The risk of holding periods across international stock exchanges.
Nowak, A.Z. ; Winkler-Drews, T. ; Shachmurove, Yochanan 等
I. INTRODUCTION
Over the past three decades, financial markets have experienced
unprecedented transformations, signs of which emerged in the late 1970s.
In the 1980s, deregulation led to integration of financial markets,
increasing competitiveness, and the gradual emergence of financial
innovation. The rapid development of information and communication
technologies in the 1990s contributed to the liberalization,
internationalization, and growth of financial markets (Budd, 2011).
Towards the end of the 1990s, cross-border investments occurred mainly
between the United States (U.S.), Western Europe and, to a lesser
extent, Japan (Clark, 2007). Currently, investment flows are still
concentrated among the three, although the importance of other areas has
been growing.
In recent years, substantial consolidation took place. The largest
stock exchanges took over smaller ones, resulting in more concentrated
transactions (Greasley, 2011). In 2011, 75% of the world's share
trading was done at four major stock exchanges, the New York Stock
Exchange (NYSE), the London Stock Exchange (LSE), Euronext, and the
Tokyo Stock Exchange (Tokyo SE). Note that the holding companies of the
NYSE and Euronext merged in 2007. These developments have generated
changing risks, various dimensions of which have been analyzed. See de
Araujo and Garcia (2013) for risk spillover among major stock exchanges,
Liang and Wei (2012) on global liquidity risk, and Esqueda et al. (2012)
about reduced volatility in emerging markets (Silver, 1995).
This paper presents the evolution of the level of risk for the
leading five stock exchanges--NYSE, LSE, Euronext, Deutsche Borse, and
Tokyo SE--from 1950 to 2012. The accepted measure of risk is the
unitized risk values (variation coefficients) for the real rate of
return. Risk levels are designated for holding periods of 1 to 30 years.
The study uses monthly data from the Global Financial Database
(www.global financialdata.com).
The remainder of the paper is organized as follows. Section II
through Section VI analyzes the U.S., United Kingdom (U.K.), German,
French, and Japanese markets. Section VII briefly concludes.
II. THE U.S. MARKET
With its robust economic growth during World War II, the U.S.
enjoyed a post-war period of economic supremacy over other capitalist
countries. The arms race arising from the outbreaks of the Cold War and
the Korean War added further momentum (the Korean boom). During the
period between 1950 and 1953, the U.S. industrial production increased
by 41%. The end of the Korean War led to a decrease in government budget
expenditures, which was accompanied by a short recession from 1953 to
1954. Inflation triggered another recession from 1957 to 1958. Expanding
industrial production in the 1950s triggered a high rate of economic
growth (Bordo, 2012).
Scientific and industrial research, propelled by the arms race,
revitalized the economy in the 1960s. Although financing the "Great
Society" programs, the space exploration missions and the Vietnam
War generated budget deficits and inflation. After 1969, fighting
inflation became the main goal -Keynesianism gave way to monetarism--but
to no avail as stagflation, a combination of low growth and high
inflation, crippled in.
During the years 1950 until 1973, the U.S. Gross Domestic Product
(GDP) grew at 3.9% annually, growth in industrial production was 5.3%
and inflation was at the 2.7% rate. The first oil crisis occurred in
1974 until 1975. The crisis slowed down the U.S. economy, increasing
both unemployment and inflation. In 1977, under President Carter, a
plethora of social programmes were initiated, which only worsened the
situation. In 1980, the inflation rate was 13.5%. In 1981, when
President Reagan took office, the inflation rate fell to 10.3%.
President Reagan introduced deregulation and spent heavily on defence
programs including the "Star Wars" missile defence system. In
1982, a decline in oil prices reduced inflation to 6.2% (World Bank
Global Economic Prospects, 2010).
Economic growth rebounded to 4.6% in 1983 after the 1981-1982
recession ended, and averaged 4.1% until 1990, when another recession
began. Technological innovation led to more exports, but it did not stop
high trade deficits. The domestic government debt was high and reached
$200 billion in 1986. Between 1974 and 1990, the American economy grew
at a rate of 2.6% annually and growth in industrial production was 2.5%,
with the inflation rate being 6.7% (Mishkin, 2002). Expenditures on
military intervention in Kuwait in 1990 and 1992 further increased the
federal deficits. In 2001, the military intervention in Afghanistan
started, and from 2003 to 2005, the Iraq War costs an estimated $802
billion; both events slowed down the economy. The market interpretation
of the aforementioned events is presented in Figure 1.
[FIGURE 1 OMITTED]
Despite expenditures on the arms race, space exploration, social
programs, and the Vietnam War, growth in the value of the Dow Jones
Industrial Average (DJIA) continued through the early 1970s. However,
the negative effects of the two energy crises did not derail the growth
in the stock market from 1973 through 1984. The development of the
information and technology sector gave impetus to the expansion of the
American economy at the turn of the 1980s and through the 1990s (Rhode,
2006). These developments are reflected by the behavior of the stock
market during the period of 1985 until 1994. A reversal of the dynamic
growth occurred in 1999 as a result of the crisis due to over expansion
of the Information Technology (IT) at the time. The housing boom that
lasted until 2006 came to a halt, triggering the great recession of
2007. Table 1 presents summary statistics for the real U.S. stock market
returns.
