EXTREME RETURNS AND VALUE AT RISK IN
INTERNATIONAL SECURITIZED REAL
ESTATE MARKETS
**
Kim Hiang LIOW and Mark Mengsheng LIM
**
Dr Kim Hiang LIOW
Associate Professor
Department of Real Estate
National University of Singapore
4 Architecture Drive
Singapore 117566
Tel: (65)65163420
Fax: (65)67748684
E-mail: rstlkh@nus.edu.sg
June 27, 2007
EXTREME RETURNS AND VALUE AT RISK IN
INTERNATIONAL SECURITIZED REAL ESTATE MARKETS
Abstract
This paper investigates and compares the extreme behavior of securitized real estate and stock market
returns as well as their value-at-risk (VaR) dynamics in international investing. Extreme value theory using
the block maxima method is applied to 10 securitized real estate and equity market indices representing
Asian, European and North American markets. The empirical evidence shows that Asian real estate and
equity maxima and minima return series are characterized by a fat-tailed Fréchet distribution. The
frequency and severity of extreme Asian real estate returns are greater than their European and North
American counterparts. Securitized real estate markets were riskier than the broader stock markets before
and during the Asian financial turmoil. In contrast, many stock markets turned riskier after the financial
crisis with their VaRs higher than the equivalent VaR estimates for the real estate series.
1
EXTREME RETURNS AND VALUE AT RISK IN
INTERNATIONAL SECURITIZED REAL ESTATE MARKETS
1.
Introduction
This paper is a contribution to the risk management literature in international real estate
investing. We make use of extreme value theory (EVT) to assess the extreme return and value at risk
(VaR) dynamics of ten major securitized real estate markets. VaR is a popular measure of market risk
that focuses on a maximum level of losses that investors would be willing to incur given the return
distribution. A unique feature of EVT is its ability to quantify the stochastic behavior of a financial
series at unusually large or small levels. In a risk management context, the use of EVT and VaR hope
to control downside risk in order to maximize investor wealth opportunities. Real estate is a major
capital asset that contributes to both investor diversification and wealth creation. Furthermore, real
estate is another large capital market in the world, comparable to the capitalization of the common
stock or bond markets. Another contribution of our study is that the real estate markets’ extreme value
results are compared with those of the broader stock markets corresponding to the individual real
estate markets, and hence their similarities and differences in the extreme market behavior and VaR
dynamics are revealed. In particular, though the literature on Asian financial crisis is extensive, no
formal analyzes have been conducted on the comparative extreme real estate market risk before,
during and after the crisis periods and their comparisons with the stock markets. This study
contributes to this literature.
While the traditional mean-variance theory focuses on a log-normal distribution where risk is
measured by the standard deviation of returns only, the EVT is the study of the tail of the return
distribution. In financial markets, extreme price movements correspond to market functioning during
ordinary periods, and also to stock market crashes, real estate market collapses, financial/currency
crises, 9/11 terrorist threats and other highly volatile periods characterized by an extreme event. A
parametric method based on EVT was developed in finance to compute the VaR of a position. More
formally, VaR measures the quantile of the projected distribution of gains and losses over a given time
2
horizon. Longin (1996) defines an extreme as “the lowest daily return (the minimum) or the highest
daily return (the maximum) of the stock market index over a given period (p. 384)”. Similarly,
investigating the empirical distribution of real estate returns and in particular those characteristics
related to the magnitude and frequency of extreme returns is equally important because real estate
market is part of larger financial market. For example, the July 1997 Asian financial crisis was
associated with large movements in real estate market returns and volatilities in some Asian
economies, and it was rather difficult to diversify away the risk associated with this systematic
extreme return movement of the market as a whole. From individual investors’ perspective, a riskaverse investor would likely to invest in a portfolio whose empirical distribution of returns has low
kurtosis since this would imply that the probability of large negative returns is comparatively small. In
contrast, downside risk would tend to be underestimated in the traditional mean-variance framework.
Although the use of EVT in finance is growing, little is known of this topic in international
real estate markets even though real estate is another large capital market in the world. One possible
reason is existing direct property performance series do not have daily frequency data required for
EVT and VaR studies. With recent studies highlighting the portfolio diversification benefits of
including securitized (public) real estate in a portfolio (Conover et al, 2002; Worzala and Sirmans,
2003),1 considerable attention has been given to examining various aspects of securitized real estate
market performance in Asia and internationally. It is therefore timely and important to investigate the
extreme behavior of securitized real estate equity returns and quantity the extreme return levels
associated with market crashes and boom. The July 1997 turmoil that occurred in Asian financial
markets provides interesting exploratory opportunities within which to estimate and compare the
extreme market risk with the conventional standard deviation measure. Given the large fluctuations
1 An investment in real estate can be made either directly, by acquiring the physical asset in the private real
estate market, or indirectly, by purchasing shares of a company holding real estate in the public real estate
market. There are two common types of indirect (or securitized) real estate investment vehicles available to
investors. The first type is Real Estate Investment Trusts (REITs) in the United States and Australia with its
dramatic growth since the beginning 2000’s in some Asian countries such as Japan, Singapore, Korea and
Hong Kong further enhancing the status and influence of the public market. The second type of public real
estate investment, popularly known in countries such as the United Kingdom, Hong Kong and Singapore,
consists of shares of property companies quoted on a stock market.
3
inherent in securitized real estate markets, these two risk measures (i.e. standard deviation and
extreme market risk) complement each other to optimally protect investor wealth opportunities.
This is believed to be the first comprehensive study to characterize the distribution of extreme
returns for a broad spectrum of international securitized real estate markets from three continents. As
both international investors and risk managers have become more concerned with events occurring
under extreme market conditions, investigating the empirical distributions of securitized real estate
market returns and in particular those characteristics relating to the magnitude and frequency of
extreme returns are therefore vitally important. Ten major securitized real estate markets are
considered in this study; those of the USA, UK, France, Australia, Japan, Hong Kong, and Singapore;
and Asian, European and North American regional markets over the period January 1990 through
October 2006. For comparative purpose, the extreme value investigation is also conducted for broader
stock markets corresponding to the individual real estate markets. This is our secondary contribution.
The remainder of this paper is organized as follows: Section 2 presents important elements of
the EVT and VaR that are relevant to this study. A selective review of some stock market studies is
included in Section 3. Section 4 explains the data and methodology. Section 5 discusses the estimation
results. Finally, Section 6 concludes the study.
2.
Essence of EVT and VaR
Pioneered by the works of Fréchet (1927) and Fisher and Tippett (1928), the main purpose of
the EVT theory is to provide asymptotic models with which portfolio managers can model the tails of
a distribution. It uses statistical techniques that focus on those parts of a sample of return data that
carry information about extreme behavior. The sample is divided into N blocks of non-overlapping
returns with say n returns in each block. The largest rise and the biggest fall in returns are extracted
from each block to create a maxima and minima series each with a total of m returns. These series are
used to model both tails of the sample return distribution which can then be employed to extrapolate
the return behavior beyond the particular dataset employed.
4
Under EVT, there are at least three limiting distribution alternatives to characterize the
distribution of extreme returns. In particular, a Generalized Extreme Value (GEV) distribution of
Jenkinson (1955) combines into a single form of the three possible types of limiting distribution,
namely the Grumbel, Fréchet and Weibull distribution, for extreme values, with a probability density
function (1). The GEV distribution enjoys support from the classical EVT. 2
FX(y) =exp [-(1 – τ y) 1/τ]
{
for y> τ -1, if τ < 0,
y< τ -1 , if τ > 0, ------------------------------------------(1)
where τ = -1 / k
The particular type of distribution in the GEV is determined by the tail index (τ); a Grumbel
distribution is represented by τ = 0 (thin tail), a Weibull distribution by τ > 0 (no tail) and a Fréchet
distribution by τ < 0 (fat-tail). The evidence in the literature appears to suggest that the Fréchet
distribution results in the best fit to stock market return series. Estimates of the tail index are negative
and are generally less than -0.5.
To proceed with the EVT analysis, one can use either the peaks over threshold (POT) (fitted
by GPD) or block maxima model (fitted by GEV). The block maxima model is suitable for large
observations collected from large samples of identically distributed observations while the POT model
is more appropriate for all large observations which exceed a high threshold and could happen many
years ago (McNeil, 1999). The block maxima method measures the maximum (minimum) values that
the return series take in consecutive periods. These selected returns, the block maxima (minima),
represent the extreme events. The estimation procedure of the asymptotic distribution of maximal /
minimal returns considers the IID maximal / minimal returns over non-overlapping time periods
(block length). Whilst Longin (1996) suggests a 21 trading days, Christoffersen et al. (2001) suggest
that block lengths of 10 to 15 days are required for IID observations.
2
The other two limiting distributions are: Generalized Pareto distribution (GPD) and Generalized Logistic
distribution (GLD).
5
The four parameters of GEV distribution, namely the tail (τ), shape (k) scale (α) and location
(β) indices are estimated using Probability Weighted Moments (PWM).3 Finally, VaR are computed
for confidence levels of 95 and 99 percent. More formally, VaR measures the quantile of the proposed
distributions of gains (maximal) and losses (minimal) over a given time horizon. If alpha is the
selected confidence level, VaR is the (1-alpha) lower-tail level.
The limiting extreme value cumulative distribution is:
(
Fy ( y ) = 1 − exp − (1 + τ ( y − β ) / α )
1/τ
)---------------------------------(2)
The confidence level or probability (p) is:
(
p = 1 − Fy ( y ) = − exp − (1 + τ ( y − β ) / α )
1/τ
)--------------------------------(3)
By expressing VaR in percentage terms and rearranging the above expression, then the VaRs
or the 95% and 99% degree of confidence, VaR95 and VaR99 are:
VaR 95 = − β +
VaR 99 = − β +
3.
[
]
[
]
α
τ
1 − (− ln p )
τ
α
τ
1 − (− ln p )
τ
------------------------------------------------------------------(4)
------------------------------------------------------------------(5)
Empirical evidence
As pointed out above, in contrast to the real estate literature where no published study
regarding EVT-based risk management is available, there are several applications of EVT in the
finance literature, with VaR being the most popular. Longin (1996) is one of the first to apply EVT in
finance. He finds that the extremes of daily returns for the S&P 500 index over 1885-1990 can be
characterized by the Fréchet distribution (a member of the GEV family). He also suggests the
potential of EVT in other aspects of risk management, such as VaR estimation and margin settings in
3
Another alternative is to use the maximum likelihood (ML) method. The PMW method originated in
hydrology and was developed by Greenwood et al. (1979) to become a credible alternative to the ML
method. They are easier to compute and almost always yield feasible values for the estimated parameters
(Hosking, et al, 1985).
