Testing an Alternative Six-Factor Asset Pricing Model in the UK Equity Market

Testing an Alternative Six-Factor Asset Pricing Model in the UK
Equity Market
Georgios A. Charalambous
School of Management, University College London
August 31, 2021
Abstract
This paper constructs and tests an alternative six-factor asset pricing model to determine whether
it can adequately describe expected returns in the UK equity market. Specifically, we conduct
Fama-Macbeth (1973) regressions using test portfolios formed from various intersecting factor
sorts to evaluate whether the factors can be consistently and reliably priced. However, our findings
indicate that the model cannot offer a satisfactory description of UK equity expected returns.
Specifically, our results indicate that the market factor is the only factor that is consistently priced
across all test portfolios. We are therefore unable to recommend the model to practitioners for UK-
based regional applications.

2
Acknowledgements
I would like to express my deepest gratitude to my parents who have supported me in my academic
endeavours throughout the years.

3
Table of Contents
1. Introduction……………………………………………………………………………………6
1.1 Background……………………………………………………………………………6
1.2 Global Versus Regional Models………………………………………………………6
1.3 Literature Review……………………………………………………………………7
1.4 Research Aim………………………………………………………………………….8
1.5 Dissertation Structure……………………………………………………………….10
2. The Empirical Model…………………………………………………………………………10
3. Data and Methodology……………………………………………………………………….10
3.1 Data………………………………………………………………………………….10
3.2 Factor Construction…………………………………………………………………11
3.2.1 Market Factor and Risk-Free Rate…………………………………………11
3.2.2 Size Factor…………………………………………………………………11
3.2.3 Value Factor………………………………………………………………12
3.2.4 Profitability Factor…………………………………………………………13
3.2.5 Investment Factor…………………………………………………………13
3.2.6 Momentum Factor…………………………………………………………13
3.3 Test Portfolio Construction…………………………………………………………14
3.4 Tests of the Factor Model……………………………………………………………14
4. Results………………………………………………………………………………………15
4.1 Factor Summary Statistics……………………………………………………………15
4.2 Correlations Between the Factors……………………………………………………16
4.3 Fama-Macbeth (1973) Tests of the Factor Model……………………………………16
4.3.1 Factor Model Tests Using (5 × 5) Intersecting Test Portfolios……………16
4.3.2 Factor Model Tests Using (2 × 4 × 4) Intersecting Test Portfolios………18
4.4 Results Discussion……………………………………………………………………21
5. Conclusion……………………………………………………………………………………22
6. References……………………………………………………………………………………24

4
1. Introduction
1.1 Background
Multifactor asset pricing models have become the de facto models of choice in various applications,
including estimating the cost of equity capital (Nagel et al., 2007), evaluating the performance of
portfolio managers (Carhart, 1997), as well as case studies that require a model of expected returns
(Fama and French, 2004). Noteworthy examples of such models include the Fama and French
(1993, 1996) three-factor model, the Carhart (1997) four-factor model, and the more recent Fama
and French (2015) five-factor model.
Specifically, the Fama and French (1993) three-factor model, which is a linear factor asset
pricing model, extended the classic Sharpe-Lintner (Lintner, 1965; Sharpe, 1964) Capital Asset
Pricing Model (hereafter CAPM) by including two additional factors that sought to explain the
value effect (as evidenced by Rosenberg et al., 1985) and size effect (as evidenced by Banz, 1981);
vis-à-vis, the value factor and size factor. Likewise, Carhart (1997) extends the Fama and French
(1993) three-factor model by including an additional factor that seeks to capture the momentum
effect, as documented by Jegadeesh and Titman (1993), as well as Asness (1994). Similarly, the
Fama and French (2015) five-factor model enhanced the Fama and French (1993) three-factor
model by adding profitability and investment factors following the evidence from Novy-Marx
(2013) and Titman, Wei, and Xie (2004), respectively.
1.2 Global Versus Regional Models
As clearly illustrated by our previously mentioned examples, we are faced with the problem
of choice. Needless to say, choosing the wrong model may lead to costly errors in capital budgeting,
portfolio evaluation, as well as risk analysis decisions (Griffin, 2002). For instance, the choice
between a factor model constructed from country-specific factors or global equivalents can result
in substantially different estimates of expected returns (Griffin, 2002). In fact, Griffin (2002) finds
evidence that country-specific asset pricing models are advantageous to their global and
international counterparts since they generally have lower pricing errors. To be exact, Griffin
(2002) investigates whether the Fama-French (1993) three-factor model can better explain
variation in international equity returns when constructed from country-specific or global factor
components by conducting Fama-Macbeth (1973) regressions. Therefore, Griffin (2002)
concludes that practical applications of multifactor models, such as estimating the cost of equity
capital and evaluating the performance of portfolio managers, are best executed on a country-
specific basis. Similarly, Fama and French (2012) report that a global version of the Fama-French
(1993) three-factor model fails to explain regional expected returns. Consequently, they do not
recommend its use in applications that seek to explain regional portfolio returns (Fama and French,
2012). Correspondingly, Fama and French (2017) conclude that global versions of both the three-
factor (Fama and French, 1993) and five-factor models (Fama and French, 2015) perform poorly
when tested on regional portfolios, and thus suggest focusing on local models in which both the
factor components and returns to be explained are from the same region in such applications.

5
1.3 Literature Review
However, to date, there is little evidence from UK-based tests to support that a regional-
based multifactor asset pricing model that can consistently and reliably describe the cross-sectional
variation of equity returns in the UK has been identified (Foye, 2018; Gregory et al., 2013). For
instance, in one of the earliest UK-based studies, Miles and Timmermann (1996), using monthly
data from May 1979 to April 1991, find evidence that the value and size factors contain
information about variation in equity returns. Indeed, in a later study, Dimson et al. (2003), using
a more extensive data sample find evidence of a strong value premium in UK equities from 1955
to 2001. Nevertheless, Miles and Timmermann (1996) report that the market factor does not
explain cross-sectional variation in returns, even when other factors are absent, thus severely
undermining the CAPM and Fama-French (1993) three-factor model.
Likewise, Gregory et al. (2001) deduce that UK value stocks have indeed yielded higher
returns between January 1975 to December 1998. Nonetheless, they conclude that the Fama-
French (1993) three-factor model can be strongly rejected. Similarly, Hussain et al. (2002) conduct
tests on portfolios formed from size-value intersecting sorts using data from 1974 to 1998 and find
that although the Fama-French (1993) three-factor model is an improvement over the CAPM, there
exists substantial mispricing in several test portfolios.
In a later study, Gregory et al. (2013) conduct Fama-Macbeth (1973) as well as Gibbons,
Ross, and Shanken (1989, hereafter GRS) tests of alternative versions of the Fama-French (1993)
three-factor and Carhart (1997) four-factor models using test portfolios formed from size-value
and size-value-momentum intersections from October 1980 to December 2010, in order to
examine whether the factors are consistently priced. However, they report that the factors are
neither consistently nor reliably priced (Gregory et al., 2013).
In a more recent study, Nichol and Dowling (2014) carry out Fama-Macbeth (1973) and
GRS (1989) tests of the Fama-French (1993) three-factor and Fama-French (2015) five-factor
models using test portfolios formed exclusively from size-value sorts from January 2002 to
December 2013. Despite Nichol and Dowling's (2014) finding that both models ultimately fail the
tests and can thus be rejected, they argue that the Fama-French (2015) five-factor model is an
improved specification. Lastly, they argue that the profitability factor appears to be a promising
candidate and recommend that future research test alternative measures of profitability (Nichol
and Dowling, 2014). Hence, Foye (2018) capitalises on Nichol and Dowling's (2014) suggestion
by conducting Fama-Macbeth (1973) tests of the Fama-French (2015) five-factor model as well as
models with alternative definitions of profitability using a wide range of test portfolios from
October 1989 to September 2016. Nevertheless, most intriguingly, Foye (2018) questions Nichol
and Dowling's (2014) findings due to the limited scope of portfolios tested. Specifically, Foye
(2018) argues that if the Fama-French (2015) five-factor model indeed constitutes an improvement,
its factors should be consistently priced across different test portfolios. Thus, Foye (2018) conducts
tests using portfolios formed from size-value, size-profitability, size-investment, size-profitability-
investment, and size-value-investment sorts. In addition to testing the Fama-French (2015) five-
factor model, which defines profitability using operating profit (minus interest expense), Foye

