2005. Dissertation Carlos Salas

Multi-Style and Rotation Equity Strategies in European Markets.
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Multi-Style and Rotation Equity Strategies in European Equity Markets
By Carlos Salas, 2005 June,
This study examines the application of different single-style and multi-style equity strategies in European
markets taking in consideration a sample of 104 companies during the period 1994-2004. Results from previous
research papers, which were mainly focus on the US and the UK Markets, provide evidence that several
fundamental ratios have strong influence on stock prices. The main conclusions in this study were the
importance of the market capitalization as primary discriminative factor in constructing equity portfolios,
whereas PER and PTB showed risk-efficient results as secondary selection factors only for medium and large
capitalization stocks. In addition, the last section includes a probabilistic quantitative analysis which sets forth
the high degree of accuracy required from an Active Portfolio Manager to top efficiently Passive strategies. This
research was completed in 2005 as final dissertation while I was attending lectures in AFI Business School´s
“MBA in Finance” during the period 2004-2005. The sources being used for data gathering were Bloomberg,
Datastream and JCF/Factset; using Eviews, Excel and VBA as key tools for computational purposes.
Contents
1. Introduction
2. Sample Data.
2.1.Data Description
2.2.Performance by industry and some theoretical concepts
3. Investment Strategies using fundamental Data.
3.1.Portfolio Classification system: Description
3.2.Single-Style Investment Strategies
3.3.Multi-Style Investment Strategies
4. Investment Strategies using Rotation Style.
4.1.Style Rotation strategies as an alternative
4.2.Indicative models for the practice of Style Rotation
5. Conclusions
Notes
Bibliography

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1. Introduction.
This paper discusses different investment strategies created from the use of fundamental
ratios as PTB (price to book value) or PER (price to earnings) during the period 1995-2004.
The use of such a kind of financial indicators as tools in analyzing and creating portfolios has
been very popular over the past 40 years, being a topic very popular in research by several
authors and starting to be used as a basis for different papers by pioneering authors like
Nicholson (1968).
Some articles such as those presented by Chen, Roll and Ross (1986) are focused on the
use of macroeconomic variables in finding additional information not provided by the market
index, while there are other research also aimed at seeking information not priced by the
markets but it can extracted from ratios and data of a fundamental nature. This work is
related to the last view and in line with other financial literature written by relevant authors:
S.Basu (1977) assesses the variable PER as determinant of higher performance, M.Levis
(1985) starts the election debate between small caps or blue chips; as well as Capaul,
Rowley and Sharpe (1993) conduct an influential work on value and growth assets. Of
paramount relevance is the work by Fama and French (1993) highlighting the importance of
market capitalization and book-to-market (inverse of price to book) variables using cross-
section regressions, pointing out the inability inherent in the CAPM model to properly
describe an asset risk-return features. These conclusions were very criticized by CAPM
advocates as Kothari, Shanken and Sloan (1995).
Concerning the sample period on this study, the fact that the first part of the data pertained to
the second half of the 90s might skew the paper conclusions as this period was a booming
one which could be allocated as an outlier whether a longer stock period were to be
appraised. Authors such as Campbell and Schiller (2001) studied the mean-reversion effects
in key ratios like PER and Dividend Yield, as well as their high values during the stock bubble
previously commented, confirming “Stock Price” as the main driver variable within the mean-
reversion phenomenon. Some critics still cast doubted about the former role played by the
stock price in the mean-reversion trend, though a lot of research has backed this conclusion
as aforementioned.

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Different types of research have been based on the former conclusions and using different
data sample as Ahmed, Lockwood and Nanda (2002) for the US markets or Levis and
Liodakis (1999) for the UK markets. This document explores different investment
methodologies concerning portfolio construction for a sample of European stocks using Excel
and VBA. In Section 2 a generic description of the sample data and a resume of portfolio
construction performance by industry sector are displayed. Section 3 is focused on the
analysis of single and multi-style strategies: portfolio creation method, discrimination criteria
and data gathering. Last but not least, results from single and multi-style strategies are
analyzed in-depth.
In Section 4 some brief comments are done regarding to style-rotation investment strategies.
A concise description of the differences between the investment strategies to be developed
in this section and the ones illustrated in section 3 is conducted, afterwards some remarks
related to advantages and requirements in carrying out an active investment strategy
overcoming passive investment strategies are discussed. The second subsection highlights
the importance of different variables in creating and developing investment strategies using
the former methodology, where some econometric models are created for this purpose using
Eviews 3.1 econometrics software.
Finally, in Section 5 are gathered and summarized all the conclusions obtained in each
section, exposing the study biases and how they could be solved in further articles.
2. Sample Data.
2.1. Data description.
The data sample is composed by 104 companies from which different types of information
have been obtained. The purpose of this study is to analyze and evaluate investment
strategies within an increasingly integrated environment such as Europe, using for that
reason a sample comprised only by European companies. This way we can make an
analysis that allows us to both assess the efficiency of European markets and introduce a
sample of data different from the one used by other authors: M.Levis and M.Liodakis (1999)
with the UK; Ahmed, Lockwood and Nanda (2002) with the US.

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The data used in this study is featured for being on a quarterly basis during a ten-year time
horizon (December 31, 1994 to December 31, 2004). The information collected is essentially
of fundamental nature: pricing, market capitalization, price to book ratio (price to stock book
value), price to earnings ratio (price to next year expected earnings), and Dividend Yield ratio
(dividends to price) 1
. This data have been chosen since previous works by Fama and
French (1992) and Campbell and Schiller (2001) analyzed the performance of portfolios built
up on criteria related to values of these ratios.
The databases used for data gathering have been JCF version 5.0 and Bloomberg. As it is
shown at Exhibit 1, the Companies used in the study are members in various market indices
representing regional areas or industries: 40 companies in Eurostoxx 50 index, 36
companies in Eurostoxx Mid while 28 companies belong to Small Eurostoxx. Unfortunately
the lack of data available made not possible add to the sample the whole member of each
one of the former indices. Likewise the sample only has been composed with companies
"active" by 31 December 1994, so companies whose start-up dated before were wiped out of
the sample.
Exhibit 1. Company detail
Abertis Casino Guichard Hochtief AG Repsol
Abn Amro Holding Celesio AG Huhtamaki Plc Sacyr Y Vallehermoso
Acerinox CEPSA Iberdrola Safran
Aegon Christian Dior SA Imerys Saint Gobain
Agf Corp Fin Alba Ing Groep Saipem
Ahold Corp Mapfre Inmobiliaria Metrovacesa Sampo Bank
Air Liquide DaimlerChrysler AG Italcementi San Paolo Imi
Alcatel Danone Kesko Sanofi-Aventis
Alleanza Delhaize Group Klepierre Sap AG
Allianz AG Deutsche Bank Kone SBM Offshore NV
Altana AG DSM Lafarge Scor
Amer Sports Corp E.On AG Linde AG Societe Generale
Autostrade Eiffage Loreal Suez
Axa Endesa Lufthansa AG Technip
Banca Fideuram FCC Lvmh Telefonica
Bankinter Fondiaria M Real Television Francaise 1
Basf AG Fortis M6 Metropole Television Thales (Ex Thomson)
Bayer AG Fresenius AG Man AG Total
BBVA Gas Natural Sdg Mondadori Unibail
Beiersdorf AG Gecina Muenchener Rueck Unicredito Italiano
Bic Generali Natexis Unilever Nv
Bnp Paribas Getronics Nokia Union Electrica Fenosa
BSCH Havas Sa Omv Ag Valeo
Buhrmann Heidelbergcement AG Outokumpu Vivendi Universal
Cap Gemini Henkel Philips Wartsila Corp Beff
Carrefour Hermes International Publicis Groupe SA Wolters Kluw er

