S. stock market. After accounting for data transformations in the

proposed modeling approaches, performance results were also insignificant against the

Fama-French Model. In addition, the EMA approach for equity and fund returns did not

reveal anything significant enough to improve or outpace the benchmark.

For question two, variables defined as human economic behavioral activity does

have a role to play in the Fama-French modeling approach. The change in the money

velocity and U-3 unemployment has statistical significance with returns under the

original approach for the Vanguard S&P 500 Fund; State Street stock returns, however,

only has a relationship with money velocity and not U-3 unemployment. So, since a few

human economic behavioral variables are decent predictors of returns, what about

causality? Is there any evidence suggesting that geomagnetic behavior might influence

human economic outcomes?

In Appendix C, this research analyzed whether causality might exist between

these two groups of data: (a) geomagnetic indices and (b) human economic behavior.

Unfortunately, the Granger test demonstrated that economic and geomagnetic data does

not contain enough information to forecast each other—in essence, there is an

insignificant direct or indirect connection among these parameters—this defeats the

research’s second null hypothesis suggesting that it does.

On the performance front, the only model worthy of mention is AdjModel2. This

model was tested against both the 3-Factor and 5-Factor model. In all cases except one,

the alternative 5-factor model outpaced Fama and French’s approach by a mean absolute

66

percentage error of roughly 3% less than the benchmark. In both a large and small

market environment, this model does have the potential to recognize swings in behavior

more accurately than the benchmark. Although this research area still needs maturing,

Eugene Fama and Kenneth French should consider environmental influences, such as

human economic behavior, legitimate factors to better estimate returns. In this research,

the evidence is clear that practitioners and academics should look outside their narrow

boarders for other significant factors that might influence research and investment

outcomes.

In conclusion, the first null hypothesis is considered half true: human economic

behavior does play, to some degree, a role in quantitative estimation on returns while

geomagnetic activity does not have strong enough influence in this research approach.

Although this study only scrapes the surface of answering the unknown, there are now

potential research gaps with additional asset classes: such as real estate, commodities,

fixed income, foreign exchange, and other investment vehicles. Among these asset

classes, regions and industries participating in any market should also be researched. In

artificial intelligence and machine learning for the financial industry, practitioners should

explore how this data might impact predicted outcomes due to the results in this research.

Lastly, although human economic behavior revealed some influence in this controlled

mathematical study with two dependent variables under one asset class, opportunities for

new research possibilities exist and should be sought-out for most academic disciplines

and practitioners.

67

Appendix A

Experiential Modeling with Adjusted Closed Prices

Chapter VII used fund and stock returns as the dependent variable. The original

Fama-French equation calls for returns, not adjusted closed prices. In this Appendix,

however, the dependent variable is changed to non-stationary adjusted closed prices. The

rationale for a dependent variable change is to analyze any impact of geomagnetic and

human economic behavior on temporal trends in price fluctuations. This chapter uses

both the original approach illustrated on Chapter IV and EMA filtered data for both asset

prices. In regards to the original approach, the monthly time-series ranges from October

1986 to November 2014. The data range derived from the EMA approach is from

December 2004 to November 2009, or 60 monthly periods; EMA is calculated from

December 2009 to November 2014, or 60 monthly periods. For variable elimination, the

focus of the regression output will include the following: (i) Adj. R2, (ii) RMSE (root-

mean-squared-error), and (iii) p-values (0.1%, 1%, or 5%). A variance inflation factor

(VIF) analysis will typically occur after the model’s parameters have been adjusted (or

removed). Robustness analysis during the 2008-2009 Financial Crisis, in addition to a

model fitness test of observed verses predict values, is displayed in this appendix. Models

are denoted with a “P” to signify that the dependent variable represents adjusted closed

prices and not returns. Section A-1 analyzes final regression results for State Street

Corporation’s closed adjusted prices.

68

Section A-1: State Street Corporation Stock Prices

Table A-1.1: STT Model Regression Results

AdjDir..EconP AdjDir..EconP2 AdjDir..EconP3

==================================================

(Intercept) 5.93391 10.20130 *** -26.60961 ***

(3.54589) (2.54811) (3.03669)

SumKp 0.01657

(0.00961)

PerConsumEx 0.00581 *** 0.00562 *** 0.00716 ***

(0.00021) (0.00018) (0.00022)

PerSavRate -3.61286 *** -3.64793 ***

(0.27851) (0.27858)

DSavKp 0.02982 *

(0.01166)

-------------------------------------------------------------------------------------

R^2 0.87265 0.87152 0.80947

Adj. R^2 0.87151 0.87075 0.80833

Num. obs. 338 338 338

RMSE 7.47867 7.5007 9.13397

==================================================

*** p < 0.001, ** p < 0.01, * p < 0.05

Variance inflation factors for the AdjDirectModelEconP equation are at 1.49

(SumKP), 1.946 (PerConsumEx), and 1.40 (PerSavRate)—variables, such as the

PerConsumEx and PerSavRate, are higher than expected inflation factors causing the