6
(2018) also tests alternative specifications, including Novy-Marx's (2013) original specification,
which uses gross profit (as a measure of profitability), as well as free cash flow and net income.
Nonetheless, Foye (2018) finds that the tests conducted fail to specify which measure of
profitability offers the best description of this asset pricing factor. Furthermore, Foye (2018)
reports that the factors are inconsistently priced across the test portfolios for all model
specifications and thus cautions practitioners from using either model in applications. Finally, in
parallel to Fama and French (2015), Foye (2018) finds evidence that the value factor could be
redundant.
Similarly, Michou and Zhou (2016) conduct tests of the Fama-French (2015) five-factor
model and models with alternative definitions of profitability, including gross profit and income
before extraordinary items. Specifically, they conduct tests using test portfolios sorted on size-
value, size-profitability, and size-investment from July 1996 to June 2006 and find evidence that
the value and size factors are redundant (Michou and Zhou, 2016). Furthermore, their tests cannot
specify which measure of profitability is a better candidate for constructing the profitability factor.
In a recent study, Fletcher (2019) conducts model comparison tests of nine linear factor
models using test portfolios sorted on size-value and size-momentum from July 1983 to December
2016. Among the models tested is a six-factor model described by Fama and French (2018), which
extends the Fama-French (2015) five-factor model by including the momentum factor. The study
concludes that the six-factor model with small spread factors is the most promising of all tested
candidates. However, in parallel to Foye's (2018) critique over Nichol and Dowling's (2014)
conclusion, we question Fletcher's (2019) findings on the premise of the limited scope of portfolios
tested.
1.4 Research Aim
Therefore, primarily, the purpose of our study is to examine the performance of an
alternative six-factor model1
which we propose and to test whether its factor components can be
consistently priced when evaluated against a wide range of test portfolios in order to determine
whether it can offer a viable choice to practitioners in UK-based regional applications. Specifically,
our proposed model augments the Fama-French (2015) five-factor model by including the
momentum factor in a similar fashion to the Fama-French (2018) six-factor model. Furthermore,
it replaces the traditional profitability and value factors as described by Fama and French with
Novy-Marx's (2013) original definition of the profitability factor and an alternative definition of
the value factor proposed by Asness and Frazzini (2013). Our model's specification is motivated
by the following evidence.
Firstly, we replace the value factor as defined by Fama and French (1992) with Asness and
Frazzini's (2013) definition2
, which they claim to be a better proxy of true value. This choice is
1
An extensive description of our alternative model's specification is given in the Empirical Model section.
2
A detailed comparison between the two definitions of value is provided in the Factor Construction section.

7
motivated by their finding that the Fama and French (1992) definition is an accidental portfolio of
80% pure value and 20% poorly constructed momentum (Asness et al., 2014). Furthermore,
Asness and Frazzini (2013) state that their definition is superior not only because it is a better
stand-alone proxy of value but also because it can better handle the complex relationship between
value and momentum. In fact, identically to Asness et al. (2014), we find that the negative
correlation between value and momentum is significantly higher than under Fama and French's
(1992) value definition.
This brings us to the second change, which is the inclusion of the momentum factor. One
could argue that the natural relationship between value and momentum (documented by Asness,
1997) and the finding that technically, the original definition of value does capture some of the
momentum effect (Asness and Frazzini, 2013) provide enough evidence for the inclusion of
momentum. However, Asness et al. (2013) find evidence of momentum's existence in 40 countries
(including the UK) in various asset classes, using more than 20 years of out-of-sample data. In fact,
there exists evidence of momentum's existence that predates its academic discovery, which
suggests that the momentum premium has likely existed for as long as financial markets existed
(Asness et al., 2014). Specifically, Geczy and Samonov (2016) conduct out-of-sample research
using US stock data between 1801 and 1926 and report that the momentum effect was found to be
significant. Similarly, Chabot, Ghysels, and Jagannathan (2009), using hand-collected UK data
between 1866 and 1907, report that the momentum effect was present during the Victorian age,
thus eliminating the possibility that momentum could be an artefact of data mining.
The last change is related to our choice of following Novy-Marx's (2013) suggestion of
using gross profit as a measure of profitability when constructing the factor. Initially, the question
regarding which measure of profitability is best suited for the task of constructing the profitability
factor arose from the fact that although Fama and French (2015) cite Novy-Marx (2013) as their
motivation for including a profitability factor in their model, they chose to define profitability
using operating profit (minus interest expense) instead of gross profit, which was Novy-Marx's
(2013) suggestion, without explaining their choice (Foye, 2018). In fact, Fama and French (2018)
implicitly validate the question by considering an alternative definition of profitability.
Specifically, Ball et al.'s (2016) suggestion of using cash profitability. Therefore, given the
inconclusive evidence from Foye (2018) and Michou and Zhou (2016), we choose to remain
neutral by selecting gross profit, which Novy-Marx (2013) claims to be the “cleanest accounting
measure of true economic profitability”.
In addition to our paper's primary concern, our secondary goal is to provide evidence
against the claims of value's redundancy in the UK (e.g., Foye, 2018; Michou and Zhou, 2016)
using a wide range of test portfolios, following Asness (2014) who finds similar evidence in the
US. Furthermore, we also wish to shed light on the relationship between value and momentum in
the UK following Asness and Frazzini's (2013) findings that the negative correlation between value
and momentum is significantly higher under their definition of value.

