Small versus Large Caps—Empirical Performance Analyses of Stock Market Indices in Germany, EU & US since Global Financial Crisis

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Journal of Financial Risk Management, 2020, 9, 434-453
https://www.scirp.org/journal/jfrm
ISSN Online: 2167-9541
ISSN Print: 2167-9533
DOI:
10.4236/jfrm.2020.94023 Dec. 8, 2020 434 J
ournal of Financial Risk Management
Small versus Large Caps—Empirical
Performance Analyses of Stock Market
Indices in Germany, EU & US since Global
Financial Crisis
Ernst J. Fahling*, Mario Ghiani, Diethard Simmert
International School of Management, Frankfurt am Main, Germany
Abstract
This academic paper applied different models in order to analyse the per-
formance of several small cap and large cap indices for the German-, Euro-
pean- and US-market since the financial crisis in 2008. Thus, the period un-
der consideration amounts to approx. 12 years. The research period starts in
July 2008 and ends in August 2020. It was found, that an investment in the
US large cap index outperformed the German as well as the European indices
with regard to the S
harpe Ratio and Sortino Ratio. Furthermore, it has been
proven that small cap indices in Germany and Europe outperformed their
counterparts in terms of return, the large cap indices in terms of their
risk/return profiles. For the US-market, this relationsh
ip turns. Thus, the
large cap index represents the better investment compared to the small cap
index. It can therefore be said that the small cap anomaly could only be de-
tected on a country-
specific basis. With regard to the maximum drawdown, it
is evident
that the German market implies a very similar risk to the American
market. The European market again clearly beats the German and the
US-market in terms of maximum drawdown and is therefore less risky.
Keywords
Stock Market Indices, Asset Management, Performance Analysis, MSCI-Index,
DAX, SDAX, MSCI Europe, MSCI USA, Small Cap Indices, Large Cap Indices,
Sharpe Ratio, Sortino Ratio, Downside Deviation, Maximum Drawdown
1. Introduction
In the asset management field, the question to invest in small or large caps is
How to cite this paper:
Fahling, E. J.,
Ghiani
, M., &
Simmert, D. (2020).
Small
versus Large Caps
—
Empirical Performance
Analyses of Stock Market Indices in Ge
r-
many, EU & US since Global
Financial Cri-
sis
.
Journal of Financial Risk Management
,
9
,
434-453.
https://doi.org/10.4236/jfrm.2020.94023
Received:
October 19, 2020
Accepted:
December 5, 2020
Published:
December 8, 2020
Copyright
© 2020 by author(s) and
Scientific Research Publishing Inc.
This work is licensed under the Creative
Commons Attribution
-NonCommercial
International License (CC BY
-NC 4.0).
http://creativecommon
s.org/licenses/by-nc/4.0/
Open Access

E. J. Fahling et al.
DOI:
10.4236/jfrm.2020.94023 435 J
ournal of Financial Risk Management
highly ranked on the investment agenda and is of major importance in the asset
allocation process.
This question is in line with the other questions “Active versus Passive” and
“Growth Stocks versus Value Stocks”. All these questions are to a large extent
determining the performance outcome of the asset allocation, measured in dif-
ferent figures and ratios.
This paper focuses its analysis on the major issue: small versus large caps.
What is the better strategy on a long term investment horizon? Some research
on this issue has already been undertaken.
To bring further clarity to the development of small cap and large cap returns
this paper investigates the performance of several small and large cap indices.
The paper analyzes the performance particularly by focusing on specific key
performance and risk ratios. Therefore, the SDAX and German Stock Index
(DAX) for the German market, the MSCI Europe Small Cap Index and the
MSCI Europe Large Cap Index for the European market as well as the MSCI
USA Small Cap Index and the MSCI USA Large Cap Index are reviewed since
the financial crisis.
In this context the following risk measurement tools have been applied:
Sharpe Ratio, Sortino Ratio, Downside Deviation and maximum drawdown. To
do so the third chapter provides information on the indices examined and their
composition. Chapter four addresses the methodology issue and explains differ-
ent performance measurement tools which are used to determine the return and
risk profile of the country-specific small cap and large cap indices. In the fol-
lowing chapter the collected indices data are examined with regard to the past 12
years, starting in July 2008 and ending in August 2020. The sixth and last chap-
ter draws a conclusion based on the main findings of the investigation.
2. Literature Review
“Small caps do tend to carry more risk, but they should over time reward inves-
tors for taking that risk, meaning they normally outperform over long periods of
time,” so Eric Marshall, President of Hodges Capital (American Entrepreneur-
ship Foundation, 2019).
While in the business world the assumption holds that equity market yields
should represent the future cash flows of companies, the so-called anomaly of
small companies is already the first challenge for this statement. The main find-
ing of that anomaly states that small cap companies outperform the large cap
firms over a long-term horizon. Over the years, this topic has gained increasing
interest from academic researchers. Accordingly, different scientists came up
with different conclusions. For example, Dhatt, Kim, & Mukherji (1999) found
out that small cap companies account for a substantial value premium in com-
parison to the large cap companies.
Whereas Switzer & Fan (2007) came to the result that the high returns of
small caps could be country-specific (Switzer, 2010). Based on the results of Fa-