For the 30-year holding period, the expected value of rates of
return is more than twofold smaller than the same value for 1-year. The
standard deviation is respectively seven times smaller. The unitized
risk values for the real rate of return for the DJIA Index are indicated
on the basis of the data presented in Table 1 and Figure 2. The dynamic
of unitized risk for the real rate of return of the DJIA Index is
presented in Table 2.
[FIGURE 2 OMITTED]
III. THE U.K. MARKET
At the conclusion of World War II, Great Britain was economically
weak. Reconstructing its economy was only possible with the help of the
United States. From 1945 until 1951, Great Britain implemented a
nationalization program. The British economy focused on colonization,
which made it difficult to benefit from the opportunity to export
significant quantities of raw materials for the U.S. arms industry
during the Korean War. The outbreak provided a renewed incentive for the
British economy with intermittent perturbations in 1952. The inflation
rate reached 9.6% in 1952. In 1956, the colonial empire started
disintegrating after its defeat surrounding the Suez Canal. In 1959,
with a conservative economy and a lower, compared with other countries,
research and development (R&D) budget, the U.K. conceded the top
European GDP spot to West Germany (Arrighi, 2010; Read, 2010).
Following an attempt to construct "the opportunity to export
the welfare society" and the subsequent nationalisation of certain
industries in 1964, the U.K. devalued the pound sterling by about 12%.
This devaluation reinvigorated exports but also reinforced inflation,
which peaked at 9.4% in 1971. The British economy was managed according
to Keynesian principles, which endorse state interventionism. From the
mid-1960s, with a larger R&D budget, the technological gap between
the U.S. and the U.K. narrowed. Inflation peaked at 24% in 1975. The
exploitation of the British oil resources and the resulting oil
self-sufficiency, lowered inflation to 8% in 1976, and it remained at
12% for the following three years. In 1979, the Tory won the elections
and introduced monetary neoliberalism (Thatcherism) in order to
reconstruct the industry, stabilize inflation, and strengthen the
currency (Bernholz, 2003).
The second oil crisis thwarted the economic reforms, causing an
economic depression from 1980 to 1981. In 1982, the introduction of new
reforms resulted in a 3.5% increase in GDP growth rate and inflation
increased by 5%. In 1983, the volume of international trade became
considerably more important. In 1986, the oil price returned to its
pre-crisis level. During the period of 1974-1990, the British economy
grew at a rate of 1.9%. Growth remained stable through the 1990s. In the
first decade of the 21st century, this development was impeded by the
subprime crisis in 2008 (Kindleberger and Laffargue, 2008). Figure 3
presents the market interpretation of the aforementioned events in the
U.K (see also Quennouelle-Corre and Cassis, 2010).
[FIGURE 3 OMITTED]
In the years 1950-1973 the London stock exchange (LSE) market
experienced a moderate upward trend. The increasing volatility of the
alternating fluctuations of the LSE benchmark shows that during the
period analyzed, the growth of the British economy was achieved with
difficulties. The behavior of the stock market from 1950 to 1955 was
fairly steady as the average GDP growth was 3% (Littlewood, 1998). The
failure of the Suez conflict in 1956 initiates the ten-year period of
major deviations of the index from the trend line.
The London stock exchange reacted with more volatile performances
as a result of the devaluation of the pound sterling in 1967, generating
a gradual increase in inflation and then stagflation caused by the first
energy crisis. The exploitation of offshore oil which mitigated the
effects of the first energy crisis, and the debilitating effects of the
second energy crisis caused by Thatcherism, largely contributed to the
non-linear upward trend of the benchmark of the London Stock Exchange in
the period 1974-1989. From 1990 until 2010, the FTSE is characterized by
large amplitude fluctuations around a strong upward trend where the
turning points define a global phenomenon - the Information Technology
(IT) crisis in 2000 and the subprime crisis of 2006-2008 (Eichengreen,
2012). Table 3 presents summary statistics for the real U.K. stock
market returns (Vickers, 2011). For the 30-year holding period, the
expected rate of return is more than one and a half times smaller than
the same value for 1-year. The standard deviation is respectively twelve
and a half times smaller. The unitized risk values for the real rate of
return for the FTSE Index are indicated on the basis of data in Figure 4
and Table 3. Table 4 presents the dynamic of unitized risk for the real
rate of return for the FTSE Index.
