Matthew Smith Dissertation

An Analysis of Value Criteria for Portfolio Construction

by

Matthew Ryan Smith, MA(Hons)


Presented to the Faculty of the Graduate Business School of

The University of Aberdeen

in Partial Fulfilment

of the Requirements

for the Degree of

MSc Finance and Investment Management

The University of Aberdeen August 2014

Word Count: 9,459

51339874

Dedication

I dedicate my dissertation to my parents who, through thick and thin, have been

there for me. Their support and drive is what has made me who I am.

iii

Acknowledgements

I would like to thank my supervisor Professor Angela Black who is one of the

most knowledgeable and helpful academics I have met. She has been most

generous with her time and expertise without which I would not have been able to

complete this dissertation.

iv


Matthew Ryan Smith MA(Hons)

Student ID: 51339874

The University of Aberdeen, 2014

Supervisor: Professor Angela J. Black

Abstract

This paper examines whether a simple stock selection criteria, based on

the fundamentals of value investing, can produce superior risk-adjusted returns

than the market. I show that these 7, seemingly simple criteria, do in fact offer

higher risk-adjusted returns than that of the market over the period 1999-2014.

The value portfolio, created from the criteria, return over 1,000% to the investor

over the period with a Sharpe ratio of 0.63. This is compared with just over 110%

cumulative return and a Sharpe of 0.06 from the market, for which I use the

Russell 3000. The findings back up many other studies of value criteria, which

show that this investment technique can offer superior returns.

v

Table of Contents

List of Formulas ................................................................................................... vi

List of Illustrations .............................................................................................. vii

Introduction ........................................................................................................... 1

Literature Review .................................................................................................. 4

Methodology ........................................................................................................ 12 Data Base ....................................................................................................... 12 Selection Criteria .......................................................................................... 13 Method of Analysis ....................................................................................... 15

Results and Analysis ........................................................................................... 18 Descriptive Statistics ..................................................................................... 19 Analysis ........................................................................................................ 22 Discussion ..................................................................................................... 26

Conclusion ............................................................................................................ 29

References ............................................................................................................ 32

Appendices ........................................................................................................... 36

vi

List of Formulas

Formula 1.1: Mis-used Graham Valuation Formala ............................................. 7

Formula 1.2: Fama French 3 Factor Model ......................................................... 16

Formula 1.3: Regression Result .......................................................................... 23

vii

List of Illustrations

Figure 1: Return of the Portfolio versus the Russell 3000 ......................... 18

Figure 2: Sharpe and Sortino Ratios .......................................................... 19

Figure 3: Comparison of varying P/E Ratio and Sharpe Ratio .................. 21

1

INTRODUCTION

Value investing is one of the most widely known and widely used investment

styles. The explanation of where the superior returns heed from is one that is

debated and discussed frequently in both the academic and professional worlds.

There are many, in both worlds, who see value investing as a very good strategy to

beat the market; amongst them Chan, Hamao and Lakonishok (1991), Fama and

French (1992, 1996, 1998), and Rosenberg, Reid and Lanstein (1984)1.

The idea behind a value investment strategy is whereby an investor purchases those

stocks which have a high book-to-market ratio. This is converse to a growth

investor who would have a portfolio of low book-to-market ratio stocks. As I will

discuss there is a great deal of debate regarding the source of this outperformance

by value strategies; many believe it to be as a result of the increased risk

supposedly inherent in value stocks whereas many see the potential outperformance

as a result of market inefficincies.

The greatest proponent of value investment, and perhaps the father of it, Benjamin

Graham has written extensively on the merits of value investing. A collection of

essays penned by Graham have been collected and published coutresy of

ValueHuntr2 and offers readers an insight into the mind of one of the most

respected and succesfull investors. Beyond these papers are the more formal books

he has published; Security Analysis (Graham and Dodd 1934) and The Intelligent

Investor (Graham 2003). It is a set of criteria for stock selection from his book The

Intelligent Investor that forms the basis of this paper.

1 For further evidence of a so-called value premium see a summary of evidence by Fama and French (1998). 2 Accessed at http://www.rbcpa.com/Common_Sense_Investing_The_Papers_of_Benjamin_Graham_1974.pdf. Last Accessed 26 August 2014

2

Whilst the copy of The Intelligent Investor I have used during my study, and the

one that is referenced above, is the 2003 edition, the book was originally published

by Graham in 1949. A time where there were very few personal investors (or retail

investors) and most investing was done on an institutional level. As a result of this,

prices moved less frequently and there were fewer analysts pouring over the

financials and other relevant materials of companies. This lead to more opportunity

for the value investor to seek out and identify those stocks which were trading at a

high book-to-market ratio. With the advent of online investment platforms and the

exponential growth in the number of investment analysts, it is hard to see that

prices could deviate from a reasonable price with great frequency or for any length

of time. Is it still possible, therefore to find these value stocks and create a portfolio

of them; one which can offer superior returns to the market?

Given this, I have set out to use Graham’s criteria and apply it to a universe of

stocks over the past 16 years in order to determine if it is still possible to achieve

superior, risk-adjusted returns in todays faster paced world.

Utilising these criteria I will create a portfolio for each of the past 16 years and

from the resultant time series data carry out various tests and analysis to determine

the answer. As part of the analysis I will be utilising the 3-factor model set out by

Eugene Fama and Kenneth French, of which you will read more about in the course

of my literature review. The authors of this model argue that the use of a 3-factor

model, with a factor acting as a proxy for the risk of the aforementioned value

premium, offers a better understanding of the returns than can be offered by the

Capital Asset Pricing Model (CAPM) created by Lintner (1965) and Sharpe (1964).

I have mentioned risk several times so far, and in my analysis it is considered at

length. It would, however, be prudent to note that there are many who offer strong

evidence that value investing is by no means more inherently risky than other

investment styles (Daniel and Titman 1997; Haughen and Baker 1996; Lakonishok,

3

Shleifer and Vishny 1994). It is the inefficiencies of the market and the excessive

weight put on past history that could explain the superior returns of this strategy.

I shall examine some past literatrure on the subject to begin, followed by an outline

of our data set and analysis method. My analysis and interpretation of the results

will come next followed by the paper’s conclusion.

4

LITERATURE REVIEW

The purpose of this literature review is to give a background to Benjamin Graham’s

thinking and his stock selection criteria. To look at and attempt to explain why he

believes that from these criteria he can obtain higher risk adjusted returns than the

market. I shall begin with a brief look at the efficient markets hypothesis.

Security prices, at any time, fully reflect all available information; this is the basis of the

efficient markets hypothesis. It is this basis that leads to the conclusion that no investor

can earn excess returns; that is returns above the market. It was Eugene Fama (1965), in

his milestone paper, who effectively defined this efficient market for first time. The

conclusion of that paper was that stock prices follow a random walk; that is that prices do

not follow any patterns and are not predictable, they are at their root random. A

conclusion like this proposes significant questions for those engaged in technical or

fundamental analysis. A subsequent paper by Fama (1970) was a decisive review of the

various studies and literature on the efficient market hypothesis. In it he puts forth the

definition; “A market in which prices always ‘fully reflect’ available information is called

‘efficient’.” He discussed three forms of the theory; strong form, semi-strong form and

weak form. He explained them as follows:

1. Weak Form: the market is efficient and reflects all market information. Historical price

information and movements are reflected in the current price and therefore cannot be

used to earn excess return. This precludes the use of technical analysis to obtain an

advantage, however it may provide for opportunities in fundamental analysis and through

the use of non-public information (however the use of non-public information is illegal in

most jurisdictions (Summers and Sweeney 1998; Wang 1981; Carlton and Fischel 1983;

Meulbroek 1992).