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ournal of Financial Risk Management
ma & French (1993), that smaller and therefore riskier firms achieve higher re-
turns than larger companies, Pandey & Sehgal (2016) identified several factors
which caused the higher risk. With their investigation Pandey & Sehgal (2016)
support the existence of anomaly caused by company size. A recent study by
Norland (2020) resumes for the US an outperformance of large versus small caps
during economic expansion, whereas small caps outperformed large caps during
economic downtrend.
LXV Research (2018) summarizes his research as follows: “In the ten years
since the global financial crisis, European stocks have underperformed US stocks
by a considerable margin.”
A recent study by Svaluto Moreolo (2019) concludes that “lack of research on
small-caps leads to higher risk but also higher alpha-generation potential”.
3. Indices at a Glance
Table 1 provides an overview of the researched indices, focusing on the market
capitalization and the number of companies included in the reviewed indices.
The market capitalisation of the DAX and SDAX is based on September 11th,
2020, the MSCI Europe indices on August 31st, 2020 as well as MSCI United
States indices.
This following provides an overview about the indices which will be analysed
in more detail in chapter five with regard to their performances. In this context,
the respective country-specific small cap and large cap indices are presented.
Chapter 3.1 focuses on the DAX and the SDAX which belong to the so-called
DAX family. The subsequent Chapter 3.2 explains the MSCI Europe Small Cap
Index as well as the MSCI Europe Large Cap Index. Subchapter 3.3 provides
some information on the MSCI USA Large Cap Index and the MSCI USA Small
Cap Index.
3.1. DAX
The DAX is a brand of the Qontigo GmbH and belongs to the German stock
exchange. The DAX family includes approximately 900 different stock indices
(Deutsche Börse Gruppe, 2020). The four best-know indices are the DAX, the
Table 1. Market caps of chosen small and large cap indices.
#
Index
Currency
Market Cap
# of Companies Included
1 DAX EUR 960,910,190,000 30
2 SDAX EUR 47,531,660,000 70
3 MSCI EU Large Cap EUR 5,866,141,960,000 193
4
MSCI EU Small Cap
EUR
1,078,551,510,000
944
5
MSCI US Large Cap
USD
27,105,897,770,000
290
6
MSCI US Small Cap
USD
3,408,855,910,000
1,722
Note. Adapted from Thomson Reuters; MSCI 2020, (3, 4, 5, 6).

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MDAX, the SDAX as well as the TecDAX (STOXX Ltd., 2020).
Companies which are included in these indices have to fulfil several basic re-
quirements. First, all companies listed in the four named indices are subject to
the prime Standard. The Prime Standard pursues the goal of creating more
transparency for international investors through extended mandatory disclosure
in English language. The Prime Standard was introduced on January 1st, 2003
(STOXX Ltd., 2020). Second, the company is continuously traded on Xetra.
Third, a minimum amount of 10% of all shares is free floating on the market.
And the last point states that legal and operating headquarters need to be located
in Germany (STOXX Ltd., 2020). The DAX represents the 30 largest and with
the strongest sales performing companies listed on the Frankfurt Stock Ex-
change. In terms of market cap the 30 DAX companies account for roughly 80%
of listed stock corporations in Germany. Following the DAX, the MDAX com-
prises the 60 largest and with the highest turnover performing companies in
Germany listed on the Frankfurt Stock Exchange.
The market capitalization of the DAX and SDAX is based on September 11,
2020, the MSCI Europe indices on August 31, 2020 as well as MSCI United
States indices.
In terms of size, these values are below those of the DAX. These two are fol-
lowed by the SDAX, which contains the 70 largest companies below the MDAX
in terms of sales. With regard to the TecDAX, it can be said that this index
represents the 30 largest and with the highest turnover performing tech compa-
nies listed on the German stock exchange (STOXX Ltd., 2020).
As the empirical analysis only focuses on the DAX as a large cap index and the
SDAX as a small cap index, these two are explained in more detail. The DAX
was introduced on July 1st, 1988 and is the most important stock index in Ger-
many. All companies listed in the DAX are also known as Blue Chips. The DAX
is based on the trading data of the electronic trading platform Xetra, an ex-
change-based trading platform of the Frankfurt Stock Exchange (STOXX Ltd.,
2020).
The DAX is published both as a performance index and as a price index.
Whereby, the performance index includes the dividend payment of the compa-
nies in the calculation while the price index does not. Both the DAX and the
SDAX are calculated on the basis of the market capitalization of the companies
included in the index. Furthermore, they are both based on the Laspeyres index
(Equation (1)) formula and only include the free float in the index calculation.
The Laspeyres index formula is described in the following:
t00
Index Base
it iT iT it
Tii
p ff q c
Kpq
∗ ∗∗
=∗∗
∗
∑∑
(1)
whereas
t
depicts the time of calculation of the index,
T
K
is describes as an in-
dex specific chaining factor which is valid from chaining date
T
. In the following
the upper half of the fracture is composed of
it
p
which is the stock price
i
at
time
t
,
iT
ff
the free float of the stock class
i
at time
T
,
iT
q
the amount of

