THE DYNAMICS OF REAL ESTATE COMPANY DISCOUNTS IN ASIAN MARKETS
Kim Hiang LIOW and Yeou Chung KOH, Department of Real Estate, National University of Singapore
Corresponding Author
Dr. Kim Hiang LIOW
Associate Professor
Department of Real Estate
National University of Singapore
4 Architecture Drive
Singapore 117566
Tel: (65)68743420
Fax: (65)67748684
Email: rstlkh@nus.edu.sg
25 May 2005
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THE DYNAMICS OF REAL ESTATE COMPANY DISCOUNTS IN ASIAN MARKETS
Abstract
There has been very little empirical research on to net asset value discounts / premium (abbreviated as NAVDISC) in
Asian real estate markets. Focusing on four major issues of NAVDISC in five major Asian markets that include Japan,
Hong Kong, Singapore, Malaysia and Philippines and the UK, we find that NAVDISC performance varies across the six
real estate markets over the last decade. The proportion of real estate firms that are struck by a NAV “discount”
increases from 33.8% in the pre-crisis period to 83.1% in the millennium period for the five Asian markets as a whole.
For all national markets, Individual real estate firms’ NAVDISC performances are closely correlated. In addition, at least
one common NAVDISC factor prevails in the five Asian and the UK markets. There are also additional common
NAVDISC factors between some pairs of real estate markets. We find that company financial factors have only a
moderate impact on the NAVDISC performance of Asian real estate companies. In the long run, none of the NAVDISC
series exhibits cointegration with their respective local stock market and real estate stock market index series
indicating absence of these two systematic components in the NAVDISC series for these countries. In the short term,
this relationship is mainly the one-way information flow from some local indexes to their respective NAVDISC series.
Finally, this study reinforces the increased potential importance of Asian securitized real estate in an investment
portfolio for US-based and European investors.
1.
INTRODUCTION
There is some evidence regarding the presence of discount to net asset value (NAV) of real estate
companies in the literature. NAV in a property context represents the underlying value of the real estate assets of a
property company. This value is generally similar to the direct value of underlying real estate values less liabilities. The
discount or premium of real estate stocks (NAVDISC) is calculated by taking the difference between the current stock
price (P) and the NAV and dividing it by the NAV. The higher the NAV to the P results in the real estate stock trading at
a discount (i.e. NAVDISC is a discount); the lower the NAV to the P results in the real estate stock trading at a
premium (i.e. NAVDISC is a premium). Given that global real estate over the coming decade is expected to become an
increasingly important component of institutional investors’ portfolios, Steinert and Crowe (2001) expect the current
discount to NAV of securitized real estate to narrow and the greatest contraction is expected to occur in Europe, UK
and the US. Interest by academia in tracking the NAVDISC trend in international securitized real estate markets and
searching for likely causes of real estate company discounts has been on the rise. Our study is one such attempt. As
there are very limited studies investigating the real estate company accounts in Asian-Pacific markets, consequently in
this paper, we focus on the behavior of NAVDISC in five Asian markets and the UK over the period July 1994 to July
2004. Our study covers four objectives:
(a)
To examine the time-series and cross-sectional performance of average monthly NAVDISC in real estate
companies There are four sub-periods involved: (i) the pre-Asian financial crisis from July 1994 to June 1997
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(36 months); which is characterized by strong growth and high asset inflation in many Asian economies (ii)
the Asian financial crisis period from July 1997 to August 1998 (14 months); (iii) the post-crisis period from
September 1998 to December 2000 (28 months); which reflects the recessionary and recovery stages of the
markets following the financial crisis; and (iv) the millennium period from January 2001 to July 2004. The
intent is to discern the degree of fluctuation in NAVDISC and their adjustments between successive periods.
(b)
To investigate the correlation and degree of linkages in NAVDISC performance across the different markets
using a combination of factor analysis and canonical correlation techniques. In respond to the increasing
trend in globalization of real estate markets, we search for the presence of common factor(s) in the
NAVDISC series across the five major Asian real estate stock markets and to further investigate whether any
of the Asian common factor(s) are correlated with those of the UK factor(s). The results will thus provide
investors with additional insights into the presence or absence of linkages across the various real estate
markets and help them make better decisions in portfolio diversification and asset allocation.
(b)
To understand key financial determinants of NAVDISC in real estate companies. We focus on five companyspecific financial factors: size, return on equity, borrowing ratio, systematic risk and total risk. The
investigations are conducted for each market and across all markets using Pearson correlation and multipleregression analyzes. If the results show that NAVDISC performances are closely associated with any
financial factor(s) or any combination of them rather than purely for idiosyncratic reasons, then investors will
need to pay more attention to those important financial factors that influence the real estate company
discounts.
(c)
To assess whether NAVDISC performances are significantly affected by the ‘noise trader’ or ‘investor
sentiment’ hypothesis. Following the literature on Closed End Funds (CEFs), we examine the pattern of
cointegration and causality between the NAVDISC series and market movements that are represented by the
respective local stock market and real estate stock market indexes. The intent is to detect any evidence of a
general systematic relationship between each market’s NAVDISC and domestic market movements in the
long run and their causal relationships in the short-term.
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This study therefore contributes to the NAVDISC literature in at least three ways. We extend our empirical
investigation to cover five major Asian real estate markets and over an extended period that includes both the crisis
and recovery periods. This wider coverage of Asian markets and time period is in line with the growing importance of
Asian securitized real estate markets in the global context in the millennium period. Second, we investigate the
presence or absence of any common factor(s) in NAVDISC across the major real estate markets and detect further
evidence of linkages through these common factor(s). Such work, which has not done before, contributes to better
understanding of international real estate market linkages and interdependence. Third, unlike earlier studies, we
search for possible explanations of NAVDISC from both the “rational” (represented by company-specific financial
factors) and “investor sentiment” (represented by domestic market movements) perspectives. The findings will enable
investors assess the utility of the two approaches in explaining real estate company discounts. Our cross-market study
thus provides a good opportunity for international investors to understand and compare the dynamic behavior of real
estate company discounts across the major Asian real estate markets and the potential portfolio implication of investing
in real estate stocks. Finally, the results of this study should be of great interest to US and European investors who
wish to invest in Asian public real estate markets. Together with the usual risk and return analyses, the time series
NAVDISC dynamics of the individual markets and their cross-market relationships over time will enable these investors
gain additional understanding into the potential benefits and pitfalls of portfolio diversification that includes the Asian
real estate markets.
To provide a background for this study, Section 2 contains a review of key studies on NAVDISC in closedend funds and real estate companies. Section 3 explains the sample and data characteristics. The time-series and
cross-sectional performance of NAVDISC are discussed in Section 4. Section 5 investigates the presence of common
factor(s) in NAVDISC and further explores whether any of the common factors are linked across the Asian and the UK
markets. Sections 6 and 7 examine the significance of company-specific financial factors and “investor sentiment”
hypothesis on the NAVDISC performance respectively. Section 8 contains concludes the study.
2.
RELATED LITERATURE
This section provides a brief review on some prior studies addressing real estate company discounts and
CEF valuation discounts. Adam and Venmore-Rowland (1989) have pointed out that real estate company valuation is
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generally related to the value of the underlying properties and less to earnings to dividends. Hence real estate
companies represent a special case of CEFs except that the true NAV is much harder to ascertain. In addition, that
real estate companies tend to trade at a discount to their net asset value has been well documented in the literature.
Adams and Baum (1989) discuss a number of potential factors that can cause the discount/premium in the UK property
investment companies: management qualities, taxation, liquidity, risk (which includes gearing, volatility and divisibility),
uncertainty as to true NAV, take-over threat and market inefficiencies. However, they do not provide empirical evidence
of these “unpriced” factors.
A long-term equilibrium NAVDISC of 25% for the UK property companies is found by Barkham and Ward
(1999). They also examine possible causes of NAVDISC in property companies and find that four company-specific
factors (contingent capital gains tax, size, holding of trading stocks and historical monthly returns) are able to explain
about 15% of the cross-sectional variance in property company discounts. They further find that the sector average
discount is equally influential in explaining the NAVDISC in property companies. Finally, they also find some support
for the hypothesis that discounts result from the interaction of noise traders and rational investors.
In the Asian context, a study by Liow (1996) examines NAVDISC of Singapore property companies over
1980 to 1994. He finds that the share prices of many Singapore property companies during the study period are above
their NAV. Consequently the 15-year average sector rating is approximately 64% premium. However, the NAVDISC
varies from one company to another and the average rating for the sector changes over the period. Furthermore there
is an inverse relationship between the size of average valuation discount of property stocks and direct property returns
even in the presence of a “pure” real estate factor in both the public and private real estate markets.
Liow (1998) updates his 1996 study to cover the Asian financial crisis period. He examines NAVDISC
performance of 14 major Singapore property companies from January 1990 to June 1998. Overall, he finds that (a) the
NAVDISC performance varies widely from one company to another and the sector average discount varies over time widening from a premium of 6.2% (1990) to 164% discount (1998) in light of Asian Financial Crisis and weakened local
real estate market. Moreover, the sector NAV “discount” happens 55% of the time (i.e. 56 of 102 months); and (b) 9 of
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14 companies report an average “discount” between 3% and 122%, with six of them having significantly higher
“discount” than the sector average discount over the full period.