6
regulating capital requirements for financial institutions. Longin (2000) presents an application of
EVT to compute the univariate VaR for the US equity market. In addition, he also uses multivariate
EVT to compute the VaR of a position decomposed on risk factors. One of the important messages
from his work is that as the extreme value method focuses on extreme events, the event risk is
explicitly taken into account. Other applications of EVT include Dannielsson and Vries (1997), Bali
(2003), Fernandez (2003, 2005), Ho et al. (2004), Longin (2005), Brooks et al. (2005), Tolikas and
Brown (2006), Gettinby et al. (2004, 2006) and Cotter (2004, 2006). These studies demonstrate in
different manners that the EVT based-methods are able to model the extreme behavior and estimate
VaR associated with the sequence of financial returns satisfactory.
4.
Data description and methodology
The real estate data are daily FTSE EPRA/NAREIT total return indexes maintained by the
European Public Real Estate Association (EPRA). The indices are constructed, which are comprised
of REIT stocks and non-REIT securities, on a consistent basis across countries from the share prices
of companies with greater than US$200 million listed capitalization as well as derive at least 60
percent of their income from property investment related activities. As such, these global real estate
series are designed to track the performance of listed real estate companies and REITs worldwide
(www.epra.com). In addition, the broader Dow Jones (DJ) stock market indices correspond to the real
estate markets are obtained extracted from Datastream. The study period is from January 1992 to
October 2006, the longest time series data available for both types of indices. Returns are calculated
by the first difference of the natural logarithm of the daily indices resulting in 3867 realizations. They
are expressed in local currencies and are representative of an investor who is fully hedged against
currency risk.
As mentioned above, seven national and three regional markets are considered in this study.
They are Australia (AUS), Hong Kong (HK), Japan (JP), Singapore (SG), France (FRA), United
7
Kingdom (UK), United States (US), Asia (ASIA), Europe (EUR) and North America (NAM).4 The
focus on these markets is of significant interest to the world investors. The US market, being the
world’s largest, most mature and transparent securitized real estate market, is an apparent choice. The
UK and FRA are two world major economies and European’s most established property markets. Of
the Asia-Pacific markets, JP is a significant world economy and has a long history of public real estate.
The AUS securitized real estate sector is a leading player in global real estate. Similarly, HK and SG
have track record of listed real estate companies that play a relative important role in general stock
market indexes. Finally, while some markets like the USA and AUS have mainly REITs and LPTs;
other markets’ real estate indexes consist of mainly real estate companies.
Table 1 show detailed descriptive statistics for the EPRA and DJ logarithmic returns
respectively. The daily log-return series is first calculated and then the minima (and maxima) of these
returns over successively weekly (5-day), fortnightly (10-day), monthly (20-day), quarterly (60-day),
half-yearly (120-day), yearly (240-day) and 2-yearly (480-day) selection intervals are determined. The
minimum (maximum) is defined as the period’s smallest (largest) return in the market.
(Table 1 here)
As the numbers indicate, the overall mean for the real estate and stock return series is slightly
positive for all ten real estate markets. The standard deviations for the daily values range between
0.59% (EUR) and 2.01% (SG) for the EPRA indices, the corresponding DJ return values range
between 0.78% (AUS) and 1.72% (FRA). Another interesting observation is that the daily standard
deviation values for the stock markets of ASIA, HK, SG and JP are (significantly) lower than those of
the real estate markets; while the opposite is true for other countries/ regions. This suggests that Asian
real estate markets are (significantly) riskier than their respective broader stock markets. It is evident
that the daily returns are non-normal in all EPRA and DJ series investigated as the skewness values
are different from zero and the excess kurtosis values are all greater than three. The normal
distribution can also be rejected as an appropriate description of these real estate and stock market
4
The North American (NAM) regional real estate market comprises the US and Canada real estate markets.
8
datasets since all Jarque-Bara statistic (JB) greatly exceed 9.21, which is the 99% quantile of the Chisquared distribution with two degrees of freedom.
Additional interesting findings emerge when the behavior of the maxima (Table 1, Panels A
and B) and minima (Table 1, Panels C and D) over different selection intervals is inspected.
According to the descriptive figures, all EPRA and DJ maxima series are positively skewed while all
EPRA and DJ minima series exhibit a negative skewness. However, both the maxima and minima
returns show different values for mean, standard deviation, skewness and kurtosisn at each selection
interval.
The mean values for the maxima EPRA and DJ returns are all positive across all selection
intervals, with the maxima EPRA returns for ASIA, HK, JP and SG greater than their DJ counterparts
for all selection intervals. In particular, the size of the mean increases with the length of selection
interval, similarly the standard deviation increases as the selection interval gets longer. For all
selection intervals except for the 2-yearly and some yearly maxima values the EPRA and DJ series are
non-normal, as the respective JB statistics exceed 5.99, which is the 95% quantile of the Chi-squared
distribution with two degrees of freedom. .
The mean values for the minima EPRA and DJ returns are all negative for the different
selection intervals, with the absolute minima EPRA returns for ASIA, HK, JP, SG and NAM greater
than their DJ counterparts for all selection intervals. The absolute size of the mean increases with the
length of the selection-interval, from a value of 0.56% (EUR-EPRA) for weekly time intervals to
7.76% (SG–EPRA) for 2-yearly intervals, similarly, the standard deviation increases for all minima
returns as the selection-interval gets longer, recording a low of 0.55 % (AUS - EPRA) for weekly
minima value to a high of 4.70% (SG - DJ) for 2-yearly minima values. As with maxima returns, the
data for the minima returns are non normal for all markets for weekly, fortnightly, monthly and
quarterly selection intervals; however the normality assumption cannot be rejected for half-yearly,
yearly and 2-yearly selection intervals.
Finally, Figure 1 shows the downside tail returns (monthly minima returns) of the ten real
estate series. For each real estate series, its Quantile-quantile (QQ) plot of the minima return is
9
compared against the normal distribution. As can be seen, all the ten QQ plots are convex, indicating
that the distribution of the minima return is negatively skewed compared to the normal. Consequently,
the normal distribution underestimates the downside tail behavior.
(Figure 1 here)
Our estimation process comprises four steps which can be summarized as follows.
Step 1: We model the maxima and minima of all return series within the EVT framework. The tail
indexes are measured using the block maxima approach that considers the maxima (and minima)
taken by a return series in consecutive time-periods (weekly, fortnightly, monthly, quarterly, halfyearly, yearly and two-yearly). Such approach involves fitting a GEV distribution to the extreme
returns over non-overlapping blocks. Thereafter, The VaR estimates derived from the EVT are derived.
Step 2: To compare the VaR estimates derived from the EVT and the normal distribution, we deploy a
backtesting process that involves an exceedance test whereby an exceedance occurs when the actual
returns exceed the VaR estimates.
Step 3: As a further refinement to the VaR estimation, we investigate the impact of clustered returns
using the extremal index (θ), with higher values of θ indicating lower dependency in the return series.
Cotter (2006) use an estimator of θ provided Embrechts et al (1997):
θ = T −1
⎛ K ⎞
Log ⎜1 − u ⎟
k ⎠
⎝
N ⎞
⎛
Log ⎜⎜1 − u ⎟⎟
⎝ (kT ) ⎠
where k represents the number of blocks, T represents the length of blocks, Nu is total number of
exceedance, u is the threshold defined by the VaR of the return series and Ku is the number of distinct
blocks in which the threshold is exceeded.
Step 4: We divide the entire sample period into thee shorter intervals that broadly corresponds to the
(a) pre-Asian financial crisis: (Jan 92 – Jun 97), (b) during –crisis (Jul 97 – Dec 98) and (c) post-crisis
(Jan 99 – Oct 2006). Both the conventional standard deviation measure and VaR method are
10
conducted to evaluate and compare the impact of the Asian financial turmoil on the real estate and
stock market risk profiles.
5.
Empirical results
The results of the extreme value analysis and VaR estimation of the 10 real estate return
series are now focused. In the interest of brevity only some stock market results will be reported and
compared. Estimation results of the asymptotic distribution for a range of block lengths are reported
and the effects of the parameter estimates are discussed. The VaR estimates generated from the
extreme return are produced describing the magnitude of losses caused by the extreme market
movements. In Section 5.1 the results are reported for the entire period ending October 2006. In
Section 5.2, the VaRs calculated by the normal distribution method and the EVT approach are
compared, for each country, using exceedance test. The results of the impact of clustered returns using
the extremal index appear in Section 5.3. Finally, in Section 5.4, VaR results and their comparisons
with the standard deviation measure are evaluated for the three shorter sub-periods that correspond to
pre-, during- and post-Asian financial crisis respectively
5.1
EVT parameters and VaR estimates
Results of the estimation for the parameters of the asymptotic extreme value distributions are
given for real estate maximal returns (Table 2) and minimal returns (Table 3). Extreme daily returns
are observed over time periods ranging from 5 days (weekly) to 480 (every 2-yearly) with a sample
size of 3867 daily returns. The four GEV extreme parameters (tail, shape, scale and location) are
estimated using the PWM method.
(Tables 2 and 3 here)
Focusing on the results for minimal daily returns that investors are most concerned with, the
tail index value is always negative for ASIA and HK for all selection intervals and is between -0.0614
and -0.4372, implying that the limiting distribution is a Fréchet distribution. Consistent with this
evidence is the highest shape value derived for Hong Kong (16.299) and ASIA (12.960) implying that
11
the probabilities of extreme losses happening in these markets are higher. In contrast, the European
and North American return series are likely indicative of Weibull distribution. The behavior of the
shape parameter is generally time-varying suggesting that the probability of extreme negative returns
occurring changes over time. The location parameter that estimates the average size of extreme returns
associated with each block length reveals the EPRA minima returns in Japan, Singapore, Hong Kong
and the Asian regional markets have higher location estimates than other developed real estate
markets. The location parameter, which is related to the mean, as expected, exhibits negative values in
all markets for all block lengths. With minor exceptions, the location parameter value increases in
every selected block lengths. This observation reinforces the conclusion that Asian real estate markets
exhibit greater downside risk. Finally, the scale parameter acting as a measure of the dispersion of
extremes is generally low and stable across all block lengths for many securitized real estate markets.
For the EPRA maxima series, the negatively signed tail index values for ASIA across all
selection intervals as well as for HK, JP and AUS in many instances are again indicative of a Fréchet
distribution, with more Weibull type distribution for the remaining EPRA maximal series. More
instances of a positive shape parameter are derived for ASIA, AUS, HK and JP suggesting that the
likelihood of extreme positive returns is higher for these markets. Additionally, a comparison of real
estate and stock market EVT results reveals some interesting similarities and differences.5 First, the
distribution for all DJ series has a positive shape parameter for the minima (except for some block
lengths in AUS and HK). Second, a Fréchet type distribution is observed for the minima series of
ASIA, AUS and HK and the maxima series of ASIA, AUS, HK and JP; but this is not consistent
across all block lengths. Third, average size for the location parameter is lower for all stock markets’
minimal and maximal return series. This implies that real estate markets exhibit both greater downside
and upside risks than the stock markets and is consistent with the earlier descriptive analysis of
extreme returns.
The VaR values determined by the extreme value method, for the maximal and minimal real
estate return series, at both the 95% and 99% intervals, are also presented in Tables 2 and 3. In general,
5
The VaR results for the stock markets are not reported in order to conserve space.