2. Semi-Strong Form: prices adjust rapidly to all newly available public information. In this

form both fundamental and technical analysis would be futile in the search for excess

returns.

5

3. Strong Form: prices reflect all information – public and private – and therefore any new

public information would not affect prices. As such there is no excess returns to be made,

even if new information was obtained.

It is widely believed that the markets exist in the semi-strong form and that, in the long

run, prices do reflect available information. Despite this however, there are many

anomalies and situations where this does not stand up. Examples of just a few are

seasonality of returns, liquidity effects, price to earnings and the small firm effect.

The seasonality effect is born out of evidence that there exist patterns in security prices

that consistently occur at specific times in a calendar year, this can be a month or even

specific days. One example is the day of the week effect; whereby evidence exists that

returns at the end of the week are regularly higher than at the beginning of the week.

There are various studies on this phenomenon, a sample include Cross (1973), French

(1980), Gibbons and Hess (1981), and Keim and Stambaugh (1984). Another widely

studied seasonal effect is the January effect. Studies, again show abnormalities in returns

based on the time of year; that is to say that there is evidence that returns in January are

often higher than any other month in the year. Studies on this include Keim (1983), Ritter

and Chopra (1989), and Ritter (1988).

Another prominent anomaly is that of price bubbles. Even in just the past 10-15 years we

have experienced this anomaly; namely the tech bubble and the real estate bubble. Many

of the other anomalies that exist create only a small effect on the markets and the

economy, so whilst they may show to be statistically significant they are often less

economically significant. Bubbles however can have massive and potentially very

damaging effects on the markets and the economy as a whole. One of the first papers to

discuss bubbles, (Diba and Grossman 1988), provides the following definition:

“A rational bubble reflects a self-confirming belief that an asset’s price depends on a

variable (or a combination of variables) that is intrinsically irrelevant – that is, not part

of market fundamentals – or on truly relevant variables in a way that involves parameters

that are not part of market fundamentals.”

6

Camerer (1989) discussed that these rational bubbles can occur when seemingly rational

traders expect to profit merely by participation in the bubble. He believed however that

the main component of a bubble was in fact a departure from rationality and potentially

the existence of overconfidence.

A final anomaly I will look at is that of the price to earnings effect. This forms an integral

part of our criterion and there have been several studies around this effect. The price to

earnings ratio (P/E) simply shows how much the investor is paying per unit of income (be

that £1, $1, €1 etc.). If we were to follow the efficient markets thought process we would

argue that the P/E for a company is at a level that reflects all relevant information, be it a

low or high P/E. There is however many views and studies which show the possibility of

excess returns linked to P/E ratios. There are many studies (Anderson and Brooks 2005;

Basu 1983) which show the potential for excess returns through investing in low P/E

stocks. Benjamin Graham was one such investor that saw the potential in low P/E, or

value stocks. Graham, as well as using P/E, also took into consideration those companies

which also had a low price to book (P/B) ratio. He saw these as potential indicators of a

value stock, the “book value, or net worth, as a […] possible guide to the selection of

common stocks.” (Graham 1974) Graham also noticed that these two often go hand in

hand, “For the most part, these issues selling below book value [low P/B] are also in the

low-multiplier group [low P/E]” (Graham 1974).

It is various criteria put forward by Graham that I will be using in our analysis in the

latter half of this paper and so I will now look at some of Graham’s work and his thoughts

on investing. Let us first look at his views on what we have just been discussing; the

efficient markets hypothesis. Graham agrees in principal with the hypothesis that markets

have all the information and so no consistent profits can be made by attempting to seek

out further information. What Graham vehemently disagrees with is that because of this

completeness of information, security prices are correct (or reasonable). He has stated this

many times in his books and various papers. Put very succinctly by Graham, “The market

may have had all the information it needed about [a stock]; what it has lacked is the right

7

kind of judgement in evaluating its knowledge.” (Graham 1974). A favoured quote of

Graham’s, from a long time ago, is that of René Descartes written in Discours de la

Méthode (Descartes 1637). It, however, is not the most famously quoted line in the book,

that being “Je pense, donc je suis” – I think, therefore I am. The line Graham often refers

to is

“Ce n’est pas assez d’avoir l’esprit bon, mais le principal est de l’appliquer bien.”

“It is not enough to have a good intelligence, the principal is to apply it well.”

A fitting quote, Graham would say, to apply to the many thousands of equity analysts in

the business. Graham has further insight into that of analysts later in the paper, “financial

analysts have not shown any more prudence and vision than that of the general

public….They too have largely put aside the once vital distinction between investment

and speculation” (Graham 1974).

Speculation in stock selection runs through many of Graham’s writings; he believes that

through his value stock selection technique that investors can make less risky, less

speculative investments.

As I have said, Graham has produced many papers and various books in his time. In these

are many methods for stock valuation and selection, including the criteria I use for this

analysis. Among these are formulas that he never intended to be solidified as stock

valuation formulas. One of which is a formula from his most notable book, The

Intelligent Investor (Graham 2003). Despite studies and papers (Morris 1976; Lin and

Sung 2014) showing its use yields excess returns, a commonly used graham formula (1.1)

was never intended to be used to calculate intrinsic value, or for stock selection.

Value = Current (Normal) Earnings X

(8.5 + double the expected growth rate)

In his book, The Intelligent Investor, Graham discusses this formula in relation to growth

stocks. What is often missed however is the footnote attached to this formula, which

reads:

1.1

8

“Note that we do not suggest that this formula gives the ‘true value’ of a growth stock,

but only that it approximates the results of the more elaborate calculations in vogue.”

Despite his warning that this formula yields a mere approximation, studies such as those

above have taken this formula to be an accurate judge of a stocks intrinsic value. It is

possible much of the confusion surrounding this formula is due to how later editions of

his book were formatted. In newer editions, with commentary by Jason Zweig, the

footnotes have been moved to the end of the book, unlike at the bottom of the page as in

the original editions. This does not, however, excuse academics and professionals from

utilising a formula intended for approximation as an accurate predictor of firm value;

appropriate due diligence should have been carried out.

Graham discusses his views on investor’s asset allocations (Graham 1974), and does

not propose that an investor rely solely on these value stocks to create a portfolio. In

fact his minimum allocation to equity is just 25%. His view of asset allocation was

initially a base of 25% in each of equities and bonds. Developing this further he

suggests that the remaining 50% should be split between the two as the investor sees

fit; that is to say whichever asset class looks to present more value. As we will see

later there are periods in which our criteria yields no suitable stocks for investment,

this itself could be a sign for the investor to move most of their money into bonds as it

would appear the market is overvalued in general.

There have been several studies over the year into both value investing and the

theories and criteria put forth by Graham in particular. One such paper, (Oppenheimer

1984), which examines a set of criteria put forth by Graham, shows that it is possible

to earn excess returns. Through the paper he discusses Graham’s views on the efficient

markets, and his believe that emotional swings can cause ‘central values’ to depart

significantly from security prices. Perhaps the further values depart the more

overpriced the market, and a potential warning sign for market corrections.