In a 3rd study on the same subject matter, Liow (2003) investigates the relationship between Singapore
property company stock prices and their NAV from a mean reversion perspective. He finds that there is absence of a
long-term linear relationship between the two series. However, there is some evidence of mean reversion behavior of
Singapore property stock prices toward the property companies’ NAV, both at individual company level and in the
sector as whole. Additionally, his results also reveal that NAV is significant in capturing the dynamics of the changes in
property stock prices. Hence NAV is relevant in property company valuation.
In the USA, Capozza and Lee (1995) examine the variation in discount / premium by property type on 75
equity REITs (the US equivalent of real estate stocks). They also assess causes of discount /premium including
differences in leverage, concentration (sector and location), administrative expenses and yield. They find that small
REITs are heavily discounted than larger REITs. Furthermore, retail REITs have the lowest discount with high industry
concentration and low administrative expenses. Gentry et al. (2004) find that REIT stock prices deviate substantially
from Green Street NAV from January 1990 through December 2003.1 In addition, they find large positive excess
returns to a strategy of buying stocks that trade at a discount to NAV, and shorting stocks trading at a premium to NAV.
Also, NAV premiums are positively related to recent and future NAV growth.
To the best of our knowledge, only two studies have extended this NAVDISC issue into an international
context. Bond and Shilling (2004) examine the variation in the NAVDISC performance across 50 European public real
estate companies (of which 29 are UK property companies) from March 1998 to May 2003. They find that 54% of the
companies (27 companies) trade at discounts to NAV and this proportion increase substantially as at May 2003 to 88%
(44 of 50). They are also significant variations in the NAVDISC performance across the sample countries. Another
important aspect of the study is to examine the impact of company risk (total, systematic and unsystematic), company
financial indicators (size, return on enterprise, value, gearing and interest cover), economic focus and country effect on
the NAVDISC performance. Overall, they find that company risk is the most important determinant of the NAVDISC
performance. There is also some evidence of a positive (and statistically significant) influence for the economic focus
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factor on NAVDISC, suggesting some benefits might result from a diversification strategy. Moreover, real estate
companies with high financial gearing have significantly higher NAVDISC. Finally, other company financial factors
appear to have no significant impact on NAVDISC of European property companies..
Employing panel unit root test, heterogeneous panel cointegration test and dynamic panel error-correction on
real estate company discounts in eight Asian-Pacific markets, Liow and Li (2005) find that long-run NAVDISC persist in
individual Asian-Pacific markets and the regional market. All discount series display mean-reversion and that the
respective disequilibrium errors fluctuate around the mean values. Moreover, the authors find that NAV is an important
factor that statistically explains the price variations in real estate stock price regardless of their speed of mean
reversion in NAVDISC.
In the finance literature, it has been documented that CEFs and investment trusts usually sell at a discount to
NAV. Moreover, there are additional research studies in the CEF literature that aim to understand the main causes of
NAVDISC. Two popular approaches have appeared in the literature. First, the “rational” approach seeks to link the
NAVDISC performance to company-specific factors such as management quality, tax liability and the type of stocks
held by the fund (Malkiel, 1995; Lofthhouse, 1999). For example, Malkiel (1975) suggests that unrealized capital
appreciation in CEFs is a potential liability to shareholders. Second, the “noise trader” or “investor sentiment”
approaches to discounts of De Long et al. (1990) and Lee et al. (1990), on the other hand, postulates that the
operation of noise traders provides an additional risk that is reflected in the value and returns of stocks, and that stock
prices will be settled below NAVs in equilibrium. A more recent study by Bennett (2002) shows evidence of a general
systematic relationship between CEF’s discount / premium and domestic market movements to support the presence
of “noise” induced sentiment trading by the UK institutional CEF shareholders. Finally, Gasbarro et al. (2003) find that
CEF discounts vary widely over time due to changes in share prices, NAV or both. In addition, they also find that bond
and equity CEF display stationary time-series properties and detect statistically significant error correction that
quantifies the speed of mean reversion.
3.
RESEARCH DATA
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The research sample consists of 183 real estate companies that are publicly traded in the stock markets of
five Asian countries (Hong Kong, Japan, Singapore, Malaysia and Philippines) and the UK which is included to provide
a useful comparison. The choice of this Asian sample is expected to be of significant interest to the US and other
international investors and policy makers. The ten-year period of study is from July 1994 to July 2004 that covers the
boom and bust phases of the most recent real estate market cycle in Asia. Many of these companies are investment
with some undertaking property development and trading.2 Real estate is an important asset in these economies and it
also plays a very crucial role in individuals’ investment portfolio. Japan is a significantly developed economy in Asia
and also a world industrialized economy. There has been a long history of Japanese real estate companies. Other
markets like Hong Kong, Malaysia and Singapore are major economic forces in the region. Also Hong Kong and
Singapore have track record of listed real estate companies that play a relative important role in the general stock
indexes. Other Asian public real estate markets such as Malaysia and the Philippines are developing and still need to
take a longer time to become established. The UK property market plays a key role in the European property markets.
Of the major institutional property markets, the global share of Japan, HK/China and the UK are about 12%, 9% and
8% respectively (UBS Warburg, 2003). Table 1 provides additional information on the key macroeconomic and stock
market indicators for the six markets. Finally, REITs have been successfully introduced in Japan and Singapore; HK
will likely to have its first REIT introduced in 2004-05. With bullish sentiment about real estate investment opportunities
in Asia, our study reinforces the increased potential importance of Asian listed real estate in investment portfolios for
both local and international investors.
(Table 1 here)
In order to increase the sample size, a company will be included in the study if it has at least eight years (i.e.
96 monthly observations) of full-period NAV and stock price (P) data from the Datastream International. The final
number of real estate companies derived for each market is thus: 14 (Singapore), 53 (HK), 45 (Malaysia), 28 (Japan),
14 (the Philippines) and 29 (the UK). Table 2 provides further breakdown of the sample companies by market and
study period. These 183 real estate companies pass the Augmented Dickey-Fuller (ADF) test of I(1).3 A monthly
database is created for the 183 real estate firms as well as one averaged series for P and NAV of all six markets. The
variable NAV is defined as net tangible assets per share calculated by dividing shareholders’ equity less intangible
assets and preference capital by the number of ordinary shares. Barkham and Ward (1999) argue that property
companies’ NAV, derived from contemporaneous estimates of the market value of property assets, provide acceptable
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proxies for true NAVs. This is because UK property companies have their investment properties appraised annually by
independent professional valuers. Furthermore, the use of tangible (balance sheet) value as a proxy for the appraised
NAV can be justified in the context of the local institutional accounting framework that is broadly based on historical
cost convention modified by revaluation of fixed assets and investment properties. Unlike the USA where its real estate
operating companies practice strictly historical cost accounting, all five Asian real estate markets, as in the UK and the
Netherlands, do not have a strict historical cost system but one in which assets may be revalued. As such, real estate
companies in these countries use a mixture of historical cost and current value accounting, showing most fixed assets
at costs but revaluing investment properties. Nevertheless, it is a normal business policy for real estate companies to
revalue their properties annually in order to keep investors well informed of the market values of their property portfolio.
Hence, the NAV metrics employed in the study, as a proxy for appraised NAV, is appropriate for time-series analysis.
Finally, whilst the NAV definition may be driving some of the results, any systematic bias should be smoothed out and
should not affect significantly the results since the individual NAVs are analyzed cross-sectionally across a reasonable
homogeneous sample of Asian real estate stocks.
(Table 2 here)
4.
TIME-SERIES AND CROSS-SECTIONAL BEHAVIOUR OF NAVDISC
Figure 1 displays the time series movement in the NAVDISC performance of the six markets over the last ten
years. Figure 2 shows the corresponding movement in price-NAV ratios (P/NAV) for the same period. The P/NAV ratio
contains the same information as NAVDISC. The P/NAV ratio is greater than one when the NAVDISC is negative (i.e.
premium).The ratio becomes smaller than one when real estate companies trade at a discount (i.e. NAVDISC is
positive).
(Figures 1 and 2 here)
As the descriptive statistics in Table 3 indicate, over the last ten years, the average performance of the six
real estate stock markets stands at a NAV “discount “ of 36.36% (HK) and 12.67% (UK) and a NAV “premium” each of
8.37% (Singapore), 31.02% (Malaysia), 53.22% (Philippines) and 66.62% (Japan) respectively. Among the six
markets, Hong Kong reports consistently a NAV “discount” in all four sub-periods. The discounts are: 20.02% (precrisis period), 35.53% (crisis period), 44.87% (post-crisis period) and 44.56% (millennium period). On the contrary,
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Japan is the only real estate market that reports a NAV “premium” consistently in all four sub-periods but this NAV
“premium” has decreased from 141% in the pre-crisis period to 23% in the millennium period. Singapore and Malaysia
also report a widening trend in their NAV “discount” from the pre-crisis to the millennium periods. For the UK, its
average NAVDISC performance widens from 5% “discount” in the pre-crisis period to 22.1% “discount” in the postcrisis period and contracts to a smaller “discount” of 17.1% in the millennium period. Table 4 further indicates over the
past ten years, the Japanese real estate market is only hit by NAV “discount” in one of the 121 months (i.e. 0.74%
discount in April 2003). On the other hand, the Hong Kong market trades at NAV “discount” in 116 of the 121 months
(i.e. 95.9%). The numbers of NAV “discount” months (out of 121) for Singapore, Malaysia, Philippines and the UK were
73, 66, 62 and 99 respectively.