SumKP’s p-value to be inflated. With the SumKP removed, AdjDirectModelEconP2’s

variance inflation factors are at 1.393 (PerConsumEx) and 1.393 (PerSavRate). To further

enhance the geomagnetic Kp Index, an independent variable difference calculation was

conducted between PerSavRate and SumKp with a new variable entitled “DSavKp”—

using this variable along with PerConsumEx, the AdjDirectModelEconP3 equation

decreased the p-value of the Kp Index below 5%, but greater than 1% when modeled with

human economic behavior—this model, however, suffers from a lowered Adjusted R2

69

and a higher RMSE; variance inflation actors are at 1.45 for both PerConsumEx and

DSavKp. All alternative models have an Adj. R2 of at least 80%.

The intercept of AdjDirectModelEconP suggests that the expected State Street

stock return rate is $5.93 (USD) per month; the slope can be viewed as the expected one-

unit increase of the stock return, per month, results in an escalation of SumKp’s

coefficient by 0.02, personal consumption expenditure (PerConsumEx) by 0.00581, and

personal savings rate (PerSavRate) by -3.612, respectively. Regarding

AdjDirectModelEconP2, the intercept suggests that the expected State Street stock return

rate is $10.20 (USD) per month; the slope can be viewed as the expected one-unit

increase of the stock return, per month, results in an escalation of personal consumption

expenditure’s coefficient (PerConsumEx) by 0.00562 and personal savings rate

(PerSavRate) by -3.64, respectively. Lastly, AdjDirectModelEconP3’s intercept

concludes that the expected State Street stock return rate, per share, is -$26.61 (USD) per

month; the slope can be viewed as the expected one-unit decrease of the stock return, per

month, results in an escalation of personal consumption expenditure’s coefficient

(PerConsumEx) by 0.00716 and the difference between personal savings rate and the KP

index (DSavKp) by 0.02982, respectively. Section A-2 analyzes regression results for the

Vanguard S&P 500 Fund.

Section A-2: Vanguard S&P 500 Fund Prices

Table A-2.1: Van500 Regression Results

AltRefitMod1 AltRefitMod2 AdjDir..EconP3

==================================================

(Intercept) -70.28248 ** -76.81129 *** 41.10021 ***

(24.84088) (21.64883) (3.45093)

PerSavRate -2.24614 ** -2.08346 **

(0.69629) (0.69371)

M2MoneyEMA 0.03500 *** 0.03565 ***

70

(0.00095) (0.00100)

APEMA -11.99171 **

(3.45945)

CPEMA -272.32490 ***

(72.87854)

C9 -0.88783

(0.62934)

M2Money 0.01731 ***

(0.00030)

U3Unemploy -11.12161 ***

(0.43383)

-------------------------------------------------------------------------------------

R^2 0.96408 0.96508 0.93283

Adj. R^2 0.96216 0.96321 0.93222

Num. obs. 60 60 338

RMSE 5.57431 5.49619 10.68677

==================================================

*** p < 0.001, ** p < 0.01, * p < 0.05

Variance inflation factors, for AltRefitMod1, are at 1.04 (PerSavRate), 1.14

(M2MoneyEMA), and 1.14(APEMA). For AltRefitMod2, inflation factors are now at

1.06 (PerSavRate), 1.30 (M2MoneyEMA), and 1.31(CPEMA). Using the Cp

geomagnetic index, compared to the AP Index, the variable slightly inflates the variance.

The intercept of AltRefitMod1 suggests that the expected Vanguard S&P 500 Index Fund

return rate is -$70.28 (USD) per month; the slope can be viewed as the expected one-unit

stock return decrease, per month, results in a de-escalation of personal savings rate’s

coefficient by -2.24, money velocity by 0.035, and APEMA by -11.991, respectively. For

AltRefitMod2, the model’s intercept suggests that the expected Vanguard S&P 500 Index

Fund rate is $-76.81 (USD) per month; the slope can be viewed as the expected one-unit

fund return decrease, per month, results in a de-escalation of personal savings rate’s

coefficient by -2.08, M2MoneyEMA by 0.035, and CPEMA by -272.32, respectively.

The Fama-French model is still expected to outpace both alternative models, but

regardless of those metrics, these models will be back-tested. Under AdjDirectModel-

71

EconP3, the inflation factors are at 1.43 (C9), 1.65 (M2Money), and 1.25(U3Unemploy).

The intercept of AdjDirectModelEconP3 suggests that the expected Vanguard S&P 500

Index Fund return rate is $41.10 (USD) per month; the slope can be viewed as the

expected one-unit fund return increase, per month, results in an escalation of the velocity

of money’s (M2Money) coefficient by 0.0173, unemployment (U3Unemploy) by -

11.121, and the geomagnetic C9 Index (C9) by -0.887, respectively. Section A-3 analyzes

model fitness and robustness for single stock prices.

