1. An Analysis of Value Criteria for
Portfolio Construction
by
Matthew Ryan Smith, MA(Hons)
An Analysis of Value Criteria for Portfolio Construction
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
2. 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.
3. 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.
4. iv
An Analysis of Value Criteria for Portfolio Construction
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.
5. 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
6. 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
7. 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
8. 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
9. 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,
10. 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.
11. 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.
12. 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.”
13. 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
14. 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
15. 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
16. 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.
17. 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.
18. 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.
19. 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
20. 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
21. 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.
22. 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
23. 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
24. 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.
25. 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
26. 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.
27. 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.
29. 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
30. 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
31. 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
32. 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.
33. 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
34. 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
35. 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.
36. 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
37. 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.
38. 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.
39. 32
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43. 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_RETURN
Sample 1/01/1999 12/31/2014
Observations 3774
Mean 0.000740
Median 0.000000
Maximum 0.162249
Minimum -0.084179
Std. Dev. 0.013658
Skewness 0.588607
Kurtosis 12.43677
Jarque-Bera 14221.46
Probability 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_RETURN
Sample 1/01/1999 12/31/2014
Observations 3774
Mean 0.000288
Median 0.000694
Maximum 0.114750
Minimum -0.092752
Std. Dev. 0.013226
Skewness -0.026305
Kurtosis 10.10308
Jarque-Bera 7934.290
Probability 0.000000
44. 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)
45. 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
R-squared 0.024219 Mean dependent var 0.000161
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
46. 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
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 Wald F-statistic 97.34375
Prob(Wald F-statistic) 0.000000