[FIGURE 4 OMITTED]
IV. THE GERMAN MARKET
War damages and reparations for the First World War considerably
weakened the German industry. The U.S. and the U.K. helped the German
economy. Raw material exports from Germany helped the U.S. arms industry
during the Korean boom. Additionally, increases in non-arms expenditures
helped create the "German economic miracle." In 1959, Germany
started leading the GDP rankings. In the 1960s, it received monetary
support from the U.S., and scientific/technological progress became a
driving force behind its economic expansion. From 1950 to 1973, West
Germany's industrial production was five times larger, and German
exports grew by 30 times (Alpert, 1951; Bairoch, 1993; Glossner, 2010).
This effect caused annual GDP to rise by 5%, with a simultaneous
inflation increase. The first oil crisis increased inflation to 7% in
1974 and resulted in an economic downturn. The German economy, based
mostly on coal, overcame the crisis in a short time, reaching a $14.3
billion balance of payments surplus. The second oil crisis prevented
inflation from falling, reaching 6.3% in 1981. In the early 1980s,
foreign investments decreased and as a result the German Mark weakened.
Limited budget expenditures, coupled with increases in export and
investment volumes led to a 2.3% GDP increase between 1974 and 1990.
After 1990, changes in Central and Eastern Europe triggered economic
development with a controlled inflation rate (Alpert, 1951). The German
economy was developing steadily, despite high government expenditures as
the country was going through the re-unification process (Flandreau,
Holtfrerich, and James, 2003). The subprime crisis weakened the economy.
Figure 5 shows the impact of German events on the market.
[FIGURE 5 OMITTED]
From 1950 to 1958 the German stock exchange enjoyed a boom as its
benchmark fluctuation trends show. Despite the energy crisis, the German
economy experienced modest growth, as depicted by the upward trend of
the stock market for the two-decade period from 1959 to 1982. A strong
upturn of the German stock market from 1983 to 1995 represents the
condition of the economy during the late 1980s and 1990s (Haug and
Dewald, 2004). Significant fluctuations of the DAX Index around the
economic trend are adequate for the economic burden associated with the
reunification of Germany. The upward trend in 1996-2012 confirms the
modest growth of the German economy in the first decade of the 21st
century. The impact of externalities on the German economy is manifested
in other areas of the economy due to large fluctuations of the
benchmark. Table 5 provides summary statistics for the real German stock
market returns.
For the 30-year holding period, the expected value for the rate of
return is over twofold smaller than the same value for 1-year and the
standard deviation is respectively seventeen times smaller. On the basis
of the data shown in Table 5, Figure 6 shows the unitized risk values
for the real rate of return for the DAX Index, whose dynamic is
presented in Table 6.
[FIGURE 6 OMITTED]
V. THE FRENCH MARKET
The American Marshall Plan was crucial for the reconstruction of
the French economy. Central planning and the nationalization of energy,
coal mining, aviation, and banking sectors were pillars of French
economic policy (Maddison, 2000). With its military involvement in
Indochina, France was not able to take full advantage of the opportunity
to export significant quantities of raw materials for the U.S. arms
industry during the Korean War. There was a drop in the GDP growth rate
between 1952 and 1953 (Giersch, 1978). The military involvement in
Indochina and Algeria resulted in France's fragility toward the
worldwide economic downturn from 1958 until 1959. French exports became
more competitive with the initiation of the Great France programme,
which devalued the currency (Schroter, 2005).
Due to capital and technological inputs from the U.S., the French
GDP increased 5.7% between 1960 and 1970. The recession caused by the
first oil crisis had a lower impact on the French economy as compared
with other European countries or the United States (1980). France had
the second highest GDP growth rate after West Germany. The end of the
second oil crisis coincided with political changes in France. In 1981,
the leftist defeated the right wing political party in presidential
elections. France, weakened by the oil crises and nationalization, which
promoted high worker compensations, made its economy less competitive
and witnessed inflation upwards of 12% (Rivoire, 1980).
During the years 1981-1983, trade difficulties prompted currency
devaluations. In 1986, the rightist political party took over the
government and once again privatized banks and enterprises. Throughout
the years 1974 until 1990, the French economic development reached the
level of Germany, and progressed much faster than that of the United
Kingdom. The changes in Eastern and Central Europe did not benefit the
French economy as they favoured Germany. In the first decade of the 21st
century, French economic growth was stable. The subprime mortgage crisis
of 2008 and 2009 impacted the French economy to a much lesser degree as
compared with the U.S. and the U.K. Figure 7 presents the market
interpretation of the aforementioned events in France.
[FIGURE 7 OMITTED]
The relatively small amplitude in fluctuations of the French stock
exchange index, around a moderate upward trend in the period 1950-1962,
suggest that the loss of the war in Indochina (1945-1954) and in Algeria
(1954-1962) did not substantially affect the behavior of the market. The
large deviation of the index from the trend line in 1958 indicates low
resistance of the French economy to the global economic downturn. The
currency devaluation in 1960 stimulated export and technological
progress, which boosted the French economy in the 70s (Allen, 2011).
Both the soundness of the French economy and a better reaction to the
negative effects of the two energy crises led to favorable stock market
performances. However, it was accompanied with less than the previous
upward trend and with greater volatility in the stock index (Fridson,
1998).