Oppenheimer’s study tests a selection of criteria that was put forward in Blustein

(1977). He found the best returns were linked to the use of the criterion for price to

9

earnings and a criterion looking at the companies’ debt level (criterion 1 and 6). His

study also showed that inclusion of a measure for earnings growth provided an

increment in risk-adjusted returns. These are amongst the criteria that form the basis of

my analysis and, I believe, the addition of my further criteria offer further controls for

risk and therefore offer higher risk-adjusted returns.

The debate as to where the excess return from value stocks arises from is on going.

Whilst many believe that the additional return achieved is the result of the additional risk

taken (Fama and French 1993; Fama and French 1995; Liew and Vassalou 2000) the

opposing camp believes that this excess return is achieved as a result of market

inefficiencies (Lakonishok, Shleifer and Vishny 1994; Haugen and Baker 1996). Whether

it is as a result of the non-diversifiable risk inherent in these stocks, or whether it is as a

result of informational inefficiencies, I will look to examine whether our simple value

selection criteria can create a simple investment strategy to take advantage of this, and

achieve excess return.

In the course of my analysis I will utilise the Fama French 3 factor model (Fama and

French 1996); this model expands on the well-known Capital Asset Pricing Model

(CAPM), which looks at individual returns simply using the return of the market. The

Fama French model incorporates further factors relating to firm size and value. The

model considers the vast evidence, as we have discussed, that small market cap stocks

and value stocks regularly outperform the market. Fama and French built the model out

of the realisation and evidence that those stocks considered to be small cap and those with

high ratio of book value to equity have historically exhibited higher returns than that

predicted by the CAPM. They take their additional factors to be proxies for risk not

explained by the CAPM, in particular beta of the CAPM.

Now to look at the criteria that Graham discusses in The Intelligent Investor. In chapter

14 of his book he discusses the methodology suitable for the defensive investor; it is here

where our criteria start.

10

His first criterion discusses the importance that the firm be of adequate size; this is of

importance to ensure that small firms are excluded as they are most likely to experience

“more than average vicissitudes” (Graham 2003); that is to say that they may be more

prone to changes, financially. In order to ensure this, he excluded all firms with sales of

less than $100 million (or in the case of public utility companies, those firms with no less

than $50 million of total assets). I shall exclude the asset criteria for our study and focus

merely on the sales figures. As you will see I have inflation adjusted this figure for today

to continue to ensure I exclude small companies by today’s standards.

The second criterion is that of financial strength; here he looks to ensure the selected

firms will continue as an ongoing concern well into the future. Here he considers the

company’s current ratio for which he recommends at least 2-to-1. Furthermore, long-term

debt should not exceed the net current assets of the company. Combined these criteria

ensure those firms which do not have a strong financial foundation are excluded from the

portfolio.

Thirdly, Graham looks to ensure long term earnings stability. He puts forth a criterion of

some level of earnings each year for the preceeding 10 years. Given recent financial

crises and the bear markets we have experienced, I have reduced this requirement, but

still require that over the past 10 years that earnings per share have grown, by at least

10%.

His next criterion, following the form of his previous, is that there be uninterrupted

dividends for at least the past 20 years. Again for the reasons detailed before I have

altered this criterion, so as to ensure that there has been some level of dividend but not as

stringent. I have proposed a criterion of dividend yield being greater than 2%; I am

confident this yield level will include, in general, only those companies commited to a

culture of ongoing dividends.

His next criterion concerns earnings growth, as I mentioned above I have altered the

earnings stability criterion to one concerned with growth so this element has been met

already.

11

The price to earnings ratio comes next. He outlines that the company’s price to earnings

ratio should be no greater than 15, I see this as still being a reasonable ratio in todays

market and have thus left the criterion as he originaly described it.

Finally, and in terms of value investing importantly, is his criterion for a moderate ratio

of price to assets (book value to price). As with the price to earnings ratio I see the figure

he proposes as still being reasonable today. Therefore I have left his criterion as a price to

book ratio of no more than 1.5.

The combination of these criterion into a stock selection strategy will, I believe, allow us

to find those stocks which offer value but which, through controls for financial strength

and earnings and dividends, have limited downside. The result being superior risk-

adjusted returns.

Following is a detail of the dataset I am using and further detail and summary of the

criteria to be applied to the dataset.

12

METHODOLOGY

The following research design was utilised to look at the potential use of stock selection

criteria outlined by the father of value investing, Benjamin Graham, as an investment

strategy. In each annual period a portfolio of stocks was created using the criteria set forth

by Graham as a screen. I then examined the risk-return relationship of the portfolio

comparing it to a selected market benchmark, as well as considering whether the strategy

can create positive alpha. For the study, the portfolio was created and back tested using

software provided by portfolio123.com, I then used the econometric software eViews for

the analysis.

Data Base

As mentioned, the data for the study was drawn from an online stock screening tool,

portfolio123.com, which it itself draws the underlying data from Compustat. At present

the tool does not allow the analysis of the UK stock market, I will therefore be analysisng

the US market. Compustat is a database of stocks and financial information provided by

S&P CapitalIQ. The database allows access to over 9000 US stocks; however further

examination of the available universe shows that many of these stocks are not readily

tradable on any exchange or market. Therefore I created, from this selection, my own

universe for use in my study.

The universe created consists of all stocks listed on the Russell 3000 in each year of the

screen, as well as stocks available over the counter (OTC); namely those available form

the OTC Bulletin Board, a regulated electronic trading service. Large investments banks

and investment advisers will have ready access to these OTC securities, however with the

advent of, and great improvements in retail investment platforms, such as Hargreaves

Lansdown, these OTC securities are becoming more readily available to all investors,

retail and institutional alike. It is for this reason I have decided to include these OTC

securities in the study and increase the pool of available securities for the portfolio. The

13

Russell 3000 is an annually rebalanced market-capitalisation weighted index that consists

of the 3000 largest publicly traded companies in the United States. The index represents

around 98% of the investable US market.

At its peak during our timeframe, this new universe (of OTC stocks and Russell 3000

stocks) offers over 5,100 stocks to screen from; which, whilst considerably less than 9000

still offers a vast universe to screen from.

The Compustat database offers historical financial information from 1999 to present for

analysis. My study period will therefore be the period from January 2nd 1999 to January

2nd 2014, utilising daily stock prices.

Selection Criteria

As discussed previously, I will be drawing my criteria for stock selection from Benjamin

Graham’s seminal book, The Intelligent Investor (2003). To reiterate, the 7 criteria I will

be using are as follows:

1. A price to earnings ratio below 15;

2. A price to book ratio below 1.5;

3. A current ratio greater than 2;

4. Dividend yield greater than 2%;

5. Annual Sales greater than $375 million;

6. 10 year earnings per share growth greater than 10%;

7. Net current assets greater than long-term debt.

Again, in order to be added to the portfolio, a stock must meet each requirement. In order

to ensure that the criteria are comparable with stocks during our timeframe, I have

adjusted the minimum sales figure for inflation. The new criterion of $375 million is

Graham’s $100 million figure inflation adjusted to the start of our analysis, January 2nd

1999. Additionally, for some of our criteria there were multiple options; for example I

14

could have used trailing or forward-looking price to earnings ratios. Where multiple

options existed I have selected what I believe to be the most appropriate:

1. There are several price to earnings ratios that I could have employed for this criterion;

the one I have chosen to use is the trailing twelve month ratio, excluding extraordinary

items. To be more exact, this is the current price divided by the sum of the previous

four diluted earnings per share from continuing operations, before extraordinary items

and accounting changes. This is used to avoid any large unusual financial transactions

affecting our selection.