8
1.5 Dissertation Structure
The remainder of this paper is organised as follows. In the “Empirical Model” section, we
extensively describe our alternative six-factor asset pricing model. The “Data and Methodology”
section provides information regarding the data used, the methods adopted for the factor and test
portfolio construction, and the tests we conduct. The “Results” section presents the findings of our
Fama-Macbeth (1973) regressions for our proposed factor model against various test portfolios.
Finally, the “Conclusion” section concludes our research's findings, discusses limitations, and
provides suggestions for further research.
2. The Empirical Model
This section provides a comprehensive description of the alternative six-factor model, which we
briefly mentioned earlier. Algebraically, the model is:
𝑅𝑖𝑡 − 𝑅𝐹𝑡 = 𝛽𝑖(𝑅𝑀𝑡 − 𝑅𝐹𝑡) + 𝑠𝑖𝑆𝑀𝐵𝑡 + h𝑖𝐻𝑀𝐿𝑡
𝐷𝐸𝑉
+ 𝑟𝑖𝑅𝑀𝑊𝑡
𝐺𝑃
+ 𝑐𝑖𝐶𝑀𝐴𝑡 + 𝑢𝑖𝑈𝑀𝐷𝑡 + 𝜀𝑖𝑡
Where 𝑅𝑖 is the return on a risky asset 𝑖, 𝑅𝐹 is the risk-free rate, (𝑅𝑀𝑡 − 𝑅𝐹𝑡) is the excess return
of the market portfolio, 𝑆𝑀𝐵 (Small Minus Big) is the size factor, 𝐻𝑀𝐿𝐷𝐸𝑉
(High Minus Low) is
the alternative value factor proposed by Asness and Frazzini (2013), 𝑅𝑀𝑊𝐺𝑃
(Robust Minus
Weak) is the profitability factor based on gross profit as initially proposed by Novy-Marx (2013),
𝐶𝑀𝐴 (Conservative Minus Aggressive) is the investment factor, and 𝑈𝑀𝐷 (Up Minus Down) is
the momentum factor. The terms 𝛽𝑖, 𝑠𝑖, h𝑖, 𝑟𝑖, 𝑐𝑖, and 𝑢𝑖 represent the respective factor loadings
of each factor for asset 𝑖. Lastly, the term 𝜀𝑖𝑡 represents the error term.
3. Data and Methodology
3.1 Data
The data used for our research is obtained from Datastream and covers the period of March 1985
to March 2021. Specifically, we use the Worldscope UK database, which almost covers the entirety
of the total market capitalisation (Otten and Bams, 2002) and is relatively free of survivorship bias
due to its inclusion of active, dead, as well as delisted firms.
In addition, similarly to previous UK-based research (e.g., Dimson et al. 2003; Foye 2018;
Nagel 2001), our sample includes only companies that trade on the main market of the London
Stock Exchange and excludes financial companies, investment trusts, foreign companies, GDRs,
as well as companies that are listed on the Alternative Investment Market (AIM). Finally,
following Gregory et al. (2013), we exclude companies with negative or missing book values.

9
3.2 Factor Construction
3.2.1 Market Factor and Risk-Free Rate
Similarly to Gregory et al. (2013) and Foye (2018), we choose the FTSE All Share Index as our
proxy for the market portfolio, where 𝑅𝑀 is the total monthly return (including dividends that we
assume are reinvested). Furthermore, following Gregory et al. (2013) and Foye (2018), our choice
of proxy for the risk-free rate is the monthly return on three-month UK Treasury Bills.
Before we proceed, we note that the size factor (𝑆𝑀𝐵), profitability factor (𝑅𝑀𝑊𝐺𝑃
), and
investment factor (𝐶𝑀𝐴) are formed at the beginning of October of each year and are rebalanced
on an annual basis. In contrast, the value factor (𝐻𝑀𝐿𝐷𝐸𝑉
) and momentum factor (𝑈𝑀𝐷) are
formed and rebalanced on a monthly basis at the beginning of each month. Our choice of forming
the factor portfolios at the beginning of October (similarly to the previously mentioned UK-based
research) instead of the end of June is motivated by Agarwal and Taffler's (2008) finding that 22%
of UK firms have a March fiscal year-end, and 37% have a December fiscal-year end. Moreover,
the decision of using end of March fundamentals for the first time the following October, which is
also applied to the value factor, allows us to avoid look-ahead bias. In addition, all factor portfolios
are value-weighted. Furthermore, following previous literature, all factor portfolios are formed
using the largest 350 UK-based firms (in terms of market capitalisation) at the time of each
rebalancing.
3.2.2 Size Factor
For instance, for the size factor (𝑆𝑀𝐵), we form two size groups; Small (S) and Big (B), using the
median market capitalisation of the largest 350 firms as the size breakpoint (following Dimson et
al. 2003 and Gregory et al. 2001, 2013). Additionally, we form three value groups; High (H),
Medium (M), and Low (L), using the 70th and 30th percentiles of the book-to-market ratio
(hereafter B/P) sorts of the largest 350 firms as the value breakpoint similarly to Gregory et al.
(2001, 2013)3
. Then, using the aforementioned size and value groups, we form six intersecting
portfolios: SH, SM, SL, BH, BM, and BL, in order to construct the size factor (SMB), which is
equal to:
𝑆𝑀𝐵 =
(𝑆𝐿 + 𝑆𝑀 + 𝑆𝐻) − (𝐵𝐿 + 𝐵𝑀 + 𝐵𝐻)
3
Moreover, we note that similarly to previous UK-based research (e.g., Foye 2018; Gregory et al.
2001 and 2013), we employ the same 70/30 percentile breakpoints for the creation of all factor
portfolio groups formed on value, profitability, investment, and momentum, as our choice of the
appropriate breakpoints.
3
We note that the B/P ratio of the value breakpoint for the size factor is calculated on a yearly basis following Fama
and French's (1992) standard approach (denoted as bpa,𝑙
) and is different from the B/P ratio used for the alternatively
defined value factor (𝐻𝑀𝐿𝐷𝐸𝑉
).

10
3.2.3 Value Factor
The value factor (𝐻𝑀𝐿𝐷𝐸𝑉
), which is rebalanced every month, is constructed using six intersecting
portfolios between the two previously mentioned size groups and three value groups formed using
the 70/30 percentile breakpoints for B/P. However, unlike the size factor, the B/P ratio used to
construct the value factor (which we denote as bpm,𝑐
) is calculated at a mismatch of dates between
the date of book value (updated yearly) and the date of share price (updated every month).
To clarify the differences between bpm,𝑐
and bpa,𝑙
, in Exhibit 1 presented below, we
reproduce Exhibit 1 from Asness and Frazzini (2013); however, our example firm has a fiscal year
ending in March instead of December. This is because, unlike Asness and Frazzini (2013), which
use a book value of equity obtained at the end of December to calculate bpm,𝑐
, we use a book
value of equity obtained at the end of March. Our choice is motivated by Agarwal and Taffler's
(2008) finding, as mentioned earlier. Therefore, we form six alternative intersecting portfolios
based on size and value: 𝑆𝐻𝑚
, 𝑆𝑀𝑚
, 𝑆𝐿𝑚
, 𝐵𝐻𝑚
,𝐵𝑀𝑚
, 𝑎𝑛𝑑 𝐵𝐿𝑚
(where the superscript 𝑚
indicates their monthly rebalancing frequency) in order to construct the value factor (𝐻𝑀𝐿𝐷𝐸𝑉
),
which is equal to:
𝐻𝑀𝐿𝐷𝐸𝑉
=
(𝑆𝐻𝑚
+ 𝐵𝐻𝑚) − (𝑆𝐿𝑚
+ 𝐵𝐿𝑚)
2
Exhibit 1
Example: B/P Calculation for a Firm with Fiscal Year Ending in March 2000.
This exhibit illustrates the approach used to compute the B/P ratio used for 𝐻𝑀𝐿𝐷𝐸𝑉
, denoted as 𝑏𝑝𝑚,𝑐
, and the
traditional approach by Fama and French (1992) used for 𝐻𝑀𝐿, 𝑏𝑝𝑎,𝑙
, for a firm with a fiscal year ending in March
2000. 𝑏𝑝𝑚,𝑐
is equal to the book value of equity per share (B) divided by the current price per share and is updated
monthly. In comparison, 𝑏𝑝𝑎,𝑙
is equal to the book value per share (B) divided by the share price at fiscal year-end
(𝑃𝑓𝑦𝑒) and is updated yearly. Lastly, the first superscript indicates the refreshing frequency (where 𝑎 is annual and m
is monthly), and the second indicates the lag used to update the share price (where l is lagged price and c is current
price). Finally, in this illustrated example, the date is assumed to be October 1st, 2001.