12
the VaR estimates increase with longer block lengths. At the 95% level, the average VaR values for
the minimal series (across all block lengths) range from 1.58% (Europe) to 6.01% (HK). Similarly, the
average minimal VaR values at the 99% level range from 1.59% (Europe) to 8.11% (HK). Further
investigations reveal that real estate market crashes are probably more severe than market booms with
the VaR99% (2-yearly minima) larger than VaR99% (2-yearly maxima) for 6 of the 10 EPRA series
analyzed. However, this observation only applies to 5 of the 10 stock market series analyzed. Finally,
the VaR values for the EPRA series of ASIA, JP, HK and SG are significantly higher than those of the
US and European markets and this again highlights the more extreme nature of the Asian real estate
markets. Similar observations are made from the stock market series.
5.2
VaR backtesting
Back-testing the VaR results from the EVT and normal distribution method involves an
exceedance test. One important observation is that VaRs based on the extreme value distributions are
much higher than VaRs which assume the normal distribution; this is especially the case at high
confidence levels.6 The exceedance results for the maxima and minimal VaR results derived from
using 10-day and 20-day block lengths are presented in Table 4.
(Table 4)
Results are encouraging. As anticipated, the average number of exceedances per year is
greatest at the 95% level for the VaR normal distribution estimates. With the extreme value method at
the 95% level, only AUS and NAM has a greater number of exceedances per year, 64 (Australia) and
23 (NAM) respectively. At the 99% level, the EVT performance is even better with AUS and the UK
have no exceedances for their maxima series for 10-day (AUS) and 20-day (UK) selection intervals.
The exceedance results are qualitatively similar for the DJ stock series.
6
The individual VaR results based on the normal distribution method are not reported in order in order to
conserve space. The average VaR values for the EPRA indices at the 95% level are 0.10% (10 trading days)
and 0.14% (20 trading days), at the 99% level are 0.14% (10 days) and 0.20% (20 days). The corresponding
average VaR values for the DJ indices are 0.10%, 0.14% (95%) and 0.10%, 0.19% (99%).
13
As an example, Figure 2 illustrates the US EPRA daily returns over the entire study period.
Superimposed are the 95% and 99% VaR values estimated by the EVT. It is apparently from the
figure that there are several cases where the daily changes are far in excess of the 99% and 95% VaR
values estimated by the EVT. On average, only 9 (10) exceedances per year are expected at the 99%
(95%) levels. Clearly the average number of exceedances per year would have been even greater with
VaR values estimated based on normal distribution.
(Figure 2 here)
5.3
Extremal index results
Table 5 indicates that all EPRA and DJ market returns series exhibit different degrees of
clustering as the reciprocal of the extremal index deviate from 1. However, most of the extremal index
values are above 0.7 with some index values exceeding 0.90. This indicates although all financial
return series are not IID variables, the degree of clustering is not so substantial as to affect the
accuracy of EVT results significantly. Consequently all extreme return levels would not be adjusted
by the extremal indices. Here the highest level of dependence occurs for the negative extreme returns
of ASIA (real estate) and NAM (equity) whereas the smallest clustering effect occurs for upper tail
realizations of the AUS (real estate) and JP (equity) return series.
(Table 5 here)
5.4
Extreme value VaRs before, during and after the Asian Financial Crisis
Though the literature on Asian financial crisis is extensive, no formal analyzes have been
conducted on the comparative extreme real estate market risk before, during and after the crisis
periods and their comparisons with the stock markets. Following literature, we divide the entire study
period into: (a) Pre-crisis period (Jan 92-Jun 97), (b) During the crisis period (Jul 97 – Dec 98) and (c)
Post-crisis period (Jan 99 – Oct 06) for both maxima and minima return series of EPRA and DJ
indices. By comparing the estimated extreme value VaRs with the standard deviation measure, we
14
hope to observe changes in the extreme risks over the three sub-periods and detect which markets
exhibit the greatest propensity for experiencing crashes and booms.
Table 6 first describe the behavior of the left (minima) and right (maxima) tails of the
distribution of EPRA and DJ indices’ daily returns during the Asian financial crisis period. We focus
on the frequency of returns which are lower (left tail) and higher (right tail) (exceedances) than four
thresholds defined as
and
μ − 4σ (left tail) or μ + 4σ (right tail) where μ is the overall daily means
σ is the overall daily standard deviation for the period. Because of leptokurtosis the frequencies
expected under normality are higher than that observed for exceedances of
μ − 4σ and
μ − 3σ (minima) as well as μ + 4σ and μ + 3σ (maxima) threshold. However, the frequencies of
exceedances of the thresholds
μ − 2σ , μ − σ , μ + 2σ and μ + σ are higher than expected under
normality in the majority of the indices. These results indicate that investors who assume normality
would tend to underestimate the risk of investing in major real estate and stock markets arising from
returns below the
μ − 3σ and μ − 4σ thresholds (downside risk).
(Table 6 here)
The extreme value VaR and standard deviation results for the three sub-periods are
represented graphically in Figures 3(a) (EPRA maxima), 3(b) (EPRA minima), 3(c) (DJ maxima) and
3(d) (DJ minima). In order to conserve space, only the VaR95 results are included. At least five
interesting findings emerge from the analysis. First, the maxima and minima VaRs increase with
longer block length. This suggests that investors with a longer horizon are more likely to experience
extreme returns during these turbulent periods. Second, higher VaRs are also accompanied by higher
standard deviations; however the standard deviation values are lower or significant lower than the
VaR estimates in all EPRA and DJ series. Third, extreme return levels associated with market crashes
are generally more severe than booms especially in Asian markets. This confirms that Asian real
estate markets exhibit more downside risk. Forth, Asian real estate markets exhibit greater propensity
for experiencing booms and crashes because the respective maxima and minimal VaR estimates are
higher (or significant higher) than those for the European and North American counterparts. This
15
observation applies to the stock markets too. Finally, it further appears that securitized real estate
markets were riskier than the broader stock markets before and during the Asian financial turmoil
because the respective real estate VaR estimates were of higher magnitudes. In contrast, many stock
markets became riskier after the crisis with the DJ VaR values (significantly) higher than the
equivalent VaR estimates for the EPRA series. In particular, the development of REITs after the Asian
financial crisis has helped stabilize Asian real estate markets. Consequently, the probabilities of
extreme negative real estate market price movements were reduced relative to the general stock
markets. The overall implications for investors emerge from this event can be significant as this means
that the investment decisions with respect to the portfolio structure and hedging strategy that consider
both VaR and standard deviation could be different from those investment decisions that solely based
on the standard deviation measure.
(Figures 3(a) – 3(d) here)
6.
Conclusion
In this study, EVT methods are used to model tail returns and estimate VaRs of 10 major
international securitized real estate markets and stock markets over the period 1992 to 2006. We hope
to provide international investors with another risk perspective in addition to the traditional meanvariance approach. The July 1997 financial turmoil that occurred in the Asian markets indicates the
need for investors and financial institutions to understand and model the maxima and minima return
distributions of various financial markets (including real estate markets) as well as generating VaR
estimates in order to manage and control extreme risk in financial markets.
The paper offers investors a number of interesting findings. First, several Asian real estate
and stock market’s maxima and minima return series produce negative tail indices implying that the
limiting extreme value distributions are characterized by a Fréchet distribution and hence are fat-tailed.
Second, the EVT parameters do change through time and with the length of the selection interval.
However, the performance of extreme value VaRs is still much better than the normal VaRs,
particularly in terms of the number of exceedances of VaR estimates. Third, the extreme return levels
16
of Asian real estate market indices are found to be higher than their US and European counterparts
suggesting that the frequency and severity of extreme Asian real estate market returns are greater.
Together with a higher standard deviation measure, the overall picture is investing in Asian real estate
markets is associated with higher return fluctuations compared to the developed markets. This
observation also applies to the maxima and minima stock market returns. Finally, securitized real
estate markets were riskier than the broader stock markets before and during the Asian financial
turmoil. In contrast, many stock markets turned riskier after the crisis with their VaR values
(significantly) higher than the equivalent VaR estimates for the real estate market series. Accordingly,
investors and fund managers should be aware of such changing market dynamics when formulating
their portfolio strategies that include securitized real estate and stock markets.
Overall, important contributions of this study include significant evidence of extreme return
and VaR in major real estate and stock markets. Focusing on international real estate investing, these
results are important because knowing real estate market returns exhibit extreme behavior can help
investors and fund managers understand the distribution of real estate market returns better and obtain
potentially more accurate real estate return forecasts. In particular, higher VaRs are accompanied by
higher standard deviations; however the standard deviation values are lower or significant lower than
the VaR estimates in all EPRA and DJ series. In this respect, our results also have practical
implications, because they suggest international real estate portfolio risk management should include
both extreme risks and standard deviations. Accordingly, global investors should be even more
cautious in formulating their diversification strategies since gains from diversification can be reduced
significantly by the severity of extreme return levels. Further research includes addressing the
question of whether the stochastic behavior of extreme return parameters can be explained and
predicted using macroeconomic variables or implied volatilities in international real estate investing.
Additionally, the extension from considering separate univariate distributions for the minima and
maxima returns to employing an appropriate bivariate (multivariate) distribution, using both the
unconditional and conditional EVT approaches, to describe their joint behavior would be fruitful.