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2.2 Performance by industry and some theoretical concepts.
Performance sorted by sector is illustrated in Exhibit 2 on a YoY basis (annual returns) as
well as a risk-return proxy ratio:
Exhibit 2. Sector Performance
Market Financials Industrials Energy Technology Construction Retail Media Chemicals Transport
1995-1999 28,47% 21,38% 12,56% 17,27% 38,58% 6,39% 17,69% 33,66% 12,62% 22,98%
2000-2004 -7,13% -12,75% -1,90% 3,81% -25,57% 4,72% -14,25% -24,02% -5,33% 5,14%
1995-2004 9,23% 2,91% 5,08% 10,33% 1,56% 5,56% 0,46% 0,78% 3,26% 13,71%
Mdo Financials Industrials Energy Technology Construction Retail Media Chemicals Transport
1995-1999 1,29 0,81 0,52 0,99 1,34 0,29 1,25 1,28 0,63 1,27
2000-2004 -0,28 -0,22 -0,10 0,21 -0,57 0,33 -0,42 -0,61 -0,20 0,26
1995-2004 0,37 0,10 0,23 0,58 0,04 0,26 0,02 0,02 0,14 0,71
beta 1 1,152 0,740 0,584 1,446 0,577 0,836 1,211 0,761 0,590
YoY Performance / Standard Deviation
YoY Performance
Each industry index has been built using the JCF industry system for classifying only
companies of the sample. Nevertheless there are some as chemical, multimedia sectors,
distribution and transportation which do not reflect the reality of the sector as they only
consist of 3 or 7 companies.
Regarding Exhibit 2 figures, “Transport” is shown as best performer, being only exceeded by
“Technologicals” and “Media” during the second half of the 1990s due to both industries
booming trend. Sectors highlighted by its steady performance were “Energy”, “Construction”
and “Transport”; since at no time any of these sectors have endured losses, being this fact
closely related to low-beta profile shown by them. The outstanding results of the “Transport”
industry are biased by previously commented sample shortage which hides the true level of
risk embedded in the sector.
Main feature to underline is the fact that European markets do not seem to meet efficiency as
the concept proposed by authors as Sharpe or Markowitz. This claim is based on the highest
performance obtained by sectors with low-beta profile such as “Energy” or “Construction” in
relation to high-beta profile sectors as ”Technology” or “Media”.

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3. Investment Strategies using fundamental data.
3.1 Portfolio Classification System: Process description.
Different methodologies to create portfolios/indices will be developed following a given
criteria using Excel XP as a working tool. In a first step some portfolios will be created based
on the value of a single variable (market capitalization, price to book ratio, etc), commonly
called in financial literature as single-style strategies. This type of strategy is based on
classifying sample stocks in three different portfolios each December 31, representing each
portfolio a concrete percentile chosen as a reference to the portfolio. For example in building
three indexes based on market capitalization, those stocks whose market capitalization was
less than or equal to the sample percentile who accumulate 33.33% in terms of capitalization
will be considered members of the “Small” index. In the same way those stocks with market
capitalization higher than percentile 66,66% will be considered within the “Large” index, while
the “Mid” index contains assets with size between both percentiles. Similarly other indexes
will be constructed based on ratios as Price to earnings, Price to book and Dividend Yield.
In Section 3.3 a pair of variables instead of a single one will be used as allocating factors
also known as multi-style strategies. Such strategies consist of 2 breakdown stages that will
take place every December 31. The first stage consists in a classification in terms of its size,
building three groups named “primary”: medium, large and small capitalization stocks. The
second stage begins by choosing a ratio as a criterion for classifying each of the stocks of
each primary group in portfolios of assets according to the value of the ratio of each company
in comparison with the percentile ratio chosen for the primary group to which that company
belongs. By this way each primary group spawns three portfolios based on a ratio chosen as
a secondary criterion: portfolio Low (stocks with a ratio figure equal or lower to 33.33% of
those stocks in the primary group), High (stocks with a ratio greater than or equal to the
percentile 66,66% ratio) and Mid (assets with a value of the ratio between the percentiles
33.33% and 66,66%). In this way, if for example we choose as a secondary criterion the
price-to-book ratio book we can create 9 portfolios: Smallcap-Low, Smallcap-Mid, Smallcap-
High, Midcap-Low, Midcap-Mid, Midcap-High, Largecap-Low, Largecap-Mid and Largecap-
High.

7
The reasons for using market capitalization (size) as primary criteria to filter data rely on
conclusions by Fama and French (1992) 2
. Also previously named authors demonstrated in
cross-section regressions a relatively higher reliability of ratios as, for example, price to book
to market capitalization.
3.2 Single-style investment strategies.
Filter variables as market capitalization as well as the ratio price-to-book are presented as
those that financial literature has stressed more: Fama and French (1992) or Chan,
Jegadesh and Lakonishok (1995). Other ratios, as the Price-to-earnings and Dividend Yield,
have been studied as a starting point for developing investment strategies: Basu (1977) or
Campbell and Schiller (2001).
Regarding portfolios created by selecting securities according to their size, three different
groups are obtained: Small, Mid and Large. Each one of these indexes is composed by a
33,33% of stocks presented in the sample and are re-allocated every December 31. Results
on a YoY basis as well as in terms of risk-return are presented in Exhibit 3, where small caps
is the asset class with higher profitability (10,58%) and adjusted risk-return (0.48 and 0.137) 3
over the entire period. On the other hand, blue chips (Large index) were the winners during
the first 5 years (23.32% annualized profitability and 1.08 return on deviation), though the
market capitalization-weighted index got the best results.
Exhibit 3. Performance by size.
Mkt Small Mid Large
1995-1999 28,47% 18,46% 16,89% 23,32%
2000-2004 -7,13% 3,21% -9,78% -14,36%
1995-2004 9,23% 10,58% 2,69% 2,77%
beta 1 0,774 0,861 1,085
Mkt Small Mid Large
1995-1999 1,29 0,89 0,89 1,08
2000-2004 -0,28 0,14 -0,40 -0,47
1995-2004 0,37 0,48 0,12 0,10
YoY / beta 0,092 0,137 0,031 0,026
YoY
YoY risk adjusted