(Tables 3 and 4 here)
For each market, the changes in NAVDISC between successive sub-periods are estimated from Table 3. As
expected, except for the UK, the largest decline in the NAVDISC performance is reported during the Asian financial
crisis period. The declines are 86.23%, 15.31%, 154.70%, 179.40% and 69.69%, respectively, for Singapore, Hong
Kong, Malaysia, Philippines and Japan. On the contrary, the UK real estate market is not affected by the Asian
financial crisis and instead reports a NAVDISC improvement of 5.34% from the pre-crisis period. Furthermore, there
are only four instances where the NAVDISC performance improves between two successive periods. Specifically, the
average NAVDISC performance in the Singapore and Malaysia markets improve by 3.23% and 5.17% respectively
from the crisis to post crisis periods. From the post-crisis to millennium periods, Hong Kong and the UK real estate
markets report an improvement each of 0.31% and 4.92% respectively in their average NAVDISC performance.
Overall, the average NAVDISC performance appears to decline than recover by a larger magnitude in the sample
markets
In term of NAVDISC volatility as measured by its standard deviation, Table 3 shows that over the last ten
years, Philippines (standard deviation = 99.56%) and UK (standard deviation = 11.74%) were the most and least
volatile markets respectively. Similarly, Malaysia and Japan also report a higher standard deviation each (respectively
83.93% and 54.15%) associated with their NAV “premium”. Hence, as in price-earnings (P/E) ratios, it appears a
higher NAV premium is associated with too much volatility in the NAVDISC performance as revealed by the three
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markets. Two other major findings emerged when comparing the volatility in the NAVDISC of different sub-periods.
They are: (a) Singapore, Hong Kong, Malaysia and Philippines real estate markets report a higher NAVDISC volatility
each in the financial crisis period. As expected, return and NAVDISC performance of many real estate companies in
these markets fluctuated significantly during the Asian financial crisis period; and (b) The NAVDISC volatility for
Singapore, Hong Kong and Malaysia report a significant fall from the crisis to millennium periods suggesting less
fluctuating NAVD performance in these three countries in recent years, in line with the improving economic outlook in
Asia.
The disaggregate results of NAVDISC performance across the six real estate markets are provided in Table
5. Over the full ten-year period, the number (proportion) of real estate companies trade at NAV “discount” are 9
(64.3%), 46 (86.8%), 18 (40%), 8 (57.1%), 9 (32.1%) and 24 (82.8%), respectively, for Singapore, Hong Kong,
Malaysia, Philippines, Japan and the UK. For the five Asian markets as a whole with 154 real estate firms, the number
of firms that are struck by NAV “discount” were 52 (33.8%), 109 (70.8%), 114 (74.0%) and 128 (83.1%) in the precrisis, crisis, post-crisis and millennium periods respectively. Moreover, the average NAV “discount” for the Asian
market increases from 8.63% to 11.83% during the last six years (i.e. from post-crisis to millennium). Overall, although
the global NAV “discount” for public real estate is expected to narrow, our results suggest that any consistent
contraction in the NAV “discount” for the Asian real estate markets has yet to come. Could a REIT type structure help
narrow the NAV “discount” consistently in Asian markets is definitely of concern to local and international investors.
(Table 5 here)
Based on the real estate companies’ NAVDISC performance over the full ten-year period, Table 6 (Panel A)
lists the top 20 Asian real estate companies. Japan (6), Malaysia (6), Philippines (3), Singapore (3) and Hong Kong (2)
dominate the top 20, with Kabuki Theatrical (Japan), Metro Pacific (Philippines) and Petaling Tin (Malaysia) being the
top 3 Asian real estate companies. To assess the percentage representation in the top 30 amongst the Asian countries
over the four sub-periods, Table 6 (Panel B) shows Malaysia (35.6%), Japan (39.3%), Japan (35.7%) and Japan
(32.1%) having the highest representation in the top 30 from their respective sample of real estate companies in the
pre-crisis, crisis, post-crisis and millennium periods respectively.
(Table 6 here)
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5.
COMMON FACTORS IN NAVDISC
We appeal to a combination of factor analysis and canonical correlation technique to investigate whether
there are common factors found in the real estate company NAVDISC performance of the UK and five Asian markets
and the degree of linkages of these common factors (if any) across the markets. This analysis will provide alternative
evidence as to whether international real estate markets are integrated or segmented in addition to the usual return (1st
moment) and variance (2nd moment) evidence and consequently the findings will thus has significant implication for
international portfolio diversification.
In the first stage, the NAVDISC series of individual companies for each market are subject to maximumlikelihood factor extraction and varimax rotation. In accordance with the literature, the Kaiser criterion (1960) is used to
decide on the common factors that should be retained. Accordingly only those common factors with latent roots greater
than or equal to one will be retained. Table 7 contains the numbers of factors and the proportions of NAVDISC
variance explained by the identified factors. As can be seen, the first 4 (UK), 4 (Japan), 5 (HK), 2 (Singapore), 2
(Malaysia) and 1 (Philippines) factors have eigenvalues greater than one and together they are able to explain
approximately 75.63%, 91.54%, 78.80% , 76.55%, 86.34% and 74.06% of the NAVDISC variance in the UK, Japan,
HK, Singapore, Malaysia and Philippines respectively. Moreover, the first factor for the respective markets is the most
important since it is able to explain between 39.26% (UK) and 74.06% (Philippines) of the total sample NAVDISC
variance. A final point to note is that the number of significant factors is an increasing function of the size of the group
analyzed and since there are fewer factors in the NAVDISC series for Philippines, it might give rise to some biased
results obtained in the subsequent canonical correlation analyses.
(Table 7 here)
In the 2nd stage, canonical correlation analysis (CCA) is conducted to investigate the extent of linkages
between the NAVDISC series for 15 pairs of markets (i.e. UK and Japan, UK and HK, UK and Singapore, UK and
Malaysia, UK and Philippines, Japan and UK, Japan and Singapore, Japan and Malaysia, Japan and Philippines, HK
and Singapore, HK and Malaysia, HK and Philippines, Singapore and Malaysia, Singapore and Philippines, and
Malaysia and Philippines). For each pair, the canonical correlations are the association between the factor scores of
market 1’s NAVDISC and the factor scores of market 2’s NAVDISC. Essentially, CCA is a multivariate technique
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between two sets of inter-correlated variables. Each set may contain several correlated variables, and vectors of
weights for each set are derived so that the correlations between the linear combinations contained by using the
derived canonical weights are maximized. The linear combinations are known as the canonical variables and the
composite derived from using these “best possible” weights are called variate scores. An overall measure of any
relation between the two sets of variables is indicated by the canonical correlation coefficient. Next, canonical loadings
are the correlations between the original variables and canonical scores. Normally, loadings greater than some
selected lower bound, commonly 0.30 to 0.50 in absolute value, are used to decide whether a loading coefficient is
significant (Fornell and Larcker, 1980). Further, if a canonical variate pair is significantly associated with certain
predictor variable(s) and certain criterion variable(s), it is inferred that these original variables are related, although
cross loadings are sometimes used. Finally, Stewart and Love’s (1968) redundancy index provides a summary index
of the average ability of the predictor variable to explain the variability in a set of criterion variables.
Panel A of Table 8 reports the main canonical correlation results between the NAVDISC factor scores of
each Asian market and the UK market. As can be seen, there are four significant pairs between the NAVDISC factors
scores of Japan and the UK and between those of Hong Kong and the UK. The first canonical correlation is between
0.971 and 0.975, representing about 94.3%-95% of the shared variance for the first pairs of canonical variates. The
second canonical correlation is between 0.914 and 0.923, explaining between 83.5% and 85.2% of overlapping
variance for the second pair of canonical variates. On the other hand, there are only two significant pairs of canonical
relationship each between the NAVDISC factor scores of Singapore and the UK (first pair canonical correlation is
0.933) and those of Malaysia and the UK (first pair canonical correlation is 0.854); and one significant pair between the
NAVDISC factor scores of Philippines and the UK (canonical correlation is 0.896). Additionally, canonical redundancy
analyses show that the factor scores of the UK NAVDISC performance are able to explain 63.5%, 50.1%, 38.7%,
29.4% and 20.2%, respectively, of the factor scores of NAVDISC performance in Japan, Hong Kong, Singapore,
Malaysia and Philippines. Panel B of the same Table reports the canonical correlation results between 10 pairs of
Asian markets. Overall, there are between one and four significant NAVDISC canonical pairs across the five Asian
markets. The first canonical correlation is between 0.925 and 0.975, representing about 85.6%-95% of the shared
variance for the first pairs of the canonical variates. Furthermore, the factor scores of Japan NAVDISC performance
are able to account for 73.4%, 40.5%, 31.5% and 23.4%, respectively, of the factor scores of NAVDISC performance in
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Hong Kong, Singapore, Malaysia and Philippines. For another major Asian economy Hong Kong, its NAVDISC factor
scores explain 32.8%, 30.1% and 19%, respectively, of the factor scores of NAVDISC performance in Singapore,
Malaysia and Philippines respectively.
(Table 8 here)
Taking the results as a whole, the evidence has implied at least one common NAVDISC factors can be found
in the five Asian and the UK markets. There are also additional common NAVDISC factors between some pairs of real
estate markets. Furthermore, it appears that there are close NAVDISC linkages between the Asian markets of Japan,
Hong Kong, Singapore and Malaysia and the UK. Our results thus provide additional support to the belief that
globalization of capital markets has resulted in increasing linkages across the major real estate markets. Specifically, in
addition to possible linkages in return and volatility, international real estate markets are also closely linked in their
NAVDISC performances. Overall, support is thus offered that common factors are present in securitized real estate
markets from the NAVDISC perspective. This learning is useful to international real estate investors, and even policy
makers who might be interested in understanding how changes in one real estate market’s NAVDISC performance can
impact upon another real estate market’s NAVDISC performance
6.