72

Section A-3: STT Robustness Analysis & Model Fitness

Figure A-3.1 illustrates model performance for alternative models using only closed adjusted price data from October

1986 to November 2014 with the exception of AltRefitModel1, which used 60 monthly periods after the 2008-2009 Financial

Crisis at 8.8% MAPE. The best historical performer, by MAPE, is AdjDirectModelEconP2 with an MAPE of 41.78%; P and

P3 have a MAPE of 42.07% and 43.14%, respectively. As visualized, extreme swings in stock behavior (i.e., STT AdjClose)

are not predicted accurately among these models. To further analyze this, Figure A-3.2 compares equity prices against the

models during the 2008-2009 Financial Crisis.

73

During the market crisis, AdjDirectModelEconP appears to recognize pattern

behavior slightly stronger than other alternative models between September 2008 to

August 2009; this model contains three variables to estimate closed adjusted prices: such

as (i) Kp Index, (ii) personal consumption expenditures, (iii) and personal savings rate.

The second model (P2) contains all variables except the Kp Index which slightly under-

performs compared to model (P1). The third model (P3) uses personal consumption

expenditures plus the difference between personal savings rate and the Kp Index—this

model can only predict, to some degree, the overall historical trend increase in stock

behavior and not volatility or market swings. Table A-3.1 illustrates predicted values

among these models and actual equity prices during the Financial Crisis. The Kp Index,

under model P compared to model P2 without geomagnetic activity, can slightly improve

model performance in this market shock by an average of 80¢ per share from January to

March 2009. Overall, despite this improvement, neither model is sensitive to extreme

market behavior (see Table A-3.1). Section A-4 analyzes the Vanguard fund in the same

fashion.

74

Table A-3.1: 2008-2009 Financial Crisis (STT) Predicted vs. Observed Prices

Column1 Dec-08 Jan-09 Feb-09 Mar-09 Apr-09 May-09

STTAdjClose (USD) 35.048183 20.736618 22.518881 27.437977 30.42424 41.406563

Predict.AdjDirectModelEconP (USD) 40.730626 41.048973 42.711146 42.0710226 39.739094 34.5756186

Predict.AdjDirectModelEconP2 (USD) 41.597521 41.866624 43.598454 42.684597 40.490221 35.4831193

Predict.AdjDirectModelEconP3 (USD) 45.29521 45.71013 45.51953 45.77006 45.45998 45.16978

75

Section A-4: Vanguard S&P 500 Robustness Analysis & Model Fitness

The Vanguard alternative models are using closed adjusted price data from October 1986 to November 2014 with the

exception of AdjDirectModelEconEMAP, which used 60 monthly periods after the 2008-2009 Financial Crisis at 2.7% MAPE.

The best historical performer, by MAPE, is AdjDirectModelEconP3 with an MAPE of 21.22%; Mod 2 & 3 have a MAPE of at

least 124%. As visualized, extreme swings in fund behavior (i.e., Van500IndexAdjClose) are not predicted accurately among

76

these models. To further analyze model performance, Figure A-4.2 compares Fund prices

against the models during the 2008-2009 Financial Crisis.

Model shock performance in AltRefitMod1 appears to recognize pattern behavior

slightly stronger than other alternative models between October 2007 and July 2009—but

AdjDirectModelEconP3 has a stronger historical forecasting error rate—this model

contains three variables to estimate closed adjusted prices: such as (i) C9 Index, (ii) U-3

unemployment rate, and (iii) velocity of money. The second model (AltRefitMod1)

contains personal savings rate, EMA of money velocity, and EMA of the Ap Index. The

third model (AltRefitMod2) uses the same variables from AltRefitMod1, but with the

EMA version of the CP Index. Table A-4.1 illustrates predicted values among these

models and actual fund prices during the Financial Crisis. The variable selection in

AltRefitMod1, compared to AltRefitMod2, could slightly improve model performance,

during this market shock, by an average of 78¢ per share from January to March 2009. In

conclusion, despite shock improvement, neither model is absolutely sensitive to extreme

market behavior (see Table A-4.1).

77

Table A-4.1: 2008-2009 Financial Crisis (Vanguard) Predicted vs. Observed Prices

Dec-08 Jan-09 Feb-09 Mar-09 Apr-09 May-09

Van500IndexAdjClose (USD) 71.26239 65.2674 58.31183 63.43016 69.49334 73.39727

Predict.AltRefitMod1 (USD) 99.771088 96.781252 90.647497 87.93043 85.801662 81.838106

Predict.AltRefitMod2 (USD) 99.48135 97.52685 91.10097 89.04749 87.61287 83.39575

Predict.AdjDirectModelEconP3

(USD) 100.61908 96.577631 91.375937 87.822392 84.906052 81.542762

78

Appendix B

Data Transformation Approach for Returns

This section will use transformed independent variables, outside absolute delta, in

time-series regression; the only exception in this exercise is that Fama-French’s market

parameters are not modified nor included in other models—this is to better understand

the variables’ impact before being included into the Fama-French Model for both State