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Drawing conclusions from Exhibit 3 according to both absolute and risk-adjusted
performance figures, Small capitalization companies outperformed Large and Medium
capitalization issuers. For which reason it can be confirmed that the European companies in
the sample performed similarly to other international capital markets during the 1995-2004
period. It is remarkable that the amount of negative correlation between profitability and size
is not satisfied in comparing absolute performance between Medium and Large capitalization
companies but it is significant on a risk-return adjusted basis.
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Chart 1. Spread trend: Small-Large vs Market index.
Small vs Large
Market Index
Looking at Chart 1, the performance of large capitalization companies has been positively
and strongly related to the Market index movements (which remind is weighted by
capitalization). This statement is corroborated looking at the higher beta profiles in large
capitalization securities (1.085), by this it can be inferred a pro-cyclical fashion from this sort
of issuers as it was expected and once again points out some caveats in the CAPM model as
a framework to assessing accurately rates of required risk-adjusted return.
As regards the set of indexes created from classifying the stocks using multifarious ratios as
the price-to- book value per share (PTB), the price-to-earnings per share (PER) or Dividend
Yield (DY), 3 types of assets classification are arranged:

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 Value assets: stocks whose earning trend evolution is quite stable and characterized
by low PER and PTB ratios as well as moderately high Pay-out ratios (Dividend per
share to earnings per share) that generally are turned into high Dividend yields.
 Growth assets: stocks in which investors deposited high hopes for growth in profits,
but with irregular figures, characterized by high PTB and PER ratios while their
Dividend yield is quite scarce mainly caused by low Pay-out ratios.
 Blend assets: hybrid stocks whose main features are halfway to those shown by their
value and growth counterparts.
Under the hypothesis of mean-reversion observed in PER PTB or DY ratios, along with the
conclusions by Campbell and Schiller (2001) showing the stock price as the main driver in
bringing these ratios to their long term average 4
variable; different performance paths may
be displayed depending on the inner features of each stocks.
A first sight of the later is shown in Exhibit 4, where three indexes were created similarly to
those built earlier when we analyze the effect size, but using the PTB as filter ratio. This time
the stocks classification comes as it follows: low PTB (Value assets), Medium PTB (Blend
assets) and High PTB (growth assets).
Exhibit 4. Performance by PTB.
Mkt Low Mid High
1995-1999 28,47% 18,51% 17,02% 23,04%
2000-2004 -7,13% 0,91% -7,73% -14,07%
1995-2004 9,23% 9,36% 3,91% 2,82%
beta 1 0,846 0,939 0,937
Mkt Low Mid High
1995-1999 1,29 0,84 0,82 1,20
2000-2004 -0,28 0,04 -0,29 -0,54
1995-2004 0,37 0,40 0,16 0,12
YoY/ beta 0,092 0,111 0,042 0,030
Rentabilidad Anualizada
YoY risk adjusted
Exhibit 4 shows the Low PTB portfolio as the best performer in absolute (9.36%) and risk-
weighted terms, 0.4 and 0,111 respectively. Once again high PTB stocks outperformed Low
PTB during the first sample period, though its performance stood still below the Market
portfolio. This time the nearly 7% performance spread Low PTB- High PTB portfolios is not
possible being explained by the CAPM model as the difference between both portfolios betas
is negative.

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Q10431/03/2004
Q30430/09/2004
Chart 2. Spread Trend: Market vs Low PTB
Market vs Low PTB
Market iIndex
In Chart 2 it is shown what was commented previously: Low PTB portfolio outperforms the
market in those stages in which market wanes, while in those years when market flourishes
Low PTB is outpaced. It is also remarkable that, as it happened with the market capitalization
when used as selection factor, the PTB ratio generated portfolios yield outcomes within the
mean-reversion hypothesis only concerning Low PTB stocks, being this hypothesis unable to
explain the results obtained between Mid PTB and High PTB indices.
Another ratio used for the construction of indexes has been Price-to-earnings, from which the
conclusions achieved emphasized even more the difference between value and growth style
assets. Comparison between both types of stocks by various authors as Capaul, Rowley and
Sharpe (1993) have led to empirical findings concluding in better value stocks performance
over extended periods of time, findings also present in our sample as it is pointed in Chart 3
(Value index is created by Low PER stocks and Growth by High PER stocks) .

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0
0,5
1
1,5
2
2,5
3
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Chart 3. Accumulated Return Value vs Growth.
Value
Growth
As a reflection of Chart 3, figures in Exhibit 5 show better results for Low PER companies
(Value asset class) than High PER stocks (Growth asset class). Nevertheless the extreme
bull period 1995-1999 resulted in a better performance for Growth and Blend stocks,
although once again the best portfolio turned out to be the Market index.
Exhibit 5. Performance by PER.
Mkt Low Mid High
1995-1999 28,47% 19,41% 20,23% 18,74%
2000-2004 -7,13% 1,22% -6,88% -15,57%
1995-2004 9,23% 9,94% 5,81% 0,13%
beta 1 0,907 0,836 0,976
Mkt Low Mid High
1995-1999 1,29 0,81 1,07 1,00
2000-2004 -0,28 0,05 -0,30 -0,53
1995-2004 0,37 0,39 0,27 0,00
YoY/ beta 0,092 0,110 0,069 0,001
YoY
YoY risk adjusted
Portfolios with blend and growth style as well as the Market index sank from 2000 to 2004,
while Value style stocks outperformed during this sub-period and caught up other investment
styles for the whole period of study. Checking out the former results along with Chart 4 5
one
could say that mean-reversion hypothesis cannot be rejected while CAPM theory fails

12
stunningly, since one more time systematic risk, represented by beta, is not a performance
explanatory variable as assets with high beta-profile are not rewarded.
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Chart 4. Average PER and QoQ Average Performance
Average PER
PER Long term Average
QoQ Average Performance (right)
Finally, portfolios created filtering sample data using Dividend Yield ratio are shown in Exhibit
6. The ratio denominator is the variable “Stock price” contrary to what happened in previous
ratios, being the High DY portfolio undoubtedly the best investment vehicle6
(11.39%
annualized profitability and 0,142 return to beta). This High DY portfolio can also be
interpreted as a Value index composed of companies with a high dividend profitability and
generally high payout rates as well as stable profits.
Exhibit 6. Performance by DY.
Mkt Low Mid High
1995-1999 28,47% 21,05% 18,02% 19,46%
2000-2004 -7,13% -18,50% -5,89% 3,86%
1995-2004 9,23% -0,68% 5,39% 11,39%
beta 1 1,051 0,865 0,804
Mkt Low Mid High
1995-1999 1,29 1,03 0,87 0,93
2000-2004 -0,28 -0,61 -0,24 0,16
1995-2004 0,37 -0,02 0,23 0,51
YoY/ beta 0,092 -0,006 0,062 0,142
YoY
YoY risk adjusted

13
This slight appreciation becomes even more overwhelming observing the beta figures: High
DY beta (0,804) is below Low DY beta (1,051), jointly with Chart 5 helps to understand the
stronger cyclical bias regarding Low DY stocks. In particular, Low-High DY spread becomes
generally more positive over bull markets while negative spreads were bound to arise during
bear markets. As it happened in earlier sections, CAPM null hypothesis can be rejected as
beta continues showing no signs of significance in explaining relative performance among
portfolios.
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Chart 5. Spread trend: Low DY vs High DY and Market index
Low DY vs High DY
Market Index
To sum up, a common feature among best performer indices in each ratio-class filtering
method is the low sensitivity to market fluctuations or systematic risk. This feature was crucial
especially during the period 2000-2005, when the market slumped violently causing an even
more radical drop to those stocks with high beta features. An easy way to notice the last is by
looking at Chart 6 since this figure highlights quite intuitively how the best single-style
portfolios (Small index along with Low PER, Low PTB and High DY portfolios) share together
the lower market sensitivities, yet this relationship is flawed by the short observational period
chosen.