17
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- 19 -
Table 1
Panel A:
MAXIMA
AUS
Daily
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
HK
Daily
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
JP
Daily
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
SG
Daily
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
FRA
Daily
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
Descriptive Statistics for Extremes of Daily Returns over Various Selection Intervals for the Period 1992-2006: EPRA versus DJ
Maxima (AUS, HK, JP, SG and FRA)
Real estate (EPRA)
Stock (DJ)
N
Mean
Max
Min
SD
Skew
Kurt
JB
Mean
Max
Min
SD
Skew
Kurt
JB
3867
773
386
192
64
32
16
8
0.00055
0.0086
0.0114
0.0140
0.0182
0.0213
0.0249
0.0289
0.05278
0.0528
0.0528
0.0528
0.0528
0.0528
0.0528
0.0528
-0.05554
-0.0032
0.0011
0.0045
0.0088
0.0102
0.0133
0.0219
0.00709
0.0054
0.0055
0.0060
0.0069
0.0080
0.0095
0.0115
-0.010
1.614
1.994
2.125
2.423
2.296
1.875
1.395
5.925
10.171
12.788
12.852
12.163
9.544
6.149
3.287
1378.64
1991.87
1796.63
921.00
286.54
85.22
15.99
2.62
0.00049
0.0091
0.0120
0.0146
0.0187
0.0216
0.0248
0.0296
0.05991
0.0599
0.0599
0.0599
0.0599
0.0599
0.0599
0.0599
-0.07231
-0.0028
0.0000
0.0058
0.0094
0.0095
0.0104
0.0205
0.00783
0.0057
0.0058
0.0061
0.0074
0.0088
0.0108
0.0131
-0.378
1.564
2.062
2.500
2.867
2.636
2.186
1.783
7.651
11.481
14.878
17.558
16.469
12.630
8.155
4.732
3576.85
2631.68
2542.71
1895.42
571.44
160.71
30.46
5.24
3867
773
386
192
64
32
16
8
0.00037
0.0194
0.0270
0.0349
0.0475
0.0580
0.0688
0.0755
0.19677
0.1968
0.1968
0.1968
0.1968
0.1968
0.1968
0.1968
-0.13991
-0.0362
0.0019
0.0059
0.0144
0.0235
0.0311
0.0370
0.01869
0.0179
0.0198
0.0234
0.0294
0.0350
0.0414
0.0511
0.239
3.012
3.300
3.081
2.697
2.475
2.102
1.893
11.982
21.649
21.695
17.318
12.909
9.517
6.994
5.266
13036.70
12370.84
6321.96
1943.67
339.46
89.29
22.42
6.49
0.00045
0.0156
0.0215
0.0270
0.0364
0.0431
0.0490
0.0562
0.13958
0.1396
0.1396
0.1396
0.1396
0.1396
0.1396
0.1396
-0.12785
-0.0107
0.0018
0.0082
0.0101
0.0168
0.0177
0.0303
0.01493
0.0131
0.0146
0.0168
0.0225
0.0271
0.0285
0.0347
-0.238
2.897
3.156
3.247
2.673
2.405
2.183
2.017
12.271
21.260
21.027
18.873
11.842
8.603
7.658
5.553
13886.21
11820.40
5867.56
2352.94
284.72
72.71
27.17
7.60
3867
773
386
192
64
32
16
8
0.00020
0.0218
0.0303
0.0389
0.0557
0.0690
0.0856
0.0997
0.13270
0.1327
0.1327
0.1327
0.1327
0.1327
0.1327
0.1327
-0.10671
-0.0088
0.0017
0.0076
0.0187
0.0234
0.0333
0.0578
0.02000
0.0190
0.0207
0.0232
0.0285
0.0306
0.0314
0.0291
0.552
2.034
1.961
1.740
1.065
0.574
-0.076
-0.322
7.469
9.552
8.279
6.479
3.442
2.340
1.917
1.698
3415.15
1916.09
695.54
193.74
12.62
2.34
0.80
0.70
0.00005
0.0133
0.0179
0.0223
0.0309
0.0375
0.0443
0.0512
0.07024
0.0702
0.0702
0.0702
0.0702
0.0702
0.0702
0.0702
-0.06382
-0.0063
0.0017
0.0041
0.0105
0.0159
0.0252
0.0325
0.01181
0.0098
0.0102
0.0113
0.0137
0.0146
0.0143
0.0157
0.065
1.634
1.747
1.708
1.164
0.855
0.447
-0.182
5.949
8.145
8.079
6.802
3.874
2.722
1.880
1.328
1403.59
1196.41
611.25
208.98
16.50
4.00
1.37
0.98
3867
773
386
192
64
32
16
8
0.00023
0.0205
0.0285
0.0375
0.0504
0.0619
0.0743
0.0910
0.22747
0.2275
0.2275
0.2275
0.2275
0.2275
0.2275
0.2275
-0.14407
-0.0224
0.0000
0.0090
0.0149
0.0171
0.0337
0.0452
0.02011
0.0212
0.0243
0.0289
0.0344
0.0419
0.0516
0.0595
0.819
3.423
3.413
3.092
2.740
2.331
1.945
1.697
14.919
23.624
21.062
16.350
13.134
9.147
6.027
4.630
23321.46
15209.84
5996.45
1731.91
353.94
79.34
16.20
4.73
0.00030
0.0123
0.0170
0.0219
0.0312
0.0388
0.0501
0.0639
0.17732
0.1773
0.1773
0.1773
0.1773
0.1773
0.1773
0.1773
-0.16862
-0.0072
0.0000
0.0036
0.0085
0.0127
0.0183
0.0240
0.01245
0.0124
0.0147
0.0183
0.0251
0.0329
0.0416
0.0542
0.129
4.894
4.906
4.424
3.763
2.780
2.082
1.342
28.185
51.199
44.321
32.487
20.573
11.501
6.684
3.370
102213.70
77909.66
29009.91
7582.41
974.55
137.55
20.61
2.45
3867
773
386
192
64
32
16
8
0.00060
0.0088
0.0119
0.0154
0.0215
0.0267
0.0329
0.0408
0.08326
0.0833
0.0833
0.0833
0.0833
0.0833
0.0833
0.0833
-0.04584
-0.0038
-0.0001
0.0032
0.0081
0.0128
0.0182
0.0235
0.00765
0.0068
0.0076
0.0086
0.0111
0.0132
0.0158
0.0192
0.285
2.856
3.258
3.410
3.119
2.695
2.255
1.529
9.791
24.048
25.484
23.489
16.735
11.853
7.705
4.058
7482.08
15319.95
8813.91
3730.44
606.84
143.23
28.32
3.49
0.00039
0.0147
0.0193
0.0231
0.0290
0.0337
0.0388
0.0465
0.08086
0.0809
0.0809
0.0809
0.0809
0.0809
0.0809
0.0809
-0.71509
-0.0050
0.0028
0.0082
0.0106
0.0139
0.0186
0.0264
0.01720
0.0099
0.0101
0.0112
0.0128
0.0152
0.0174
0.0198
-18.663
1.617
1.947
1.937
1.870
1.511
1.123
0.685
777.181
8.246
9.216
8.336
7.212
4.780
3.300
1.926
96795843.00
1223.40
865.34
347.80
84.61
16.40
3.42
1.01
- 20 -
Table 1 (Panel B):
MAXIMA
UK
Daily
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
US
Daily
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
ASIA
Daily
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
EUR
Daily
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
NAM
Daily
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
Maxima (UK, US, ASIA, EUR, NAM)
Real estate (EPRA)
Stock (DJ)
N
Mean
Max
Min
SD
Skew
Kurt
JB
Mean
Max
Min
SD
Skew
Kurt
JB
3867
773
386
192
64
32
16
8
0.00050
0.0101
0.0138
0.0177
0.0244
0.0313
0.0396
0.0497
0.08829
0.0883
0.0883
0.0883
0.0883
0.0883
0.0883
0.0883
-0.04882
-0.0061
0.0015
0.0055
0.0080
0.0126
0.0165
0.0254
0.00921
0.0087
0.0098
0.0117
0.0157
0.0190
0.0219
0.0236
0.631
3.145
3.319
3.094
2.297
1.615
1.156
0.785
10.008
22.082
20.643
15.915
8.818
5.064
3.198
2.139
8169.84
13002.37
5714.91
1640.60
146.53
19.58
3.59
1.07
0.00037
0.0103
0.0133
0.0161
0.0211
0.0255
0.0294
0.0363
0.05809
0.0581
0.0581
0.0581
0.0581
0.0581
0.0581
0.0581
-0.05486
-0.0102
0.0020
0.0069
0.0086
0.0096
0.0117
0.0206
0.00936
0.0077
0.0079
0.0087
0.0109
0.0128
0.0140
0.0151
-0.165
1.809
2.017
1.987
1.555
1.059
0.788
0.319
6.870
8.646
8.993
7.982
5.132
3.129
2.436
1.464
2430.74
1448.02
839.46
324.95
37.90
6.00
1.87
0.92
3867
773
386
192
64
32
16
8
0.00063
0.0079
0.0106
0.0132
0.0180
0.0215
0.0255
0.0308
0.04930
0.0493
0.0493
0.0493
0.0493
0.0493
0.0493
0.0493
-0.05509
-0.0060
0.0003
0.0031
0.0060
0.0100
0.0131
0.0155
0.00735
0.0062
0.0065
0.0071
0.0084
0.0096
0.0110
0.0122
-0.474
1.601
1.690
1.708
1.566
1.252
0.804
0.211
8.745
8.364
8.384
7.972
5.908
4.018
2.608
1.689
5462.59
1256.97
650.04
291.17
48.72
9.74
1.83
0.63
0.00038
0.0110
0.0146
0.0179
0.0230
0.0266
0.0311
0.0347
0.05414
0.0541
0.0541
0.0541
0.0541
0.0541
0.0541
0.0541
-0.06988
-0.0035
0.0025
0.0057
0.0095
0.0111
0.0160
0.0166
0.00991
0.0083
0.0087
0.0097
0.0117
0.0133
0.0146
0.0149
-0.147
1.809
1.720
1.520
1.101
0.761
0.383
0.268
7.438
7.790
6.659
5.136
3.161
2.114
1.467
1.398
3187.75
1160.65
405.70
110.38
13.01
4.14
1.96
0.95
3867
773
386
192
64
32
16
8
0.00038
0.0149
0.0200
0.0253
0.0333
0.0397
0.0456
0.0509
0.10614
0.1061
0.1061
0.1061
0.1061
0.1061
0.1061
0.1061
-0.09411
-0.0165
-0.0003
0.0071
0.0151
0.0161
0.0247
0.0282
0.01388
0.0117
0.0124
0.0141
0.0163
0.0188
0.0215
0.0238
-0.018
2.143
2.475
2.436
2.256
2.068
1.813
1.727
7.750
13.008
13.620
11.677
9.549
7.254
5.478
4.912
3635.03
3817.58
2208.20
792.21
168.63
46.93
12.86
5.19
0.00014
0.0133
0.0180
0.0221
0.0295
0.0353
0.0424
0.0508
0.09974
0.0997
0.0997
0.0997
0.0997
0.0997
0.0997
0.0997
-0.06422
-0.0046
0.0013
0.0070