FINANCIAL DETERMINANTS OF NAVDISC
In order to understand whether company-specific financial factors can partially explain the cross-sectional
variation in the NAVDISC performance of our sample, we express the NAVDISC as a function of five hypothesized
variables in the following model:
NAVDISC = f ( SIZE , ROE , BR, BETA, TRISK )
Five independent variables are defined for inclusion in the analysis. These variables are chosen mainly
based on data availability. SIZE is the natural log of market value and is expected to show a positive coefficient. ROE
is a summary measure of corporate performance and is also regarded as a reflection of management quality. Following
Malkiel (1995), ROE is the earned net operating income divided by equity capital and less reserves. Company risk is
taken to be (a) the BETA of the real estate stock (which is the extent to which the company returns co-vary with the
14
overall market index). As beta increases, the NAVDISC gets larger; and (b) total risk (TRISK) which is simply the
variance of monthly continuous returns time series and is expected to be positively related to NAVDISC too. Finally,
BR is the variable that measures leverage, is debt as a percentage of total tangible asset value and is expected to be
positively associated with the NAVDISC.
Table 9 provides the sample means of the five financial variables grouped at a national level. The means
reported are un-weighted and not adjusted for company size.
(Table 9 here)
The bivariate correlations between NAVDISC and the five financial factors are reported in Table 10. Both
Pearson and Spearman correlation coefficients are estimated. In general, there is some evidence regarding the
significant impact of some company financial characteristics on the NAVDISC performance. It appears from the results
that the variable SIZE has the most number of significant correlation coefficients. However, the sign of the SIZE
coefficient is negative implying that larger market capitalized Asian real estate companies trade at a smaller discount to
NAV than the smaller real estate companies. The variable ROE is significantly negatively associated with NAVDISC of
Singapore, Hong Kong, UK real estate companies suggesting the effect of positive “momentum“ in raising investors’
valuation of relative performance. Finally, the remaining company-specific financial factors (borrowing ratio, beta and
volatility) are only statistically significant in some instances.
(Table 10 here)
As many of the explanatory financial factors are highly correlated, stepwise regressions are run to overcome
the influence of multicollinearilty and determine the most important variable (s) that explains the variation in the
NAVDISC performance. Table 11 provides the regression results for all six individual markets as well as for the
regional Asian market. The adjusted R2 of the models is between 3.8% (Asian regional market) and 68% (UK).
According to the models, the SIZE variable emerges as the most important factor in explaining the NAVDISC
performance of Hong Kong and the regional Asian market. Specifically, its significant negative impact implies that as
the market value of a real estate company increases by one percentage point, the NAVDISC reduces by approximately
0.21 percentage point (Asian market) and 0.34 percentage point (HK) respectively. The ROE variable appears to be
15
the most significant financial factors in influencing the NAVDISC performance of Singapore and the UK real estate
companies. The coefficient is negative and statistically significant at a 1% level. Furthermore, as ROE rises by one
percentage point, the NAVDISC falls by about 0.76 percentage point (Singapore) and 0.83 percentage point (UK)
respectively. Further interesting results are observed from the regressions. The total risk variable (TRISK) emerges as
the most important factor that influences the NAVDISC of real estate companies in Malaysia and Japan. In Japan, a
positive coefficient implies that more volatile real estate firms are valued less relative to their underlying real estate
assets than firms that are less volatile. On the other hand, Malaysian real estate firms have a significantly negative
TRISK coefficient implying that firm stock volatility reduces the NAVDISC. This is somewhat at odd with the theoretical
prediction that volatility should be positively associated with the NAVDISC. Finally, there is lack of a statistical
significant relationship between the variables BR and beta and the NAVDISC series in all sample countries.
(Table 11 here)
Comparing the results of this study to the findings of Bond and Shilling (2004) for a sample of European
property companies, three major conclusions can be drawn. First, size is the most important factor of NAVDISC of
major Asian real estate companies; whereas for European property companies, company risk is the most significant
determinant of NAVDISC and there is no significant relationship between size and NAVDISC. Second, another two
significant determinants of NAVDISC for Asian real estate companies are ROE and total risk. In addition, the
relationship between ROE and NAVDISC is highly significant for the UK market. On the contrary, Bond and Shilling
(2004) find that the relationship between ROE and NAVDISC is statistically insignificant for European property
companies. Finally, similar to European property companies, company financial factors have only a moderate impact
on the NAVDISC performance of Asian real estate companies. One main implication arising from this finding is that the
variation in the NAVDISC performance is only moderately related to fundamental and that a larger portion of NAV
discount / premium may deviate from the average value for some idiosyncratic reasons.
7.
RELATIONSHIP BETWEEN NAVDISC AND DOMESTIC MARKET MOVEMENTS
Lee et al. (1991) argue that discounts on CEFs reflect (individual) investor sentiment. By examining the
pattern of cointegration and causality between average NAVDISC of real estate companies and their respective local
stock market and real estate stock market indexes, we hope to detect evidence of a general systematic relationship
16
between each market’s average NAVDISC and domestic market movements thereby supporting the ‘investors
sentiment’ hypothesis of Lee et al. (1991). More specifically, cointegration analysis will identify any long-run equilibrium
relationship between the NAVDISC series and the two proxies for investor sentiment. Granger causality will identify the
causal direction between changes in the NAVDISC and changes in levels of the indexes that proxy domestic stock
market and real estate market sentiment.
We extract monthly stock market index (MKT) and real estate market index (PMKT) for the respective
markets from the Datastream from July 1994 to July 2004. They are: Singapore All-Equity and Singapore All-Equity
Property indexes (Singapore), Hang Seng market index and Hang Seng Property Index (Hong Kong), KSLE
Composite and KSLE Property Indexes (Malaysia), Philippines SE All-Share and Philippines SE Property Indexes
(Philippines), Tokyo SE (TOPIX) and Tokyo SE Property Indexes (Japan), and FTSE 350 All-share and FTSE 350
Real Estate Indexes. All stock market indexes (MKT) and real estate stock market indexes (PMKT) are respective
proxies for general local investor sentiment and real estate market sentiment.
Briefly, the concept of cointegration is developed from the belief that certain economic variables should not
diverge from each other by too far a distance or diverge without bound. Such variables may drift apart in the short-run
but if they continue to be too far apart in the long-run, then economic forces will bring them together again (Granger,
1986). As such, an error correction model (ECM) can be established to capture the short-run disequilibrium. A fairly
extensive formal literature has been developed on the cointegration methodology. As far as this section is concerned,
first, the different time series are examined for their stationarity on the level and first difference using the standard
Augmented Dickey-Fuller (ADF) and Phillips Perron (PP) unit root tests. The tests are necessary, as the finding of a
unit root in any of the series indicates non-stationarity, which has implications for modeling the relationship between
any of the two series (i.e. NAVDISC and market index). To overcome the problem of taking log transformation of
negative NAVDISC in the analysis, we use the price-NAV (P/NAV) ratio as the proxy for the premium / discount value.
Since all P/NAV ratios are positive numbers, the log transformation can be applied to create stationary series. To test
for cointegration, we appeal to Johansen's (1988) Full Information Maximum Likelihood method (FIML). The basis of
Johansen method is essentially a Vector autoregressive model (VAR) with some non-linear cross-equation restrictions.
Specifically, if the P/NAV series are cointegrated with their respective MKT (or PMKT) in the system, then a
17
relationship (taking P/NAV as the dependent variable) between the two series would have a zero mean stationary error
term (u t):
LN (P/NAV) t = a + b* LN (MKT/ PMKT) t + ut …………………………(XX)
Hence, if u t is stationary, then the two series would display a fairly constant relationship over time although
they might have diverged in certain shorter periods. Evidence of cointegration implies a long-term, equilibrium reverting
relationship and the possibilities of long-term arbitrage opportunities. Finally, Granger causality tests are conducted to
investigate causal relations between P/NAV and MKT (/PMKT). More specifically, we are interested in finding out
whether changes in the MKT / PMKT cause changes in P/NAV, or are MKT /PMKT and P/NAV both exogenously
determined. If the MKT (/PMKT) Granger causes P/NAV, then changes in the former should precede changes in the
later. If the null hypothesis is rejected, then the stock market (MKT) / (property market – PMKT) is said to Granger
cause P/NAV. If the null is accepted, the MKT (/PMKT) is exogenous to the P/NAV series. The Granger test for
causality relies on the estimation of bivariate VAR models for all possible pairs of indexes and P/NAV series in the
group. Up to 12 lags are included to describe adequately the dynamics in a VAR system using monthly data.4
Table 12 displays the Pearson correlations of the NAVDISC series with the respective stock market and real
estate market indexes. As the figures indicate, the NAVDISC series of all Asian markets are significantly (p <0.001)
negatively correlated with their respective local stock market (MKT) and real estate market (PMKT) indexes implying
that higher stock market and real estate market prices are associated with higher “premium” to NAV. Except for
Philippines, the correlations are higher with the real estate market than with the stock market indexes. Although the
NAVDISC for the UK market is significantly negatively correlated with its stock market index, the correlation coefficient
of -0.252 is much lower than those of Asian markets (ranged between -0.596 and -0.989). Finally, the UK’s NAVDISC
is positively correlated with its real estate market index implying that higher real estate market prices are linked to
higher real estate company discounts. Moreover, the correlation coefficient of 0.321 is also statistically significant at the
1% level.