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0,820
0,840
0,860
0,880
0,900
0,920
0,940
0,960
0,980
1,000
Small
Mid
Large
Low
Mid
High
Low
Mid
High
Low
Mid
High
I.Capitaliz I.Ptb I.PER I.DY
Chart 6. Market Correlations.
All in all, the best outcomes in absolute and risk-adjusted terms during the sample period of
study came from high dividend securities (Exhibit 7). However, as it was previously
underlined, High DY portfolio does not have a lower beta or lower correlation coefficient in
comparison with the rest of investment strategies. In the last column of the exhibit a “Value”
strategy proxy is depicted, being constructed by averaging PTB Low, Low PER and High DY
outcomes. In short, Small caps strategies still outperformed this “Value” proxy indicator as it
can be reflected from the figures.
Exhibit 7. Optimal Portfolios by Performance.
Mkt I.Small Low PTB Low PER High DY Value
1995-1999 28,47% 18,46% 18,51% 19,41% 19,46% 19,13%
2000-2004 -7,13% 3,21% 0,91% 1,22% 3,86% 2,00%
1995-2004 9,23% 10,58% 9,36% 9,94% 11,39% 10,23%
beta 1 0,774 0,846 0,907 0,804 0,852
1995-1999 22,12% 20,79% 21,93% 24,12% 20,97% 22,34%
2000-2004 25,76% 23,00% 25,26% 26,76% 23,41% 25,14%
1995-2004 25,05% 21,91% 23,68% 25,49% 22,21% 23,79%
1995-1999 8,06% 19,35% 20,58% 15,61% 15,44% 17,21%
2000-2004 45,98% 41,44% 37,83% 47,98% 37,70% 41,17%
1995-2004 44,06% 41,38% 37,49% 47,98% 37,70% 41,06%
1995-1999 128,70% 88,80% 84,39% 80,50% 92,79% 85,90%
2000-2004 -27,67% 13,98% 3,61% 4,57% 16,50% 8,22%
1995-2004 36,85% 48,26% 39,52% 39,01% 51,27% 43,26%
YoY/ beta 0,092 0,137 0,111 0,110 0,142 12,07%
YoY
Stand Deviation annualized
VAR 95%
YoY risk adjusted

15
3.3 Multi-style investment strategies.
Multiple articles as Ahmed, Lockwood and Nanda (2002) have suggested and demonstrated
the fact that applying different criteria to build portfolios may give rise to greater
performances than those obtained through single-style investment strategies. Then the next
step will be to develop a composition of portfolios based on a double-filter methodology: the
first discriminating factor to apply is size (market capitalization), while the second filtering
factor will depend on the chosen (PTB, PER or DY). To begin with PTB as first secondary
discriminatory factor, Exhibit 8 shows nine portfolios built up following the previously
commented methodology.
Exhibit 8. Performance by PTB.
M kt Low M id High M kt Low M id High M kt Low M id High
1995-1999 28,47% 18,75% 7,65% 27,79% 28,47% 19,39% 11,75% 18,30% 28,47% 26,18% 15,84% 27,05%
2000-2004 -7,13% 3,61% 6,71% -1,28% -7,13% -2,71% 11,75% -14,04% -7,13% -14,47% -13,43% -16,20%
1995-2004 9,23% 10,92% 7,18% 12,32% 9,23% 7,78% -1,72% 0,84% 9,23% 3,89% 0,14% 3,19%
beta 1 0,876 0,709 0,731 1 0,798 0,930 0,857 1 1,181 1,065 1,007
M kt Low M id High M kt Low M id High M kt Low M id High
1995-1999 1,29 0,82 0,33 1,37 1,29 0,82 0,64 0,89 1,29 1,11 0,70 1,30
2000-2004 -0,28 0,12 0,31 -0,06 -0,28 -0,12 0,39 -0,54 -0,28 -0,41 -0,42 -0,58
1995-2004 0,37 0,41 0,33 0,58 0,37 0,33 -0,07 0,03 0,37 0,13 0,01 0,12
YoY/ beta 0,092 0,125 0,101 0,169 0,092 0,098 -0,018 0,010 0,092 0,033 0,001 0,032
YoY risk adjusted
YoY YoY
MID LARGESMALL
YoY risk adjusted YoY risk adjusted
YoY
From the last figure some useful insights can be extracted: Smallcaps – High PTB portfolio
got the better results (12.32% annualized return of 12.32% and 0,169 beta-adjusted return).
Results vary depending on the size of enterprises, being medium and large capitalization
enterprises with Low PTB those who better reflect the size premium effect. This figures seem
to unveil some degree of subordination in the PTB criterion to the previous filter by size,
since the results we initially expected according to the indexes created in section 3.2 did
believe that a portfolio consisting of small caps with low ratios PTB would yield superior
performance. However, the results seem to show a greater importance of the size variable
(especially in small caps), being this market capitalization effect offset during the irrational
exuberance fashion which ruled the markets during the first sub-period (1995-1999).
Under the results shown in Exhibit 8, some comments may be made: due to the short time
horizon used (10 years) results could be spurious as the boom and bursts periods in the
sample could have flawed the true role played by both the “Size” and “PTB” variables.