0.0125
0.0138
0.0211
0.0287
0.01175
0.0097
0.0102
0.0114
0.0144
0.0169
0.0195
0.0237
0.111
2.045
2.450
2.622
2.247
1.914
1.691
1.116
6.548
13.378
15.431
14.834
10.544
7.782
5.677
3.204
2036.63
4007.90
2871.66
1340.36
205.61
50.03
12.41
1.68
3867
773
386
192
64
32
16
8
0.00048
0.0064
0.0086
0.0109
0.0148
0.0183
0.0225
0.0281
0.04217
0.0422
0.0422
0.0422
0.0422
0.0422
0.0422
0.0422
-0.04497
-0.0038
-0.0001
0.0018
0.0062
0.0086
0.0129
0.0165
0.00590
0.0050
0.0055
0.0063
0.0075
0.0088
0.0083
0.0085
-0.176
2.260
2.420
2.289
1.817
1.209
0.961
0.156
8.530
13.231
12.313
9.789
6.239
3.659
2.938
2.191
4947.70
4029.54
1771.43
536.43
63.20
8.38
2.46
0.25
0.00039
0.0126
0.0164
0.0198
0.0260
0.0308
0.0357
0.0391
0.06023
0.0602
0.0602
0.0602
0.0602
0.0602
0.0602
0.0602
-0.05074
-0.0050
0.0029
0.0048
0.0085
0.0137
0.0175
0.0199
0.01131
0.0089
0.0093
0.0101
0.0122
0.0142
0.0151
0.0150
-0.185
1.603
1.691
1.652
1.272
0.807
0.415
0.220
5.704
7.186
6.882
6.188
3.860
2.242
1.689
1.752
1200.24
895.69
426.42
168.69
19.24
4.24
1.61
0.58
3867
773
386
192
64
32
16
8
0.00064
0.0111
0.0149
0.0186
0.0239
0.0279
0.0315
0.0375
0.05835
0.0583
0.0583
0.0583
0.0583
0.0583
0.0583
0.0583
-0.05804
-0.0053
0.0000
0.0051
0.0099
0.0176
0.0192
0.0262
0.00971
0.0074
0.0072
0.0071
0.0077
0.0086
0.0099
0.0108
-0.259
1.136
1.197
1.516
1.884
1.675
1.423
0.959
5.629
6.279
6.984
8.441
8.744
6.579
4.603
2.731
1156.81
512.73
347.37
310.42
125.87
32.05
7.11
1.25
0.00039
0.0108
0.0143
0.0175
0.0225
0.0260
0.0303
0.0340
0.05336
0.0534
0.0534
0.0534
0.0534
0.0534
0.0534
0.0534
-0.07114
-0.0033
0.0019
0.0056
0.0083
0.0098
0.0151
0.0164
0.00974
0.0082
0.0086
0.0096
0.0115
0.0131
0.0143
0.0148
-0.177
1.813
1.715
1.514
1.095
0.766
0.414
0.295
7.599
7.775
6.635
5.127
3.176
2.157
1.526
1.395
3428.28
1158.13
401.71
109.57
12.87
4.08
1.90
0.97
- 21 -
Table 1 (Panel C):
MINIMA
AUS
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
HK
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
JP
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
SG
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
FRA
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
Minima (AUS, HK, JP, SG and FRA)
Real Estate (EPRA)
Stock (DJ)
N
Mean
Max
Min
SD
Skew
Kurt
JB
Mean
Max
Min
SD
Skew
Kurt
JB
773
386
192
64
32
16
8
-0.0073
-0.0099
-0.0124
-0.0170
-0.0209
-0.0258
-0.0313
0.0045
0.0000
-0.0040
-0.0069
-0.0089
-0.0141
-0.0233
-0.0555
-0.0555
-0.0555
-0.0555
-0.0555
-0.0555
-0.0555
0.0055
0.0058
0.0063
0.0077
0.0089
0.0094
0.0103
-1.829
-2.150
-2.382
-2.220
-1.855
-1.989
-1.845
12.102
13.784
14.312
11.013
8.359
7.415
5.070
3099.04
2167.60
1205.14
223.80
56.64
23.55
5.97
-0.0081
-0.0110
-0.0140
-0.0199
-0.0243
-0.0306
-0.0393
0.0052
0.0013
-0.0034
-0.0077
-0.0104
-0.0134
-0.0210
-0.0723
-0.0723
-0.0723
-0.0723
-0.0723
-0.0723
-0.0723
0.0068
0.0074
0.0082
0.0107
0.0132
0.0158
0.0183
-2.454
-2.930
-3.186
-2.764
-2.103
-1.456
-0.689
18.075
20.053
19.770
12.560
7.532
4.291
2.249
8095.65
5229.48
2574.71
325.21
50.97
6.76
0.82
773
386
192
64
32
16
8
-0.0176
-0.0244
-0.0311
-0.0441
-0.0545
-0.0694
-0.0841
0.0180
0.0000
-0.0052
-0.0137
-0.0190
-0.0324
-0.0371
-0.1399
-0.1399
-0.1399
-0.1399
-0.1399
-0.1399
-0.1399
0.0167
0.0179
0.0203
0.0261
0.0305
0.0277
0.0306
-2.284
-2.333
-2.198
-1.614
-1.178
-0.912
-0.355
12.269
11.725
9.943
5.878
3.867
3.683
2.806
3438.96
1574.47
540.23
49.89
8.41
2.53
0.18
-0.0144
-0.0201
-0.0257
-0.0375
-0.0475
-0.0620
-0.0775
0.0054
-0.0011
-0.0033
-0.0108
-0.0163
-0.0256
-0.0330
-0.1278
-0.1278
-0.1278
-0.1278
-0.1278
-0.1278
-0.1278
0.0143
0.0156
0.0182
0.0244
0.0294
0.0305
0.0333
-2.746
-2.708
-2.600
-1.856
-1.263
-0.792
-0.184
16.526
15.061
12.334
6.356
3.628
2.587
1.789
6864.20
2811.32
913.40
66.78
9.03
1.79
0.53
773
386
192
64
32
16
8
-0.0205
-0.0270
-0.0335
-0.0428
-0.0513
-0.0627
-0.0736
0.0110
0.0000
-0.0067
-0.0123
-0.0246
-0.0258
-0.0440
-0.1067
-0.1067
-0.1067
-0.1067
-0.1067
-0.1067
-0.1067
0.0155
0.0158
0.0167
0.0192
0.0216
0.0234
0.0218
-1.430
-1.494
-1.369
-1.287
-0.970
-0.363
-0.271
6.491
6.575
6.020
4.863
3.344
2.365
1.790
655.97
349.13
132.94
26.93
5.17
0.62
0.59
-0.0124
-0.0170
-0.0215
-0.0292
-0.0365
-0.0448
-0.0505
0.0058
-0.0011
-0.0065
-0.0098
-0.0161
-0.0184
-0.0361
-0.0638
-0.0638
-0.0638
-0.0638
-0.0638
-0.0638
-0.0638
0.0099
0.0102
0.0110
0.0127
0.0129
0.0112
0.0093
-1.407
-1.362
-1.246
-0.701
-0.142
0.485
0.243
5.931
5.493
4.556
2.851
2.256
3.133
2.034
531.72
219.27
69.03
5.31
0.85
0.64
0.39
773
386
192
64
32
16
8
-0.0186
-0.0251
-0.0316
-0.0455
-0.0558
-0.0674
-0.0776
0.0109
-0.0020
-0.0072
-0.0143
-0.0198
-0.0277
-0.0380
-0.1441
-0.1441
-0.1441
-0.1441
-0.1441
-0.1441
-0.1441
0.0164
0.0179
0.0205
0.0257
0.0290
0.0291
0.0327
-2.129
-2.135
-1.973
-1.503
-1.158
-1.057
-0.931
11.253
10.645
8.976
5.677
4.169
4.068
3.252
2777.75
1233.04
410.24
43.22
8.97
3.74
1.18
-0.0115
-0.0158
-0.0203
-0.0304
-0.0389
-0.0509
-0.0616
0.0099
0.0000
-0.0025
-0.0095
-0.0113
-0.0173
-0.0242
-0.1686
-0.1686
-0.1686
-0.1686
-0.1686
-0.1686
-0.1686
0.0121
0.0143
0.0173
0.0249
0.0317
0.0377
0.0470
-4.501
-4.522
-4.255
-3.150
-2.399
-2.051
-1.655
45.223
39.656
31.754
16.474
9.941
7.003
4.496
60030.22
22925.85
7193.91
589.98
94.93
21.90
4.40
773
386
192
64
32
16
8
-0.0075
-0.0103
-0.0316
-0.0186
-0.0224
-0.0274
-0.0326
0.0036
0.0000
-0.0072
-0.0086
-0.0093
-0.0159
-0.0168
-0.0458
-0.0458
-0.1441
-0.0458
-0.0458
-0.0458
-0.0458
0.0063
0.0066
0.0205
0.0084
0.0095
0.0099
0.0105
-1.924
-2.015
-1.973
-1.428
-0.932
-0.657
0.051
9.436
9.117
8.976
4.905
3.353
2.244
1.777
1811.00
863.01
410.24
31.42
4.80
1.53
0.50
-0.0141
-0.0196
-0.0256
-0.0394
-0.0552
-0.0813
-0.1307
0.0200
0.0000
-0.0048
-0.0136
-0.0175
-0.0205
-0.0300
-0.7151
-0.7151
-0.7151
-0.7151
-0.7151
-0.7151
-0.7151
0.0274
0.0371
0.0512
0.0867
0.1212
0.1697
0.2366
-21.717
-17.116
-12.807
-7.571
-5.281
-3.566
-2.252
553.981
320.649
172.804
59.528
29.277
13.849
6.103
9838574.00
1641670.00
235914.80
9132.46
1069.35
112.38
9.97
- 22 -
Table 1 (Panel D):
MINIMA
UK
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
US
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
ASIA
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
EUR
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
NAM
Weekly
Fortnightly
Monthly
Quarterly
Half-yearly
Yearly
2-yearly
Minima (UK, US, ASIA, EUR, NAM)
Real Estate (EPRA)
Stock (DJ)
N
Mean
Max
Min
SD
Skew
Kurt
JB
Mean
Max
Min
SD
Skew
Kurt
JB
773
386
192
64
32
16
8
-0.0090
-0.0123
-0.0159
-0.0209
-0.0251
-0.0300
-0.0352
0.0072
0.0002
-0.0038
-0.0077
-0.0127
-0.0182
-0.0217
-0.0488
-0.0488
-0.0488
-0.0488
-0.0488
-0.0488
-0.0488
0.0074
0.0076
0.0079
0.0087
0.0091
0.0092
0.0095
-1.259
-1.306
-1.157
-1.060
-0.829
-0.592
0.016
5.681
5.495
4.849
4.014
3.213
2.443
1.845
435.77
209.84
70.17
14.72
3.73
1.14
0.44
-0.0094
-0.0126
-0.0158
-0.0211
-0.0256
-0.0299
-0.0338
0.0047
0.0000
-0.0035
-0.0082
-0.0123
-0.0130
-0.0208
-0.0549
-0.0549
-0.0549
-0.0549
-0.0549
-0.0549
-0.0549
0.0083
0.0088
0.0093
0.0105
0.0118
0.0123
0.0113
-1.744
-1.622
-1.499
-1.376
-1.037
-0.732
-0.622
7.396
6.408
5.752
4.659
3.156
2.653
2.564
1014.26
356.05
132.46
27.53
5.76
1.51
0.58
773
386
192
64
32
16
8
-0.0066
-0.0094
-0.0125
-0.0185
-0.0234
-0.0290
-0.0356
0.0079
0.0008
-0.0013
-0.0050
-0.0070
-0.0119
-0.0186
-0.0551
-0.0551
-0.0551
-0.0551
-0.0551