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ournal of Financial Risk Management
stocks of firm
i
at time
T
and
it
c
which represents the adjustment factor of firm
i
at time
t
. The denominator of the fraction contains
0i
p
which stands for the
closing price of stock
i
on the trading day before its initial inclusion in the index.
In contrast to this
0i
q
describes the amount of stocks of firm
i
on the trading
day prior to the first inclusion in the index. Finally, “Base” describes the value of
the index on the base day (STOXX Ltd., 2020).
3.2. MSCI Europe
For more than 40 years the MSCI forms the most widely used equity-based in-
dices for institutional investors (MSCI, 2020a). A subset of the various indices is
represented by the MSCI Europe. The MSCI Europe is composed of 435 stocks
which represent about 85% FreeFloat MCap of the entire European industrial-
ized countries. Further subcategories of the MSCI Europe are represented by the
MSCI Europe Large Cap Index and the MSCI Europe Small Cap Index. The last
two indices are examined in more detail below (MSCI, 2020b).
With regard to the composition of the MSCI Europe Large Cap Index, it cov-
ers several companies out of 15 developed market countries in Europe. These
developed market countries include Austria, Belgium, Denmark, Finland, France,
Germany, Ireland, Italy, The Netherlands, Norway, Portugal, Spain, Sweden,
Switzerland and the UK. With 193 different companies spread across 15 differ-
ent countries, the large cap index covers about 70% of FreeFloat MCAP of the
European equity market, while the largest company has a market capitalization
of EUR 299,060.65 million and the small one of EUR 1772.51 million. The Index
was introduced in June 5th, 2007 (MSCI, 2020c).
The construction of the MSCI Europe Large Cap Index is based on the Global
Investable Market Indices methodology. The indices of the MSCI family are all
based on the Laspeyres index formula (Equation (1)) as already described for the
calculation of the DAX indices. The MSCI Europe Large Cap as well as the Small
Cap index is calculated both in local currency and in USD. The indices calcula-
tion incorporates data from Monday until Friday (MSCI, 2020e).
The selection criteria of the MSCI indices are based on the following five
points. The first step is to determine the equity universe. This point is divided
into the identification of suitable shares and the allocation of these to only one
country. The second step is to determine the market investable equity universe.
This includes the identification of companies with local and foreign listing. The
purpose is to determine whether certain companies with foreign listing are eligi-
ble for inclusion in the index. Furthermore, the individual securities will be
checked for investability such as the minimum size requirement, minimum Free
Float MCAP, liquidity standards, foreign inclusion factor, minimum length of
trading and the foreign room specifications. The third factor is the definition of
the size-segments based on the securities market capitalization, while the fourth
step ensures index continuity by setting a minimum number of companies for a
developed market standard index. Based on the previous evaluation, the fifth

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ournal of Financial Risk Management
step is to compile the index and calculate it using the Laspeyres index formula
(Equation (1)) (MSCI, 2020e).
Both the large cap and small cap index are updated on quarterly and
semi-annual basis. While the quarterly review takes place in February, May,
August and November, the aim is to indicate changes in the stock market in
time and thus restrict undue index turnover. In contrast, the semi-annual ad-
justment is intended to rebalance the index on the basis of current developments
and update the large capitalization cut-off points. The six-monthly adjustments
take place in May and November (MSCI, 2020c; MSCI, 2020d).
In contrast to the large cap index, the MSCI Europe Small Cap Index focuses
on companies with low market cap. It contains 944 companies from 15 different
European developed market countries. These are the same as the MSCI Europe
Large Cap Index incorporates. However, the small cap index only covers 14% of
the FreeFloat MCAP for the European equity market. The largest company in
the index has a market capitalization of EUR 9880.50 million and the smallest
one of EUR 76.62 million. The MSCI Europe Small Cap Index was launched on
January 1st, 2001 (MSCI, 2020d).
3.3. MSCI USA
Another country specific index of the MSCI is the in 1986 launched MSCI USA
Index. It displays the performance with regard to the large cap and small cap
segments within the United States share market. Therefore, the index includes
616 different companies which represent roughly 85% of the US FreeFloat Mar-
ket Cap. While the largest company accounts for a market capitalization of USD
1,859,754.02 million and the smallest for USD 3029.18 million (MSCI, 2020f).
As this paper aims to compare the large and small cap segments, the MSCI USA
Large Cap Index and the MSCI USA Small Cap Index are presented below. In
comparison to the MSCI USA its large cap index contains only 290 companies
which still cover 70% of the Free Float Market Cap. Within the 290 companies, the
largest market capitalisation is USD 1,859,754.02 million and the smallest is USD
3398.02 million. The Index was established on January 5th, 2007 (MSCI, 2020g).
Like the MSCI Europe, the MSCI USA is also part of the MSCI family and is ac-
cordingly also compiled on the Global Investable Market Indices methodology. As
a result, the US-index is also based on the Laspeyres index formula (Equation (1)).
The selection procedure follows the same steps as described in chapter 3.2.
On the other hand, the MSCI USA Small Cap Index contains 1772 companies
which account for approximately 14% of the Free Float Market Cap in the US.
The market capitalization ranges from the largest company with USD 14,038.84
million to the smallest with USD 84.61 million. The introduction of the MSCI
USA Small Cap Index dates back to January 1st, 2001 (MSCI, 2020h).
4. Methodology
The current chapter provides an overview about the performance analysis in-