16
In Chart 7, the performance trend of the Smallcaps-High PTB portfolio during the T&IT
Bubble shown the excessive optimism regarding profit growth expectations placed by the
investors in such a kind of companies. As it can be observed, the Small-High PTB portfolio
even outpaced the results obtained by the Small caps index or the low PTB portfolio, which
were the two best single-style investment strategies. So it can be pointed that two elements,
short sample period and irrational exuberance, could have been skewing the final
conclusions about the size and PTB variables effects.
0,50
1,00
1,50
2,00
2,50
3,00
3,50
Q19531/03/1995
Q39530/09/1995
Q19631/03/1996
Q39630/09/1996
Q19731/03/1997
Q39730/09/1997
Q19831/03/1998
Q39830/09/1998
Q19931/03/1999
Q39930/09/1999
Q10031/03/2000
Q30030/09/2000
Q10131/03/2001
Q30130/09/2001
Q10231/03/2002
Q30230/09/2002
Q10331/03/2003
Q30330/09/2003
Q10431/03/2004
Q30430/09/2004
Chart 7. Accumulated Performance Small caps vs PTB.
Small Index
Small-Low PTB
Low PTB
Small-High PTB
Likewise in Exhibit 9 are shown the results using the PER ratio as secondary selection
variable. In this case the results do not differ from those expected from the single-style
strategies: small capitalization stocks with lower PER ratios performed the best regardless
the size group but in small caps. This phenomenon may have a similar explanation to the
one exhaustively exposed regarding Exhibit 8 data.
Exhibit 9. Performance by PER.
Mkt Low Mid High Mkt Low Mid High Mkt Low Mid High
1995-1999 28,47% 9,35% 27,49% 18,73% 28,47% 21,78% 10,64% 17,46% 28,47% 26,74% 18,77% 23,40%
2000-2004 -7,13% 6,64% 3,26% -1,11% -7,13% -3,34% 10,64% -19,12% -7,13% -11,55% -12,35% -19,98%
1995-2004 9,23% 7,99% 14,74% 8,35% 9,23% 8,50% 1,23% -2,53% 9,23% 5,88% 2,03% -0,63%
beta 1 0,857 0,711 0,748 1 0,822 0,769 0,982 1 1,188 0,951 1,103
1995-1999 1,29 0,37 1,41 0,91 1,29 1,00 0,54 0,89 1,29 1,00 0,92 1,20
2000-2004 -0,28 0,23 0,15 -0,05 -0,28 -0,14 0,49 -0,59 -0,28 -0,34 -0,45 -0,59
1995-2004 0,37 0,30 0,70 0,40 0,37 0,36 0,06 -0,09 0,37 0,19 0,08 -0,02
YoY/ beta 0,092 0,093 0,207 0,112 0,092 0,103 0,016 -0,026 0,092 0,049 0,021 -0,006
YoY
YoY risk adjusted YoY risk adjusted YoY risk adjusted
YoY YoY
MID LARGESMALL

17
Chart 8 (graph below) highlights in accumulated terms how the performance of the
Smallcaps–Mid PER portfolio exceeded sharply that of the other investment strategies,
including passive single-style strategies like Small caps or Low PER indices.
0,50
1,00
1,50
2,00
2,50
3,00
3,50
4,00
Q19531/03/1995
Q39530/09/1995
Q19631/03/1996
Q39630/09/1996
Q19731/03/1997
Q39730/09/1997
Q19831/03/1998
Q39830/09/1998
Q19931/03/1999
Q39930/09/1999
Q10031/03/2000
Q30030/09/2000
Q10131/03/2001
Q30130/09/2001
Q10231/03/2002
Q30230/09/2002
Q10331/03/2003
Q30330/09/2003
Q10431/03/2004
Q30430/09/2004
Chart 8. Accumulated Performance Small caps vs PER.
Small Index
Small-Mid PER
Low PER Index
Small-Low PER
Finally, Exhibit 10 shows the performance for portfolios created using the Dividend Yield as
secondary discriminatory criterion. From this data it can be inferred that market investors
rewarded income generating stocks, regardless the size of the company. A clear evidence of
this income effect is observed on the Small-High DY (14.27% annualized performance and
0,22 beta-adjusted return), being previously anticipated by the aforementioned single-style
results on Small and High DY indices constructed in earlier sections. Once again a graph
showing accumulated returns is present in Chart 9, where the outstanding return of the
Small-High DY portfolio and other related strategies are concisely
depicted.

18
Exhibit 10. Performance by DY.
1995-1999 28,47% 24,54% 13,30% 16,01% 28,47% 14,60% 14,03% 20,88% 28,47% 23,45% 21,02% 24,60%
2000-2004 -7,13% -6,75% 3,91% 12,55% -7,13% -20,24% 14,03% 0,76% -7,13% -21,10% -11,72% -10,44%
1995-2004 9,23% 7,77% 8,51% 14,27% 9,23% -4,39% -0,03% 10,36% 9,23% -1,31% 3,36% 5,64%
beta 1 0,924 0,752 0,643 1 1,073 0,751 0,768 1 1,140 0,990 1,116
1995-1999 1,29 1,00 0,53 0,94 1,29 0,62 0,84 1,01 1,29 1,22 0,94 0,96
2000-2004 -0,28 -0,26 0,17 0,54 -0,28 -0,59 0,58 0,03 -0,28 -0,60 -0,44 -0,33
1995-2004 0,37 0,30 0,36 0,71 0,37 -0,15 -0,00 0,48 0,37 -0,04 0,13 0,19
YoY/ beta 0,092 0,084 0,113 0,222 0,092 -0,041 0,000 0,135 0,092 -0,011 0,034 0,051
YoY risk adjusted YoY risk adjustedYoY risk adjusted
YoY YoY
MID LARGESMALL
YoY
0,50
1,00
1,50
2,00
2,50
3,00
3,50
4,00
Q19531/03/1995
Q39530/09/1995
Q19631/03/1996
Q39630/09/1996
Q19731/03/1997
Q39730/09/1997
Q19831/03/1998
Q39830/09/1998
Q19931/03/1999
Q39930/09/1999
Q10031/03/2000
Q30030/09/2000
Q10131/03/2001
Q30130/09/2001
Q10231/03/2002
Q30230/09/2002
Q10331/03/2003
Q30330/09/2003
Q10431/03/2004
Q30430/09/2004
Chart 9. Accumulated Performance Small caps vs DY.
Small Index
Small-High DY
High DY Index
In Exhibit 11 there is a summary of the 6 best strategies both multi-style and single-style.
Overall, the only single-style strategies displayed in the box are those which main investment
themes are high Dividend Yield (High DY) as well as those related to low market
capitalization (Small). The 3 best strategies are multi-style portfolios with small size features:
Small High DY, Small-Mid PER and Small High PTB. An important takeaway from the last
results is the astonishing importance of considering the size factor as primary discriminator.