-0.0551
-0.0551
0.0072
0.0080
0.0092
0.0112
0.0125
0.0137
0.0151
-2.296
-2.287
-2.010
-1.437
-1.103
-0.733
-0.219
11.785
10.432
8.069
4.964
3.552
2.328
1.380
3164.87
1224.80
334.87
32.31
6.89
1.73
0.94
-0.0136
-0.0171
-0.0236
-0.0289
-0.0355
-0.0402
-0.0009
-0.0017
-0.0077
-0.0131
-0.0165
-0.0188
-0.0699
-0.0699
-0.0699
-0.0699
-0.0699
-0.0699
0.0096
0.0108
0.0137
0.0164
0.0191
0.0199
-2.096
-2.076
-1.764
-1.282
-0.795
-0.535
10.835
9.592
6.220
3.741
2.213
1.682
1270.13
485.56
60.86
9.50
2.10
0.96
773
386
192
64
32
16
8
-0.0141
-0.0189
-0.0242
-0.0337
-0.0406
-0.0489
-0.0568
0.0134
0.0017
-0.0041
-0.0099
-0.0202
-0.0311
-0.0319
-0.0941
-0.0941
-0.0941
-0.0941
-0.0941
-0.0941
-0.0941
0.0119
0.0123
0.0136
0.0161
0.0173
0.0161
0.0180
-1.879
-1.862
-1.715
-1.348
-1.341
-1.291
-0.911
9.572
8.597
7.529
5.473
4.601
4.933
3.630
1846.02
726.88
258.20
35.70
13.01
6.93
1.24
-0.0125
-0.0169
-0.0212
-0.0290
-0.0357
-0.0441
-0.0494
0.0095
-0.0006
-0.0057
-0.0107
-0.0158
-0.0249
-0.0271
-0.0642
-0.0642
-0.0642
-0.0642
-0.0642
-0.0642
-0.0642
0.0096
0.0099
0.0106
0.0125
0.0130
0.0119
0.0129
-1.488
-1.520
-1.477
-0.924
-0.533
-0.137
0.386
6.725
6.581
5.696
3.417
2.574
2.260
2.116
732.17
354.84
127.97
9.58
1.76
0.42
0.46
773
386
192
64
32
16
8
-0.0056
-0.0079
-0.0105
-0.0144
-0.0181
-0.0231
-0.0273
0.0053
0.0010
-0.0020
-0.0059
-0.0093
-0.0117
-0.0160
-0.0450
-0.0450
-0.0450
-0.0450
-0.0450
-0.0450
-0.0450
0.0054
0.0057
0.0062
0.0076
0.0089
0.0100
0.0117
-2.013
-2.259
-2.267
-2.191
-1.619
-0.994
-0.548
11.136
11.880
11.091
8.463
5.246
3.100
1.726
2654.12
1596.56
688.24
130.81
20.71
2.64
0.94
-0.0119
-0.0160
-0.0200
-0.0260
-0.0298
-0.0340
-0.0381
0.0109
-0.0009
-0.0049
-0.0080
-0.0153
-0.0180
-0.0239
-0.0507
-0.0507
-0.0507
-0.0507
-0.0507
-0.0507
-0.0507
0.0097
0.0099
0.0101
0.0107
0.0114
0.0115
0.0096
-1.271
-1.248
-1.058
-0.786
-0.502
-0.082
0.207
4.899
4.306
3.613
2.567
1.891
1.657
1.984
324.13
127.69
38.83
7.09
2.99
1.22
0.40
773
386
192
64
32
16
8
-0.0099
-0.0138
-0.0181
-0.0255
-0.0308
-0.0368
-0.0407
0.0076
0.0000
-0.0047
-0.0068
-0.0173
-0.0235
-0.0302
-0.0580
-0.0580
-0.0580
-0.0580
-0.0580
-0.0580
-0.0580
0.0084
0.0088
0.0095
0.0104
0.0102
0.0102
0.0103
-1.578
-1.685
-1.519
-1.122
-0.932
-0.706
-0.698
7.501
7.029
5.794
4.154
3.506
2.539
1.973
973.41
443.65
136.27
16.97
4.98
1.47
1.00
-0.0098
-0.0134
-0.0169
-0.0233
-0.0284
-0.0348
-0.0395
0.0042
-0.0007
-0.0016
-0.0083
-0.0127
-0.0164
-0.0192
-0.0711
-0.0711
-0.0711
-0.0711
-0.0711
-0.0711
-0.0711
0.0088
0.0095
0.0108
0.0136
0.0164
0.0192
0.0202
-2.039
-2.116
-2.126
-1.836
-1.359
-0.880
-0.635
11.135
11.141
10.024
6.591
4.007
2.368
1.806
2667.19
1354.01
539.39
70.36
11.20
2.33
1.01
Notes: This table (with four panels) shows the descriptive statistics for daily returns as well as the maxima (Panels A and B) and minima (Panels C and D) of
EPRA and DJ indices over the different selection intervals: weekly, fortnightly, monthly, quarterly, half-yearly, yearly and 2-yearly. The number of observations
(N), the mean and standard deviation (SD), the maximum, the minimum, the raw coefficients of skewness (Skew) and kurtosis (Kurt) as well as the test statistic
for the Jarque-Bara test (JB) are reported.
- 23 -
Table 2
EVT Parameters and Value-at-Risk (VaR) Estimates for EPRA Daily Maximal Returns: Jan 92 to Oct 06
Tail Index
(τ)
Shape
(k)
Scale (α)
Location
(β)
VaR95
VaR99
AUS
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
-0.3857
-0.8954
-0.1049
-0.1980
-0.1740
0.2558
0.6555
2.5924
1.1168
9.5314
5.0494
5.7462
-3.9088
-1.5255
0.0001
0.0003
0
0.000011
0.000004
0.000022
0.0002
0.0085
0.0138
0.0140
0.0182
0.0213
0.0250
0.0290
0.88%
1.78%
1.40%
1.83%
2.14%
2.50%
2.92%
0.92%
3.20%
1.40%
1.83%
2.14%
2.50%
2.93%
HK
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
-0.0979
0.2108
0.2087
-0.0718
-0.2750
-0.2735
0.2004
10.2120
-4.7440
-4.7912
13.9212
3.6364
3.6565
-4.9905
0
0.0003
0.0004
0
0.0006
0.0006
0.0001
0.0194
0.0323
0.0412
0.0475
0.0583
0.0691
0.0776
1.94%
3.30%
4.20%
4.75%
6.10%
7.16%
7.78%
JP
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
0.6018
0.2918
0.2474
-0.1698
-0.5236
-0.3628
-0.5168
-1.6616
-3.4274
-4.0421
5.8894
1.9098
2.7566
1.9351
0.0001
0.00003
0.00004
0.000002
0.0064
0.0051
0.0083
0.0220
0.0304
0.0391
0.0557
0.1111
0.1864
0.1724
SG
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
0.2148
0.2007
0.2042
0.2318
0.2297
-0.1248
0.3323
-4.6554
-4.9820
-4.8962
-4.3143
-4.3526
8.0116
-3.0095
0.0002
0.00003
0.0002
0.0002
0.0004
0
0.00001
FRA
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
0.2546
0.2449
-0.1048
0.5906
0.1940
0.2437
0.6589
-3.9279
-4.0841
9.5457
-1.6933
-5.1545
-4.1028
-1.5177
0.0001
0.00001
0
0.0002
0.0012
0.0001
0.0006
Tail Index
(τ)
Shape
(k)
Scale (α)
Location
(β)
VaR95
VaR99
UK
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
0.9946
4.1623
-0.4678
0.4077
1.0473
1.5864
0.3348
-1.0054
-0.2402
2.1379
-2.4530
-0.9548
-0.6303
-2.9867
0.000004
0.0007
0.0028
0.0003
0.0002
0.0021
0.00001
0.0100
0.0138
0.0098
0.0247
0.0300
0.0392
0.0492
1.00%
1.39%
2.79%
2.53%
3.01%
4.05%
4.92%
1.00%
1.39%
5.54%
2.54%
3.01%
4.05%
4.92%
1.94%
3.32%
4.23%
4.75%
6.37%
7.42%
7.78%
US
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
0.5638
0.5693
0.7067
0.7766
0.5506
0.1916
0.9501
-1.7737
-1.7565
-1.4150
-1.2877
-1.8161
-5.2197
-1.0525
0.0001
0.0001
0.0004
0.0003
0.0002
0.0029
0.0002
0.0079
0.0111
0.0133
0.0180
0.0216
0.1232
0.0306
0.80%
1.13%
1.38%
1.84%
2.18%
12.98%
3.08%
0.80%
1.13%
1.38%
1.84%
2.19%
13.21%
3.08%
2.22%
3.04%
3.92%
5.57%
15.64%
21.36%
23.10%
2.22%
3.05%
3.92%
5.58%
23.38%
24.69%
32.96%
ASIA
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
-0.2315
-0.2421
-0.2081
-0.4253
-0.3446
-0.1906
-0.2315
4.3188
4.1305
4.8052
2.3513
2.9019
5.2456
4.3206
0.0001
0.0001
0.0001
0.0023
0.0017
0.0001
0.0004
0.0149
0.0200
0.0253
0.0314
0.0369
0.0456
0.0509
1.53%
2.07%
2.56%
4.51%
4.58%
4.59%
5.26%
1.56%
2.13%
2.59%
6.43%
5.63%
4.62%
5.42%
0.0230
0.0292
0.0420
0.0521
0.0653
0.0700
0.0901
2.34%
2.93%
4.25%
5.26%
6.61%
7.00%
9.01%
2.35%
2.93%
4.27%
5.28%
6.63%
7.00%
9.01%
EUR
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
0.2616
0.3006
0.6853
0.6219
0.2083
-0.1056
0.9424
-3.8231
-3.3269
-1.4592
-1.6079
-4.8016
9.4719
-1.0611
0.0001
0.0002
0.0002
0.0002
0.0010
0.0000
0.0001
0.0070
0.0090
0.0109
0.0149
0.0363
0.0200
0.0281
0.73%
0.93%
1.12%
1.52%
3.86%
2.00%
2.82%
0.74%
0.94%
1.12%
1.52%
3.93%
2.00%
2.82%
0.0088
0.0120
0.0154
0.0216
0.0629
0.0306
0.0409
0.90%
1.20%
1.54%
2.19%
6.56%
3.08%
4.17%
0.91%
1.20%
1.54%
2.19%
6.65%
3.08%
4.18%
NAM
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
-0.0861
-0.2482
0.9545
-0.2691
0.2279
0.7627
0.5343
11.6178
4.0290
-1.0476
3.7155
-4.3876
-1.3112
-1.8714
0
0.0007
0.0000
0.0009
0.0001
0.0001
0.0001
0.0100
0.0092
0.0186
0.0205
0.0287
0.0315
0.0375
1.00%
1.23%
1.86%
2.45%
2.89%
3.17%
3.76%
1.00%
1.53%
1.86%
2.86%
2.90%
3.17%
3.76%
Notes: This table reports the EVT parameters and VaRs of the EPRA maxima indices fitted by PWM using different block lengths over the 14 year period for the
national real estate indices of Australia (AUS), Hong Kong (HK), Japan (JP), Singapore (SG), France (FRA), United Kingdom (UK) and United States (US) and
the regional real estate indices of Asia (ASIA), Europe (EUR) and North America (NAM).