Street stock and Vanguard S&P 500 Fund returns. Since most geomagnetic variables

have not shown promising results, they have undergone heavier data transformations

compared to the human economic behavioral variables. The objective of this analysis is

to understand if there is any meaningful information that can be used to improve the

Fama-French model. The data transformation methods are located in Chapter V. In

addition, the monthly time-series range is from October 1986 to November 2014. This

section will not follow typical equation patterns located in Chapter IV. Instead, the

analysis uses a linear regression matrix format, then compares the multiple outputs to the

Fama-French model. For variable elimination, the focus of the regression output includes

the following: (i) Adj. R2, (ii) RMSE (root-mean-squared-error), and (iii) p-values (0.1%,

1%, or 5%). A variance inflation factor (VIF) analysis will typically occur after the

model’s parameters have been adjusted (or removed). The following matrix is expressed

below:

Yt = Xt + t (15)

79

Section B-1: State Street Corporation Stock Returns

Table B-1.1: STT Transformed Data Approach, Part 1

TransModel 1 TransModel 2 TransModel 3 FFModel

========================================================

(Intercept) 9.79023 6.11946 -1.3108 -0.06705

(13.78657) (29.68894) (3.57921) (0.13014)

Kppwhalf 0.46999

(0.82055)

Appw8 0.00565

(0.02967)

Cppwnine -16.69977

(25.18379)

C9pwsqurt -0.03646

(0.11436)

KPLN 0.61833

(4.74959)

ApLn -0.34917

(1.40881)

CpLn 5.84214

(6.98404)

C9Ln -5.29675

(4.05846)

KpSqrt 0.05211

(0.94232)

APSqrt -0.19308

(0.75467)

CpSqrt 24.04645

(26.37132)

C9Squrt -10.42755

(8.34498)

MktRF 0.36832 ***

(0.02967)

SMB -0.09350 *

(0.04236)

HML 0.21147 ***

(0.04613)

------------------------------------------------------------------------------------------------

R^2 0.00182 0.00844 0.00576 0.32647

Adj. R^2 -0.01017 -0.00347 -0.00619 0.32042

Num. obs. 338 338 338 338

RMSE 2.86964 2.8601 2.86397 2.3537

========================================================

*** p < 0.001, ** p < 0.01, * p < 0.05

80

Models 1 to 3 contain geomagnetic data that was transformed by either natural

log, square-root, or squared. The overall conclusion is that neither of these variables are

good candidates to be included in the FFModel due to their lack of statistical significance

with the Corporation’s stock returns including model fit based on the following: such as

Adj. R2, RMSE (root-mean-squared-error), and p-values (0.1%, 1%, or 5%) of

independent variables in conjunction with the dependent variable. Table B-1.2 illustrates

the regression output of models 4 to 5 against the Fama-French model (i.e., FFModel).

Table B-1.2: STT Transformed Data Approach, Part 2

TransModel 4 TransModel 5 FFModel

==============================================

(Intercept) 0.57513 0.21068 -0.06705

(0.98488) (0.15551) (0.13014)

SumKPInv -115.3632

(412.16274)

APInv 4.18831

(16.32573)

CpInv -0.1196

(0.86818)

C9Inv 0.45633

(1.29350)

SumKPInvDelta 46.44955

(381.00475)

APInvDelta 11.14549

(13.87255)

CpInvDelta -0.48137

(0.78585)

C9InvDelta 0.71424

(1.07142)

MktRF 0.36832 ***

(0.02967)

SMB -0.09350 *

(0.04236)

HML 0.21147 ***

(0.04613)

-------------------------------------------------------------------------------

R^2 0.0033 0.00926 0.32647

Adj. R^2 -0.00868 -0.00265 0.32042

Num. obs. 338 338 338

RMSE 2.86751 2.85893 2.3537

==============================================

*** p < 0.001, ** p < 0.01, * p < 0.05

81

As defined in Chapter V, TransModel 4 takes on the rate for geomagnetic activity

at (1 ÷ xt). TransModel 5 uses the derivative calculated in TransModel 4 where each

variable is then transformed into its delta form. Overall, neither of these variables have

revealed any parameter significance with single stock returns including overall model fit;

therefore, neither of the transformed variables are included in the Fama-French model for

model performance analysis. The next section will follow the same approach with these

transformed parameters, but within a larger market environment.

82

Section B-2: Vanguard S&P 500 Fund Returns

Table B-2.1: Van500 Transformed Data Approach, Part 1

Models 1 to 3 contains geomagnetic data that was transformed by either natural

log, square-root, or squared (see Chapter V for further details). The overall conclusion is

TransModel 1 TransModel 2 TransModel 3 FFModel

=========================================================

(Intercept) 0.10393 -0.09912 -0.00638 0.00257 ***

(0.21401) (0.46226) (0.05566) (0.00032)

Kppwhalf 0.00243

(0.01274)

Appw8 -0.00024

(0.00046)

Cppwnine -0.13499

(0.39094)

C9pwsqurt 0.00066

(0.00178)

KPLN 0.03217

(0.07395)