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ournal of Financial Risk Management
struments which will be applied in chapter five in order to examine the per-
formance behaviour of large and small cap indices. Chapter 4.1 explains the
Sharpe Ratio, a tool for measuring the risk/return ratio of an investment. The
explanation of the Sortino Ratio is provided, a measure which, as a modification
of the Sharpe Ratio, concentrates solely on the volatility caused by downward
price movements. Thus, the explanation of the downside deviation is also ad-
dressed in Chapter 4.2. Chapter 4.3 covers the explanation of the maximum
drawdown, which provides information about the largest maximum loss of value
that has ever occurred within a given time frame based on a specific investment.
4.1. Sharpe Ratio
In 1966 William F. Sharpe developed a measurement tool to evaluate the per-
formance of mutual funds in terms of expected return and risk, originally named
Reward-to-Variability Ratio (later known as Sharpe Ratio). The idea behind the
Sharpe Ratio is to achieve easier comparability between investments by simulta-
neously considering return and risk. The return, also called yield (from the Ital-
ian “rendita”) is based on a time series of prices
12
, , ,
k
pp p⋅⋅⋅
and calculates
the return between two periods. Therefore, the simple return is defined as fol-
lowed (Equation (2)):
1
1
tt
tt
PP
RP
−
−
−
=
(2)
where
Rt
depicts the return at time
t
and
Pt
the price at time
t
(Franke, Härdle, &
Hafner, 2004). The risk, also called volatility, is defined as the standard devia-
tion. The standard deviation is the square root of the variance (Equation (3))
and is composed as follows:
( )
( )
2
1
μ
σ
ni
i
x
VAR X n
=
−
= =
∑
(3)
where σ expresses the volatility or standard deviation. In more detail
xi
represents the return at time
i
, μ denotes the average return and
n
is the number
of data points (Franke et al., 2004).
Nowadays it is without any doubt the most used model to determine the
risk-adjusted return. The Sharpe Ratio measures the return on an investment
above the risk-free interest rate, also described as excess return, associated with
each risk taken. This means that only the reward for the additional risk is taken
into account as return, since investors could have earned the risk-free interest
rate even without any risk by investing into a risk-free security. In the following
the excess return is adjusted for the risk associated with it and can be more
transparent compared with other risk/return combinations (Sharpe, 1966). The
ex post/historic Sharpe Ratio (
Sh
) is explained by the following formula (Equa-
tion (4)):
σ
hD
SD
=
(4)

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ournal of Financial Risk Management
where
D
depicts the average value of
Dt
which is defined as the difference in
excess return achieved by a fund in period t and the excess return generated by a
benchmark portfolio or security in period
t
.
σD
is the standard deviation of
D
and
Dt
. Approximately 30 years later Sharpe introduced the ex-ante Sharpe Ra-
tio, which uses expected returns and an expected standard deviation instead of
the actual parameters. This is the main difference to the ex post Sharpe Ratio
(Sharpe, 1994).
The Sharpe Ratio concept is based on the portfolio theory of Markowitz
(1952), which as the first theory made the formation of optimal portfolios de-
pendent on return and standard deviation possible. Both the Sharpe Ratio and
the portfolio theory are based on the assumption that a risk-free security exists
on the market. In this case risk-free means that the variance or standard devia-
tion of the return of the risk-free investment is equal to zero (Markowitz, 1952).
Regardless of the application, it is important to take into consideration that
the Sharpe Ratios do not take correlations into account. Nevertheless, the Sharpe
Ratio provides a convenient summary of two important aspects of any strategy
(return and risk) that affect the difference between the return of a fund and the
return of a related benchmark (Sharpe, 1994).
4.2. Sortino Ratio
This chapter focuses on the explanation of the Sortino Ratio, a variation of the
Sharpe Ratio. Compared to the Sharpe ratio, the Sortino ratio uses only the
downward deviation instead of the total standard deviation of portfolio returns.
Accordingly, it distinguishes between harmful volatility and non-harmful vola-
tility (Hoechner, Reichling, & Schulze, 2019). This means that the Sortino Ratio
takes into account the standard deviation of negative portfolio returns. The fol-
lowing outlines the Downside deviation then follows the description of the
Sortino Ratio.
Downside deviation, also named downside risk, takes the risk preference of
investors into account by introducing the Minimum Acceptable Return (MAR).
The MAR focuses more on the interests of the investors and thus solves the
problem of the downside deviation, as it considers only these. Therefore, good
volatility is said to exist as soon as the deviations are above the minimum ac-
ceptable return. Conversely, one speaks of bad volatility when the deviations are
below the MAR. Sortino described the minimum acceptable return (MAR) based
on the following formula (Equation (5)):
( )
2
1
δT
MAR t t MAR
ti pr r
=
= +−
∑
(5)
where
i
represents the index to be examined,
rt
stands for the return of the index
investigated in month
t
, the probability of an investigation is depicted by
pt
=
1/
T
, while
r
MAR is the minimum acceptable return (Van der Meer, Sortino, &
Plantinga, 2001).
Having already explained, the Sharpe ratio does not give us any information