Two devaluations of the French franc in the period 1981-1983
initiated a fifteenyear period of strong growth of the CAC40 Index. This
substantial boost was a market response to shaky political and economic
changes in the late twentieth-century Europe (Pomfret, 2011). The
significant volatility of the Paris stock exchange benchmark around the
downward trend in the period 1997-2012 is a manifestation of the growing
scale of market interactions as a result of the ongoing globalization
process. Table 7 presents summary statistics for real French stock
market returns.
For the 30-year holding period, the expected value for the rate of
return is more than twofold smaller than the 1-year and the standard
deviation is respectively nine times smaller. Figure 8 derives the
unitized risk values for the real rate of return for the CAC 40 Index on
the basis of data in Table 7. The dynamic of unitized risk for the real
rate of return for the CAC 40 Index is presented in Table 8.
[FIGURE 8 OMITTED]
VI. THE JAPANESE MARKET
The loss of colonies and the considerable damages from World War II
led Japan into an economic depression. The Communist party victory in
China in 1949 forced the U.S. to change their policy toward Japan. The
drastic reforms and the $2 billion invested by the U.S. in Japan did not
reinstate industrial production to its pre-war level. The Korean War was
a strong trigger in increasing the Japanese growth. Japan received $1.4
billion from the U.S. for military support, and exports increased. The
Vietnam War (1964-1973) led to further economic development for Japan.
During the period 1950-1973, the "economic miracle"
period, political stabilization and government interventions helped the
Japanese economy to reach annual growth rates as follows: GDP 9.2%,
industrial production 14.6%, and inflation 5.2% (Mosk, 2008).
Furthermore, the economy became dependent on imports, GDP increased
moderately and inflation grew (24%) as a consequence of the first oil
crisis. In 1976, inflation decreased to 10% as a result of a reduction
in budget expenditures. In the following year, inflation decreased even
further to 4.2%, which caused the yen to appreciate. Although the second
oil crisis was less severe, the Japanese economy contracted and the yen
depreciated. In 1980, the Japanese capital exports grew and the country
became a leader in foreign investments, hence causing the yen to
re-appreciate. A dynamically increasing domestic demand and low
inflation in the second part of the 1980s, helped Japan to leverage its
investments, leading to a "speculative bubble" (Rockoff,
2003).
During the period 1974 until 1990, the Japanese economy was the
fastest developing economy among capitalist countries. The annual
average Japanese GDP grew at 3.9%, industrial production at 3.5%, and
inflation by 5.2%. Since 1989, fearing the consequences of a
"bubble burst," the Bank of Japan started raising interest
rates, which led to a bubble burst and yen appreciation. The first
post-war slowdown occurred when the Japanese GDP increased at a rate
lower than other developed countries, causing the Heisei recession in
the years 1991-1993. In 1995-1996, an economic revival followed an
increase in investments and consumption, but rising tax rates pushed the
economy once again into recession. Poor credit policy in the 1980s and
the Asian financial crisis of 1997-1999 promoted the Japanese banking
crisis (Cassis, 2011). Consequently, the requirements for obtaining
loans became stricter, resulting in the 2000-2002 recession (Arestis,
Sobreira, and Oreiro, 2011). Moreover, deflation of the 1990s affected
the Japanese economic growth ("lost decade"). It started in
the last decade of the 20th century, and continued throughout the first
decade of the 21st. Figure 9 presents the market interpretation of the
aforementioned events.
[FIGURE 9 OMITTED]
The Japanese "economic miracle" can be observed on the
Tokyo Stock Exchange as a sharp upward trend during the period 1950 to
1958, then weakened slightly from 1959-1968 and peaked in the final
phase from 1970 to 1972. The negative economic growth caused by the
energy crisis did not change the economic outlook of the Tokyo Stock
Exchange during the 1969-1982 timeframe (Ferguson, 2008). The Japanese
stock market explosion, mainly in exports, during the 80s and the
"wake-up policy in domestic consumption" are symptoms of
exponential trend in the Tokyo Stock Exchange benchmark over the period
1983-1989. A consequence of the "bubble economy" was the
crisis of the early 1990s, which triggered a downward stock exchange as
a result of the Asian and the subprime crises. Table 9 presents summary
statistics for the Japanese real stock market returns.
For the 30-year holding period the expected value for the rate of
return is more than one and a half times smaller than the same value for
1-year and the standard deviation is respectively nine times smaller.
Figure 10 indicates the unitized risk values for the real rate of return
for the NIKKEI 225 on the basis of data in Table 9.
[FIGURE 10 OMITTED]
Table 10 presents the dynamic of unitized risk for the real rate of
return for the NIKKEI 225 Index.
VII. CONCLUSION
Figure 11 depicts the unitized risk values for the real rate of
return for the FTSE Index, and is the highest for holding periods 1-5
years. The unitized risk values for the real rate of return for the CAC
40 Index are highest for holding periods 5-30 years. The unitized risk
values for the real rate of return for the DAX Index are the lowest for
all holding periods.