ApLn -0.0102

(0.02194)

CpLn 0.01451

(0.10874)

C9Ln -0.02629

(0.06319)

KpSqrt 0.00281

(0.01465)

APSqrt -0.00529

(0.01174)

CpSqrt 0.18269

(0.41013)

C9Squrt -0.08842

(0.12978)

MktRF 0.01004 ***

(0.00007)

SMB -0.00195 ***

(0.00010)

HML 0.00027 *

(0.00011)

-------------------------------------------------------------------------------------------------

R^2 0.00295 0.00358 0.00321 0.98361

Adj. R^2 -0.00903 -0.00839 -0.00876 0.98347

Num. obs. 338 338 338 338

RMSE 0.04455 0.04453 0.04454 0.0057

=========================================================

*** p < 0.001, ** p < 0.01, * p < 0.05

83

that neither of these variables are good candidates to be included in the FFModel due to

their lack of statistical significance with Fund returns. Table B-2.2 includes model results

for models 4 to 5 against the Fama-French model (i.e., FFModel).

Table B-2.2: Van500 Transformed Data Approach, Part 2

TransModel 4 TransModel 5 FFModel

===============================================

(Intercept) 0.01676 0.00900 *** 0.00257 ***

(0.01530) (0.00242) (0.00032)

SumKPInv -4.85218

(6.40120)

APInv 0.12521

(0.25354)

CpInv 0.00737

(0.01348)

C9Inv -0.00976

(0.02009)

SumKPInvDelta -0.55865

(5.92493)

APInvDelta 0.09679

(0.21570)

CpInvDelta -0.00041

(0.01222)

C9InvDelta 0.00216

(0.01666)

MktRF 0.01004 ***

(0.00007)

SMB -0.00195 ***

(0.00010)

HML 0.00027 *

(0.00011)

-------------------------------------------------------------------------------

R^2 0.00353 0.00706 0.98361

Adj. R^2 -0.00844 -0.00487 0.98347

Num. obs. 338 338 338

RMSE 0.04453 0.04445 0.0057

===============================================

*** p < 0.001, ** p < 0.01, * p < 0.05

TransModel 4 takes on the rate of geomagnetic activity at (1 ÷ xt). TransModel 5 uses the

derivative calculated in TransModel 4 where each variable is then transformed into its

84

delta form. Overall, neither variable tested provides any statistical significance to be

included into the Fama-French model for model performance analysis.

Overall, the data transformation approach for both dependent variables revealed

that neither parameter could improve model estimation due to insignificant p-values with

its dependent variable. The next appendix discusses the Granger test for causality.

85

Appendix C

Causality of Earth’s Magnetic Field and Human Economic Behavior

To test causality among the geomagnetic field indices and the proposed human

economic behavioral variables, the Granger Causality test is utilized. The human

economic variables includes their raw monthly average form. Each variable is tested

separately and not through multivariate analyses which uses vector auto-regression. The

final result does not necessarily warrant a 100% certainty that X causes Y—but,

according to Granger (1988), the method may reveal a causal relationship of causality

between or among variables for prediction—this research is statistically trying to show if

there is enough information in X that could help predict Y. In addition, optimal lag order,

for each variable, is revealed through this test. A p-value near (or above) 5% suggests no

causality between the variables (i.e., fail to reject the null hypothesis). The test will also

use a reverse approach were the independent variable becomes dependent, as well as the

dependent to independent.

After all variables were tested, the analysis indicated that geomagnetic activity

does not Granger-cause human economic behavior—this is also true for the reverse

approach. Despite the results not adhering to minimal standards, the Cp and Ap indices

were closest to testing positive for causality with personal savings rate at 9.3% and 6.2%,

respectively. Table C-1 illustrates the results for this test. The time-series is from October

1986 to November 2014 for all raw monthly averaged data.

86

Table C-1: Results for Causality of Earth’s Magnetic Field and Human Economic Behavior2

Independent

Variable Dependent Variable

P-

Value Reject Null?

Lag

Order

Reverse

Order P-

Val

Reverse

Order

Lag

Reject Null?