11
3.2.4 Profitability Factor
The profitability factor (𝑅𝑀𝑊𝐺𝑃
) is calculated using the six intersecting portfolios (SR, SM, SW,
BR, BM, and BW) formed between the two size groups and the following three profitability groups
using the gross-profit-to-assets ratio as a measure of profitability (following Novy-Marx, 2013);
Robust (R), Medium (M), and Weak (W). Therefore, 𝑅𝑀𝑊𝐺𝑃
is calculated as:
RMWGP
=
(𝑆𝑅 + 𝐵𝑅) − (𝑆𝑊 + 𝐵𝑊)
2
3.2.5 Investment Factor
The investment factor (𝐶𝑀𝐴) is obtained using the six intersecting portfolios (SC, SM, SA, BC,
BM, and BA) formed between the two size groups and the following three investment groups using
the yearly per cent change in total assets as a measure of investment; Conservative (C), Medium
(M), and Aggressive (A). Thus, 𝐶𝑀𝐴 is calculated as:
𝐶𝑀𝐴 =
(𝑆𝐶 + 𝐵𝐶) − (𝑆𝐴 + 𝐵𝐴)
2
3.2.6 Momentum Factor
Lastly, the momentum factor (𝑈𝑀𝐷) is obtained using the six intersecting portfolios (SU, SM, SD,
BU, BM, and BD) formed between the two size groups and three momentum groups using a firm's
(2-12) returns4
as described by Gregory et al. (2013) and Asness and Frazzini (2013) as a measure
of momentum instead of Carhart's (1997) definition which does not interact with size. The three
momentum groups are Up (U), Middle (M), and Down (D). Ergo, UMD is calculated as:
𝑈𝑀𝐷 =
(𝑆𝑈 + 𝐵𝑈) − (𝑆𝐷 + 𝐵𝐷)
2
3.3 Test Portfolio Construction
Following the same principles applied to the construction of the factors, we construct value-
weighted test portfolios formed based on various intersecting sort portfolios. However, we draw
attention to the fact that not all factor portfolios are rebalanced yearly in October; particularly,
value and momentum are rebalanced monthly. Thus, similarly to Gregory et al. (2013), all test
portfolios that involve intersections based on value and momentum are rebalanced monthly,
4
The prior (2-12) return of a firm at the end of month 𝑡 is the cumulative return from month 𝑡 − 11 to month 𝑡 − 1.
We note that by not including month 𝑡 in the cumulative return estimate, we avoid look-ahead bias.

12
whereas those that do not are rebalanced yearly in October. In addition, unlike the factors that are
formed using only the largest 350 firms, the test portfolios are developed using all firms within the
sample.
Specifically, we form the following four groups of 25 intersecting portfolios (5 × 5)
formed between intersections on size and intersections based on value, momentum, profitability,
and investment: size-value, size-momentum, size-profitability, and size-investment. Following the
same approach as Foye (2018) and Gregory et al. (2013), the five size portfolios are formed from
quartiles of the largest 350 firms, plus one portfolio from the rest of the sample. Lastly, the
remaining five portfolios based on either value, momentum, profitability, or investment are formed
from quintile breakpoints of all firms in the sample.
In addition to the aforementioned four (5 × 5) groups, similarly to Foye (2018), we form
the following six groups of 32 intersecting portfolios (2 × 4 × 4) that are formed using intersecting
sorts on size, value, profitability, investment, and momentum: size-profitability-investment, size-
value-investment, size-value-profitability, size-value-momentum, size-profitability-momentum,
and size-investment-momentum. Following the approach of Fama and French (2015), we form
two size groups using the median market capitalisation of the entire sample as the size breakpoint.
Finally, we apply Foye's (2018) approach for the value, profitability, investment, and momentum
breakpoints, where quartiles obtained from the largest 350 firms are used as breakpoints for all
firms of the sample.
3.4 Tests of the Factor Model
As previously stated, the primary goal of this paper is to examine whether the factors of our
alternative six-factor model can be reliably priced. Specifically, we conduct Fama-Macbeth (1973)
two-step regressions for each one of the ten previously mentioned test portfolio groups under the
assumption of constant parameter estimates across the data sample. After obtaining the average
factor premia for each Fama-Macbeth regression, we conduct t-tests in order to evaluate whether
the factors are significantly priced against that specific group of test portfolios. In addition, we
conduct chi-squared tests (similarly to Cochrane, 2001, Ch. 12) of the null hypothesis that the
pricing errors are all jointly equal to zero, which can also be interpreted as a test whether our
proposed model is ex-ante mean-variance efficient (Cochrane, 2001). Finally, we note that the
Fama-Macbeth (1973) procedure standard errors do not account for autocorrelation (Cochrane,
2001). Thus, we apply the Newey-West (1987) procedure in order to obtain standard errors that
correct for autocorrelation and conditional heteroskedasticity.

13
4. Results
4.1 Factor Summary Statistics
We begin by reporting the summary statistics of our factors in Table 1. Our first observation is that
in contrast to Nichol and Dowling (2014) and Foye (2018), we find that the market risk premium
is significantly different from zero at the 5% significance level. Furthermore, comparably to
Gregory et al. (2013) and Nichol and Downling (2014), we find that the size risk premium is not
significantly different from zero, which contrasts with Foye's (2018) finding of high statistical
significance. Moreover, the alternatively defined value premium has the second-highest mean
(0.71% per month), which is statistically significant at the 1% significance level, exhibits the
highest positive skewness, and the largest kurtosis. Our finding contradicts with Foye's (2018)
finding that the value factor is not statistically significant, but most importantly, disputes Fletcher's
(2019) finding that the value factor is not significant under Asness and Frazzini's (2013) definition
which we use to construct our alternative value factor. Additionally, we report that the profitability
factor's risk premium (𝑅𝑀𝑊𝐺𝑃
), as defined by Novy-Marx (2013), is found to be statistically
significant at the 1% significance level. In parallel to Foye (2018) and Nichol and Downling (2014),
the investment factor risk premium is not significantly different from zero. In addition, we find
that the investment factor, in contrast to the other factors, has a platykurtic distribution. Lastly,
likewise to Gregory et al. (2013), we find that the momentum factor has the highest mean return
(0.89% per month), which is significant at the 1% level but also displays the greatest negative
skewness.
Table 1
The table reports summary statistics for the factors of our alternative six-factor model. Specifically, the table presents
the mean, standard deviation (SD), skewness, maximum, minimum, median, and kurtosis for each factor. Lastly, the
***, **, and * superscripts represent statistical significance at 1%, 5%, and 10% significance levels, respectively.