19
Exhibit 11. Optimal Peformance: Multi-Style and Single-Style.
Small-High DY Small-Mid PER Small-High PTB High DY Small Small-Low PTB
1995-1999 16,01% 27,49% 27,79% 19,46% 18,46% 18,75%
2000-2004 12,55% 3,26% -1,28% 3,86% 3,21% 3,61%
1995-2004 14,27% 14,74% 12,32% 11,39% 10,58% 10,92%
beta 0,643 0,711 0,731 0,804 0,774 0,876
1995-1999 16,99% 19,53% 20,26% 20,97% 20,79% 22,98%
2000-2004 23,13% 21,83% 20,35% 23,41% 23,00% 29,75%
1995-2004 20,03% 21,13% 21,13% 22,21% 21,91% 26,42%
1995-1999 16,81% 14,69% 11,83% 15,44% 19,35% 28,47%
2000-2004 36,39% 40,37% 44,81% 37,70% 41,44% 42,86%
1995-2004 35,23% 38,86% 38,56% 37,70% 41,38% 42,23%
1995-1999 0,94 1,41 1,37 0,93 0,89 0,82
2000-2004 0,54 0,15 -0,06 0,16 0,14 0,12
1995-2004 0,71 0,70 0,58 0,51 0,48 0,41
YoY/ beta 0,222 0,207 0,169 0,142 0,137 0,125
YoY
Stand Dev annualized
VAR 95%
YoY risk adjusted
Something quite remarkable is the fact that Multi-Style strategies offer a Market correlation
coefficient lower than the Single-Style 7
strategies (Chart 10). However, observing the best
strategies for each type there is little distinction among them in sensitivity terms: Single-Style
optimal strategies coefficients are ranging from 0,885 to 0,906 while Multi-Style optimal
strategies coefficient are allocated from 0,804 to 0.96.
0,700
0,750
0,800
0,850
0,900
0,950
1,000
LowPtb
MidPtb
HighPtb
Lowptb
Midptb
Highptb
Lowptb
Midptb
Highptb
LowPER
MidPER
HighPER
LowPER
MidPER
HighPER
LowPER
MidPER
HighPER
LowDY
MidDY
HighDY
LowDY
MidDY
HighDY
LowDY
MidDY
HighDY
Small Mid Large Small Mid Large Small Mid Large
Chart 10. Market Index Correlations.

20
4. Investment strategies using Style Rotation.
4.1 Style rotation strategies as an alternative.
Multiple investment strategies based on different criteria have been released in the previous
sections. In section 2, Single-Style strategies were built using a single variable; meanwhile in
Section 3 efforts were made to elaborate a more complex portfolio construction process from
using a pair of factors to creating portfolios (primary and secondary discrimination factors)
named Multi-Style strategies.
Single-style and Multi-Style strategies have similar and divergent points, but a great feature
both share is their intrinsic element of passivity. With reference to this inner passivity is the
fact that each 31st December a new portfolio(s) are created based on some parameters and
held until the next allocation window (12 months later), so the name of “Passive Investment
Strategies” is fairly assigned.
However, various authors as Ahmed, Lockwood and Nanda (2001) have tried to analyze the
effect of not betting continuously in a single style strategies over 12-month periods and
experimented with investment style changes, commonly known as Style Rotation, to optimize
portfolio returns. Style rotation strategies may belong to the same group, as changing from
Large Caps to Small Caps, or being a much more sharp change like passing from Large
Caps to Value stocks. The last example is illustrated in Chart 118
, where the optimal strategy
is constructed by using the right timing to picking strategies. The quarterly turnover between
styles is useful as the investor may avoid serious drawdowns and manage to get a smooth
returns pattern over the investment horizon. As a result, better absolute and risk-adjusted
returns are achieved in comparison with Passive Investment Strategies.

21
-15,00%
-10,00%
-5,00%
0,00%
5,00%
10,00%
15,00%
20,00%
25,00%
Q19531/03/1995
Q39530/09/1995
Q19631/03/1996
Q39630/09/1996
Q19731/03/1997
Q39730/09/1997
Q19831/03/1998
Q39830/09/1998
Q19931/03/1999
Q39930/09/1999
Q10031/03/2000
Q30030/09/2000
Q10131/03/2001
Q30130/09/2001
Q10231/03/2002
Q30230/09/2002
Q10331/03/2003
Q30330/09/2003
Q10431/03/2004
Q30430/09/2004
QoQReturns
Chart 11. Spread Trend: Multi-Style and Optimal Strategies .
Small-Large
Value-Growth
Optima
The key in order to achieve a higher performance following active strategies is based on
knowing and anticipate changes in the market cycle. Hence an investor must know a lot of
variables that can explain the change in the leading investment style, besides holding a fairly
outstanding prediction ability whether the investor aims at improving or at least matching
passive strategies performance.
Therefore it is important to find out those expected results linked to a certain level of
prediction under a specific probability of occurrence. To perform the next analysis a set of
previously constructed indexes has been used, choosing the minimum and maximum
performance for each date (accounted for a Rotation fee of 2%) and applying 4 different
levels of prediction. It is assumed that each of the 4 performance generated series are
normally distributed with mean and distribution equal to the computed for each series. Last
step was to implement the inverse normal distribution to find the return linked to each of the
probability values.
For example in Chart 12 some indexes created in Section 2 (Small, Mid and Large) where
used. For each date, the higher and lower returns from these indexes have been gathered;
resulting in 2 data series (minimums data and maximums data) on which we have applied 4
different levels of forecasting to obtain 4 simulated series of expected returns. To put it
another way, the expected returned series of an individual with predictive level of 80% will be

22
simulated as the multiplication of the pair of maximum and minimum series by 80% and 20%
respectively. Thus although by this method the true distribution of expected returns is not
truly forecasted, this rudimentary process is enough to demonstrate some useful insights. To
obtain the true distribution of expected returns for each prediction level, several Style rotation
simulations should be run though is topic up to further research articles.
-15,00%
-10,00%
-5,00%
0,00%
5,00%
10,00%
15,00%
100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 39% 34% 29% 24% 19% 14% 9% 4%
QoQreturns
Level of Confidence
Chart 12. Returns Distribution: Size Rotation.
Forecast Level 80% Forecast Level 70%
Small Index
-15,00%
-10,00%
-5,00%
0,00%
5,00%
10,00%
15,00%
100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 39% 34% 29% 24% 19% 14% 9% 4%
QoQreturnsl
Level of confidence
Chart 13. Returns Distribution: Style Rotation.
Value Index
Both Chart 12 and Chart 13 yielded similar conclusions. Regarding the former one, taking a
level of confidence equal or lower to 55% only an investor with an 80% level prediction would

23
obtained a return equal to the passive strategy (Small caps). In other words, the probability of
outperforming the Small Index for an investor whose forecast accuracy is 80% would be
equal or lower to 45%. An investor with only a 50% forecast ability would only match passive
strategies at a level of confidence equal or lower to 65%, so his chance of getting a higher
profitability would be reduced to 35%.
In Chart 14 a similar process has been followed but using all indices and portfolios created in
sections 2 and 3, in this way we have obtained a series of maximum and minimum for each
date and rotation possibilities include Single-style and Multi-Style strategies. Conclusions to
be drawn from Chart 12, Chart 13 and Chart 14 could be summarize in the difficulty of
outperforming the passive investment strategies without having considerable levels of
prediction.
-15,00%
-10,00%
-5,00%
0,00%
5,00%
10,00%
15,00%
20,00%
100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 39% 34% 29% 24% 19% 14% 9% 4%
QoQreturns
Level of Confidence
Chart 14. Returns Distribution: Total Style Rotation.
Forecast Level
80%
Forecast Level
70%
Forecast Level
60%
Forecast Level
50%
Small Index
4.2 Indicative models for the practice of Style Rotation.
In Section 4.1 some insights regarding the application of rotation strategies were underlined,
being the most important one the necessity to have certain superior forecasting skills to
anticipate market and style changes. This section will introduce two types of econometric
models whose main objective is to enhance this forecasting ability concerning changes in
cycle and whose explicative variable are 2 sort of spreads: size or style value/growth).