2. There are two options for price to book, the option for previous quarter price to book

or current quarter price to book, in order to ensure that the most up to date ratio is

screened I have used the current quarter ratio.

3. As with price to book there were two options for current ration and I opted for the

current quarter current ratio.

4. Dividend yield can be screened for current yield or a 5-year average yield. Despite

Graham’s concern for long-term dividend commitment, I have opted for the current

yield so as to ensure we get the current dividend picture of the company.

5. There were several options for sales figures, namely quarterly previous trailing twelve

month, latest year, previous year etc. I have used the latest years sales, again to get the

most up to date picture of the company.

6. Various timeframes were available for earnings per share growth, however I have

chosen 10 years to ensure a long history of growth in the company, which is an

important factor in Graham’s considerations.

7. Finally for each of the variables used to calculate this criterion I have used the latest

years figure.

15

Method of Analysis

In order to identify stocks that match all of my 7 criteria, and are therefore suitable for

inclusion in the portfolio I will apply these criteria to our universe of stocks, beginning on

January 2nd 1999. An equally weighted portfolio of these stocks was then formed and held

until the next screening period. Unfortunately the back testing tool is, as yet, unable to

operate on an annual rebalancing period and at present works on a 52-week period, this

discrepancy results in some drift from the original date (this can bee seen in the dates

shown in the summary of annual results in Appendix 9). The screen is then ran again at

the end of the 52 week period and the portfolio rebalanced so that only stocks that meet

the criteria at that point in time are included in the portfolio. This can mean anything

from no turnover to 100% turnover rate in the portfolio each year. This was done

annually for the period being studied and daily and annual return data obtained from

poirtfolio123.com’s back testing tool.

By only rebalancing once a year, I take a slightly passive approach to the investments,

and because of this I may miss the peaks of a stocks price. Doing so, however, simplifies

the strategy and furthermore reduces the costs to just one rebalancing per year.

I have set no criterion for minimum holdings, meaning that in any year there can

potentially be no holdings in the portfolio (as you will see is the case in more than one

period). Additionally I have no criterion for maximum holdings. Despite Graham’s

recommendation not to be completely out of the market, I have done this to ensure a pure

test of the criteria; you will see during the discussion that this portfolio of value stocks

forms part of a larger portfolio.

Given that investors are assumed to be risk averse, and that returns incorporate risk, the

most apt performance measure will be one that has a consideration of risk as well as

return. There are several risk adjusted performance measures available such as those

developed by Treynor, Jensen and Sharpe (Friend and Blume 1970). For my study I have

16

chosen to begin my analysis with a consideration of the market and the portfolio’s Sharpe

ratio and Sortino ratio.

Following this I will then move on to evaluate the performance of the portfolio using

econometric software, eViews. Using data provided by Kenneth French, one of the

economists behind the Fama French 3 factor model, I ran regressions on the data to

evaluate whether or not our method could add positive alpha and also to consider what

may be the contributing factors to the portfolio’s returns.

For my analysis I used the following Fama French model:

𝑅!" − 𝑅!" = ∝!+ 𝛽!(𝑅!" − 𝑅!")+ 𝑆𝑀𝐵 + 𝐻𝑀𝐿 + 𝜀!"

where:

𝑅!" = Portfolio return on day t;

𝑅! = the risk-free (Treasury Bill) rate of return on day t;

𝛼! = the measure of daily abnormal return of the portfolio;

𝛽! = the portfolio’s risk relative to that of the market portfolio;

𝑅!" = the return on the market on day t. To elaborate further, a value-

weighted return of all CRSP firms incorporated in the US, specifically

those listed on the NYSE, AMEX, or the NASDAQ that have a CRSP

share code of 10 or 11;

SMB = small minus big, this accounts for the spread in return between small

and large sized firms, in terms of their market capitalization;

HML = high minus low, this accounts for the spread in returns between value

and growth stocks, this is constructed using book-to-market values;

𝜀!" = error term, which is assumed to be zero and to have no serial correlation.

The equation is the Fama French 3 factor model I discussed in the literature review. It

states that the portfolio return in excess of the risk free rate is a function of 5 terms – that

is to say it is a function of a risk premium (the product of the return on the market above

1.2

17

the risk free rate and the portfolio’s risk), a factor accounting for firm-size, a factor

accounting for value versus growth, a random error, and finally an estimate of the

portfolio’s return that is not explained for by any of the other factors. Whilst I have

referred to this model as the 3 factor model then actually discussed 5 factors, both the

random error and alpha term are expected to be zero, therefore, with both of these

variables equalling zero, we return to the aforementioned 3 factor model. As mentioned

above I am using the alpha term as a test of the strategy’s ability to provide us with

returns above those expected by the market, so despite our expectation of zero for this

term, I am in reality aiming for a statistically significant positive value.

Before using the above model, I also carried out additional tests of the data to ensure that

there was no serial correlation as well as tests and, if necessary, corrections for any

heteroscedasticity.

Due to the point-in-time nature of the Compustat database our analysis is not impacted by

survivorship bias. At each screen date any stocks that existed at that point, which no

longer exist, will be included in the portfolio, and therefore included in our analysis.

Additionally, any effect from dividends or stock split will be included in our analysis.

18

RESULTS AND ANALYSIS

In order to determine whether the screen is effective or not, we must look at various

measures of success. The first, and most obvious measure is return. As we can see

from Figure 1, the portfolio created from the screen clearly offers substantially higher

returns than the market. Over the 16-year period the portfolio has returned over

1,000% compared to just over 100% from the market.

Figure 1

Whilst this return is substantially higher, simply considering return does not offer the

whole story. We must consider what level of risk was taken to achieve these high

returns. In order to do this I have utilised the Sharpe ratio and the Sortino ratio as a

measure of risk-adjusted return.

The Sharpe ratio is simply a measure of how much additional return you are achieving

from taking on the extra level of risk. The Sortino, whilst still a measure of risk

adjusted return, looks at just downside deviation in order to calculate it. The Sharpe

ratio takes into account both downside and upside risk, whereas the Sortino ratio

-‐50.00% 50.00% 150.00% 250.00% 350.00% 450.00% 550.00% 650.00% 750.00% 850.00% 950.00% 1050.00%

1999 2001 2003 2005 2007 2009 2011 2013

Por$olio Return vs Russell 3000 Return

Por2olio Return

Market Return

19

considers just the negative downside risks. The ratios for our portfolio and the market

can be seen in figure 2.

Sharpe Ratio Sortino Ratio

Market 0.06 0.08

Portfolio 0.63 0.85 Figure 2

We can see that although I may have taken on additional risk to achieve the returns in

our portfolio that on a risk adjusted basis, both the Sharpe and Sortino ratios show that

the portfolio offers markedly higher returns over the market.

Descriptive Statistics

In order to examine further whether our criteria can help produce a superior portfolio, I

made use of the econometric software eViews. Through the use of this software I can

observe various statistical information as well as test models based on our data.

From the histogram and corresponding statistics, which can be seen in Appendix 1, we

can note certain things regarding the portfolio return data. Firstly we can observe that

the largest one-day fall over the observed 3,774 days was 8.4%, smaller than the

largest fall of the market of 9.3% (Appendix 2). This shows us that, as discussed in

Petkova and Zhang (2005), value investing does not necessarily expose the investor to

a greater degree of downside risk. Whilst interesting to see that the largest one day fall

in value was from the market and not the portfolio, it does not tell us too much about

the actual data. We can further examine the data through the measures of skewness

and kurtosis.