14
4.2 Correlations Between the Factors
In Table 2, we report the correlations between the factors for the period of October 1986 to March
2021. Firstly, in parallel to Gregory et al. (2013) and Foye (2018), size and value are positively
correlated to the market factor, whereas profitability, investment, and momentum are negatively
correlated to the market factor. Secondly, we find that value has a very high negative correlation
with momentum of -71%. Of course, this relationship between value and momentum is well
documented since Asness (1997); thus, it is no surprise. Nevertheless, our alternative definition of
value reveals that this relationship is significantly stronger than Gregory et al.'s (2013) finding of
-50%. Again, this is to be expected given Asness and Frazzini's (2013) observation that the
traditional definition of value (HML) is approximately equivalent to a portfolio composed of 80%
timely value (HML-DEV) and 20% momentum. Thirdly, the significantly high positive
relationship between value and investment of 64% reported by Foye (2018) appears to diminish to
just 10% under our definition of value, similarly to Asness's (2014) finding for the United States.
Furthermore, a particularly interesting finding is the relatively high negative correlation between
profitability and value (at -50%) and the relatively high positive correlation between profitability
and momentum (at 40%). Last but not least, the absence of a linear association between the
momentum factor and the investment factor (at 0.26%) is particularly intriguing.
Table 2
The table reports the correlations between the factors of our alternative six-factor model.
4.3 Fama-Macbeth (1973) Tests of the Factor Model
4.3.1 Factor Model Tests Using (𝟓 × 𝟓) Intersecting Test Portfolios
We now turn to the results of our Fama-Macbeth (1973) regressions on our test portfolios. Apropos,
in Table 3 we report the results obtained from the Fama-Macbeth regressions, under the
assumption of constant parameter estimates, on each of the four groups (presented in panels A-D)
of 25 intersecting portfolios (5 × 5) obtained by intersecting sorts based on size and sorts based
on either value, momentum, profitability, or investment.

15
In Panel A, we report the results of the Fama-Macbeth regression on the 25 test portfolios
formed on size and value. We find that given our six-factor model specification, the market risk
premium is significant at the 5% significance level and is equal to 0.46% per month. Furthermore,
the value and momentum premia appear to be statistically significant at the 5% significance level
and are equal to 0.63% and -3.35% per month, respectively. However, we find that the size,
profitability, and investment premia are not significant. Lastly, we note that the likely explanation
of the greatly significant negative momentum premium is the negative correlation between value
and momentum (-70%) and the fact that the test portfolios were formed using value intersections.
In Panel B, we present the results obtained from the Fama-Macbeth regression on the 25
test portfolios formed on size and momentum. Similarly to Panel A, we observe that the market,
value, and momentum risk premia are significant at the 5% significance level and are equal to
0.62%, -2.08%, and 0.82% per month, respectively. Again, we do not find evidence that the size,
profitability, and investment risk premia are significant. In parallel to Panel A, the significant
negative value premium is likely due to the negative correlation between value and momentum
and the fact that the test portfolios were formed using momentum intersections.
In contrast to Panels A and B, when testing on 25 portfolios formed on size and profitability
in Panel C, we notice that the only factors that are priced are the market and profitability factors.
Furthermore, they are both statistically significant at the 5% significance level, and their risk
premia are equal to 0.48% and 0.66%, respectively. Lastly, although statistically insignificant, a
likely explanation of the negative value premium, which is equal to -0.91%, is the relatively high
negative correlation between value and profitability (at -50%) and the fact that the test portfolios
were formed using profitability intersections.
In Panel D, when testing on 25 portfolios formed on size and investment, we notice that in
parallel to our previous findings, the market premium, which is equal to 0.65%, is statistically
significant at the 5% significance level. However, the value premium, equal to -1.76%, is only
marginally significant at the 10% significance level. Nonetheless, the momentum premium, equal
to 3.52%, is highly significant at the 1% significance level. Finally, similarly to our previous
observations, the size, profitability, and investment premia are not statistically significant.
To summarize, when conducting Fama-Macbeth regressions on (5 × 5) test portfolios
formed on intersections of size and value, momentum, profitability, or investment, we find that the
only factor that is consistently priced across all panels is the market factor. Nonetheless, with the
exception of tests on portfolios sorted on size and profitability, the value factor and momentum
factor appear to be consistently priced. However, we do not find evidence that the size, profitability,
and investment factor premia are significant. Furthermore, when comparing the results of Panels
A, C, and D, to Foye's (2018) Tables 4, 5, and 6, we notice that the adjusted 𝑅2
increases
significantly from 54%, 59%, and 66% to 68.77%, 75.19%, and 73.74% respectively, likely due
to the inclusion of the momentum factor and the alternative definition of the value factor. Lastly,
we notice that with the exception of test portfolios formed on size and value, all (5 × 5) test
portfolios reject the null hypothesis that the pricing errors are jointly equal to zero. This implies

16
that we do not have sufficient evidence in order to claim that our model does not have significant
pricing errors in its estimates.
Table 3
The table reports the results obtained from each Fama-Macbeth (1973) regression on each of the four groups of 25
intersecting portfolios (5×5) formed by intersecting sorts on size and sorts based on value, momentum, profitability,
and investment. Specifically, the table presents the factor premia (denoted as λ), their respective t-statistics (displayed
in parentheses), the adjusted 𝑅2
, as well as a test statistic (and its corresponding p-value) of a chi-squared test which
tests under the null hypothesis that the pricing errors are jointly zero. Lastly, the ***, **, and * superscripts represent
statistical significance at 1%, 5%, and 10% significance levels, respectively.
4.3.2 Factor Model Tests Using (𝟐 × 𝟒 × 𝟒) Intersecting Test Portfolios
We now turn our attention to the results of the Fama-Macbeth (1973) regressions on the (2 × 4 × 4)
test portfolios displayed in Table 4. Specifically, in Panels A-F, we present each of the six groups
of 32 intersecting (2 × 4 × 4) test portfolios formed from intersections based on size, value,
profitability, investment, and momentum.
In Panel A, the results of the Fama-Macbeth regression on the 32 test portfolios formed on
size, profitability, and investment, are reported. The value risk premium, equal to -2.35%, is highly
significant at the 1% level. Furthermore, the market and momentum risk premia are statistically
significant at the 5% significance level and equal to 0.54% and 3.41%, respectively. The
profitability premium, which is equal to 0.55%, is only marginally significant at the 10% level.
However, the size and investment premia appear to be insignificant. Similarly to Panel C of Table
3, we note that a likely explanation of the negative value premium is the relatively high negative