For the 5-year holding period, the dynamic of unitized risk is
higher for the DJIA, DAX, and FTSE indices (ranging from 32.5%-30.3%),
and smaller for CAC 40 and NIKKEI 225 (23.4%, 21.7%). For the 10- year
holding period, it is higher for FTSE (50.6%), and the DAX has a
unitized risk of 47.2%. The DJIA and NIKKEI 225 indices are at
comparable levels (42.6%, 42%), and the CAC 40 is 33.5%. For the 15-year
holding period, the FTSE and DAF are higher and comparable (61.4% and
60.8% respectively), while the NIKKEI 225, DJIA, and CAC40 have unitized
risk values of 51.8%, 49%, and 44.8%.
[FIGURE 11 OMITTED]
For the 20-year holding period, it is comparable for the FTSE and
DAX (68.3%, 67.9%), while the NIKKEI 225, DJIA, and CAC 40 respectively
have unitized risk values of 62.5%, 51.9%, and 48.7%. For the 25-year
holding period, the dynamic is higher for DAX (78.3%), while the NIKKEI
225 and FTSE are at comparable levels (75.9%, 75.8%) and so are the CAC
40 and DJIA indices (58.9%, 58.7%). For the 30year holding period, the
dynamic is higher and comparable for the DAX and FTSE indices (86.1%,
85.5%), while the NIKKEI 225, CAC 40 and DIJA indices respectively are
80.2%, 74% and 70.5%. For the 5-year holding period, the dynamic of
unitized risk is the highest for the DJIA. For the 10-20-year holding
period, it is the highest for the FTSE index. The DAX has the highest
level for the 25-30-year holding period. For the 5-20-year holding
period, the dynamic is the smallest for the CAC 40. For the 25-30 year
period, the dynamic is smallest for the DJIA.
Acknowledgements: Shachmurove acknowledges that partial support for
this project was provided by a PSC-CUNY Award, jointly funded by The
Professional Staff Congress and The City University of New York, and by
the Schwager Fund of the City College of The City University of New
York. Shachmurove also gives special thanks to Ivana Harrington, Fatjon
Kaja, Akim Mahmud, Henry Semanjarrez, and Gregg Stevens, from the City
College of New York, and to University of Pennsylvania students Modibo
Camara, Jamie Lee and Kevin Yang and, for their research assistance.
Yochanan Shachmurove has benefitted from discussions on the topic of
this paper with Emanuel, Amir and Tomer Shachmurove.
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www.globafinancialdata.com.
A.Z. Nowak (a), T. Winkler-Drews (b), Yochanan Shachmurove (c)
(a) Warsaw University, Poland Anowak@mail.wz. uw. edu.pl
(b) Department of Banking and Insurance, Kozminski University in
Warsaw, Poland tadeusz@kozminski. edu.pl
(c) Department of Economics and Business, The City College of New
York, The Graduate School and University Center of The City University
of New York, USA yshachmurove@ccny. cuny. edu
Table 1
Summary statistics for the real U.S. stock market returns
Holding Standard
Period [years] Min Max Mean Deviation
1 -42.67% 46.72% 4.33% 16.30%
2 -29.66% 37.28% 3.60% 11.61%
3 -18.16% 28.25% 3.29% 9.34%
4 -13.94% 22.91% 3.11% 8.25%
5 -12.08% 22.20% 3.06% 7.79%
6 -13.06% 18.20% 3.00% 7.19%
7 -11.19% 16.64% 2.92% 6.75%
8 -9.97% 15.14% 2.87% 6.44%
9 -9.99% 14.89% 2.85% 6.23%
10 -9.45% 13.17% 2.77% 5.98%
11 -8.45% 12.89% 2.72% 5.81%
12 -7.74% 12.47% 2.70% 5.62%