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ournal of Financial Risk Management
whether the deviation from the mean is positive (above) or negative (below), the
Sortino Ratio takes into account the asymmetry of risk. Instead of applying the
standard deviation the Sortino ratio uses the semi-variance downwards. This
means that only those yields are penalized that fall below an investor specified
rate, namely the MAR. As a result, this ratio is a performance measurement of
return deviation under a minimum acceptable rate (Le Sourd, 2007). Whereas
the Sharpe Ratio takes the risk-free-rate into consideration the Sortino Ratio re-
placed this term by the minimum acceptable rate. The Sortino Ratio (SR) is de-
scribed with the following formula (Equation (6)):
( )
( )
2
0
1
pt MAR
p MAR
Ttpt MAR
Rr
ER r
SR
Rr
T
=
<
−
=
−
∑
(6)
where
( )
p
ER
denotes the expected return of portfolio
p
, rMAR the minimal ac-
ceptable rate,
T
is interpreted as the number periods and
pt
R
denotes the return
generated by portfolio
p
within the sub-period
t
(Sortino & Van der Meer, 1991).
As can be seen, the Sortino Ratio focuses on negative deviation and thus ig-
nores the upside volatility which is favourable for investors. Similar to a higher
Sharpe ratio, a higher Sortino ratio expresses a better result. This means that an
investment with a higher Sortino Ratio per additional unit of negative risk taken
will generate more return than an investment with a lower Sortino Ratio. It can
therefore be concluded that the Sharpe ratio penalises the investor for positive
volatility, above the MAR, whereas the Sortino ratio does not (Pekar, Čičková, &
Brezina, 2015).
4.3. Maximum Drawdown
The maximum drawdown is an asymmetric risk measurement tool frequently
used in reality. For example, it finds application in the area of commodity trad-
ing. A drawdown denotes the loss of an investment with regard to a specific pe-
riod. In contrast, the draw-up stands for a profit that ranges from the lowest
point of an investment to the maximum. In contrast, the maximum drawdown
outlines the largest loss that has ever occurred within a period for a particular
investment (Reza & Baghdadabad, 2015). Grossman & Zhou (1993) defined the
maximum drawdown as the loss generated when buying an asset at its maximum
and sold it at its minimum. In comparison to the downside risk the maximum
drawdown accounts for serial correlation within the returns in a non-parametric
way. Another point is that the maximum drawdown is independent of the time
during which the fall has occurred (Hamelink & Hoesli, 2004). The maximum
drawdown considers the lower partial moments (LPM) as risk below the target
risk in addition to the maximum loss suffered by an investor during the holding
period. Therefore, the maximum drawdown (MDD) is defined as follows (Equa-
tion (7)):
( )
( )
( )
{ }
1
1
1
, Min ,0 n
kt it
i
MDD n t D R E
k−
=
= +−

∑
(7)

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where
() ( )( )
high high low low close close
1 0 1 010 1
ln Max , , ln Min , , ln ln μ
t t tt
D P P PP P P
− − −−
= ⋅⋅⋅ − ⋅⋅⋅ + − −
,
additionally
k
depicts the number of data whereas
E
is the target return. The
component  stands for the return of fund
i
with respect to time
t
. The
maximum loss that an investor can be hit by from 0 to
t
− 1, is shown by
1t
D
−
.
Furthermore,
D
0 = 0 and
n
depicts the degree of the maximum drawdown risk
(Reza & Baghdadabad, 2015). Equation seven represents an important risk
measurement tool for institutional investors in terms of choosing a portfolio
since it shows the loss from the former maximum point (prior outermost loss) to
the nearest minimum point (next maximum loss) (Reza & Baghdadabad, 2015).
In the following chapter, the models described above are used for empirical
performance analysis of small cap and large cap portfolios with regard to the
German, European and American market.
5. Empirical Analysis
The following analysis investigates the performance differences between small
cap and large cap indices. In this context small and large cap indices from Ger-
many, Europe and the US are analysed with regard to their return and risk ratio.
To do so, the following three performance measurement tools will be applied.
Chapter 5.1 characterizes and presents the collected data. Chapter 5.2 analyses
the small and large cap indices regarding their annualized returns, volatilities
and Sharpe Ratios. Subsequently Chapter 5.3 covers the Sortino ratio, a modified
form of the Sharpe ratio. In this context, the downside deviation as well as the
Sortino Ratio will be presented and interpreted. Finally, Chapter 5.4 focuses on
the maximum drawdown with reference to the country-specific indicators.
5.1. Data
Several country-specific indices have been downloaded in order to analyze the
performance behaviors of small and large cap indices. In detail, the DAX as large
cap index and the SDAX as small cap index were taken for the German market.
For the European market, the MSCI Europe Large Cap Index and the MSCI Eu-
rope Small Cap Index were retrieved. The US-market comprises the MSCI USA
Large Cap Index and the MSCI USA Small Cap Index. All indices were down-
loaded on a monthly basis and cover a period of 145 months (roughly 12 years)
starting from July 2008 and ending in August 2020. Both the German and the
European indices were taken in euros, the US-indices in US-dollars. All indices
were retrieved via the business information services provider Thomson Reuters.
In addition, the risk-free rate has been taken for a similar period of time. With
regard to the risk-free rate for the German the average risk-free rate has been
taken from Statista. The Euro area yield curve based on AAA-rated euro central
government bonds and all euro area central government bonds (including
AAA-rated) has been downloaded from the European Central Bank. Whereas
for the US-market the risk-free rate based on the 10-year Treasury bill has been
obtained from Bloomberg.