We observe that the data exhibits positive skew, which is to say that there are a greater

number of higher observations in the data. When comparing this to the observed

negative skew of the market returns it would suggest that the portfolio offers a greater

number of days with positive returns.

20

We can also see that the data appears to have a high level of leptokurticity; that is to

say that the data is more peaked than a normal distribution and has fatter tails. This

observation of fat tails, may have some bearing on our consideration of the portfolio,

as fatter tails increase the probability of an extreme observation and that a great deal of

the risk is coming from outlier events. We see, however that the market returns also

exhibit leptokurticity. Furthermore, given that I earlier noted the largest negative

return of the portfolio was smaller than the markets, we can assume that the more

extreme outliers are in fact in the positive return area.

I was interested in how much effect the price to earnings criterion had on the results. I,

therefore, ran the back test several times, altering the maximum P/E ratio from 5 to 20

whilst holding all other criteria constant. The effects can be seen on the next page

(Figure 3) and it is clear to see that whilst the P/E has a strong effect on the risk-

adjusted return, in most instances the risk-adjusted return is still higher than the

Russell 3000. The range of 13 to 17 for the ratio seems to offer the highest Sharpe

ratio’s, with a P/E of 14 offering the highest risk-adjusted returns, ceteris paribus.

What is interesting form the results is the lower end, those that do not offer superior

returns compared to the market. In his paper, The Future of Common Stocks (Graham

1974), Graham identifies 3 groups of stocks (P/E ≤ 7, 7 < P/E < 20 and P/E ≥ 20) and

those with a P/E of 7 or less (which fall below the market in our study) he classifies as

unpopular stocks. Our study would appear to solidify his classification of these stocks,

given their inferior returns compared to the market.

Following this more visual observation of the data, I proceeded to test the data using

the Fama French 3 Factor Model, as outlined above.

21

Figure 3

22

Analysis

The first step in my analysis was to consider the possibility of serial correlation in the

error terms; that is to say whether there is the presence of a relationship between the

return variable and itself. I first plotted the residuals in a scatter diagram to identify

any clear presence, as can be seen (Appendix 4) there is no clear evidence of serial

correlation. In order to affirm this, I then proceeded to use the Durbin-Watson test to

examine its possible presence. In using this test I am testing the null hypothesis of no

serial correlation against the alternative hypothesis of its presence. In order to ascertain

the test statistic for the test, I ran the regression utilizing the aforementioned model,

the results can be seen in Appendix 3. Upon running the regression, a Durbin-Watson

statistic of 1.6127 is observed. When comparing this with the values for the lower and

upper bound of the test3, at the 5% significance level (𝑑! = 1.59 𝑎𝑛𝑑 𝑑! = 1.76), I

come to a conclusion of inconclusive, as our test statistic falls between the two

bounds; as such I assume no serial correlation and therefore do not reject the null

hypothesis.

The next step is to consider the possibility of heteroscedasticity; whereby the standard

deviation of my returns variable is not constant over time. In order to test for this I use

the White Test. Here I am testing a null hypothesis of homoscedasticity (i.e. no

heteroscedasticity) against the alternative hypothesis of heteroscedasticity. The results

of the test can be seen in Appendix 5. Given that the p-value for the test result is lower

than the 95% critical value then we must reject the null hypothesis in favour of the

alternative; that is to say that there is the presence of heteroscedasticity.

Given this finding I now re-run the test using a White adjusted regression; results can

be viewed in Appendix 6. In this regression, corrected standard errors are applied. The

resultant coefficients remain the same, however the standard errors are now smaller.

3 Durbin-Watson test statistic table obtained from: http://s120.ul.ie/drupal/sites/default/files/Durbin-Watson%20Stat%20Tables.pdf Last Accessed 26 August 2014

23

This means that this heterosceasticity consistent covariance method has reduced the

size of the t-statistic for the coefficients.

Now that I have adjusted for the presence of heteroscedasticity we can interpret the

results, which as can be seen in Appendix 6 are all statistically significant (p-value <

0.05).

𝑅!" − 𝑅!" = 0.000498+ 0.003408 𝑅!" − 𝑅!" + 0.002970𝑆𝑀𝐵 + 0.002063𝐻𝑀𝐿,

𝑠𝑒𝑟 = 0.013,𝑅! = 0.135

The key factor I was looking at in this test was whether, by using the criteria, I have

added alpha. This alpha measure shows whether the strategy I have employed has

introduced a level of return, which cannot be explained by the market as a whole

(Sharpe 1992; Sharpe 2007). “In order to earn alpha, one effectively has to ‘beat the

market’ either through good timing or stock picking” (Holmes 2009). By this

definition, the method I have used in this study to create the portfolio involved a

method of stock picking in order to obtain alpha. Whilst I have set the portfolio to

rebalance at a set time, there is no attempt to ‘time the market’; that is to say I do not

try to enter at the trough and sell at the peak, sales and purchases are down

simultaneously every 52 weeks. We may consider that whilst there is no conscious

effort at timing, the criteria themselves introduce an element of timing; when the

market is high it is likely that there are fewer value stocks and therefore our number of

positions in the market is reduced, whereas at times of seemingly low market values

the number of positions increases.

Alpha in our results can be taken as the coefficient for C. We can see above that our

alpha here is 0.000498. Many assume the presence of alpha represents the skill of the

investment manager, however, given that I have positive alpha using a very simplistic

stock picking criteria, skill is not necessarily needed to create alpha. If, as discussed

earlier in the paper, markets are informationally efficient, then there should be no

1.3

24

opportunity to create alpha; as is evidenced by our results however, the opportunity

clearly exists.

The existence of alpha itself implies that markets are not necessarily as efficient as

many believe and that security prices often deviate from their fundamental values. Our

criteria take advantage of these deviations from fundamentals, and seek out those

stocks that are believed to be undervalued. Given that our criteria do not require stocks

to be at a price below book value, it may be more prudent to describe our strategy as

seeking growth at a reasonable price, however I believe that the key elements of the

criteria lie in the domain of value investing.

Moving to the other coefficients in our analysis, it is interesting to note that the

coefficient for the value element (HML = 0.002) is lower than the coefficient for firm

size element (SMB = 0.003). It may be that, whilst still targeting value stocks, the

combination of our criterion creates a bias towards smaller sized firms.

Given the low 𝑅!value, future analysis of the data may find it prudent to test the same

situations using a GARCH model (Bollerslev 1986; Engle 1982). Use of this model

may better examine the volatility of the returns and take into account any shocks in the

equation.

As with any equity investment, the portfolio can fluctuate both up and down. It would

be prudent therefore, to look at whether I can identify a potential minimum holding

period. As we can see from Appendix 7 there are 2 instances where an investor in the

value portfolio would have experienced a negative return with a 3 year holding period

(assuming the investor makes the investment at the same time the portfolios are

rebalanced). Moving on to a longer period this falls to just 1 instance of negative

return form the twelve 5 year holding periods. Finally, with a long time frame of 10

years, the investor would not have experienced any negative returns if they held the

portfolio for the entire 10-year period. Whilst no investor wishes to lose money and

will therefore look to minimise risk wherever possible, for many investors a 10-year

25

time horizon can be quite long. Accepting that there is an historic 14% chance of loss

over a 3-year period, I believe that the 86% chance of making a gain (typically well

above the market) makes 3 years an acceptable minimum holding period. Whilst an

investor could move to a 5-year time frame, reducing the historic loss percentage to

just 8%, I believe it is not necessary. Many investors, often on the advice of financial

advisors and other financial services companies, will look to investments as a

minimum 5 year period anyway, but with our strategy, should the investor require

there money before this there is a high likelihood that they will have made an excellent

positive gain. Compared to the market returns over these periods, Appendix 8, it is

clear to see that a 3-year timeframe, when invested in the market, introduces a high

probability (43% historically) that you will have made a loss over the period. This

reduces to a still quite high, 29% for a 10-year holding period. When compared to the

strategies’ returns over 10 years, where there are no instances of loss, this looks highly

risky with a good chance of loss.