(Table 12 here)
18
The results of the ADF and PP unit root tests are contained in Table 13. The ADF and PP statistics for the 18
series (6 each for P/NAV, MKT and PMKT series) in the first difference are lower than the critical values for 5% and 1%
level of significance. Hence, all 18 series are integrated of order 1.
(Table 13 here)
The Johansen bivariate cointegration results are presented in Table 14. The log-likelihood ratio test statistics
for determining the existence of an equilibrium relationship between the P/NAV and market indexes using the maximal
eigenvalue procedure are evaluated. The results clearly indicate there is no cointegration between the P/NAV series
and their respective general market and real estate stock indexes as all
λ max (max-eigen statistic) and λtrace
(trace
statistic) are below the 99 per cent and 95 per cent critical values of the tests. The only exception is Malaysia’s
cointegrating model between its P/NAV and its KSLE real estate index. Although the
the 95 per cent critical value (15.41), the
(1995, p. 393) recommends that the
λtrace
value of 16.23 is above
λ max value of 13.08 is below the 95 per cent critical value (14.07). Enders
λ max test is more reliable than the λtrace
test. Consequently, we conclude that
there is no cointegrating relationship between the P/NAV and KLSE real estate index series.
(Table 14 here)
The Granger causality results reported in Table 15 shows significant one-way causal relationship from the
stock market indexes of HK, Malaysia and Philippines to their respective P/NAV series. Unidirectional causality implies
an information transmission. Specifically for HK and Philippines, this information flow is from the local market to P/NAV
in the short term (up to three lags). For Malaysia, its MKT is linked to P/NAV at lags 3, 4 and 5. For the UK, Japan and
Singapore, there is no evidence of information flow between the P/NAV series and local market index series as all test
statistics are statistically insignificant at the conventional probability levels.
There is some indication of significant lagged feedback or bilateral causality between Singapore real estate
stock market index (PMKT) and its P/NAV series at lag 1 implying that there are simultaneous adjustments in the two
variables. No evidence of bilateral causality is found between the PMKT and P/NAV series for other countries. A
significant one-way causal relationship is indicated from the Hong Kong P/NAV series to its PMKT index at lags of 4 to
19
12 months. Finally, there is some evidence of UK P/NAV series Granger caused its PMKT index and Malaysia PMKT
index Granger caused its P/NAV series at lag 12.
(Table 15 here)
In summary, the ADF unit root tests indicate that all P/NAV, MKT and PMKT are non-stationary, but are
stationary in their first-differences. The Johansen cointegrating results reject the presence of a long-run equilibrium
relationship between the real estate company discounts (represented by P/NAV) and their respective stock market
(MKT) and real estate stock market (PMKT) indexes for all countries. Granger causality tests indicate some variations
across the countries. There is a significant one-way causal relationship from the MKT series of the HK, Malaysia and
Philippines to their respective P/NAV series; and from the UK P/NAV series to its PMKT series. Additionally, there is
some evidence of bilateral causal relationship between Singapore P/NAV series and its PMKT series. Our findings that
none of the P/NAV series exhibits cointegration with the respective local MKT and PMKT index series indicating
absence of these two systematic components in the P/NAV series for these countries. Hence the relationships
between the NAVDISC series and these two local indexes would imply only a general relationship which is supported
mainly by the one-way information flow from some local indexes to their respective P/NAV series.
8.
CONCLUSION
In this paper, we find that the average NAVDISC performance varies across the six major real estate markets
over the past decade. The average ten-year performance is approximately 36.3 % “discount”, 12.7% “discount”, 8.4%
“premium”, 31.0% “premium”, 53.2% “premium” and 66.6% “premium”, respectively, for Hong Kong, the UK,
Singapore, Malaysia, Philippines and Japan. The average NAVDISC performance rating also varies significantly over
the four shorter sample periods. In particular, whilst Hong Kong and Japan report consistently a NAV discount and a
NAV premium respectively throughout the pre-crisis, crisis, post-crisis and millennium periods, the remaining three
Asian markets’ NAVDISC performance fluctuate widely across the four shorter periods. On the contrary, the UK - the
largest European real estate market, is the least volatile in its NAVDISC performance. While Singapore, Hong Kong
and Malaysia report a widening trend in their NAV “discount” from the pre-crisis to the millennium periods, their
NAVDISC volatilities experience a significant fall from the crisis to millennium periods suggesting less fluctuating
NAVDISC performance for these three countries in recent years. Finally, for the five Asian markets as a whole, the
20
proportion of real estate firms that are struck by a NAV “discount” increases from 33.8% in the pre-crisis period to
83.1% in the millennium period.
For all national markets, Individual real estate firms’ NAVDISC performances are closely correlated. There
are between one and five common factors that influence the NAVDISC performance of individual real estate firms.
Moreover, at least one common NAVDISC factor is found across the five Asian and UK markets. There are also
additional common NAVDISC factors between some pairs of real estate markets. Hence, in addition to possible
linkages in return and volatility, international real estate markets are also closely linked in their real estate company
discounts.
In understanding whether company-specific financial factors can influence NAVDISC performance, this study
finds that size is the most important factor of NAVDISC for many Asian real estate companies. Another two significant
determinants of NAVDISC for Asian real estate companies are ROE and total risk. Similar to European property
companies, company financial factors have only a moderate impact on NAVDISC of Asian real estate companies. Our
results are therefore inconclusive with regard to the impact of company financial factors on real estate company
discount / premium in Asian real estate markets.
Finally, the NAVDISC series of all Asian markets are significantly negatively correlated with their respective
local stock market (MKT) and real estate market (PMKT) indices implying that higher stock market and real estate
market prices are associated with a higher “premium” to NAV. However, none of the P/NAV series exhibits
cointegration with their respective local MKT and PMKT series indicating absence of these two systematic components
in the P/NAV series for these countries. The relationships between the NAVDISC series and some local indexes would
thus imply only a general relationship supported mainly by the one-way information flow from some local indexes to
their respective P/NAV series.
Any possible sources of error in the real estate company sample (i.e. not a pure real estate investment
company sample) and in the NAV calculations provided by the Datastream to account for development activity have to
be noted. Nevertheless, this study is very significant as to-date no other research has considered these NAVDISC
21
issues comprehensively in major Asian real estate markets. As more and more Asian economies are interested in
developing REIT type securitized real estate products, our study provide investors and regulators with the dynamics of
real estate company discounts in major international markets. Specifically, the US-based and European investors will
be interested in understanding the NAVDISC performance variation of major Asian markets and any cross-market
linkages to help manage their exposure in Asian real estate markets. Regulators will be more concerned with
identifying any common factor(s) that drive(s) the NAVDISC performance of real estate markets within the same
economic region and take appropriate corrective measures. Finally, our study also reinforces the increased potential
importance of Asian securitized real estate in an investment portfolio for both local and international investors
Acknowledgement
The original version of this paper was presented at the at the 21st ARES Annual Meeting, 13-16 April 2005, Santa Fe,
USA. We are grateful to Professor Graeme Newell and conference participants for their helpful comments in improving
the paper. Thank you.