17
correlation between value and profitability (at -50%) and the fact that the test portfolios were
formed on intersections of profitability.
In Panel B, when testing on portfolios formed on size, value, and investment, we find that
the market and value premia are highly statistically significant at the 1% level and equal to 0.59%
and 1.37%, respectively. However, the size, profitability, investment, and momentum premia
appear to be statistically insignificant.
In Panel C, the results of the Fama-Macbeth regression on the 32 test portfolios formed on
size, value, and profitability are presented. The market risk premium, which is equal to 0.59%, is
highly statistically significant at the 1% significance level. Furthermore, the value risk premium is
found to be statistically significant at the 5% significance level and is equal to 1.05%. Nevertheless,
the size, profitability, investment, and momentum risk premia are statistically insignificant.
When conducting tests on portfolios formed on size, value, and momentum in Panel D, we
find that the profitability factor, which is equal to 2.97%, is highly statistically significant at the
1% significance level. In addition, the market, value, and momentum risk premia are statistically
significant at the 5% significance level and are equal to 0.56%, 1.52%, and 1.24%, respectively.
Nonetheless, the size and investment risk premia are statistically insignificant.
In contrast to Panels A-D, when testing on portfolios formed on size, profitability, and
momentum in Panel E, we find that the value risk premium is statistically insignificant. Likewise,
the size and investment risk premia are also statistically insignificant. Nevertheless, the
profitability and momentum risk premia are both highly statistically significant at the 1%
significance level and are equal to 0.95% and 1.13%, respectively. Furthermore, the market risk
premium, which is equal to 0.54%, is found to be statistically significant at the 5% level.
In Panel F, we present the results of the Fama-Macbeth regression on the 32 test portfolios
formed on size, investment, and momentum. We notice that the profitability risk premium, which
is equal to 1.54%, is statistically significant at the 1% level. In addition, the market risk premium,
which is equal to 0.54%, is statistically significant at the 5% level. However, we do not find
evidence that the size, value, investment, and momentum risk premia are statistically significant.
In summary, when conducting Fama-Macbeth regressions on the (2X4X4) test portfolios
obtained from intersections on size, value, profitability, investment, and momentum, we observe
that the only consistently priced factor across all panels is the market factor. In addition, the value
factor appears to be priced across most test portfolio groups with the exception of size-
profitability-momentum and size-investment-momentum test portfolios. Similarly, the
profitability factor is priced across all but two test portfolio groups, specifically, size-value-
investment and size-value-profitability. This finding is a striking contrast to the factor's poor
performance observed in the (5X5) test portfolios. Furthermore, although the momentum factor is
priced by test portfolios formed from intersecting sorts on size-profitability-investment, size-
value-momentum, and size-profitability-momentum, it does not appear to be priced by test
portfolios formed on size-value-investment, size-value-profitability, and size-investment-
momentum. In parallel to the results of our tests on (5X5) test portfolios, the size and investment
factors do not seem to be priced by any of the test portfolios. Interestingly, we note that the adjusted

18
𝑅2
is significantly lower in Fama-Macbeth regressions on (2X4X4) test portfolios than on (5X5)
test portfolios. Lastly, similarly to the (5X5) test portfolios, all (2X4X4) test portfolios strongly
reject the null hypothesis that the pricing errors are jointly equal to zero. This finding suggests that
we do not have sufficient evidence to claim that our model's estimates are free from substantial
pricing errors.
Table 4
The table reports the results obtained from each Fama-Macbeth (1973) regression on each of the six groups of 32
intersecting portfolios (2×4×4) formed from intersecting sorts on size, value, profitability, investment, and momentum.
Specifically, the table presents the factor premia (denoted as λ), their respective t-statistics (displayed in parentheses),
the adjusted 𝑅2
, as well as a test statistic (and its corresponding p-value) for a chi-squared test which tests under the
null hypothesis that the pricing errors are jointly zero. Lastly, the ***, **, and * superscripts represent statistical
significance at 1%, 5%, and 10% significance levels, respectively.

19
4.4 Results Discussion
In conclusion, when conducting Fama-Macbeth (1973) regressions on a wide range of test
portfolios defined from intersecting factor sorts, we find evidence that the market factor appears
to be capable of explaining cross-sectional variation in expected returns consistently across all test
portfolios. With the exclusion of Nichol and Downling (2014), this finding is a stark contrast to
the majority of previous UK-based research.
Furthermore, although value (𝐻𝑀𝐿𝐷𝐸𝑉
) and momentum (𝑈𝑀𝐷) are not consistently priced
across all test portfolios, given the fact that they are priced in the majority of test portfolios, both
in (5 × 5) and (2 × 4 × 4) specifications, they provide the most substantial evidence across all
other alternative factors of being capable of explaining cross-sectional variation in expected
returns. This finding parallels the findings of Gregory et al. (2013) regarding value and momentum,
as well as Nichol and Dowling's (2014), Dimson et al.'s (2003), and Miles and Timmermann's
(1996) findings regarding the value factor.
Moreover, our results regarding the value factor under Asness and Frazzini's (2013)
definition (𝐻𝑀𝐿𝐷𝐸𝑉
) dispute Foye's (2018) and Michou and Zhou's (2016) findings of value's
redundancy. Importantly, we note that this observation regarding equity returns in the UK is
identical to Asness's (2014) critique of Fama and French's (2015) claims of value's redundancy in
the US. In addition, we find evidence that Asness and Frazzini's (2013) statement that 𝐻𝑀𝐿𝐷𝐸𝑉
“sheds light on the dynamic relationship between value and momentum” due to its capability of
better handling the complex relationship between the two factors also applies to the UK equity
market on a regional level. For this reason, we warn that, given Asness and Frazzini's (2013)
finding that the traditional 𝐻𝑀𝐿 factor is a portfolio composed of 80% momentum (𝑈𝑀𝐷) and 20%
of timely value (𝐻𝑀𝐿𝐷𝐸𝑉
) plus noise, the traditionally defined value factor could potentially lead
to misleading conclusions regarding value and momentum as asset pricing factors and their
relationship.
Another finding is that the profitability factor, as Novy-Marx (2013) defined, is
indecisively priced in half of the test portfolios tested. However, it seems that the factor performs
significantly better when tested against (2 × 4 × 4) test portfolios than it does against (5 × 5) test
portfolios. This finding contrasts with Foye (2018), who finds that the profitability factor, besides
size, is one of the two main drivers of UK equity returns. One likely explanation is the fact that
the evidence by Foye (2018) and Michou and Zhou (2016) is inconclusive regarding which
specification of the profitability factor is capable of providing better insights. Thus, similarly to
Nichol and Dowling's (2014) statement, we conclude that further research is required.
Additionally, we observe that all of our test portfolios are incapable of pricing the size and
investment factors. This finding contradicts Foye (2018), who suggests that the size factor, besides
profitability, is one of the two main drivers of UK equity returns. Nevertheless, there is also
evidence (e.g., Gregory et al. 2013 and Nichol and Dowling, 2014) that supports our finding
regarding size. On a similar note, Nichol and Dowling (2014) and Foye (2018) find that the
investment factor appears to be ineffective in a UK context.