26

Discussion

Despite the evidence above showing that our simple investment strategy can offer

substantially higher risk adjusted returns (as shown by the Sharpe and Sortino ratios)

as well as the ability to generate alpha (an important measure in the hedge fund

industry), it is most likely used by very few, or no, institutional investors. In order to

justify the, sometimes lofty, fees charged by these funds they will engage in costly,

and possibly unnecessary, analysis of industries, companies, economics etc. Without

these fund managers, however, and other investment analysts conducting research and

determining their own stock prices it is likely that the returns form out method would

diminish or even disappear. This is because it is the individual interpretation by each

of these analysts that cause stocks to fluctuate from their reasonable value; each

analyst will determine their own view on a stock and will price it accordingly, without

this stocks would have significantly less fluctuations. It is these fluctuations from

fundamentals that create the opportunities required for our strategy to be effective.

As mentioned, the strategy I have employed is simple to use. Institutional investors

can employ it as just easily as retail investors. The retail investors can, for a small fee,

make use of the same tools I did in screening for our stocks. Graham, however, offers

an even simpler method than that which I have utilised here, he put forward the idea

that an investor could purchase common stocks at two thirds or less of book value and

hold these stocks until they reach net asset value (or for a maximum of two years). He

does note that they should meet some other criteria of financial strength also, perhaps

similar to our criteria such as current ratio greater than 2 or net current assets being

greater than long-term debt. Despite this even simpler strategy though, I believe that

the criteria I have applied allows us to increase the requirements for book value and

price to earnings to identify those stocks which are still undervalued, but which offer

less risk. By incorporating both value identifying criterion (price to earnings, book

ratio, dividend yield) with those criteria designed to identify fundamentally strong

27

companies (current ratio, earnings per share growth, strong financial position, strong

annual sales) I have shown a strategy that can provide strong risk-adjusted returns.

Moreover, because I rebalance annually I ensure a continuous margin of safety. As a

stock price appreciates (holding all else equal) the price will likely progressively

reflect the fundamental value of the stock and thus reduce the margin of safety. I

believe my method of annual rebalancing will reduce risk further, by ensuring a

sufficient margin of safety each year.

If one had the time, resources or inclination it may, in fact, be possible to achieve even

higher returns than I have shown. An investor who, as mentioned, has the time or

ability could utilise our initial screen of stocks, but merely as a starting point from

which to then conduct detailed analysis on, identifying the strongest of the options for

addition to the portfolio. Use of this method would, however, remove the simplicity

that our strategy offers. Additionally given the potentially large amount of time

required to conduct thorough analysis on each company, the opportunity to buy the

stock at a reasonable value may pass. Nevertheless, Graham in Security Analysis does

argue that the importance of further analysis, “A major activity of security analysis is

the analysis of financial statements.” (Graham and Dodd 1934). Given this, there

potentially exists even greater risk adjusted rewards by engaging in further analysis of

the securities. Whilst there are private investor with the time and ability, it is more

likely that a fund or investment manager with a team of analysts could undertake this.

Despite the large universe of stocks to choose from, there are times whereby the screen

identifies no stocks suitable for investment. In my analysis I have held the capital in

cash over the year (with no interest rate) to look at just the returns presented by the

criteria. Perhaps, however, in these periods when the screen identifies no suitable

investments, the minimum 25% equity portion of an investor’s portfolio, which I

mentioned during the literature review, could be invested in a tracker fund. It would be

prudent to not have all the investible capital held as cash. Graham discusses holding

short-term obligations during periods when market levels appear high and stocks are

28

generally trading well above market or book value. As I have mentioned, however, he

does not believe an investor should be entirely out of the market for, as he puts it “For

the shorter or longer pull – who can really tell? – it may turn out to be wiser to have at

least an indirect interest – via the common stock portfolio.” (Graham 1974). As I have

mentioned an investor can look to an option like a tracker fund, which offers low costs

and exposure to the entire market. Whilst I have not had the time to conduct an

analysis of the effects holding a tracker fund when no stocks are identified, I believe

that it may not be preferential. If no stocks are identified from the entire universe

available, it leads one to believe that the market is overvalued. With no stocks

identified as being of reasonable value it could be that a market correction may be in

the offing, which if a tracker fund were bought would result in losses during the year

rather than maintaining the investors capital.

29

CONCLUSION

I set out in this paper to examine a set of stock selection criteria discussed by

Benjamin Graham over 30 years ago, and to find whether these criteria can still

provide investors with superior risk adjusted returns today. Whilst I based these

criteria on the original views Graham put forth in his papers and books, I have, in

some instances, updated or altered the criteria to ensure they are closer to a like for

like comparison with original studies when his theories were first published; for

example adjusting the criteria for annual sales based on inflation. Value investing, and

its close relative growth at a reasonable price, are used by many institutional investors

in some form; Warren Buffet being a prime example, a student of Graham’s, he has

gone on to be one of the most successful investors, not just in the value universe but in

general. Many others follow the value approach, but are perhaps less well known;

those such as Seth Klarman and Irving Kahn (Graham’s teaching assistant at Columbia

University) but also even lesser knowns such as Tom Dobell of M&G and, Kevin

Murphy and Nick Kirrage of Schroders. Each of these value investors has achieved

varying levels of success for their funds, but in general these successes have been high

returns. It is obvious, however, that they do not employ such a simplistic strategy as

the one I have outlined here. As I have said, further analysis could be done beyond the

simple criteria I use, however, at least for retail investors this may not be possible, and

I have shown a clear opportunity for spectacular gains, based just on this simple

strategy.

We can clearly see from both the annual and cumulative returns, that there is strong

growth potential from the investment strategy. The strategy portfolio returned a

cumulative 1,051% over the 16-year period against just 113% for the Russell 3000; a

return I am sure any investor would be very happy to experience. Whilst the market’s

113% may still seem like a strong return, in comparison to our strategy it is

significantly lower and furthermore, when inflation adjusted, our strategy portfolio

30

still returned a cumulative 713% whereas, compared with the inflation adjusted return

of the market, it returned just 46%, cumulatively, over the 16 years.

I explained, however, that we must consider the significance of risk involved with

measuring returns. Whilst I have shown the possibility of experiencing stellar

performance through using the strategy, the investor and fund managers must consider

what level of risk is being taken to achieve these results. In considering this important

principal I discussed the use of both the Sharpe and Sortino ratios. When examined,

both these ratios were found to be greater than that of the Russell 3000 over the same

period. These findings show that when adjusted for risk, our strategy portfolio is still

able to significantly outperform the performance of the market, a very positive finding.

One other significant finding to emerge from my study comes from the analysis of the

data using the Fama French 3 factor model, discussed in the literature review and

outlined in my methodology. Using this model I was able to analyse the data to

determine whether the strategy was able to add positive alpha. As I discussed this is a

measure, used often by fund managers but particularly hedge fund managers, to show

the return added beyond that explained by the market. Additionally, given the

simplistic nature of our strategy, I have shown the misconception only skilful

managers can add alpha to be false.