- 24 -
Table 3
EVT Parameters and Value-at-Risk (VaR) Estimates for EPRA Daily Minimal Returns: January 1992 – October 2006
Tail Index
(τ)
Shape
(k)
Scale (α)
Location
(β)
VaR 95
VaR 99
AUS
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
-0.3037
-1.0169
-0.7073
-0.7534
-0.7657
1.0222
0.2174
3.2922
0.9834
1.4139
1.3273
1.3060
-0.9783
-4.5993
-0.0060
-0.0002
-0.0003
-0.0010
-0.0017
-0.00002
-0.0005
0.0025
-0.0003
-0.0135
-0.0208
-0.0279
-0.0250
-0.0375
-2.66%
-0.34%
-1.67%
-3.17%
-4.75%
-2.50%
-3.86%
-5.78%
-1.71%
-2.46%
-6.12%
-10.17%
-2.50%
-3.89%
HK
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
-0.1081
-0.0614
-0.1218
-0.2519
-0.2946
-0.4372
-0.4114
9.2473
16.2990
8.2122
3.9693
3.3941
2.2872
2.4310
0
0
0
-0.0006
-0.0016
-0.0083
-0.0081
-0.0176
-0.0244
-0.0311
-0.0451
-0.0555
-0.0605
-0.0789
-1.76%
-2.44%
-3.11%
-4.76%
-6.29%
-11.13%
-12.60%
JP
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
0.2559
0.2063
0.2306
0.2467
-0.2286
-0.3937
-0.3905
-3.9080
-4.8473
-4.3365
-4.0537
4.3746
2.5403
2.5610
-0.00004
-0.0001
-0.0003
-0.0001
-0.0003
-0.0040
-0.0052
-0.0212
-0.0289
-0.0364
-0.0433
-0.0514
-0.0607
-0.0710
SG
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
0.2044
0.2133
0.2374
0.2113
0.2400
0.2113
0.2369
-4.8922
-4.6885
-4.2131
-4.7335
-4.1671
-4.7329
-4.2215
-0.0001
-0.0002
-0.0001
-0.0004
-0.0001
-0.0006
-0.0002
FRA
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
0.2743
0.6034
-0.1821
0.9377
0.1928
0.5285
0.7259
-3.6461
-1.6573
5.4920
-1.0664
-5.1866
-1.8922
-1.3777
-0.0002
-0.0001
-0.00004
-0.0001
-0.0036
-0.0002
-0.0009
Tail Index
(τ)
Shape
(k)
Scale (α)
Location
(β)
VaR
95
VaR
99
UK
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
1.1126
1.7374
0.4558
0.2623
0.2204
0.3207
0.2373
-0.8988
-0.5756
-2.1941
-3.8129
-4.5379
-3.1185
-4.2149
-0.0001
-0.0006
-0.00005
-0.00002
-0.0007
-0.00005
-0.0018
-0.0090
-0.0119
-0.0160
-0.0210
-0.0337
-0.0301
-0.0490
-0.90%
-1.22%
-1.61%
-2.10%
-3.53%
-3.02%
-5.29%
-0.90%
-1.22%
-1.61%
-2.11%
-3.58%
-3.02%
-5.41%
-1.76%
-2.44%
-3.11%
-5.01%
-7.07%
-18.39%
-18.97%
US
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
0.7507
0.8731
-0.2608
0.2036
0.1971
0.8440
0.5124
-1.3320
-1.1453
3.8341
-4.9115
-5.0742
-1.1848
-1.9515
-0.0002
-0.0001
-0.0017
-0.0005
-0.0010
-0.0005
-0.0002
-0.0070
-0.0090
-0.0135
-0.0282
-0.0490
-0.0291
-0.0357
-0.73%
-0.91%
-2.09%
-2.92%
-5.11%
-2.95%
-3.60%
-0.73%
-0.91%
-2.82%
-2.96%
-5.19%
-2.96%
-3.60%
-2.13%
-2.91%
-3.70%
-4.35%
-5.25%
-8.34%
-9.99%
-2.13%
-2.92%
-3.72%
-4.35%
-5.35%
-11.30%
-13.73%
ASIA
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
-0.1934
-0.1751
-0.2865
-0.3680
-0.2029
-0.3116
-0.0772
5.1712
5.7113
3.4909
2.7175
4.9284
3.2097
12.9599
-0.00003
-0.00001
-0.0005
-0.0019
-0.0001
-0.0014
0
-0.0141
-0.0189
-0.0245
-0.0326
-0.0406
-0.0502
-0.0568
-1.42%
-1.89%
-2.66%
-4.26%
-4.10%
-5.72%
-5.68%
-1.43%
-1.89%
-2.89%
-5.51%
-4.13%
-6.48%
-5.68%
-0.0209
-0.0288
-0.0322
-0.0523
-0.0565
-0.0774
-0.0787
-2.12%
-2.93%
-3.24%
-5.32%
-5.67%
-7.88%
-7.92%
-2.13%
-2.95%
-3.24%
-5.35%
-5.68%
-7.93%
-7.93%
EUR
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
0.4296
0.2338
0.3239
0.9098
0.6056
0.2799
0.2610
-2.3277
-4.2766
-3.0871
-1.0991
-1.6512
-3.5728
-3.8317
-0.0001
-0.00003
-0.00001
-0.0001
-0.0004
-0.00002
-0.0009
-0.0057
-0.0082
-0.0105
-0.0144
-0.0182
-0.0201
-0.0312
-0.58%
-0.82%
-1.05%
-1.45%
-1.87%
-2.01%
-3.30%
-0.58%
-0.83%
-1.05%
-1.45%
-1.88%
-2.01%
-3.35%
-0.0081
-0.0100
-0.0100
-0.0186
-0.1380
-0.0275
-0.0328
-0.84%
-1.01%
-1.02%
-1.87%
-14.62%
-2.79%
-3.38%
-0.85%
-1.01%
-1.03%
-1.87%
-14.91%
-2.79%
-3.39%
NAM
Weekly
Fortnightly
Monthly
Quarterly
Half Yearly
Yearly
2 Yearly
0.5159
0.7338
0.2228
0.9560
0.2048
0.6100
0.9615
-1.9382
-1.3628
-4.4874
-1.0460
-4.8837
-1.6395
-1.0400
-0.00004
-0.0002
-0.0015
-0.00005
-0.0001
-0.0002
-0.0001
-0.0099
-0.0138
-0.0344
-0.0255
-0.0312
-0.0369
-0.0407
-0.99%
-1.40%
-3.76%
-2.55%
-3.13%
-3.71%
-4.07%
-0.99%
-1.41%
-3.86%
-2.55%
-3.14%
-3.71%
-4.07%
Notes: This table presents the EVT parameters and VaRs of the EPRA minima indices fitted by PWM using different block lengths over the 14 year period for the
national real estate indices of Australia (AUS), Hong Kong (HK), Japan (JP), Singapore (SG), France (FRA), United Kingdom (UK) and United States (US) and
the regional real estate indices of Asia (ASIA), Europe (EUR) and North America (NAM).
- 25 -
Table 4
Daily VaR Backtesting : Exceedances for Return Series: Jan 92 – Oct 06
AUS
HK
JP
NVar95
NVar99
EVar95
EVar99
118
114
3
0
108
103
8
8
102
97
14
14
NVar95
NVar99
EVar95
EVar99
114
109
8
8
103
96
4
4
97
92
8
8
NVar95
NVar99
EVar95
EVar99
102
98
64
2
102
98
16
16
109
104
13
13
NVar95
NVar99
EVar95
EVar99
98
94
3
1
98
91
9
9
104
98
7
7
Real estate markets (EPRA)
SG FRA UK US ASIA EUR NAM ALL AUS HK JP
Panel A: Maxima returns (block length: 10 days)
106 117 117 120 116
125
121 1149 118 112 107
101 113 112 116 111
121
117 1106 114 107 102
13
14
14
14
14
11
23
128
9
16
14
13
14
14
14
13
11
14
115
5
16
14
Panel B: Maxima returns (block length: 20 days)
101 113 112 116 111
121
117 1106 114 107 102
94
107 106 109 106
116
111 1047 109
99
97
5
6
2
8
7
7
8
64
0
8
1
5
6
0
8
7
7
8
62
0
8
0
Panel C: Minima returns (block length: 10 days)
106 100 103 96
107
99
101 1026 100
98 107
101
96
100 81
104
94
97
983
96
92 103
12
15
16
17
15
14
14
196
13
16
16
12
15
15
17
15
14
14
134
11
16
16
Panel D: Minima returns (block length: 20 days)
101
96
100 91
104
94
97
983
96
92 103
95
91
94
85
99
88
92
928
91
85
97
9
14
8
2
7
8
1
69
6
9
8
9
14
8
1
6
8
1
64
5
9
8
SG
Stock markets (DJ)
FRA UK US ASIA
EUR
NAM
ALL
110
105
14
14
114
109
14
14
117
113
14
14
116
111
14
13
115
111
13
13
120
116
15
14
117
112
14
14
1146
1101
137
132
105
98
7
7
109
101
8
8
113
106
10
10
111
105
8
8
111
104
1
0
116
111
9
9
112
106
8
8
1101
1036
61
59
104
99
15
15
98
94
13
13
101
97
16
16
99
95
17
17
111
106
14
14
104
99
16
16
98
94
17
17
1020
974
152
149
99
91
9
9
94
86
6
6
97
92
11
11
95
88
10
10
106
100
8
8
99
94
10
10
94
88
10
10
974
913
88
86
Notes: This table compares the number of excceedances (i.e. actual return> VaR) between VaRs derived using the EVT(EVaR95 and EVaR99) and VaRs based
on normal distribution (NVar95 and NVaR99) using fortnightly (10 days) and monthly (20 days) blocks for the upper and lower tail of the EPRA and DJ indices
at the 95% and 99% confidence levels.