20
Therefore, given the previously mentioned evidence, we find that we have been unable to
demonstrate that the factors of our alternative six-factor model that were investigated are
consistently and reliably priced when tested against a wide range of test portfolios. Ergo, we cannot
recommend our alternative six-factor model to practitioners and to applications that seek to
estimate a measure of the expected cost of equity. Finally, we note that although we are critical of
relying on test portfolios formed on the same characteristics as the factors, as claimed by Lewellen
et al.'s (2010) critique, we believe that the use of a broad spectrum of test portfolios, as suggested
by Foye (2018), can provide a clearer picture.
5. Conclusion
The purpose of our study was to investigate whether the factors of our alternative six-factor model
could be consistently and reliably priced and whether our model could offer a viable choice to
practitioners and to applications which aim to estimate the cost of equity capital. However, our
evidence from conducting Fama-Macbeth (1973) regressions on a wide range of test portfolios
formed from intersecting sorts based on size, value, profitability, investment, and momentum
suggests that the test portfolios are incapable of consistently pricing all six factors. Thus, we are
unable to recommend our alternative factor model for practical application uses.
Specifically, our results indicate that the market factor is the only factor that is consistently
priced across all test portfolios. As previously noted, this is a relatively uncommon finding in
comparison to previous UK-based literature. In addition, similarly to Gregory et al. (2013), we
find evidence that the value factor (as defined by Asness and Frazzini, 2013) and momentum factor
are mostly capable of explaining cross-sectional variation in expected returns. However, they are
not priced in all test portfolios. Nevertheless, as previously mentioned, given Asness and Frazzini's
(2013) finding that the traditional definition of value (HML) can be viewed as a portfolio of a more
accurate proxy for true value (𝐻𝑀𝐿𝐷𝐸𝑉
), momentum (𝑈𝑀𝐷), and noise, we warn that the choice
of 𝐻𝑀𝐿 as a definition of value is likely to lead towards misleading conclusions, as evident from
previous claims over value's redundancy, as well as momentum's capability in explaining cross-
sectional variation.
Furthermore, the contrast between the poor performance of the profitability factor (as
defined by Novy-Marx, 2013) when tested against (5 × 5) test portfolios and its relatively strong
performance on (2 × 4 × 4) test portfolios may stand as evidence that the profitability factor has
the potential to explain cross-sectional variation. Nonetheless, the factor's definition appears to be
empirically problematic. Therefore, in parallel to Nichol and Dowling's (2014) initial suggestion
and motivated by the fact that Foye's (2018) results have failed to identify which specification of
profitability best describes equity returns in the UK, we believe that further research is required
due to the factor's overall potential. In addition, we believe that the alternative definition of
profitability based on cash profitability, which is unaffected by accruals, as proposed by Ball et al.
(2016), which has not been considered by Foye (2018), could prove to be a potential candidate.

21
Our view is motivated by the US-based evidence from various tests conducted by Fama and French
(2018). Another finding is that both the size factor and investment factor appear to be ineffective
in a UK context, given that all of our test portfolios were unable to price them.
Of course, our research is not without its shortcomings. For instance, given the fact that all
but one of our test portfolio groups have failed to reject the null hypothesis of the chi-squared test,
that the pricing errors are jointly equal to zero, following Lewellen et al.'s (2010) critique, we are
forced to be sceptical of our results concerning which factors are priced. Furthermore, given Lo
and MacKinlay's (1990) and Lewellen et al.'s (2010) critique against solely relying on test
portfolios formed using the same characteristics as the factors, we are critical of the fact that all of
our test portfolios are formed from the same characteristics as our factors. Nonetheless, we believe
that using a wide range of test portfolios, as advocated by Foye (2018), can help provide a clearer
view. For this reason, as mentioned earlier, we are sceptical of Fletcher's (2019) conclusion that
the six-factor model of Fama and French (2018) with small spread factors provides the best
performance compared to all factor models tested in the UK, which is entirely based on the results
from size-value and size-momentum intersecting test portfolios.
Another potentially limiting factor is the fact that our factors are constructed using only the
largest 350 firms in terms of market capitalisation. However, as recognised by Fama and French
(2012), the choice of appropriate breakpoints when forming regional factor portfolios is crucial.
Ergo, if one wishes to construct the factors from a broader firm sample must carefully choose the
appropriate breakpoints for that particular sample, as we did following Gregory et al. (2001, 2013).
Additionally, one does not have to limit oneself to the Fama-Macbeth (1973) procedure as
we have chosen. The same tests that we have conducted in our research could be applied using the
GMM two-stage procedure for linear factor models as described by Cochrane (2001, Ch.13).
Alternatively, suppose one wishes to conduct comparison tests on multiple model specifications.
In that case, one can choose to deploy the Bayesian approach described by Barillas and Shanken
(2018) or the squared Sharpe ratio method explained by Barillas et al. (2020).
Throughout our study, our primary concern has been to evaluate the performance of our
alternatively defined six-factor model and to conduct tests using a wide range of test portfolios in
order to examine its applicability to the UK equity market. Given our findings, we conclude that
our model specification is not a valid candidate and that further research is required. Of course, as
is always the case, the quest for the most parsimonious model that is capable of explaining asset
price behaviour continues (Ilmanen, 2012). Therefore, we remain optimistic that the appropriate
model specification for explaining UK equity returns may yet be found.

22
6. References
Agarwal, Vineet and Richard Taffler. 2008. “Does Financial Distress Risk Drive the
Momentum Anomaly?” Financial Management. 37:3, pp. 461–84.
Andrew, Lo W. and Archie C. MacKinlay. 1990. “Data–Snooping Biases in Tests of Financial
Asset Pricing Models.” The Review of Financial Studies. 3:3, pp. 431–67.
Asness, Clifford S. 1994. “Variables That Explain Stock Returns.” Ph.D. Dissertation,
University of Chicago.
Asness, Clifford S. 1997. “The Interaction of Value and Momentum Strategies.” Financial
Analysts Journal. 53:2, pp. 29–36.
Asness, Clifford S. 2014. “Our Model Goes to Six and Saves Value From Redundancy Along
the Way.” AQR. December 17.
Asness, Clifford S. and Andrea Frazzini. 2013. “The Devil in HML’s Details.” The Journal of
Portfolio Management. 39:4, pp. 49–68.
Asness, Clifford S., Andrea Frazzini, Ronen Israel and Tobias J. Moskowitz. 2014. “Fact,
Fiction and Momentum Investing.” The Journal of Portfolio Management. 40:5, pp. 75–92.
Asness, Clifford S., Tobias J. Moskowitz and Lasse H. Pedersen. 2013. “Value and
Momentum Everywhere.” Journal of Finance. 68:3, pp. 929–85.
Ball, Ray J., Joseph J. Gerakos, Juhani T. Linnainmaa and Valeri V. Nikolaev. 2016.
“Accruals, Cash Flows, and Operating Profitability in the Cross Section of Stock Returns.” Journal
of Financial Economics. 121, pp. 28–45.
Banz, Rolf W. 1981. “The Relationship Between Return and Market Value of Common Stocks.”
Journal of Financial Economics. 9:1, pp. 3–18.
Barillas, Francisco and Jay A. Shanken. 2018 “Comparing Asset Pricing Models.” Journal of
Finance. 73:2, pp.715–54.
Barillas, Francisco, Raymond Kan, Cesare Robotti and Jay A. Shanken. 2020. “Model
Comparison with Sharpe Ratios.” Journal of Financial and Quantitative Analysis. 55:6, pp. 1840–
74.
Carhart, Mark M. 1997. “On Persistence in Mutual Fund Performance.” Journal of Finance.
52:1, pp. 57–82.