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ournal of Financial Risk Management
In order to gain a first glimpse of the development of the indices, Figure 1
shows the index point development over the entire period under investigation.
It can be seen that the global financial crisis, which began as a real estate crisis
on the subprime market in the USA in 2007, has pulled down all indices
(Bundeszentrale für politische Bildung, 2017). On closer inspection, however,
one can see that small caps have fallen a little further in both the German and
the US-market. Only in Europe the large caps have fallen lower within that pe-
riod. With regard to February 2009 it can be seen that the SADX has been fallen
to 54.86 index points while the DAX only fell to 59.89 index points, based on the
indexed values of Figure 1. The same applies to the US market its small cap in-
dex fell 55.94 index points whereas the American large cap index decreased to
59.22 with regard to the same point in time. In the following years, prices rose
again until the beginning of March 2011 when the nuclear reactor of the Japa-
nese nuclear power plant in Fukushima exploded due to a tidal wave caused by
an earthquake (Krumrey, 2011).
In rising market phases such as this one, however, it becomes clear that the
small cap indices perform better than the large cap indices. The scissor-like de-
velopment between small cap and large cap indices shows that the small cap in-
dex outperforms the respective large cap index in its region. In our case, scis-
sors-shaped implies the ever-growing index points difference between the small
and large cap indices.
The MSCI US S outperformed the MSCI US L starting roughly in the last
quarter of 2009 until January 2020, the beginning of the corona crisis. This effect
is also known in economic research as the small company anomaly and means
that shares with low market cap perform better than shares with high market cap
during longer holding periods (Hawawini & Keim, 1998).
The following figure shows the development of the Euro/Dollar exchange rate
and its potential influence on the return.
Figure 1. Index development of the past 12 years. Data from Thomson Reuters.

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ournal of Financial Risk Management
Figure 2 shows that the euro/dollar exchange rate fell from 1.56 at the end of
June 2008 to 1.19 at the end of August 2020. This represents a percentage de-
crease of −23.72% within 12 years. It is a significant revaluation of the US-Dollar
versus the Euro, leading for US-companies to a competitive disadvantage. And
the EU-corporates have taken the windfall-profits of the continuous devaluation
of the Euro against the US-dollar. In the end the economic result has been re-
flected in the profit and loss accounts and finally in the stock market perfor-
mance of EU- and US-companies. Therefore, it is regarded as appropriate to ap-
ply the EU-data on Euro-basis, whereas US-data are kept in US-Dollars.
5.2. Sharpe Ratio Analysis
This chapter analyses the performance, volatility and Sharpe Ratio in order to
find out whether country specific small cap and large cap indices performed dif-
ferently within the last 12 years, on average. Table 2 depicts the results of the
Sharpe Ratio analysis.
Looking at the six investigated country specific indices it is striking, that the
MSCI US S has outperformed its counterpart, the MSCI US L index, by only 0.21
percentage points over the entire period with an annual return of 11.01% to
10.80% respectively. The second strongest small cap and large cap indices are the
German ones. Here too, the SDAX clearly outperformed the DAX with an an-
nual return of 10.83% compared to 7.56%.
Figure 2. Euro/US-Dollar spot rate history last 12 years. Data from Thomson Reuters.
Table 2. Sharpe Ratio analysis—July 8th, 2008 until August 20th, 2020.
SDAX
DAX
MSCI EU
S
MSCI EU
L
MSCI US
S
MSCI US
L
Rounded figures on annual basis
Return (%)
10.83
7.56
9.95
2.08
11.01
10.80
Risk-free (%)
0.80
0.80
−0.47
−0.47
0.76
0.76
Volatility (%)
18.99
18.78
18.98
14.52
20.46
15.31
Sharpe Ratio 0.53 0.36 0.55 0.18 0.50 0.66