- 26 -
Table 5
Country
AUS
HK
JP
SG
FRA
UK
US
ASIA
EUR
NAM
Extremal Index of Return Series: Jan 92 – Oct 06
Tail
Maxima
Minima
Maxima
Minima
Maxima
Minima
Maxima
Minima
Maxima
Minima
Maxima
Minima
Maxima
Minima
Maxima
Minima
Maxima
Minima
Maxima
Minima
Real estate markets (EPRA)
VaR95
VaR99
Fortnightly
Monthly
Fortnightly
Monthly
0.89
0.89
0.98
0.89
0.90
0.86
0.90
0.91
0.84
0.78
0.84
0.78
0.70
0.59
0.70
0.59
0.80
0.70
0.80
0.70
0.80
0.70
0.80
0.70
0.73
0.67
0.73
0.67
0.74
0.59
0.74
0.59
0.86
0.83
0.86
0.83
0.85
0.79
0.85
0.76
0.79
0.81
0.79
0.91
0.79
0.80
0.79
0.80
0.80
0.74
0.80
0.77
0.69
0.70
0.69
0.74
0.56
0.48
0.54
0.45
0.60
0.42
0.60
0.38
0.82
0.73
0.82
0.73
0.81
0.73
0.81
0.73
0.91
0.89
0.94
0.89
0.84
0.91
0.84
0.89
Stock Markets (DJ)
VaR95
Fortnightly
Monthly
0.93
0.97
0.81
0.74
0.83
0.65
0.75
0.57
0.90
0.94
0.78
0.70
0.75
0.64
0.66
0.61
0.83
0.71
0.76
0.61
0.78
0.58
0.69
0.58
0.82
0.67
0.72
0.57
0.88
0.98
0.86
0.68
0.60
0.63
0.65
0.58
0.81
0.67
0.72
0.56
VaR99
Fortnightly
Monthly
0.93
0.94
0.81
0.72
0.83
0.65
0.75
0.58
0.90
0.98
0.78
0.70
0.75
0.64
0.66
0.61
0.83
0.71
0.76
0.62
0.78
0.58
0.69
0.58
0.81
0.68
0.72
0.58
0.88
0.94
0.86
0.66
0.61
0.63
0.65
0.58
0.81
0.67
0.72
0.54
Notes: This table shows the extremal index θ for the lower and upper tails of each real estate (EPRA) and equity (DJ) returns series for countries consisting of
Australia (AUS), Hong Kong (HK), Japan (JP), Singapore (SG), France (FRA), United Kingdom (UK) and United States (US) and the regions of Asia (ASIA),
Europe (EUR) and North America (NAM).The VaRs at the 95% and 99% confidence intervals, computed using EVT, are used as thresholds. The extremal index
values presented represent average estimate over all values of Nu.
- 27 -
Table 6 Frequencies of Large Positive and Negative Daily Returns during the Asian Financial Crisis Period (July 1997 – December 1998)
< μ −σ
Expected
AUS
HK
JP
SG
FR
UK
US
ASIA
EUR
NAM
ALL
227
50
44
57
41
18
59
31
52
46
40
438
> μ +σ
Expected
AUS
HK
JP
SG
FR
UK
US
ASIA
EUR
NAM
ALL
227
53
34
40
42
53
56
35
44
39
44
440
Panel A: Large negative returns
Real estate markets (EPRA indices)
< μ − 2σ
32
8
7
12
7
6
9
10
7
14
11
91
< μ − 3σ
< μ − 4σ
< μ −σ
2
0
227
1
1
55
3
1
47
2
0
56
2
0
46
2
1
56
2
1
52
7
5
41
3
0
48
3
1
50
7
3
43
32
13
494
Panel B: Large positive returns
Real estate markets (EPRA indices)
> μ + 2σ
32
10
13
11
14
12
7
8
14
6
7
102
> μ + 3σ
2
1
5
6
5
2
3
5
5
2
1
35
> μ + 4σ
0
1
1
1
2
1
2
1
1
1
0
11
> μ +σ
227
50
39
48
42
60
52
43
52
55
43
484
Equity markets (DJ indices)
< μ − 2σ
32
6
7
10
10
13
14
10
9
14
10
103
< μ − 3σ
2
1
3
3
2
0
0
4
0
5
3
21
Equity markets (DJ indices)
> μ + 2σ
32
7
12
12
10
11
8
8
14
5
8
95
> μ + 3σ
2
1
4
3
5
1
3
3
3
2
3
28
< μ − 4σ
0
1
1
0
1
0
0
2
0
0
2
7
> μ + 4σ
0
1
2
1
2
1
0
0
1
1
0
9
Notes: This table includes the total number of daily return which exceeded four thresholds during the Asian financial crisis period (Jul 97 – Dec 98) for the
EPRA (real estate market) and DJ (stock market) indices. The thresholds are defined as: Panel A: the mean ( μ ) minus one, two, three and four standard
deviation ( σ ); Panel B: the mean ( μ ) plus one, two, three and four standard deviation ( σ ). The table also includes the expected frequency under the
assumption that the daily returns are normally distributed.
- 28 -
Figure 1
Quantile-quantile (QQ) plot of real estate (EPRA) monthly minima returns against the normal distribution
Theoretical Quantile-Quantile
4
4
2
2
Normal Quantile
Normal Quantile
Theoretical Quantile-Quantile
0
-2
-4
-2
-4
-6
-6
-8
-.06
0
-.05
-.04
-.03
-.02
-.01
-8
-.16
.00
-.12
-.08
-.04
.00
Minima returns (Hong Kong)
Minima returns (Australia)
Theoretical Quantile-Quantile
Theoretical Quantile-Quantile
3
4
2
2
Normal Quantile
Normal Quantile
1
0
-1
-2
0
-2
-4
-3
-6
-4
-5
-.12
-.10
-.08
-.06
-.04
-.02
-8
-.16
.00
Minima returns (Japan)
2
2
1
1
0
-1
-2
-2
-4
-4
-.02
-.01
.00
-1
-3
-.03
-.04
0
-3
-.04
-.08
Theoretical Quantile-Quantile
3
Normal Quantile
Normal Quantile
Theoretical Quantile-Quantile
3
-5
-.05
-.12
Minima returns (Singapore)
.00
-5
-.05
Minima returns (France)
-.04
-.03
-.02
Minima returns (UK)
- 29 -
-.01
.00
Theoretical Quantile-Quantile
3
3
2
2
1
1
Normal Quantile
Norm al Q uantile
Theoretical Quantile-Quantile
0
-1
-2
-3
0
-1
-2
-3
-4
-4
-5
-5
-6
-.06
-.05
-.04
-.03
-.02
-.01
-6
-.10
.00
-.08
-.06
-.04
-.02
Minima returns (US)
Minima returns (Asia)
Theoretical Quantile-Quantile
Theoretical Quantile-Quantile
4
3
2
2
.00
Normal Quantile
Norm al Q uantile
1
0
-2
-4
0
-1
-2
-3
-6
-8
-.05
-4
-.04
-.03
-.02
-.01
.00
-5
-.06
Minima returns (Europe)
-.05
-.04
-.03
-.02
-.01
Minima returns (North America)
- 30 -
.00
Figure 2
Estimated extreme return levels and actual return levels from January 1992 to October 2006
Notes: This figure plots the estimated extreme levels at the 95 and 99 percentiles (VaR maxima and minima) against the actual returns for the US EPRA index.
- 31 -
Figure 3
VaR and standard deviation measures: pre-, during- and post-Asian financial
crisis
The entire study period is divided into three shorter sub-periods: (a) before Asian financial crisis (AFC): Jan92-Jun97, (b)
during AFC: Jul97-Dec98 and (c) After AFC: Jan99-Oct06. This figure compares the extreme VAR95 and the standard
deviation measures for (a) EPRA maxima (b) EPRA minima (c) DJ maxima and (d) DJ minima, before, during and after
the AFC.
Panel A:
EPRA (Real Estate) Maxima Returns
EPRA Maxima VaR95 (N=10) for Period Jan 1992 to Oct 2006
9.00%
8.00%
Maxima VaR
7.00%
6.00%
5.00%
4.00%
3.00%
2.00%
1.00%
0.00%
AUS
HK
JP
SG
FRA
UK
US
ASIA
EUR
NAM
ASIA
EUR
NAM
EUR
NAM
EPRA M axima VaR95 (N=20) for Pe riod Jan 1992 to Oct 2006
Before AFC
During AFC
After AFC
12.00%
Maxima VaR
10.00%
8.00%
6.00%
4.00%
2.00%
0.00%
AUS
HK
JP
SG
FRA
Before AFC
UK
During AFC
US
After AFC
Standard Deviation
EPRA Maxima Standard Deviation for Period Jan 1992 to Oct 2006
4.50%
4.00%
3.50%
3.00%
2.50%
2.00%
1.50%
1.00%
0.50%
0.00%
AUS
HK
JP
SG
Bef ore AFC
FRA
UK
During AFC
- 32 -
US
Af ter AFC
ASIA
Panel B:
EPRA (Real Estate) Minima Returns
EPRA Minima VaR95 (N=10) for Period Jan 1992 to Oct 2006
AUS
HK
JP
SG
FRA
UK
US
ASIA
EUR
NAM
EUR
NAM
EUR
NAM
0.00%
Minima VaR
-1.00%
-2.00%
-3.00%
-4.00%
-5.00%
-6.00%
EPRA M inima VaR95 (N=20) for Period Jan 1992 to Oct 2006
Before AFC During AFC After AFC
AUS
HK
JP
SG
FRA
UK
US
ASIA
0.00%
Minima VaR
-1.00%
-2.00%
-3.00%
-4.00%
-5.00%
-6.00%
-7.00%
EPRA Minima StandardBefore
Deviation
Period
1992
AFC for
During
AFC Jan
After
AFCto Oct 2006
AUS
HK
JP
SG
FRA
UK
US
0.00%
Standard Deviation
-0.50%
-1.00%
-1.50%
-2.00%
-2.50%
-3.00%
-3.50%
-4.00%
-4.50%
Before AFC
During AFC
- 33 -
After AFC
ASIA
Panel C:
Dow Jones (DJ) (Stock Market) Maxima Returns
DOW Maxima VaR95 (N=10) for Period Jan 1992 to Oct 2006
8.00%
7.00%
Maxima VaR
6.00%
5.00%
4.00%
3.00%
2.00%
1.00%
0.00%
AUS
HK
JP
SG
FRA
UK
US
ASIA
EUR
NAM
EUR
NAM
EUR
NAM
DOW Maxima VaR95Before
(N=20)
for Period
Jan 1992
Oct 2006
AFC
During AFC
After to
AFC
18.00%
16.00%
Maxima VaR
14.00%
12.00%
10.00%
8.00%
6.00%
4.00%
2.00%
0.00%
AUS
HK
JP
SG
FRA
UK
US
ASIA
DOW Maxima StandardBefore
Deviation
Period
1992
to Oct 2006
AFC for
During
AFCJanAfter
AFC
3.00%
Standard Deviation
2.50%
2.00%
1.50%
1.00%
0.50%
0.00%
AUS
HK
JP
SG
FRA
Before AFC
UK
During AFC
- 34 -
US
After AFC
ASIA
Panel D:
Dow Jones (DJ) (Stock Market) Minima Returns
DOW Minima VaR95 (N=10) for Period Jan 1992 to Oct 2006
AUS
HK
JP
SG
FRA
UK
US
ASIA
EUR
NAM
EUR
NAM
EUR
NAM
0.00%
Minima VaR
-1.00%
-2.00%
-3.00%
-4.00%
-5.00%
-6.00%
DOW Minima VaR95Before
(N=20)
for Period
Jan 1992
Oct 2006
AFC
During AFC
Afterto
AFC
AUS
HK
JP
SG
FRA
UK
US
ASIA
0.00%
-2.00%
Minima VaR
-4.00%
-6.00%
-8.00%
-10.00%
-12.00%
-14.00%
-16.00%
DOW Minima Standard Before
Deviation
Period
1992
to Oct 2006
AFC for
During
AFCJanAfter
AFC
AUS
HK
JP
SG
FRA
UK
US
0.00%
Standard Deviation
-0.50%
-1.00%
-1.50%
-2.00%
-2.50%
-3.00%
Before AFC
During AFC
- 35 -
After AFC
ASIA