The results show significant risk adjusted returns and the ability to generate positive

alpha, which may provide an improved investment strategy for both retail and

institutional investors. It is important to consider, however, that these results are based

on historical data, and bearing in mind the traits of historical returns, we know that the

past is no predictor of the future; so whilst the results are positive, any investor

looking to employ this strategy should exhibit caution before its use.

Future analysis of these criteria may find it interesting to look at the why the value

element of the three factor model was found to have less impact on returns than that of

the firm size element. Perhaps a bias towards small cap stocks is inherent in the

criteria and the returns are not in fact due to a value strategy but a firm size strategy.

31

Perhaps the inflation adjusted sales figure I have used is still insufficient to exclude

today’s small market cap firms.

Furthermore, an analysis of the data utilising a GARH form model may more

accurately consider the volatility of the returns and any shocks in the data, such as the

2007/8 financial crisis. Finally one more area of study, that I looked at briefly, would

be the effect of altering the criterion based on the P/E ratio. Whilst I used a P/E of 15,

as suggested by Graham, it would appear from my brief analysis that a P/E of 14 may

actually be the optimum; further study would be required to back this up however.

The evidence from this study suggests that costly fund managers and analysts are not

necessary to achieve risk-adjusted, market beating returns. Through sound principals

put forth by Benjamin Graham and developed through the years we can create a

successful investment strategy using just 7 simple criteria.

32

REFERENCES

Anderson, Keith P, and Chris Brooks. The Long-Term Price-Earnings Ratio. Available at SSRN: http://ssrn.com/abstract=739664 , 2005. Basu, Sanjoy. “The Relationship Between Earnings Yield, Market Value and Return for NYSE Common Stocks: Further Evidence.” Journal of Financial Economics 12, no. 1 (1983): 129-156. Blustein, P. “Ben Garham's Last Will and Testament.” Forbes, 1 August 1977: 43-45. Bollerslev, Tim. “Generalized autoregressive conditional heteroskedasticity.” Journal of Econometrics 31, no. 3 (1986): 307-327. Camerer, Colin. “Bubbles and Fads in Asset Prices.” Journal of Economic Surveys 3, no. 1 (1989): 3-41. Carlton, Dennis W, and Daniel R Fischel. “The Regulation of Insider Trading.” Stanford Law Review 35, no. 5 (1983): 857-895. Chan, L, Y Hamao, and J Lakonishok. “Fundamentals and Stock Returns in Japan.” Journal of Finance, 1991: 1739-1789. Cross, Frank. “The Behaviour of Stock Prices on Fridays and Mondays.” Financial Analysts Journal 29, no. 6 (1973): 67-69. Daniel, K, and S Titman. “Evidence on the Characteristics of Cross Sectional Variation in Stock Returns.” Journal of Finance, 1997: 1-33. Descartes, René. Discours de la Méthode. Paris: Hachette, 1637. Diba, Behzad T, and Herschel I Grossman. “Explosive Rational Bubbles in Stock Prices?” The American Economic Review 78, no. 3 (1988): 520-530. Engle, Robert F. “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation .” Econometrica 50, no. 4 (1982): 987-1007.

33

Fama, Eugene F. “Efficient Capital Markets: A Review of Theory and Empirical Work.” The Journal of Finance 25, no. 2 (1970): 383-417. Fama, Eugene F. “The Behaviour of Stock-Market Prices.” The Journal of Business 38, no. 1 (1965): 34-105. Fama, Eugene F, and Kenneth R French. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics 33, no. 1 (1993): 3-56. Fama, Eugene F, and Kenneth R French. “Size and Book-to-Market Factors in Earnings and Returns.” The Journal of Finance 50, no. 1 (1995): 131-155. Fama, Eugene F, and Kenneth R French. “The Cross-Section of Expected Stock Returns.” The Journal of Finance 47, no. 2 (1992): 427-465. Fama, Eugene, and Kenneth French. “Multifactor Explanations of Asset Pricing Anomolies.” Journal of Finance, 1996: 55-84. —. “Value Versus Growth: The International Evidence.” Journal of Finance, 1998: 1975-1999. French, Kenneth R. “Stock Returns and the Weekend Effect.” Journal of Financial Economics 8, no. 1 (1980): 55-69. Friend, Irwin, and Marshall Blume. “Measurement of Portfolio Performance Under Uncertainty.” The American Economic Review 60, no. 4 (1970): 561-575. Gibbons, Michael R, and Patrick Hess. “Day of the Week Effects and Asset Returns.” The Journal of Business 54, no. 4 (1981): 579-596. Graham, Benjamin. “The Future of Common Stocks.” Financial Analysts Journal 30, no. 5 (1974): 20-30. —. The Intelligent Investor. London: Harper Business, 2003. Graham, Benjamin, and David Dodd. Security Analysis. NYC: McGraw-Hill, 1934. Haugen, Robert A, and Nardin L Baker. “Commonality in the Determinants of Expected Stock Returns.” Journal of Financial Economics 41, no. 3 (1996): 401-439. Haughen, R A, and N L Baker. “Commonality in the Detriments of Expected Stock Returns.” Journal of Financial Economics, 1996: 401-439.

34

Holmes, Christopher. “Seeking Alpha or Creating Beta? Charting the Rise of Hedge Fund Based Financial Ecosystems.” New Political Economy 14, no. 4 (2009): 431-450. Keim, Donald B. “Size-Related Anomolies and Stock Return Seasonality: Further Empirical Evidence.” Journal of Financial Economics 12, no. 1 (1983): 13-32. Keim, Donald B, and Robert F Stambaugh. “A Futher Investigation of the Weekend Effect in Stock Returns.” The Journal of Finance 39, no. 3 (1984): 819-835. Lakonishok, Josef, Andrei Shleifer, and Robert W Vishny. “Contrarian Investment, Extrapolation, and Risk.” The Journal of Finance 49, no. 5 (1994): 1541-1578. Liew, Jimmy, and Maria Vassalou. “Can Book-to-Market, Size and Momentum be Risk Factors the Predict Economic Growth?” Journal of Financial Economics 57, no. 2 (2000): 221-245. Lin, Jason, and Jane Sung. “Assessing the Graham's Formula for Stock Selection: Too Good to be True?” Open Journal of Social Science 2 (2014): 1-5. Lintner, F. “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” Review of Economics and Statistics, 1965: 13-37. Meulbroek, Lisa K. “An Empirical Analysis of Illegal Insider Trading.” The Journal of Finance 47, no. 5 (1992): 1661-1699. Morris, Victor F. “A Proposed Revision of Benjamin Graham's 1974 Valuation Formula.” Financial Analysts Journal 32, no. 6 (1976): 21-26. Oppenheimer, Henry R. “A Test of Benjamin Graham's Stock Selection Criteria.” Financial Analysts Journal 40, no. 5 (1984): 68-74. Petkova, Ralitsa, and Lu Zhang. “Is Value Riskier than Growth.” Journal of Financial Economics 78, no. 1 (2005): 187-202. Ritter, Jay R. “The Buying and Selling Behaviour of Individual Investors at the Turn of the Year.” The Journal of Finance 43, no. 3 (1988): 701-717. Ritter, Jay R, and Navin Chopra. “Portfolio Rebalancing and the Turn-of-the-Year Effect.” 44, no. 1 (1989): 149-166.