13 -8.13% 12.79% 2.71% 5.47%
14 -7.74% 12.97% 2.71% 5.30%
15 -7.58% 12.91% 2.68% 5.14%
16 -7.39% 12.48% 2.62% 4.96%
17 -6.97% 12.92% 2.56% 4.78%
18 -6.36% 11.71% 2.48% 4.60%
19 -5.25% 10.93% 2.39% 4.42%
20 -4.84% 9.96% 2.32% 4.20%
21 -4.84% 8.95% 2.28% 4.01%
22 -4.23% 8.94% 2.22% 3.84%
23 -4.36% 8.53% 2.16% 3.65%
24 -3.03% 8.20% 2.11% 3.44%
25 -3.05% 8.50% 2.09% 3.25%
26 -3.12% 7.95% 2.09% 3.08%
27 -2.70% 7.05% 2.06% 2.86%
28 -2.01% 6.70% 2.02% 2.64%
29 -1.67% 6.71% 1.99% 2.42%
30 -1.15% 6.62% 1.98% 2.19%
Holding
Period [years] Kurtosis Skewness Observations
1 -0.130 0.040 745
2 -0.013 0.131 733
3 -0.450 0.184 721
4 -0.768 0.216 709
5 -0.756 0.175 697
6 -0.856 0.005 685
7 -1.035 -0.051 673
8 -1.102 -0.159 661
9 -1.051 -0.292 649
10 -1.141 -0.304 637
11 -1.209 -0.265 625
12 -1.202 -0.236 613
13 -1.076 -0.233 601
14 -0.985 -0.188 589
15 -0.929 -0.138 577
16 -0.886 -0.117 565
17 -0.914 -0.081 553
18 -1.014 -0.043 541
19 -1.122 -0.004 529
20 -1.214 0.015 517
21 -1.326 0.026 505
22 -1.385 0.085 493
23 -1.403 0.102 481
24 -1.441 0.138 469
25 -1.381 0.167 457
26 -1.423 0.174 445
27 -1.521 0.197 433
28 -1.495 0.270 421
29 -1.403 0.307 409
30 -1.296 0.398 397
Source: Own analysis based on Global Financial Data
Table 2
Dynamic of unitized risk for the real rate of return
for the DJIA Index
Holding Period [years] 1 5 10 15
St. dev./ unit 3.77 2.54 2.16 1.92
rate of return
Change [%] 32.45 42.58 48.98
Holding Period [years] 20 25 30
St. dev./ unit 1.81 1.56 1.11
rate of return
Change [%] 51.90 58.65 70.5
Source: Own analysis
Table 3
Summary statistics for the real U.K. stock market returns
Holding Standard
Period [years] Min Max Mean Deviation
1 -65.32% 89.06% 3.56% 19.02%
2 -52.03% 40.04% 2.57% 13.19%
3 -37.52% 30.37% 2.34% 10.43%
4 -25.41% 22.90% 2.14% 8.48%
5 -22.87% 23.70% 2.03% 7.50%
6 -22.24% 21.61% 2.01% 6.74%
7 -16.45% 16.70% 2.02% 6.16%
8 -13.91% 14.20% 2.01% 5.67%
9 -11.72% 11.60% 2.00% 5.34%
10 -10.64% 11.48% 1.93% 5.09%
11 -10.68% 12.23% 1.85% 4.82%
12 -9.22% 11.55% 1.83% 4.52%
13 -8.85% 11.90% 1.86% 4.29%
14 -8.68% 9.83% 1.89% 4.08%
15 -8.55% 10.53% 1.90% 3.93%
16 -6.48% 9.50% 1.92% 3.73%
17 -5.75% 9.29% 1.92% 3.54%
18 -4.28% 9.16% 1.92% 3.38%
19 -4.72% 9.12% 1.88% 3.27%
20 -4.65% 8.51% 1.85% 3.13%
21 -3.89% 8.26% 1.82% 2.95%
22 -3.44% 8.29% 1.79% 2.80%
23 -2.98% 8.60% 1.73% 2.65%
24 -2.92% 8.57% 1.72% 2.49%
25 -2.59% 8.98% 1.77% 2.29%
26 -1.80% 8.15% 1.85% 2.07%
27 -1.75% 7.14% 1.91% 1.86%
28 -1.07% 5.86% 1.94% 1.68%
29 -1.06% 5.94% 1.95% 1.59%
30 -1.01% 5.92% 1.96% 1.52%
Holding
Period [years] Kurtosis Skewness Observations
1 1.260 -0.040 745
2 1.320 -0.462 733
3 0.948 -0.595 721
4 0.487 -0.571 709
5 0.400 -0.500 697
6 0.369 -0.536 685
7 -0.007 -0.451 673
8 -0.221 -0.476 661
9 -0.557 -0.527 649
10 -0.891 -0.453 637
11 -0.964 -0.393 625
12 -1.030 -0.313 613
13 -0.959 -0.297 601
14 -0.921 -0.282 589
15 -0.907 -0.148 577
16 -0.906 -0.052 565
17 -0.798 0.069 553
18 -0.772 0.143 541
19 -0.786 0.189 529
20 -0.826 0.162 517
21 -0.831 0.235 505
22 -0.863 0.338 493
23 -0.735 0.503 481
24 -0.621 0.618 469
25 -0.460 0.634 457
26 -0.510 0.539 445
27 -0.800 0.347 433
28 -1.061 0.229 421
29 -0.973 0.294 409
30 -0.807 0.346 397