23
Chabot, Benjamin, Eric Ghysels and Ravi Jagannathan. 2009. “Price Momentum in Stocks:
Insights from Victorian Age Data.” National Bureau of Economic Research. Working Paper 14500.
Cochrane, John H. 2001. Asset Pricing. Princeton, NJ: Princeton University Press.
Dimson, Elroy, Stefan Nagel and Garrett Quigley. 2003. “Capturing the Value Premium in
the United Kingdom.” Financial Analysts Journal. 59:6, pp. 35–45.
Fama, Eugene F. and James D. MacBeth. 1973. “Risk, Return, and Equilibrium: Empirical
Tests.” Journal of Political Economy. 81:3, pp. 607–36.
Fama, Eugene F. and Kenneth R. French. 1992. “The Cross-Section of Expected Stock
Returns.” Journal of Finance. 47:2, pp.427–65.
Fama, Eugene F. and Kenneth R. French. 1993. “Common Risk Factors in the Returns on
Stocks and Bonds.” Journal of Financial Economics. 33, pp. 3–56.
Fama, Eugene F. and Kenneth R. French. 1996. “Multifactor Explanations of Asset Pricing
Anomalies.” Journal of Finance. 51:1, pp.55–84.
Fama, Eugene F. and Kenneth R. French. 2004. “The Capital Asset Pricing Model: Theory
and Evidence.” Journal of Economic Perspectives. 18:3, pp. 25–46.
Fama, Eugene F. and Kenneth R. French. 2012. “Size, Value, and Momentum in International
Stock Returns.” Journal of Financial Economics. 105:3, pp. 457–72.
Fama, Eugene F. and Kenneth R. French. 2015. “A Five–Factor Asset Pricing Model.” Journal
of Financial Economics. 116:1, pp. 1-22.
Fama, Eugene F. and Kenneth R. French. 2017. “International Tests of a Five–Factor Asset
Pricing Model.” Journal of Financial Economics. 123:3, pp. 441–63.
Fama, Eugene F. and Kenneth R. French. 2018. “Choosing Factors.” Journal of Financial
Economics. 128, pp. 234–52.
Fletcher, Jonathan. 2019. “Model Comparison Tests of Linear Factor Models in U.K. Stock
Returns.” Finance Research Letters. 28, pp. 281–91.
Foye, James. 2018. “Testing Alternative Versions of the Fama–French Five–Factor Model in the
UK.” Risk Management. 20, pp. 167–83.

24
Geczy, Christopher and Mikhail Samonov. 2016. “Two Centuries of Price–Return
Momentum.” Financial Analysts Journal. 72:5, pp. 32–56.
Gibbons, Michael R., Stephen A. Ross and Jay A. Shanken. 1989. “A Test of the Efficiency
of a Given Portfolio.” Econometrica. 57:5, pp. 1121–52.
Gregory, Alan, Rajesh Tharyan and Angela Christidis. 2013. “Constructing and Testing
Alternative Versions of the Fama–French and Carhart Models in the UK.” Journal of Business
Finance & Accounting. 40:1–2, pp. 172–214.
Gregory, Alan, Richard D.F. Harris and Maria Michou. 2001. “An Analysis of Contrarian
Investment Strategies in the UK.” Journal of Business Finance & Accounting. 28:9–10, pp.1192–
228.
Griffin, John M. 2002. “Are the Fama and French Factors Global or Country Specific?” The
Review of Financial Studies. 15:3, pp. 783–803.
Hussain, Syed I., Steven Toms and Steve Diacon. 2002. “Financial Distress, Market Anomalies
and Single and Multifactor Asset Pricing Models: New Evidence.” Available at SSRN:
https://ssrn.com/abstract=313001.
Ilmanen, Antti. 2012. Expected Returns: An Investor's Guide to Harvesting Market Rewards.
Hoboken: John Wiley & Sons, Inc.
Jegadeesh, Narasimhan and Sheridan Titman. 1993. “Returns to Buying Winners and Selling
Losers: Implications for Stock Market Efficiency.” Journal of Finance. 48:1, pp. 65–91.
Lintner, John. 1965. “The Valuation of Risk Assets and the Selection of Risky Investments in
Stock Portfolios and Capital Budgets.” Review of Economics and Statistics. 47:1, pp. 13–37.
Michou, Maria and Hang Zhou. 2016. “On the Information Content of New Asset Pricing
Factors in the UK.” University of Edinburgh. Working Paper.
Miles, David and Allan Timmermann. 1996. “Variation in Expected Stock Returns: Evidence
on the Pricing of Equities from a Cross-section of UK Companies.” Economica. 63, pp. 369–82.
Nagel, Gregory L., David R. Peterson and Robert S. Prati. 2007. “The Effect of Risk Factors
on Cost of Equity Estimation.” Quarterly Journal of Business and Economics. 46:1, pp. 61–87.
Nagel, Stefan. 2001. “Accounting Information Free of Selection Bias: A New UK Database
1953–1999.” London Business School. Working Paper.

25
Newey, Whitney K. and Kenneth D. West. 1987. “A Simple, Positive Semi–definite,
Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica. 55:3, pp.
703–08.
Nichol, Eoghan and Michael Dowling. 2014. “Profitability and Investment Factors for UK
Asset Pricing Models.” Economics Letters. 125:3, pp. 364–66.
Novy-Marx, Robert. 2013. “The Other Side of Value: The Gross Profitability Premium.”
Journal of Financial Economics. 108, pp. 1–28.
Otten, Roger and Dennis Bams. 2002. “European Mutual Fund Performance.” European
Financial Management. 8:1, pp. 75–101.
Rosenberg, Barr, Kenneth Reid and Ronald Lanstein. 1985. “Persuasive Evidence of Market
Inefficiency.” Journal of Portfolio Management. 11, pp. 9–17.
Sharpe, William F. 1964. “Capital Asset Prices: A Theory of Market Equilibrium Under
Conditions of Risk.” Journal of Finance. 19:3, pp. 425–42.
Titman, Sheridan, K. C. John Wei and Feixue Xie. 2004. “Capital Investments and Stock
Returns.” Journal of Financial and Quantitative Analysis. 39, pp. 677–700.

Testing an Alternative Six-Factor Asset Pricing Model in the UK Equity Market

Recommended

Recommended

More Related Content

Similar to Testing an Alternative Six-Factor Asset Pricing Model in the UK Equity Market

Similar to Testing an Alternative Six-Factor Asset Pricing Model in the UK Equity Market (20)

Recently uploaded

Recently uploaded (20)

Testing an Alternative Six-Factor Asset Pricing Model in the UK Equity Market