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In terms of returns, the European indices performed worst. However, even
here it can be seen that the MSCI EU S beats the MSCI EU L with a return of
9.95% to 2.08% respectively. In terms of all returns, the MSCI EU L is roughly
four times smaller than the return of the next largest index, the DAX. However,
when the risk is considered, the tide turns. Here, the large cap indices prove to
be less risky than the small cap indices. In this case the European large cap in-
dex, MSCI EU L, turns out to bear the lowest risk with an annual standard devi-
ation of 14.52%.
A look at the American and German indices also shows that the large cap in-
dices are less risky than the small caps. The American MSCI US S carries the
greatest risk at 20.46%, the SDAX of 18.99%. With regard to the Sharpe Ratio, it
can be said that the MSCI US L achieved the best combination of return and
risk, depicted by an annual Sharpe Ratio of 0.66. Second place was claimed by
the European small cap index MSCI EU S with a Sharpe ratio of 0.55, closely
followed by the German SDAX with a Sharpe ratio of 0.53. By far the lowest
Sharpe Ratio Value was achieved by the MSCI EU L at 0.18 and the DAX with
0.36.
Based on the results, the following assumptions can be made. First, one
could assume that small cap indices are normally young companies and there-
fore more growth potential is seen with small caps. At the same time these
companies also represent a higher risk of default. However, this assumption
only applies to the US-market, as the Sharpe ratio demonstrates. With regard
to Europe, the small cap indices clearly have beaten the large cap indices. The
SDAX also clearly outperformed the DAX with regard to the German indices.
By contrast, the American large cap index outperformed the small cap index in
terms of volatility. In contrast, in terms of return the two indices are quite
close to each other, which Figure 3 illustrates once again with the comparison
of return and risk.
Figure 3. Return/Volatility comparison—July 8th, 2008 until August 20th, 2020.

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5.3. Sortino Ratio
The Sortino Ratio is a modified form of the Sharpe Ratio, since it only considers
bad volatility. Therefore, the downside deviation as well as the Sortino Ratio has
been analyzed from July 2008 until August 2020 for the country-specific small
and large cap indices. The results of the analysis are presented in Table 3.
With a view to the results it can be seen that the MSCI EU L depicts the lowest
downside deviation of 3.16% below the average annual return. This is followed
by the MSCI US L with a bad volatility of 3.66% and the DAX with 3.97%. As in
the previous chapter, the large cap indices are subject to lower risk also with re-
gard to downside risk.
In terms of downside deviation—or downside risk which focuses only on the
risk dimension of investments—the European large cap index turns out to be
less risky whereas the DAX appears to be the riskiest of the three large cap in-
dices. Also, with regard to the small cap indices the European MSCI EU S claims
for the smallest downside deviation of 3.86% followed by the SADX with 4.54%
downside risk and by the MSCI US S with 4.69% bad volatility. By analyzing the
Sortino Ratios it is striking, that the MSCI US L again outperformed its coun-
terpart, the MSCI US S, and the other European and German small cap and large
cap indices.
It is also interesting to note that when applying the Sortino Ratio, the Ameri-
can large cap index again beats the small cap index. One could therefore assume
that the outperformance of large cap indices by small cap indices is country de-
pendent. Since in Germany and Europe the small cap indices have dominated
the large caps, the MSCI EU S outperformed the MSCI EU L with a Sortino Ra-
tio of 2.70 to 0.81, respectively. Also, in the German market the SDAX has bea-
ten the DAX with a Sortino Ratio of 2.21 to 1.70.
In summary, small cap indices in Germany and Europe achieve a higher re-
turn per unit of downside risk than large caps. This is exactly the opposite in the
American market.
5.4. Maximum Drawdown
This chapter identifies the country-specific indices in terms of maximum draw-
down, which depicts the maximum cumulative loss over the observed 12-year
period. Since the maximum drawdown is a ratio which concentrates on the
Table 3. Sortino Ratio analysis—July 8th, 2008 until August 20th, 2020.
SDAX
DAX
MSCI EU
S
MSCI EU
L
MSCI US
S
MSCI US
L
Rounded figures on annual basis
Return (%)
10.83
7.56
9.95
2.08
11.01
10.80
Risk-free (%)
0.80
0.80
−0.47
−0.47
0.76
0.76
Downside Deviation (%)
4.54
3.97
3.86
3.16
4.96
3.66
Sortino Ratio
2.21
1.70
2.70
0.81
2.07
2.74

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conservation of capital it provides information about the maximum loss between
the lowest and highest point, before the turning point is reached. Table 4 sum-
marizes the results of the maximum drawdown calculations in six percentage
values.
The following conclusions can be drawn: The MSCI EU S exhibits the smallest
drawdown with −38.69% of the indices examined. In comparison to that, the
MSCI US S shows largest loss of −46.25% within the twelve years. Additionally,
the European indices have outperformed the German and American indices.
However, the American indices have exceeded the other indices, as shown in
Figure 1. With regard to the European market, this relationship inverted again.
Here the small cap index showed a smaller price drop than the large cap index
with −38.69% to −39.81%, respectively.
With regard to the maximum drawdown, an investment in German or Amer-
ican indices behaves relatively identically. Similar to the Sharpe Ratio and Sorti-
no Ratio comparison the MSCI EU S has dominated the MSCI EU L, which has
not changed with regard to the maximum drawdown. But exactly this has
changed with the measurement of the biggest single drop in the German indices.
In terms of the maximum drawdown, the SDAX was thus beaten by the DAX
with −40.11% to −45.14%, respectively. This is made particularly clear by Figure
4.
5.5. Summary Performance Measurement Tools
The most important results of this chapter are summarized in Figure 5 focusing
Table 4. Maximum Drawdown analysis—July 8th, 2008 until August 20th, 2020.
SDAX
DAX
MSCI EU
S
MSCI EU
L
MSCI US
S
MSCI US
L
Rounded figures in %
Maximum Drawdown
−45.14
−40.11
−38.69
−39.81
−46.25
−40.78
Figure 4. Summary Performance Measurement Ratios—July 8th, 2008 until August 20th,
2020.