24
The main difference between both models is based on the explicative/independent variables
used to explain the dependent variable 9
. The first model studies relationships between
external variables (different to the series of data which make up the spread), while the
second model is based on time series models (use of spread intrinsic information) through
ARMA models and volatility modeling when so required 10
.
For the first model, the following variables were used as explanatory regressive factors to
explain the “Small-Large Spread” returns, displaying in parentheses their name as they
appear in Exhibit 12 and Exhibit 13: European Union Inflation (inflation) 11
, the 10 years-12
months sovereign slope (slope) 12
, the 12 months maturity Spanish Bill quarterly price
change (bill), Dividend yield spread between small and large capitalization companies
(spreadSLDY) and between value and growth companies (spreadVGDY) 13
, Equity Market
Risk premium14
(EMRP) and the dollar/euro exchange rate quarterly growth (EURUSD). The
choice of these variables have its basis in research published by M.Levis and M.Liodakis
(1999) for the British market, though further improvement in the regression variables
selection and processing could be done in future research.
Exhibit 12. Small-Large Spread Regression.
Coef t-stat Coef t-stat
intercept 0,003768 1,6362 -0,092772 -2,1147
inflation 1,160985 1,0781 1,807237 2,3341
slope 0.432264 0,1842 1,660048 0,6803
bill 0.053278 0,6062 0,063465 0,8118
spreadSLDY 8,286365 2,2922 1,159402 3,5825
EMRP 0.093910 1,1347 0,226294 3,0546
EURUSD 0.322915 1,4162 0,590844 2,5796
R2 0,412
R2 adjusted 0,301
AIC -2,8345
Univariable Multivariable
In the first two columns of Exhibit 12 can be observed how using a single explanatory
variable yields rather spurious significant results for all the explicative factors (their t statistic
are lower than 1.96 so the null hypothesis “estimated coefficient equal to 0” cannot be
rejected with a 95% level of confidence) saving the variable “spreadSLDY” that is statistically
representative. Nevertheless the situation upturns considerably in considering the last two
columns, in this case all variables gain statistical significance but neither “slope” nor “bill”. To
emphasize the high sensitivity in the dividend regression factor (spreadSLDY), clearly related

25
to the importance previously commented in other sections of the Dividend Yield as key
discriminating factor in the construction of portfolios.
Exhibit 13. Value-Growth Spread Regression.
Coef t-stat Coef t-stat
intercept 0,011322 1,0784 -0,010400 -0,2135
inflation 0,420639 0,5146 0,514377 0,5238
slope -1,094735 -0,6205 -0,422141 -0,2143
bill -0,024461 -0,3674 -0,029563 -0,3930
spreadVGDY 2,161123 1,0074 1,788723 0,6620
EMRP -0,000470 -0,0074 0,026732 0,3329
USDEUR -0,105284 -0,6298 -0,105791 -0,5248
R2 0,048
R2 adjusted -0,125
AIC -2,9228
MultivariableUnivariable
The results presented in table 13 to explain the spread Value-Growth model are much less
encouraging since no variable is certainly significant. A very powerless model is clearly
observable as coefficient of determination low figures corroborates, not even reaching to
explain a 5% of the volatility inherent in the dependent variable.
With reference to the second model, Time-series approach, in Exhibit 14 an ARMA model is
shown using several the fourth, fifth and sixth dependent variable lags as explanatory
variables ((AR (4), AR (5) and AR (6)) as well as the first and fifth regression errors lags (MA
(1) and MA (5)). Despite the fact that after numerous tests this model seems to be the most
successful, the existence of material correlation among the square regression residuals
obliged to modeling also the variance using as independent variable the first lagged squared
residual and an intercept, ARCH (1). 15
Exhibit 14. Small-large Spread: Time-Series Model.
Main Regression
Coef p-val
AR(4) 0,213217 0,0000
AR(5) -0,659728 0,0000
AR(6) 0,359771 0,0046
MA(1) 0,928120 0,0000
MA(5) 1,244422 0,0000
Variance Regression
Coef p-val
intercept 0,001746 0,0002
arch(1) -0,196714 0,0005
R2 0,669
R2 adjusted 0,596
AIC -3,348

26
The model results showed in Exhibit 14 are very encouraging since all variables are
significant (p-value below the 0.05 so it means rejecting null hypothesis of coefficients not
statistically significant). Also sound figures in the coefficient of determination do more to
support the large capacity model to capture the dependent variable volatility.
Main Regression
Coef p-val
intercept 0,004681 0,0000
SPREADVG(-1) 0,606188 0,0001
MA(1) -0,883918 0,0001
MA(2) -0,604951 0,0210
R2 0,491
R2 adjusted 0,447
AIC -3,677
Exhibit 15. Value-Growth Spread: Time-Series model.
Concerning “Value-Growth Spread” dependent variable regression depicted in Exhibit 15, an
ARMA (1,0,2) was built as best alternative. No volatility modeling was required this time as
since regression bore no correlations between square residuals. With regards to the results,
these were similar to those of Exhibit 14, being all independent variables statiscally
significant and with a coefficient of determination around 50%. In this case model time series
for the Spread Value-Growth variable represents a significant leap forward in comparison
with the one presented in Exhibit 13.
Although regarding the “Value-Growth Spread” variable there is no other choice than apply
the Time-Series model, this does not happen so clearly for the “Small-Large Spread”
variable. In the latter case, a better alternative of comparing coefficients of determination is to
use the Akaike information indicator (AIC). The main reason behind this choice is that AIC
copes better with the biases inherent in both the coefficient of determination (artificial
increase by adding independent variables) and the adjusted coefficient of determination (data
set particularities damage this indicator). So the criterion followed compares AIC figures from
both the External factors model and the Time-Series model, and selects the one with smaller
AIC. Fortunately, the Time-Series model offers lower AIC as well as the higher coefficient of
determination, so in this case the choice offers no doubts. 16