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23
Table 1 Econmic & stock market statistics (2003)
Hong Kong
GDP*
US $ Billion
Exchange rate*
Local per USD
Lending rate*
%
Consumer Price*
Singapore
Japan
Malaysia
Philippines
UK
156.67
93.56
4648.19
103.16
78.144
1797.809742
7.787
1.7008
107.1
3.8
55.569
0.6118
5
5.31
1.82
6.3
9.472
3.69
92.9
101.1
98.1
104.3
112.541
106.5
7.9
5.4
5.3
3.5
11.4
3.1
Unemployment rate*
%
Stock Market Captilization**
US $ Million
463,108
101,900
2,126,075
123,872
39,021
2,412,434
Value Traded **
US $ Million
2,150,753
210,622
56,129
1,573,279
27,623
3,103
Value Traded (/market cap)**
0.45
1
1
0
0.08
0.89
No. of companies**
968
434
3,058
865
235
2,311
478.4
235
695
143
166.05
1043.89
Average firm Size**
US $ Million
Real Estate stock % of stock market***
%
P/E ratio of real estate stock***
Dividend yield of real estate stock***
%
11.44
8.49
1.27
2.68
16
1.75
22.60
21.60
35.50
14.20
16.5
22.7
2.47
2.58
0.94
2.96
0.99
2.88
Source: * data from IMF country database, the others are from Stock Market Factbook
**Standard & Poor's Emerging Stock Markets Factbook 2003 and IMF
Table 2 Distribution of the 183 real estate companies included in the study
Market /Minimum Data Period
Singapore
Hong Kong
Malaysia
Philippine
Japan
United Kingdom
Total
8 years
0
12
11
2
0
0
25
9 years
1
12
8
5
0
0
26
10 years
13
29
26
7
28
29
132
Total
14
53
45
14
28
29
183
Table 4 Number (proportion) of months with average NAV “discounts”
Full Period
Singapore
Hong Kong
73 of 121 (60.3%)
116 of 121 (95.9%)
Malaysia
66 of 121 (54.5%)
Philippine
62 of 121 (51.2%)
Japan
United Kingdom
1 of 121 (0.82%)
99 of 121 (81.8%)
Pre-Crisis
0 of 36
(0%)
34 of 36 (94.4%)
0 of 36
(0%)
0 of 36
(0%)
0 of 36
(0%)
28 of 36 (77.8%)
During Crisis
Post Crisis
Millennium
11 of 14 (78.6%)
11 of 14 (78.6%)
19 of 28 (67.9%)
28 of 28 (100%)
43 of 43 (100%)
43 of 43 (100%)
9 of 14 (64.3%)
14 of 28 (50%)
43 of 43 (100%)
11 of 14 (78.6%)
0 of 14
(0%)
6 of 14 (42.9%)
27 of 28 (96.4%)
0 of 28
(0%)
28 of 28 (100%)
24 of 43 (55.8%)
1 of 43 (2.3%)
37 of 43 (86.0%)
24
Table 5
Number (proportion) of real estate companies with NAV “discounts”
Singapore
Hong Kong
Malaysia
Philippines
Japan
Asian market
United Kingdom
Full Period
9(64.3%)
46(86.8%)
18(40.0%)
8(57.1%)
9(32.1%)
90(58.4%)
24(82.8%)
Pre-crisis
6(48.9%)
41(77.4%)
1(2.2%)
2(14.3%)
2(7.4%)
52(33.8%)
22(75.9%)
During
Crisis
10(71.4%)
44(83.0%)
34(75.6%)
11(78.6%)
10(35.7%)
109(70.8%)
19(65.5%)
Post Crisis
9(64.3%)
46(86.8%)
32(68.9%)
11(78.6%)
16(57.1%)
114(74.0%)
23(79.3%)
Millennium
12(85.7%)
45(84.9%)
41(91.1%)
11(78.6%)
19(67.9%)
128(83.1%)
23(79.3%)
Total Number of
Real Estate
Companies
14
53
45
14
28
154
29
Table 7
Proportion (%) of real estate NAVD
variance explained by factors extracted: July 1994 – July 2004
Factor
1
2
3
4
5
Total
Note
1.
2.
3.
UK
39.26
18.10
9.93
8.34
75.63
Japan
61.30
12.53
10.14
7.47
91.54
HK
41.21
17.95
9.04
7.79
2.82
78.80
Singapore
39.53
37.02
76.55
Malaysia
48.54
37.80
86.34
Philippines
74.06
74.06
Only NAVD series that have complete 10-year observations are included. The number of NAVD series
included in the factor analysis: 29(UK), 28(Japan), 29(HK), 13(Singapore), 26 (Malaysia) and 7 (the
Philippines)
For each market, the NAVD series are subject to maximum-likelihood factor analysis. The rotation method
used is varimax with Kaiser normalization
The number of factors extracted (based on eigen value > 1) are: 4 (UK) , 4 (Japan), 5 (HK), 2(Singapore), 2
(Malaysia) and 1 (Philippines)
25
Table 3 Average Net Asset Value Discounts of Real Estate Companies
Full Period: July 1994 - July 2004
Singapore
HK
Mean
-0.0837
0.3626
Median
0.1587
0.3906
Maximum
0.5018
0.7061
Minimum
-1.1663
-0.1848
Std. Dev.
0.4955
0.1775
121
121
Number
Malaysia Philippines
-0.3102
-0.5322
0.0532
0.0130
0.5861
0.6499
-2.6740
-3.0213
0.8393
0.9956
121
121
Japan
-0.6662
-0.4497
0.0074
-1.8835
0.5415
121
UK
0.1267
0.1451
0.3544
-0.1176
0.1174
121
Pre-Crisis Period:July 1994 - June 1997
Singapore
HK
Mean
-0.7735
0.2002
Median
-0.7850
0.2308
Maximum
-0.5530
0.3906
Minimum
-1.1663
-0.0326
Std. Dev.
0.1438
0.1055
36
36
Number
Malaysia Philippines
-1.4977
-1.6586
-1.3983
-1.5720
-0.9325
-0.6460
-2.6740
-3.0213
0.3989
0.5506
36
36
Japan
-1.4116
-1.3919
-0.9326
-1.8835
0.2523
36
UK
0.0499
0.0678
0.1451
-0.1152
0.0682
36
Crisis period: July 1997 - Aug 1998
Singapore
HK
Mean
0.0888
0.3533
Median
0.1107
0.4078
Maximum
0.5018
0.7061
Minimum
-0.5415
-0.1848
Std. Dev.
0.3040
0.2934
14
14
Number
Malaysia Philippines
0.0493
0.1354
0.1781
0.1711
0.5861
0.5850
-0.9882
-0.5383
0.4311
0.2854
14
14
Japan
-0.7147
-0.6971
-0.3909
-1.1558
0.2035
14
UK
-0.0035
-0.0095
0.1756
-0.1176
0.0765
14
Post-crisis period: September 1998 - December 2000
Singapore
HK
Malaysia Philippines
Mean
0.0565
0.4487
-0.0024
0.2856
Median
0.1152
0.4660
0.0044
0.2798
Maximum
0.4719
0.6841
0.4369
0.6069
Minimum
-0.5132
0.2176
-0.3441
-0.1744
Std. Dev.
0.2098
0.1140
0.2203
0.2062
28
28
28
28
Number
Japan
-0.3570
-0.3203
-0.2228
-0.5798
0.1110
28
UK
0.2211
0.2195
0.2906
0.1607
0.0363
28
Millenenium period: January 2001 - July 2004
Singapore
HK
Malaysia Philippines
Mean
0.3463
0.4456
0.3665
-0.3390
Median
0.3488
0.4643
0.3494
0.1356
Maximum
0.4899
0.5948
0.5071
0.6499
Minimum
0.1952
0.1821
0.2050
-2.1859
Std. Dev.
0.0843
0.1054
0.0873
0.8981
43
43
43
43
Number
Japan
-0.2277
-0.2108
0.0074
-0.6345
0.1628
43
UK
0.1719
0.1808
0.3544
-0.0786
0.1188
43
26
Figure 1 Average Net Asset Value Discounts (NAVDISC)
1
0.5
0
七月-94
三月-95
十一月-95
七月-96
三月-97
十一月-97
七月-98
三月-99
十一月-99
七月-00
三月-01
十一月-01
七月-02
三月-03
十一月-03
七月-04
三月-03
十一月-03
七月-04
NAVDISC
-0.5
-1
-1.5
-2
-2.5
-3
-3.5
Month
Singapore
Hong Kong
Malaysia
Philippines
Japan
UK
Figure 2 Average Price-to-NAV ratios (P/NAV)
4.5
4
3.5
P/NAV
3
2.5
2
1.5
1
0.5
0
七月-94
三月-95
十一月-95
七月-96
三月-97
十一月-97
七月-98
三月-99
十一月-99
七月-00
三月-01
十一月-01
七月-02
Month
Singapore
Hong Kong
Malaysia
Philippines
Japan
UK
27
Table 6
Asian real estate company NAV “discount” performance analysis
Panel A: Top 20 Asian real estate companies: July 1994 – July 2004
1. Kabuki Theatrical (Japan)
11. New Century Group Hong Kong (Hong Kong)
2. Metro Pacific (Philippines)
12. City Development (Singapore)
3. Petaling Tin (Malaysia)
13. Central Properties (Singapore)
4. Ayala Land (Philippines)
14. Country Heights Holding (Malaysia)
5.MK Land Holding (Malaysia)
15. Hong Leong Properties (Malaysia)
6. Bukit Sembawang Estate (Singapore)
16. Shenzen High-tech Holding (Hong Kong)
7. Mitsubishi Estate (Japan)
17. Tokyu Land (Japan)
8. Odakyu Real Estate (Japan)
18. Belle (Philippines)
9. Sagami Railway (Japan)
19. Mitsui Fudosan (Japan)
10. Sime UEP Properties (Malaysia)
20. Land & General (Malaysia)
Panel B: Top 30 Asian real estate companies: country analysis
Number (percentage of real estate companies included)
Pre-crisis period
Crisis period
Post-crisis period
Millennium period
(14)1
3 (21.4%)
3 (21.4%)
3 (21.4%)
2 (14.3%)
Hong Kong (53)
1 (1.9%)
6 (11.3%)
4 (7.5%)
8 (15.1%)
Malaysia (45)
16 (35.6%)
7 (15.6%)
8 (17.7%)
4(8.9%)
Philippines (14)
2 (14.3%)
1(7.1%)
2 (14.3%)
3 (21.4%)
Japan (28)
8 (28.6%)
11 (39.3%)
10 (35.7%)
9 (32.1%)
UK (29)
0 (0%)
2 (6.9%)
3 (10.3%)
4 (13.8%)
Singapore
1
Values in brackets indicate the sample size of real estate companies included in the study
28
Table 8
Significant canonical results on factor scores of NAVDISC1: July 1994 - July 2004
Panel A: Between Asian Markets and UK
NAVDISC (Japan and UK)
NAVDISC (HK and UK)
3
0.749
0.561
4
0.338
0.115
1
0.933
0.871
2
0.817
0.667
1
0.854
0.729
2
0.679
0.461
NAVDISC
(Philippines
and UK)
1
0.896
0.803
0.000
0.000
Redundancy (%)
0.191
0.172
0.115
0.239
0.216
0.140
0.000
0.000
0.000
0.000
0.000
0.000
0.023
0.028
0.435
0.218
0.335
0.169
0.381
0.184
0.220
0.110
0.803
0.202
Canonical pairs
Canonical correlation
Squared canonical
correlation
Significance
1
0.971
0.943
2
0.914
0.835
3
0.780
0.609
4
0.367
0.135
1
0.975
0.950
0.000
0.000
0.000
0.000
0.000
Left set
Right set
0.240
0.236
0.211
0.212
0.152
0.154
0.033
0.033
Panel B: Between Asian markets
NAVDISC (Japan and HK)
Canonical
pairs
Canonical
correlation
Squared
canonical
correlation
Significance
Redundancy
(%)
Left set
Right set
NAVDISC
(Japan &
Singapore)
1
2
NAVDISC
(Japan &
Malaysia)
1
2
2
0.923
0.852
NAVDISC
(JP &
PHI)
1
NAVDISC
(Singapore and UK)
NAVDISC
(HK &
Singapore)
1
2
NAVDISC
(HK &
Malaysia)
1
2
NAVDISC
(HK &
PHI)
1
NAVDISC
(Malaysia and UK)
NAVD
(Singapore &
Malaysia)
1
2
NAVDISC
(SIN &
PHI)
1
NAVDISC
(MAL &
PHI)
1
1
2
3
4
0.975
0.917
0.857
0.634
0.950
0.831
0.925
0.627
0.965
0.961
0.836
0.976
0.721
0.966
0.946
0.322
0.934
0.958
0.951
0.841
0.734
0.402
0.903
0.691
0.856
0.394
0.931
0.924
0.698
0.953
0.519
0.934
0.895
0.104
0.872
0.917
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.238
0.192
0.214
0.169
0.185
0.149
0.097
0.081
0.230
0.452
0.175
0.345
0.215
0.448
0.100
0.188
0.234
0.931
0.187
0.464
0.141
0.348
0.194
0.495
0.107
0.249
0.190
0.934
0.450
0.467
0.052
0.050
0.438
0.872
0.480
0.917
There are 15 pairs of cross-canonical relationships on the NAVDISC of real estate markets. The canonical correlations are the association between the factor scores of market
1’s NAVD (left set) and the factor scores of market 2’ NAVDISC.