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ournal of Financial Risk Management
on the major ratios like Sharpe ratio, Sortino ratio and Downside Deviation.
Starting with the small cap anomaly, it can be stated that in theory “compa-
nies with low market capitalization outperform large companies” can only be
proven here on a country-specific basis. This was the case for the European and
German small cap index. In the USA, the large cap index outperformed the small
cap index. It can therefore be concluded that investing in German and European
small cap indices is a much better investment proposition than investing in large
caps. The exception to this is the USA, where an investment in large caps would
have been more profitable compared to small caps.
6. Curreny Impact
Table 5 demonstrates the major performance and risk-ratios on US-Dollar cal-
culation only. The numbers are different, but they do not change the overall
conclusions.
DAX, SDAX and MSCI EU investments are denominated in Euros. A conver-
sion into US-Dollars incorporates also the volatility of the exchange rates be-
tween Euros und US-Dollars. Euro based investors are receiving returns in Euro;
DAX, SDAX and MSCI EU indices are reflecting the EUR-returns; vice versa for
Figure 5. Maximum Drawdown comparison—July 8th, 2008 until August 20th, 2020.
Table 5. Major performance and risk ratios, US-Dollar basis only; July 8th, 2008 until
August 20th, 2020.
SDAX
DAX
MSCI EU
S
MSCI EU
L
MSCI US
S
MSCI US
L
Rounded figures on annual basis
Return (%)
9.42
6.06
7.07
0.54
11.01
10.80
Risk-free (%)
0.80
0.80
−0.47
−0.47
0.76
0.76
Volatility (%)
24.57
23.52
19.40
19.33
20.46
15.31
Sharpe Ratio
0.35
0.22
0.39
0.05
0.50
0.66
Downside Deviation (%)
5.49
4.81
4.65
4.09
4.96
3.66
Sortino Ratio
1.57
1.09
1.62
0.25
2.07
2.74

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Table 6. Deviations between Euro-Dollar based numbers and only US-Dollar based
numbers (%).
Return (%)
1.41
1.10
2.88
1.54
Volatility (%)
−5.58
−4.74
−0.42
−4.81
Sharpe Ratio
0.18
0.14
0.16
0.13
Sortino Ratio
0.64
0.61
1.08
0.56
US-Dollar investors. If Dollar investors are investing in the Euro-market they
are also bearing the foreign exchange fluctuations.
During the review period the US-Dollar appreciated versus the Euro by 23.7%
in 12 years, around 2% p.a. (see Figure 2). By converting the Euro re-
turn/performance numbers into US-Dollars, the US-Dollar numbers are declining.
But the general conclusions on Return, SharpeRatio and Sortino Ratio are still
remaining valid. The paper summarizes the results how they have been realized
by the investors in the market.
7. Conclusion
This paper has shown that US large caps represented by the MSCI US Large Cap
Index outperformed since the financial crisis the MSCI US Small Cap Index with
regard to the Sharpe Ratio (0.66 vs. 0.50) the Sortino Ratio (2.74 vs. 2.07) as well
as the maximum drawdown (−40.78 vs. −46.25).
Furthermore, it was found that EU country-specific small caps account for
better risk/return ratios in comparison to large caps (0.53 vs. 0.36 and 0.55 vs.
0.18).
Looking specifically at return and volatility figures small caps in each market
are exhibiting higher rates than the corresponding large cap markets. This is a
remarkably conclusion that small caps are offering on a longer time horizon ex-
cellent investment opportunities in particular in times of low interest return for
fixed income investments, and at higher risk-return ratios in Germany and the
EU. In the US the risk-return ratios for large caps exceeds those for small caps.
Banz (1981) expected already some decades ago this conclusion. He showed in
his study that small caps outperformed the larger large caps, since they earned a
higher return. This statement can be confirmed, regardless of the country speci-
fication.
After all, it can be stated that an investment in the US-large cap index would
have outperformed both the European and the German market. In terms of ra-
tios the US-small cap index is slightly behind the equivalent ratios in Europe
(Sharpe ratio of 0.50 versus 0.53 Germany and 0.55 Europe; Sortino ratio of 2.07
versus 2.21 Germany and 2.70 Europe)
And Equation (1) shows that the MSCI US L is developing better out of the
corona crisis than the MSCI US S. This could indicate that the corona crisis has
hit smaller US-companies harder than the large US-companies
The low respective negative interest rate regime in all markets has not any

E. J. Fahling et al.
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10.4236/jfrm.2020.94023 451 J
ournal of Financial Risk Management
significant impact on the risk-return ratios.
Conflicts of Interest
The authors declare no conflicts of interest regarding the publication of this pa-
per.
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