Source: Global Financial Data
Table 4
Dynamic of unitized risk for the real rate of
return for the FTSE Index
Holding Period [years] 1 5 10 15
St. dev./ unit 5.35 3.69 2.64 2.07
rate of return
Change [%] 30.91 50.58 61.36
Holding Period [years] 20 25 30
St. dev./ unit 1.69 1.29 0.78
rate of return
Change [%] 68.31 75.82 85.49
Source: Own analysis
Table 5
Summary statistics for real German stock market returns
Holding Standard
Period [years] Min Max Mean Deviation
1 -52.60% 98.18% 7.09% 25.03%
2 -36.60% 70.75% 5.67% 18.57%
3 -32.71% 54.24% 4.88% 14.30%
4 -18.34% 39.51% 4.52% 11.87%
5 -16.05% 28.93% 4.34% 10.38%
6 -12.87% 30.95% 4.17% 9.04%
7 -10.09% 33.14% 4.04% 8.21%
8 -8.61% 27.93% 3.93% 7.53%
9 -10.66% 25.37% 3.80% 7.10%
10 -6.76% 26.18% 3.56% 6.64%
11 -6.17% 23.70% 3.33% 6.06%
12 -6.02% 19.59% 3.18% 5.42%
13 -6.74% 15.90% 3.15% 4.90%
14 -7.35% 15.87% 3.12% 4.54%
15 -5.90% 13.78% 3.08% 4.26%
16 -5.46% 11.94% 3.04% 4.02%
17 -5.06% 10.77% 3.01% 3.85%
18 -4.72% 11.36% 2.97% 3.73%
19 -4.80% 11.14% 2.91% 3.53%
20 -4.88% 10.54% 2.84% 3.22%
21 -5.07% 9.38% 2.79% 2.90%
22 -5.02% 8.86% 2.77% 2.72%
23 -3.57% 8.42% 2.77% 2.55%
24 -3.08% 6.94% 2.77% 2.31%
25 -1.57% 7.24% 2.79% 2.13%
26 -1.37% 6.91% 2.81% 1.95%
27 -1.81% 6.27% 2.86% 1.78%
28 -1.49% 5.88% 2.88% 1.63%
29 -0.47% 5.52% 2.88% 1.47%
30 -1.00% 5.27% 2.87% 1.41%
Holding
Period [years] Kurtosis Skewness Observations
1 0.193 0.538 745
2 0.511 0.652 733
3 0.380 0.672 721
4 -0.305 0.622 709
5 -0.766 0.473 697
6 -0.296 0.619 685
7 0.594 0.931 673
8 0.672 0.993 661
9 0.580 0.869 649
10 1.011 0.886 637
11 0.601 0.699 625
12 -0.287 0.348 613
13 -0.381 0.109 601
14 -0.276 0.057 589
15 -0.566 0.055 577
16 -0.596 0.036 565
17 -0.497 0.062 553
18 -0.273 0.138 541
19 -0.201 0.058 529
20 -0.032 -0.121 517
21 0.269 -0.298 505
22 0.014 -0.274 493
23 -0.508 -0.205 481
24 -0.814 -0.064 469
25 -0.997 0.261 457
26 -0.888 0.286 445
27 -0.631 -0.174 433
28 -0.487 -0.390 421
29 -0.717 -0.441 409
30 -0.601 -0.606 397
Source: Own analysis based on Global Financial Data
Table 6
Dynamic of unitized risk for the real rate
of return for the DAX Index
Holding Period
[years] 1 5 10 15
St. dev./ unit 3.53 2.39 2.64 1.38
rate of return
Change [%] 32.34 47.16 60.84
Holding Period
[years] 20 25 30
St. dev./ unit 1.13 0.76 0.49
rate of return
Change [%] 67.85 78.33 86.14
Source: Own analysis
Table 7
Summary statistics for the real French stock market returns
Holding Standard
Period [years] Min Max Mean Deviation
1 -50.02% 81.60% 4.80% 22.67%
2 -34.50% 50.00% 3.79% 16.82%
3 -26.77% 39.63% 3.37% 14.03%
4 -24.15% 34.08% 3.11% 12.41%
5 -18.74% 27.45% 2.90% 10.75%
6 -15.22% 24.03% 2.75% 9.29%
7 -13.82% 22.14% 2.65% 8.45%
8 -13.40% 18.97% 2.52% 7.96%
9 -10.90% 17.53% 2.45% 7.69%
10 -9.69% 16.03% 2.32% 7.30%
11 -9.78% 15.23% 2.22% 6.90%
12 -9.97% 14.27% 2.18% 6.52%
13 -9.11% 13.51% 2.16% 6.02%
14 -9.72% 12.50% 2.14% 5.70%
15 -10.35% 13.28% 2.13% 5.55%
16 -9.26% 13.86% 2.10% 5.40%
17 -8.25% 14.55% 2.05% 5.26%
18 -7.44% 14.25% 2.01% 5.10%
19 -7.76% 13.65% 1.99% 4.95%
20 -7.67% 11.63% 1.96% 4.75%
21 -7.03% 10.71% 1.93% 4.56%
22 -6.17% 11.32% 1.92% 4.44%
23 -5.70% 11.01% 1.91% 4.23%
24 -5.45% 9.86% 1.90% 3.97%
25 -5.26% 9.10% 1.91% 3.71%