1
29
Table 9 Summary of Real Estate Company Financial Information (July 1994 - July 2004)
Market
Singapore
Number
14
Hong Kong
53
Malaysia
45
Philippines
14
Japan
28
UK
29
Measure
Mean
Std Dev
Mean
Std Dev
Mean
Std Dev
Mean
Std Dev
Mean
Std Dev
Mean
Std Dev
Ln(MV)
6.3756
1.1352
7.4511
1.6818
6.0725
0.7056
5.2275
1.3413
10.6161
1.3453
4.7915
1.8075
ROE
0.0457
0.0690
-0.0080
0.1557
0.0183
0.1839
0.0331
0.1608
0.0321
0.0937
0.0802
0.0597
BR
0.6921
0.3512
0.3556
0.2192
0.5888
0.6257
0.4810
0.4175
3.3535
5.5275
0.6922
0.5373
BETA
1.4724
0.4848
1.0543
0.4241
1.1676
0.3675
1.1750
0.5360
1.0005
0.5142
0.5071
0.2773
T(RISK)
0.1415
0.0301
0.1653
0.0545
0.1628
0.0405
0.1927
0.0450
0.1060
0.0428
0.0708
0.0202
Table 10
Bivariate correlation coefficients (Pearson / Spearman)
between NAVDISC and financial factors: July 1994 – July 2004
Level
Aggregate
Market
Asian markets
[154]
Singapore, SP
[14]
Hong Kong, HK
[53]
Malaysia, MA
[45]
Philippine, PH
[13]
Disaggregate
Notes
(1)
(2)
(3)
Japan, JP [28]
United
Kingdom, UK
[29]
SIZE
-0.212**
(-0.218**)
-0.182
(-0.121)
-0.339*
(-0.408)**
-0.175
(-0.390**)
-0.532
(-0.600*)
-0.175
(-0.406*)
0.104
ROE
-0.031
(-0.261**)
-0.760**
(-0.670**)
-0.143
(-0.295*)
-0.151
(-0.164)
0.259
(-0.116)
0.051
-0.246
-0.831**
(-0.082)
(-0.375*)
Financial Factors *
BR
BETA
-0.088
0.005
(-0.220**)
(-0.130)
-0.032
0.282
(-0.103)
(-0.086)
-0.066
-0.269
(-0.101)
(-0.201)
-0.005
-0.151
(-0.108)
(-0.162)
-0.372
-0.298
(-0.270)
(-0.389)
-0.175
0.37
(-0.406*)
0.113
-0.001
-0.694**
0.088
(-0.485**)
TRISK
0.245
0.085
0.358
(-0.020)
-0.141
-0.041
-0.359*
(-0.283)
0.029
(-0.007)
0.420*
0.284
- 0.567**
(-0.432*)
* 5%
significant level, **1% significant level. [ ] - sample size
The first row for each market contains Pearson correlation coefficients Test. The second row, with
numbers in parenthesis, contains Spearman correlation coefficients.
Financial factors: SIZE (Market value); ROE (return on equity): BR (borrowing ratio); BETA
(systematic risk) and TRISK (total risk)
30
Table 11
Cross-sectional stepwise regression results
between NAVDISC and financial factors: July 1994 – July 2004
Dependent variable: NAV discounts (NAVDISC)
Financial Factor
Level
Aggregate
Disaggregate
Notes:
(1)
(2)
Market
Asian
markets
[154]
Singapore,
SP [14]
Hong Kong,
HK [53]
Malaysia,
MA [45]
Philippine,
PH [14]
Japan, JP
[28]
United
Kingdom, UK
[29]
Adj
R sq
F-Value
(sig)
0.109
7.123
(0.008)
16.437
(0.002)
6.620
(0.013)
6.356
(0.015)
0.145
5.575
(0.026)
0.68
60.385
(0.000)
0.038
0.543
0.098
Size
ROE
BR
BETA
TRISK
-0.212**
(-2.669)
-0.760**
(-4.054)
-0.339*
(-2.573)
-0.359**
(-2.521)
0.42**
(2.361)
-0.831**
(-7.771)
* 5%
significant level, **1% significant level. [ ] - sample size
Financial factors: SIZE (Market value); ROE (return on equity): BR (borrowing ratio);
BETA (systematic risk) and TRISK (total risk)
Table 12
Pearson correlations between NAVDISC
and local market and real estate market indexes: July 1994 – July 2004
*
Stock market index
Real estate market index
Singapore
-0.827*
-0.671*
Hong Kong
-0.792*
-0.344*
Malaysia
-0.989*
-0.856*
Philippines
-0.596*
-0.657*
Japan
-0.853*
-0.679*
UK
-0.252*
0.321*
Indicates two-tailed significance at the one percent level
31
Table 13
Unit root test results of time series of (P/NAV), stock market
index (MKT) and real estate stock market index (PMKT): July 1994 – July 2004
Augmented Dickey-Fuller
(Phillips-Perron)
ADF t-statistic
(PP t-statistic)
ADF t-statistic
(PP t-statistic)
P/NAV
Singapore
Level
-1.415
(-1.429)
-2.472
(-2.587)
-1.536
(-1.617)
-1.322
(-1.287)
-1.741
(-1.761)
-2.467
-2.571
1st Difference
-10.490**
(-10.485**)
-9.380**
(-9.309**)
-9.800**
(-9.806**)
10.803**
(-10.853**)
-10.306**
(-10.350**)
-8.321**
(-8.477**)
Level
-2.092
-2.26
-2.282
(-2.380)
-2.301
(-2.366)
-2.501
(-2.525)
-2.366
(-2.107)
-1.41
-1.482
-1.481
(-1.49)
-1.507
-1.417
-1.594
(-1.845)
-2.007
-2.097
-1.867
(-1.862)
-1.123
-1.452
1st Difference
-10.402**
(-10.401**)
-9.760**
(-9.700**)
-10.578**
(-10.590**)
-10.074**
(-10.087**)
-9.159**
(-9.090**)
-9.414**
(-9.373**)
-9.521**
(-9.448**)
-10.162**
(-10.391**)
-9.575**
(-9.677**)
-10.766**
(-10.765**)
-11.387**
(-11.385**)
-10.536**
(-10.607**)
Hong Kong
Malaysia
Philippine
Japan
United Kingdom
Indexes (MKT – stock market index); PMKT (real
estate stock market index)
MKT - Singapore
PMKT - Singapore
MKT - Hong Kong
PMKT - Hong Kong
MKT - Malaysia
PMKT - Malaysia
MKT - Philippines
PMKT - Philippines
MKT - Japan
PMKT - Japan
MKT – UK
PMKT – UK
Critical t statistic value at 1%=-3.486 and 5%=-2.889
* , ** 5% and 1% significant level (two-tailed)
32
Table 14
Co-integration test results of time series NAV discounts (P/NAV)
and stock market index (MKT) / real estate stock market index (PMKT): July 1994 to July 2004
Stock market index (MKT)
Real estate stock market index (PMKT)
MKT (Singapore)
PMKT (Singapore)
MKT (Hong Kong)
PMKT (Hong Kong)
MKT (Malaysia)
PMKT (Malaysia)
MKT (Philippines)
PMKT (Philippines)
MKT (Japan)
PMKT (Japan)
MKT (UK)
PMKT (UK)
Notes:
(1)
*
Trace Statistic
Singapore(P/NAV)
8.918
7.897
Hong Kong(P/NAV)
11.212
12.687
Malaysia(P/NAV)
8.375
16.226*
Philippine(P/NAV)
10.524
14.893
Japan(P/NAV)
6.866
11.815
UK(P/NAV)
15.339
14.266
Max-Egen Statistic
Singapore(P/NAV)
7.966
6.554
Hong Kong(P/NAV)
6.641
9.157
Malaysia(P/NAV)
6.781
13.076
Philippine(P/NAV)
6.232
9.186
Japan(P/NAV)
4.905
9.154
UK(P/NAV)
10.765
9.708