SumKp Money Velocity 0.6364 Fail to Reject 1 0.2988 9 Fail to Reject

CP Money Velocity 0.5788 Fail to Reject 1 0.1843 12 Fail to Reject

AP Money Velocity 0.6618 Fail to Reject 1 0.6029 7 Fail to Reject

C9 Money Velocity 0.6431 Fail to Reject 1 0.1299 12 Fail to Reject

SumKp U-3 Unemployment 0.2886 Fail to Reject 11 0.3998 1 Fail to Reject

CP U-3 Unemployment 0.1896 Fail to Reject 11 0.4171 1 Fail to Reject

AP U-3 Unemployment 0.7216 Fail to Reject 11 0.615 1 Fail to Reject

C9 U-3 Unemployment 0.267 Fail to Reject 17 0.4169 1 Fail to Reject

SumKp Personal Savings Rate 0.1179 Fail to Reject 19 0.2137 1 Fail to Reject

CP Personal Savings Rate 0.0929 Fail to Reject 19 0.1547 1 Fail to Reject

AP Personal Savings Rate 0.06207 Fail to Reject 19 0.5498 1 Fail to Reject

C9 Personal Savings Rate 0.1639 Fail to Reject 19 0.141 1 Fail to Reject

SumKp Personal Consumption 0.331 Fail to Reject 22 0.2359 1 Fail to Reject

CP Personal Consumption 0.3154 Fail to Reject 21 0.2497 1 Fail to Reject

AP Personal Consumption 0.7591 Fail to Reject 1 0.3714 1 Fail to Reject

C9 Personal Consumption 0.3164 Fail to Reject 21 0.2278 1 Fail to Reject

2 (Zeileis & Hothorn 2002)

87

Appendix D

Correlation Matrix for STT Prices & Returns, Part 1/3

STTAdjClose STTExcess MktRF SMB HML RF PerConsumEx PerConsumExDelta M2Money M2MoneyDelta PerSavRate PerSavDelta U3Unemploy U3UnemployDelta

STTAdjClose 1.00

STTExcess 0.10 1.00

MktRF -0.02 0.51 1.00

SMB 0.04 -0.04 0.22 1.00

HML 0.06 0.12 -0.22 -0.30 1.00

RF -0.59 0.01 -0.04 -0.12 0.01 1.00

PerConsumEx 0.90 0.03 -0.01 0.04 -0.02 -0.78 1.00

PerConsumEx

Delta 0.19 0.11 0.13 0.16 -0.05 -0.09 0.16 1.00

M2Money 0.83 0.04 0.02 0.03 -0.04 -0.81 0.97 0.13 1.00 M2MoneyDelt

a 0.45 -0.13 -0.09 -0.06 -0.07 -0.41 0.55 -0.09 0.56 1.00

PerSavRate -0.69 -0.03 0.05 -0.07 0.01 0.22 -0.53 -0.26 -0.37 -0.18 1.00

PerSavDelta 0.01 -0.01 0.00 -0.04 0.04 0.00 0.00 -0.35 0.01 0.11 0.24 1.00

U3Unemploy -0.01 -0.01 0.09 0.06 -0.03 -0.63 0.33 -0.06 0.45 0.16 0.38 -0.01 1.00

U3UnemployDelta 0.02 -0.05 -0.07 0.08 -0.10 0.01 0.02 -0.14 -0.01 0.09 0.03 0.02 0.05 1.00

Highlights: State Street adjusted closed stock price (i.e., STTAdjClose) is negatively correlated with the following variables:

(a) RF at -59%, and (b) Personal Savings Rate at -69%; positive correlations include (a) Personal Consumption Expenditures at

88

90%, (b) Velocity of Money at 83%, and (c) the absolute change in the Velocity of

Money at 45%. For State Street stock returns (i.e., STTExcess), the Fama-French factor

MktRF tested positive at 51%.

89


STTAdjClose STTExcess SumKp Kppwhalf KPLN SumKPDelta SumKPInv SumKPInvDelta Ap Appw8 ApLn APSqrt APDelta APInv APInvDelta

STTAdjClose 1.00

STTExcess 0.10 1.00

SumKp -0.47 0.00 1.00

Kppwhalf -0.47 0.00 0.99 1.00

KPLN -0.46 0.00 0.97 0.99 1.00

SumKPDelta -0.01 -0.08 0.32 0.30 0.28 1.00

SumKPInv 0.40 0.00 -0.87 -0.91 -0.96 -0.22 1.00

SumKPInvDelta 0.00 0.08 -0.24 -0.25 -0.27 -0.75 0.30 1.00

Ap -0.39 0.01 0.94 0.91 0.87 0.39 -0.73 -0.24 1.00

Appw8 -0.37 0.01 0.92 0.88 0.83 0.40 -0.69 -0.23 1.00 1.00

ApLn -0.43 0.00 0.97 0.98 0.97 0.34 -0.90 -0.28 0.94 0.91 1.00

APSqrt -0.42 0.01 0.97 0.96 0.93 0.37 -0.82 -0.26 0.99 0.97 0.98 1.00

APDelta -0.01 -0.08 0.27 0.25 0.22 0.89 -0.16 -0.55 0.43 0.45 0.32 0.38 1.00

APInv 0.38 0.00 -0.87 -0.92 -0.95 -0.25 0.99 0.30 -0.77 -0.73 -0.93 -0.86 -0.21 1.00

APInvDelta 0.01 0.09 -0.25 -0.26 -0.27 -0.77 0.29 0.95 -0.28 -0.27 -0.32 -0.30 -0.65 0.33 1.00

Highlights: State Street adjusted closed stock price (i.e., STTAdjClose) is negatively correlated with the following

geomagnetic variables: (a) SumKp at -47%, (b) Kppwhalf at -47%, (c) KPLN at -46%, (d) Ap at -39%, (e) Appw8 at -37%, (f)

ApLn at -43%, and (g) ApSqrt at -42%; positive correlations include (a) SumKPInv at 40% and (b) APInv at 38%. For State

Street stock returns (i.e., STTExcess), nothing significant was revealed.