27
5. Conclusions.
The most significant results obtained in each previous section are highlighted below. Firstly,
the best Single-Style strategies in terms of absolute and risk-adjusted performance are those
portfolios of low market capitalization stocks (Small index) and portfolios containing value
securities (Low PTB, Low PER and High DY portfolios). From the previous portfolios, the
income generating portfolio (High DY) proved to hold a more optimum performance; while the
other side of the coin is observed in the Low PER portfolios, which is displayed as the riskier
alternative since it offers a minimum risk-adjusted return along with high values in standard
deviation and maximum expected loss (VAR95%). In global terms, those indices constructed
with small companies (Size bias) seem to overcome timidly those composed with “Value”
bias, although in terms of VAR the latter submitted lower expected loss.
Regarding Multi-Style strategies, some resemblances with Single-Style strategies were
founded as some portfolios constructed using “Dividend Yield” as secondary discriminator
performed well. In this case the “Small-High DY” portfolio yielded a better performance,
phenomenon that was expected because of the sound results obtained from its Single –Style
"parents": Small index and High DY index. However the results from the rest of Multi-Style
portfolios were not as expected. Given the results obtained in Single-Style tests, it was likely
to have more optimal portfolios with Small-low P/E and Small-Low PTB features, however it
was not the case. Firstly, the PER-class ratio portfolio with best performance was Small-Mid
PER, besides the Small-Low portfolio PER was not even second ranked because it was
surpassed by the Small-High PER portfolio. Secondly, in terms of the PTB as secondary
filtering ratio results also were contrarian to the expected: Small-High PTB portfolio was the
best performer. These inconsistencies are not repeated in portfolios generated from medium
or large capitalization companies, being those portfolios with lower PTB or Low PER clear
winners. These results cast some doubt about the validity of ratios such as the PER and the
PTB, although no definitive conclusions might be made as the small available sample data
along with the irrational exuberant context chosen (T&IT Bubble) tainted the final
conclusions.
Then for the quarterly turnover style investment strategies, two basic conclusions should be
made. The first one refers to the predictive capabilities an investor must own, being advisable
to hold a forecasting accuracy of at least 80% to take advantage of an Active Strategy over a

28
Passive Strategy, as the probability to overcome or not a buy-and-hold tactic can oscillate
approximately a 0.2 between an investor with 80% predicting power and one that has only a
50%. The second conclusion focuses on how to achieve or improve this forecasting ability,
being the answer in the optimization of econometric models for the prediction of Style
spread´s sign changes. In this sense, this document shows a certain dominion of Time-
Series regression models against External variables models; yet the variables used as
external independent variables in this research may not be suitable for this sample data
because of certain sample data gathering limitations and the fact that some of this regression
external variables were chosen from the results of other similar articles whose sample data
features were completely different to the one used here.
In conclusion, the major pitfalls of this work are mainly focused in the little sample of
companies gathered (104 stocks), not being a significant number that reflects the European
Union wide range of companies. Another caveat comes in the way in which data have been
studied because it has been collected on a quarterly basis and a ten- year time horizon.
Unfortunately no database was available to collect data more frequently or with a longer
period like 20 years. Finally, it can be said that the document could be updated and improved
including comparisons with the fixed income market and changing the portfolio construction
frequency from an annual window to shorter or longer ones.
Notes
1. Price-to-book ratios as well as Dividend Yield used data from profit and dividends relating to the date in which are located. However,
although the PER its numerator takes the price corresponding to the date of its publication; the denominator reflects the benefit
expected next year rather than current data.
2. Size is used as the primary discriminator while the rest of ratios classify stocks as value, blend or growth. Size as market
capitalization can co-exist in groups of similar size members belonging to the three types previously appointed.
3. Two measures that have been used to assess the risk-adjusted profitability have been the YoY risk-adjusted (annualized return to
standard deviation) and Beta-adjusted returns (annualized return to beta). Although in this way we cannot collect the effect of risk,
premium, both measures are useful for comparing the portfolios created one to each other. Conclusions with both ratios will be
virtually the same as the created portfolios have a high diversification of specific risk.
4. Although mean-reversion studies by Campbell and Schiller are conducted for a sample of companies other than the one used here,
their conclusions may be extrapolated without dramatic consequences.
5. In Figure 4 is calculated the "Average PER " as the arithmetic mean of all ratios PER for each date, while "PER Long Term Average"
is an average for all arithmetic means in each date. Heading "QoQ Average performance" has been built on the average
performance of all stocks on a quarterly basis.
6. Index composed of securities with higher dividend yields is due to the rise in the risk premium priced by the investors. Since the
Bubble burst the majority of investors flew to safety by buying “real” earnings stocks different than the eternal promises made by
Telecommunications and IT companies .
7. Correlations of Single-Style and Multi-Style are in average 0,941's for the former and 0.895 for the later.

29
8. For "Value-Growth Spread" series has been necessary to perform three Spread Value-growth series created from different ratios as
main criterion (PTB, PER and DY).
9. Independent variables have been introduced in the model with one lag to the dependent variable. In other words, to explain the
“Small-Large Spread” at t, is necessary to introduce independent variables data at (t-1), being the logic behind this methodology
the aim at analyzing the predictive skills of the model.
10. All regressions have been corrected from heteroskedasticity by White (1980).
11. Inflation in the European Union is not gathered from any number of databases, so it has been calculated approaching as the HICP
annualized variation (Harmonized Price index) of Spain minus 1%. This 1% is the historical spread between the European
inflation and the Spanish inflation.
12. Types have been used for 10 years and 1 year of the Spanish public debt as approximation of European public debt. Could have
chosen the German debt given its most important markets, but it is also true that the process of convergence in recent years has
done that the German debt and Spanish differ by few points Basic.
13. The " Small-Large DY Spread" construction classifies all companies in 2 groups each December 31 depending on its size, being
its average dividend yield calculated on each date as the average between these 2 groups. While for the calculation of "Value-
Growth DY Spread" dividend yield calculation was made each date from the average dividend yield from the groups created using
PTB and PER ratios as allocating variables.
14. Equity Market Risk Premium (EMRP) is obtained through the CAPM model:
Em = Rf + beta * EMRP MERP = Em-Rf
where: Em: Market capitalization-weighted index returns.
Rf: Return of risk-free assets represented by the 10 yr euro sovereign bond.
EMRP: Market risk premium
Beta: sensitivity of the market to movements of the market, which by definition is 1.
15. Model used in theoretical terms is as follows:
Mean Equation: Yt = β * Y t-4 + β * Y t-5 + β * Y t-6 + ut + 1 α * or t-1 + α 2 * or t-2
Variance Equation: V(Yt/It-1) = ht = c + µ * or t-1
where: Yt: Small-Large Spread at t
ut: regression error at t, being on average 0 with a conditioned variance equal to ht and non-serially correlated
(cov(ut;ut-1) = 0) Although not standalone (cov(ut
2
;_ut-1
2
) ≠0).
Box presents the p-value rather than the t statistical t, since in this case variables are distributed by the statistician z whose critical
values not available, although Eviews 3.1 calculates automatically the p-value so that the individual significance test can be safely
done.
16. (AIC) of Akaike information criterion has been used to choose the most optimal model but there is another criterion called Schwartz
Bayesian (SBC). The formal expressions in both methods are:
AIC = T * ln(Squared Residuals Sum) + 2 * n
SBC = T * ln(Squared Residuals Sum) + T * n
n = number of parameters to estimate.
T = number of observations used in the regression.
The use of either criterion in small samples as the current (40 observations) is indifferent, however if the time horizon temporary
had been higher it would have allowed to recommend the SBC.

30
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2005. Dissertation Carlos Salas

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