35

Rosenberg, B, K Reid, and R Lanstein. “Persuasive Evidence of Market Inefficiency.” Journal of Portfolio Management, 1984: 9-17. Sharpe, W. “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk.” Journal of Finance, 1964: 425-442. Sharpe, William F. “Asset Allocation: Management Style and Performance Measurement.” The Journal of Portfolio Management 18, no. 2 (1992): 7-19. Sharpe, William F. “Expected Utility Asset Allocation.” Financial Analysts Journal 63, no. 5 (2007): 18-30. Summers, Scott L, and John T Sweeney. “Fraudulently Misstated Financial Statements and Insider Trading: An Empirical Analysis.” The Accounting Review 73, no. 1 (1998): 131-146. Wang, William K.S. “Trading on Material Non-Public Information on Impersonal Stock Markets: Who is Harmed and Who Can Sue Whom Under SEC Rule 10b-5?” Southern California Law Review 54 (1981): 1217.

36

APPENDICES

Appendix 1: Histogram and Statistics for Portfolio Daily Returns

0

400

800

1,200

1,600

2,000

-0.05 0.00 0.05 0.10 0.15

Series: PORTFOLIO_DAILY_RETURNSample 1/01/1999 12/31/2014Observations 3774

Mean 0.000740Median 0.000000Maximum 0.162249Minimum -0.084179Std. Dev. 0.013658Skewness 0.588607Kurtosis 12.43677

Jarque-Bera 14221.46Probability 0.000000

Appendix 2: Histogram and Statistics for Market Daily Returns

0

200

400

600

800

1,000

1,200

1,400

1,600

-0.10 -0.05 0.00 0.05 0.10

Series: MARKET_DAILY_RETURNSample 1/01/1999 12/31/2014Observations 3774

Mean 0.000288Median 0.000694Maximum 0.114750Minimum -0.092752Std. Dev. 0.013226Skewness -0.026305Kurtosis 10.10308

Jarque-Bera 7934.290Probability 0.000000

37

Appendix 3: eViews Original Output for Fama French 3 Factor Model Regression Dependent Variable: PORTF_RF Method: Least Squares Date: 07/30/14 Time: 11:50 Sample (adjusted): 2 3775 Included observations: 3774 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. C 0.000498 0.000207 2.402757 0.0163

MARKET___RF 0.003408 0.000158 21.51011 0.0000 SMB 0.002970 0.000340 8.724871 0.0000 HML 0.002063 0.000316 6.531710 0.0000

R-squared 0.134500 Mean dependent var 0.000656

Adjusted R-squared 0.133811 S.D. dependent var 0.013661 S.E. of regression 0.012715 Akaike info criterion -5.891075 Sum squared resid 0.609460 Schwarz criterion -5.884466 Log likelihood 11120.46 Hannan-Quinn criter. -5.888726 F-statistic 195.2879 Durbin-Watson stat 1.612724 Prob(F-statistic) 0.000000

Appendix 4: Scatter Diagram of Regression Residuals

-.10

-.05

.00

.05

.10

.15

.20

-.10 -.05 .00 .05 .10 .15 .20

RESID01

RESID01(-1)

38

Appendix 5: White Test for Heteroscedasticity Heteroskedasticity Test: White

F-statistic 10.38012 Prob. F(9,3764) 0.0000

Obs*R-squared 91.40078 Prob. Chi-Square(9) 0.0000 Scaled explained SS 558.3863 Prob. Chi-Square(9) 0.0000

Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 07/30/14 Time: 12:15 Sample: 2 3775 Included observations: 3774

Variable Coefficient Std. Error t-Statistic Prob. C 0.000121 1.04E-05 11.64438 0.0000

MARKET___RF^2 8.59E-06 2.30E-06 3.733380 0.0002 MARKET___RF*SMB 1.10E-05 7.17E-06 1.534516 0.1250 MARKET___RF*HML 2.00E-06 5.09E-06 0.392125 0.6950

MARKET___RF 1.21E-05 7.13E-06 1.699812 0.0892 SMB^2 3.33E-05 1.06E-05 3.127731 0.0018

SMB*HML -2.53E-06 1.58E-05 -0.160205 0.8727 SMB 2.36E-05 1.52E-05 1.549457 0.1214

HML^2 2.77E-05 9.10E-06 3.042636 0.0024 HML -4.56E-05 1.41E-05 -3.237937 0.0012


Adjusted R-squared 0.021885 S.D. dependent var 0.000565 S.E. of regression 0.000559 Akaike info criterion -12.13842 Sum squared resid 0.001176 Schwarz criterion -12.12190 Log likelihood 22915.20 Hannan-Quinn criter. -12.13255 F-statistic 10.38012 Durbin-Watson stat 1.696411 Prob(F-statistic) 0.000000

39

Appendix 6: White Adjusted Regression Dependent Variable: PORTF_RF Method: Least Squares Date: 07/30/14 Time: 12:48 Sample (adjusted): 2 3775 Included observations: 3774 after adjustments White heteroskedasticity-consistent standard errors & covariance

Variable Coefficient Std. Error t-Statistic Prob. C 0.000498 0.000208 2.397721 0.0165

MARKET___RF 0.003408 0.000235 14.49782 0.0000 SMB 0.002970 0.000450 6.607423 0.0000 HML 0.002063 0.000446 4.624788 0.0000


Adjusted R-squared 0.133811 S.D. dependent var 0.013661 S.E. of regression 0.012715 Akaike info criterion -5.891075 Sum squared resid 0.609460 Schwarz criterion -5.884466 Log likelihood 11120.46 Hannan-Quinn criter. -5.888726 F-statistic 195.2879 Durbin-Watson stat 1.612724 Prob(F-statistic) 0.000000 Wald F-statistic 97.34375 Prob(Wald F-statistic) 0.000000

40

Appendix 7: Portfolio Holding Periods

Year Portfolio Return (%) 3 Year 5 Year 10 Year

1 37.23 2 -‐21.75 3 41.86 52% 4 6.73 18% 5 186.02 333% 365% 6 17.00 257% 296% 7 -‐5.31 217% 380% 8 0.00 11% 238% 9 -‐29.82 -‐34% 122% 10 0.00 -‐30% -‐22% 262% 11 65.60 16% 10% 336% 12 0.00 66% 16% 458% 13 15.00 90% 34% 352% 14 16.38 34% 122% 393% 15 36.51 83% 203% 135% 16 5.25 67% 92% 112%

Negative Returns 2 1 0

Positive Returns 12 11 7

Likelihood of Loss 14% 8% 0%

41

Appendix 8: Market Holding Periods

Year Benchmark Return (%) 3 Year 5 Year 10 Year

1 18.66 2 -‐9.78 3 -‐8.36 -‐2% 4 -‐21.62 -‐35% 5 31.08 -‐6% 1% 6 11.21 14% -‐6% 7 7.53 57% 13% 8 14.93 37% 41% 9 7.38 33% 93% 10 -‐40.93 -‐27% -‐13% -‐12% 11 33.16 -‐16% 4% -‐1% 12 16.24 -‐9% 13% 27% 13 -‐2.45 51% -‐4% 35% 14 21.54 38% 8% 110% 15 29.00 53% 137% 106% 16 2.38 61% 82% 90%

Negative Returns 6 3 2

Positive Returns 8 9 5

Likelihood of Loss 43% 25% 29%

42

Appendix 9: Portfolio and Market Annual Returns

Documents

Matthew Smith Dissertation