90


STTAdjClose

STTExc

ess Cp Cppwnine CpLn CpSqrt CPDelta CpInv CpInvDelta C9 C9pwsqurt C9Ln C9Squrt C9Delta C9Inv C9InvDelta DSavKp

STTAdjCl

ose 1.00

STTExcess 0.10 1.00

Cp -0.46 0.01 1.00

Cppwnine -0.44 0.00 0.95 1.00

CpLn -0.44 -0.01 0.94 1.00 1.00

CpSqrt -0.46 0.00 0.99 0.99 0.98 1.00

CPDelta -0.01 -0.08 0.33 0.28 0.27 0.31 1.00

CpInv 0.27 0.02 -0.63 -0.80 -0.83 -0.72 -0.15 1.00

CpInvDelta 0.00 0.07 -0.12 -0.19 -0.21 -0.16 -0.37 0.42 1.00

C9 -0.46 0.00 1.00 0.96 0.94 0.99 0.33 -0.63 -0.12 1.00

C9pwsqurt -0.42 0.01 0.97 0.86 0.84 0.92 0.35 -0.50 -0.09 0.97 1.00

C9Ln -0.42 -0.01 0.92 0.99 1.00 0.97 0.26 -0.85 -0.22 0.92 0.81 1.00

C9Squrt -0.46 0.00 0.98 0.99 0.98 1.00 0.30 -0.72 -0.15 0.99 0.91 0.97 1.00

C9Delta -0.01 -0.09 0.33 0.29 0.28 0.31 0.99 -0.16 -0.38 0.33 0.35 0.27 0.31 1.00

C9Inv 0.18 0.04 -0.45 -0.63 -0.66 -0.54 -0.10 0.95 0.48 -0.45 -0.34 -0.69 -0.54 -0.11 1.00

C9InvDelta 0.00 0.06 -0.07 -0.14 -0.16 -0.10 -0.19 0.43 0.95 -0.06 -0.04 -0.18 -0.10 -0.20 0.55 1.00

DSavKp -0.45 0.01 1.00 0.96 0.95 0.99 0.32 -0.66 -0.13 0.99 0.96 0.93 0.99 0.32 -0.48 -0.07 1.00

Highlights: State Street adjusted closed stock price (i.e., STTAdjClose) is negatively correlated with the following

geomagnetic variables: (a) Cp at -46%, (b) Cppwnine at -44%, (c) CpLn at -44%, (d) CpSqrt at -46%, (e) C9 at -46%, (f)

C9pwsqurt at -42%, (g) C9Ln at -42%, (h) C9Squrt at -46%, and (I) DSavKp, which is the difference between personal savings

and the KP index, at -45%; positive correlations include (a) CpInv at 27% and (b) C9Inv at 18%. For State Street stock returns

(i.e., STTExcess), nothing significant was revealed.

91

Appendix E

Correlation Matrix for Vanguard Prices & Returns, Part 1/3

VanAdjClose Van500Excess MktRF SMB HML RF PerConsumEx PerConsumExDelta M2Money M2MoneyDelta PerSavRate PerSavDelta U3Unemploy U3UnemployDelta

VanAdjClose 1.00

Van500Excess 0.01 1.00

MktRF 0.03 0.98 1.00

SMB 0.03 0.08 0.22 1.00

HML -0.01 -0.16 -0.22 -0.30 1.00

RF -0.64 0.02 -0.04 -0.12 0.01 1.00

PerConsumEx 0.92 -0.04 -0.01 0.04 -0.02 -0.78 1.00

PerConsumExD

elta 0.23 0.09 0.13 0.16 -0.05 -0.09 0.16 1.00

M2Money 0.89 -0.02 0.02 0.03 -0.04 -0.81 0.97 0.13 1.00

M2MoneyDelta 0.51 -0.10 -0.09 -0.06 -0.07 -0.41 0.55 -0.09 0.56 1.00

PerSavRate -0.59 0.06 0.05 -0.07 0.01 0.22 -0.53 -0.26 -0.37 -0.18 1.00

PerSavDelta 0.00 0.02 0.00 -0.04 0.04 0.00 0.00 -0.35 0.01 0.11 0.24 1.00

U3Unemploy 0.08 0.05 0.09 0.06 -0.03 -0.63 0.33 -0.06 0.45 0.16 0.38 -0.01 1.00 U3UnemployD

elta -0.06 -0.07 -0.07 0.08 -0.10 0.01 0.02 -0.14 -0.01 0.09 0.03 0.02 0.05 1.00

Highlights: Vanguard closed adjusted fund price (i.e., VanAdjClose) is negatively correlated with the following economic

variables: (a) RF at -64% and (b) Personal Savings Rate at -59%; positive correlations include (a) Personal Consumption

Expenditures at 92%, (b) absolute change in Personal Consumption Expenditures at 23%, (c) Velocity of Money at 89%, and

92

(d) the absolute change in the Velocity of Money at 51%. For Vanguard fund returns (i.e.,

Van500Excess), the Fama-French factor MktRF tested positive at 98%.