26 -4.34% 9.01% 1.95% 3.44%
27 -3.74% 7.39% 2.00% 3.18%
28 -3.38% 7.55% 2.03% 2.93%
29 -2.31% 7.70% 2.03% 2.69%
30 -1.73% 7.62% 2.00% 2.46%
Holding
Period [years] Kurtosis Skewness Observations
1 0.106 0.286 745
2 -0.415 0.264 733
3 -0.573 0.361 721
4 -0.386 0.482 709
5 -0.616 0.393 697
6 -0.870 0.322 685
7 -0.943 0.265 673
8 -1.070 0.144 661
9 -1.226 0.086 649
10 -1.380 0.038 637
11 -1.401 -0.049 625
12 -1.294 -0.124 613
13 -1.227 -0.241 601
14 -1.064 -0.286 589
15 -0.789 -0.194 577
16 -0.602 -0.081 565
17 -0.470 -0.014 553
18 -0.479 0.005 541
19 -0.637 -0.039 529
20 -0.783 -0.121 517
21 -0.838 -0.080 505
22 -0.892 0.033 493
23 -0.874 0.184 481
24 -0.894 0.249 469
25 -0.979 0.234 457
26 -1.094 0.156 445
27 -1.262 0.069 433
28 -1.257 0.106 421
29 -1.234 0.278 409
30 -1.166 0.370 397
Source: Own analysis based on Global Financial Data
Table 8
Dynamic of unitized risk for the real rate of return
for the CAC 40 Index
Holding Period [years] 1 5 10 15
St. dev./ unit rate 4.73 3.70 3.14 2.61
of return
Change [%] 21.65 33.51 44.76
Holding Period [years] 20 25 30
St. dev./ unit rate 2.42 1.94 1.23
of return
Change [%] 48.72 58.86 73.95
Source: Own analysis
Table 9
Summary statistics for the real Japanese stock market returns
Holding Standard
Period [years] Min Max Mean Deviation
1 -49.60% 136.81% 6.84% 25.05%
2 -34.72% 88.85% 5.61% 18.65%
3 -26.31% 63.67% 4.82% 14.91%
4 -20.24% 35.00% 4.22% 12.62%
5 -15.82% 28.78% 4.05% 11.35%
6 -14.14% 28.05% 4.00% 10.01%
7 -13.82% 25.22% 3.92% 8.99%
8 -12.28% 23.99% 3.80% 8.36%
9 -12.01% 24.96% 3.70% 7.96%
10 -9.49% 26.82% 3.52% 7.47%
11 -9.95% 26.47% 3.34% 7.02%
12 -11.07% 22.11% 3.17% 6.48%
13 -11.66% 19.50% 3.10% 6.02%
14 -10.59% 16.69% 3.07% 5.66%
15 -8.83% 14.47% 3.06% 5.39%
16 -7.36% 14.37% 3.09% 5.10%
17 -6.44% 13.15% 3.13% 4.83%
18 -7.00% 12.45% 3.17% 4.74%
19 -8.24% 12.95% 3.23% 4.63%
20 -7.55% 12.69% 3.27% 4.49%
21 -6.69% 12.91% 3.30% 4.41%
22 -7.06% 14.22% 3.37% 4.27%
23 -6.24% 14.05% 3.41% 3.92%
24 -5.25% 11.81% 3.46% 3.46%
25 -4.70% 10.44% 3.54% 3.12%
26 -3.33% 10.03% 3.62% 2.83%
27 -1.97% 9.50% 3.67% 2.64%
28 -1.31% 9.23% 3.70% 2.62%
29 -1.15% 9.37% 3.73% 2.68%
30 -1.78% 9.12% 3.73% 2.71%
Holding
Period [years] Kurtosis Skewness Observations
1 2.070 0.894 745
2 0.840 0.658 733
3 0.060 0.473 721
4 -0.906 0.324 709
5 -0.856 0.411 697
6 -0.600 0.509 685
7 -0.633 0.491 673
8 -0.663 0.467 661
9 -0.169 0.535 649
10 0.316 0.632 637
11 0.401 0.547 625
12 0.068 0.218 613
13 -0.091 -0.068 601
14 -0.400 -0.282 589
15 -0.565 -0.357 577
16 -0.723 -0.368 565
17 -0.883 -0.328 553
18 -0.789 -0.228 541
19 -0.562 -0.250 529
20 -0.403 -0.320 517
21 -0.097 -0.268 505
22 0.269 -0.190 493
23 0.418 -0.237 481
24 0.163 -0.333 469
25 -0.102 -0.326 457
26 -0.494 -0.233 445
27 -0.798 -0.165 433
28 -0.938 -0.124 421
29 -0.985 -0.047 409
30 -0.991 0.039 397
Source: Own analysis based on Global Financial Data
Table 10
Dynamic of unitized risk for the real rate of return
for the NIKKEI 225 Index
Holding Period [years] 1 5 10 15
St. dev./ unit 3.66 2.80 2.12 1.76
rate of return
Change [%] 23.35 41.97 51.81
Holding Period [years] 20 25 30
St. dev./ unit 1.37 0.88 0.73
rate of return
Change [%] 62.49 75.88 80.16
Source: Own analysis