93


VanAdjClose Van500Excess SumKp Kppwhalf KPLN SumKPDelta SumKPInv SumKPInvDelta Ap Appw8 ApLn APSqrt APDelta APInv APInvDelta

VanAdjClose 1.00


SumKp -0.50 -0.03 1.00

Kppwhalf -0.50 -0.04 0.99 1.00

KPLN -0.49 -0.04 0.97 0.99 1.00

SumKPDelta 0.01 -0.10 0.32 0.30 0.28 1.00

SumKPInv 0.42 0.04 -0.87 -0.91 -0.96 -0.22 1.00 SumKPInvDel

ta -0.01 0.08 -0.24 -0.25 -0.27 -0.75 0.30 1.00

Ap -0.42 -0.03 0.94 0.91 0.87 0.39 -0.73 -0.24 1.00

Appw8 -0.41 -0.03 0.92 0.88 0.83 0.40 -0.69 -0.23 1.00 1.00

ApLn -0.45 -0.04 0.97 0.98 0.97 0.34 -0.90 -0.28 0.94 0.91 1.00

APSqrt -0.45 -0.04 0.97 0.96 0.93 0.37 -0.82 -0.26 0.99 0.97 0.98 1.00

APDelta 0.00 -0.10 0.27 0.25 0.22 0.89 -0.16 -0.55 0.43 0.45 0.32 0.38 1.00

APInv 0.40 0.04 -0.87 -0.92 -0.95 -0.25 0.99 0.30 -0.77 -0.73 -0.93 -0.86 -0.21 1.00

APInvDelta -0.01 0.08 -0.25 -0.26 -0.27 -0.77 0.29 0.95 -0.28 -0.27 -0.32 -0.30 -0.65 0.33 1.00

Highlights: Vanguard adjusted closed fund price (i.e., VanAdjClose) is negatively correlated with the following geomagnetic

variables: (a) SumKp at -50%, (b) Kppwhalf at -50%, (c) KPLN at -49%, (d) Ap at -42%, (e) Appw8 at -41%, (f) ApLn at -

45%, and (g) ApSqrt at -45%; positive correlations include (a) SumKPInv at 42% and (b) APInv at 40%. For Vanguard fund

returns (i.e., Van500Excess), nothing significant was revealed.

94


VanAdjClose Van500Excess Cp Cppwnine CpLn CpSqrt CPDelta CpInv CpInvDelta C9 C9pwsqurt C9Ln C9Squrt C9Delta C9Inv C9InvDelta

VanAdjClose 1.00


Cp -0.49 -0.03 1.00

Cppwnine -0.47 -0.04 0.95 1.00

CpLn -0.46 -0.04 0.94 1.00 1.00

CpSqrt -0.49 -0.04 0.99 0.99 0.98 1.00

CPDelta 0.00 -0.09 0.33 0.28 0.27 0.31 1.00

CpInv 0.28 0.04 -0.63 -0.80 -0.83 -0.72 -0.15 1.00

CpInvDelta 0.00 0.08 -0.12 -0.19 -0.21 -0.16 -0.37 0.42 1.00

C9 -0.49 -0.03 1.00 0.96 0.94 0.99 0.33 -0.63 -0.12 1.00

C9pwsqurt -0.46 -0.02 0.97 0.86 0.84 0.92 0.35 -0.50 -0.09 0.97 1.00

C9Ln -0.45 -0.04 0.92 0.99 1.00 0.97 0.26 -0.85 -0.22 0.92 0.81 1.00

C9Squrt -0.49 -0.04 0.98 0.99 0.98 1.00 0.30 -0.72 -0.15 0.99 0.91 0.97 1.00

C9Delta 0.00 -0.10 0.33 0.29 0.28 0.31 0.99 -0.16 -0.38 0.33 0.35 0.27 0.31 1.00

C9Inv 0.19 0.03 -0.45 -0.63 -0.66 -0.54 -0.10 0.95 0.48 -0.45 -0.34 -0.69 -0.54 -0.11 1.00

C9InvDelta 0.00 0.06 -0.07 -0.14 -0.16 -0.10 -0.19 0.43 0.95 -0.06 -0.04 -0.18 -0.10 -0.20 0.55 1.00

Highlights: Vanguard adjusted closed fund price (i.e., VanAdjClose) is negatively correlated with the following geomagnetic

variables: (a) Cp at -49%, (b) Cppwnine at -47%, (c) CpLn at -46%, (d) CpSqrt at -49%, (e) C9 at -49%, (f) C9pwsqurt at -

46%, (g) C9Ln at -45%, and (h) C9Squrt at -49%; positive correlations include (a) CpInv at 28% and (b) C9Inv at 19%. For

Vanguard fund returns (i.e., Van500Excess), nothing significant was revealed.

95

Chapter X

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