Critical Trace statistic: @* 5% level =15.41, @** 1% level =20.04. Critical Max-Eigen Statistic: @* 5% l
evel=14.07, @ **1%= 18.63
Max–Eigen statistic prevails over trace statistic in conflicting case (Enders, 1995, p.393)
33
Table 15
Granger Causality test results between P/NAV and MKT /PMKT: July 1994 – July 2004a
SINGAPORE:
MKT-->P/NAV
F-statistic
P
0.140
0.709
0.133
0.876
0.355
0.786
0.435
0.783
0.576
0.718
0.462
0.835
0.900
0.510
1.017
0.429
0.876
0.549
0.747
0.678
0.671
0.762
0.573
0.858
HK:MKT-->P/NAV
F-statistic
P
4.087*
0.046
5.253**
0.007
4.029**
0.009
2.242
0.069
1.971
0.089
2.106
0.059
1.690
0.120
1.668
0.116
1.779
0.083
1.617
0.115
1.341
0.216
1.065
0.400
MALAYSIA:
MKT-->P/NAV
F-statistic
p
1.035
0.311
2.013
0.138
3.800*
0.012
2.554*
0.043
2.615*
0.029
2.064
0.064
1.302
0.257
1.411
0.202
1.164
0.328
0.886
0.549
0.808
0.632
0.802
0.647
SINGAPORE:
P/NAV-->MKT
F-statistic
p
0.001
0.982
0.094
0.911
0.087
0.967
0.589
0.671
0.597
0.703
0.771
0.594
1.405
0.212
1.928
0.064
1.558
0.140
1.291
0.248
1.233
0.278
1.105
0.367
HK: P/NAV-->MKT
F-statistic
p
0.230
0.633
1.432
0.243
2.164
0.096
2.261
0.067
1.923
0.097
2.126
0.057
1.722
0.112
1.393
0.210
1.479
0.167
1.335
0.224
1.145
0.338
0.879
0.571
MALAYSIA:
P/NAV-->MKT
F-statistic
p
0.217
0.642
0.321
0.726
1.212
0.309
0.741
0.566
1.382
0.237
1.112
0.361
0.833
0.563
1.241
0.284
1.077
0.387
0.933
0.507
0.936
0.511
0.927
0.525
SINGAPORE:
PMKT--> P/NAV
F-statistic
P
12.019**
0.001
5.809**
0.004
4.205**
0.007
3.208*
0.016
2.602*
0.029
2.212*
0.048
2.636*
0.015
2.272*
0.029
1.979*
0.045
2.101*
0.032
2.217*
0.020
2.246*
0.016
HK:PMKT-->P/NAV
F-statistic
P
0.703
0.404
0.572
0.566
0.268
0.848
0.933
0.448
1.062
0.386
1.367
0.235
1.439
0.199
1.268
0.270
1.482
0.166
1.452
0.171
1.347
0.213
1.242
0.269
MALAYSIA
PMKT-->P/NAV
F-statistic
P
0.645
0.423
0.417
0.660
1.238
0.300
0.880
0.478
0.724
0.607
0.848
0.536
0.933
0.485
0.861
0.552
1.331
0.232
1.338
0.223
1.190
0.306
1.914*
0.044
SINGAPORE:
P/NAV-->PMKT
F-statistic
P
4.105**
0.045
1.983
0.142
1.726
0.166
1.685
0.159
1.332
0.257
1.155
0.336
1.230
0.294
1.219
0.296
1.095
0.375
1.076
0.389
1.580
0.119
1.599
0.108
HK: P/NAV-->PMKT
F-statistic
P
1.178
0.280
0.625
0.537
0.474
0.701
3.119*
0.018
2.455*
0.038
2.872*
0.013
2.683*
0.014
2.226*
0.032
2.090*
0.038
2.053*
0.037
*
1.984
0.042
1.895*
0.047
MALAYSIA:
P/NAV-->PMKT
F-statistic
P
0.008
0.931
0.186
0.831
0.416
0.742
0.334
0.855
0.390
0.855
0.511
0.799
0.863
0.539
0.827
0.581
1.392
0.203
1.265
0.263
1.109
0.364
1.406
0.180
Lags
1
2
3
4
5
6
7
8
9
10
11
12
Lags
1
2
3
4
5
6
7
8
9
10
11
12
Lags
1
2
3
4
5
6
7
8
9
10
11
12
34
PHILIPPINES
PHILIPPINES
PHILIPPINES
PHILIPPINES
MKT-->P/NAV
P/NAV-->MKT
PMKT-->P/NAV
P/NAV-->PMKT
F-statistic
p
F-statistic
p
F-statistic
P
F-statistic
P
5.965*
0.016
1.816
0.180
2.119
0.148
1.998
0.160
3.489*
0.034
1.537
0.219
1.436
0.242
1.469
0.235
2.652*
0.052
1.489
0.222
1.061
0.369
1.351
0.262
2.112
0.084
1.677
0.161
0.845
0.500
0.988
0.418
1.823
0.115
1.327
0.259
0.704
0.622
0.862
0.509
1.336
0.248
1.177
0.325
0.657
0.685
0.910
0.491
1.049
0.402
1.110
0.363
1.110
0.363
0.998
0.438
1.053
0.402
1.044
0.409
0.986
0.452
0.903
0.518
0.940
0.495
0.932
0.501
0.977
0.465
0.771
0.644
0.962
0.482
0.774
0.653
0.852
0.580
0.728
0.697
0.984
0.467
0.783
0.656
0.798
0.641
0.748
0.689
1.178
0.312
0.775
0.675
0.715
0.733
0.734
0.714
JAPAN:
JAPAN
JAPAN
JAPAN
MKT-->P/NAV
P/NAV-->MKT
PMKT-->P/NAV
P/NAV-->PMKT
F-statistic
p
F-statistic
p
F-statistic
P
F-statistic
P
0.11015
0.74057
0.08877
0.76628
0.27782
0.59914
0.05493
0.81512
0.21379
0.80785
1.18857
0.30844
0.6314
0.53371
0.61053
0.54484
0.17934
0.91021
1.5133
0.21509
1.29174
0.28091
1.40521
0.24515
0.12353
0.97374
1.1042
0.35846
0.94576
0.44058
1.12965
0.3465
0.17396
0.97175
0.88324
0.49517
0.78735
0.56109
0.87071
0.50352
0.14833
0.98901
0.77364
0.59242
0.64944
0.69043
0.89571
0.50116
0.22179
0.97944
0.73608
0.64187
0.67684
0.69122
0.88106
0.52445
0.24034
0.98212
0.90894
0.5126
0.67817
0.70962
0.81545
0.59076
0.19063
0.99468
0.89763
0.53081
0.95819
0.47967
1.67735
0.10567
0.20191
0.99565
0.68478
0.73592
0.79164
0.63678
1.42961
0.18043
0.18499
0.99805
0.62357
0.80404
0.81678
0.6234
1.49304
0.14889
0.34284
0.97843
0.60038
0.836
0.5891
0.84517
1.28288
0.24421
UK:
UK:
UK:
UK:
MKT-->P/NAV
P/NAV-->MKT
PMKT-->UK(P/NAV)
P/NAV-->PMKT
F-statistic
p
F-statistic
p
F-statistic
P
F-statistic
P
0.199
0.656
0.117
0.733
0.587
0.445
2.432
0.122
0.844
0.433
0.110
0.896
1.450
0.239
0.890
0.413
0.400
0.753
0.393
0.758
1.198
0.314
0.468
0.705
0.783
0.539
0.551
0.698
0.832
0.508
0.551
0.699
1.431
0.219
0.460
0.805
0.637
0.672
0.378
0.863
1.083
0.378
0.781
0.587
0.529
0.785
0.342
0.913
1.004
0.433
0.994
0.440
0.931
0.486
1.026
0.418
0.952
0.478
1.028
0.421
1.335
0.236
0.837
0.573
1.161
0.329
0.983
0.459
1.192
0.310
0.888
0.540
1.042
0.416
0.750
0.676
1.216
0.292
1.425
0.183
0.942
0.505
0.730
0.707
1.541
0.132
1.812
0.064
0.904
0.547
0.773
0.676
1.775
0.066
2.432**
0.009
Notes:
a P/NAV: price-to-NAV ratio; MKT: local stock market index; PMKT: local real estate stock market index
*, **- indicates two-tailed significance at the 5% and 1% levels respectively
Lags
1
2
3
4
5
6
7
8
9
10
11
12
Lags
1
2
3
4
5
6
7
8
9
10
11
12
Lags
1
2
3
4
5
6
7
8
9
10
11
12
35
Notes
According to the authors, Green Street Advisors, Inc focuses exclusively on real estate firms and each of its analysts
follows only a few firms. The analysts specialize by type of property and compute NAV by determining the fair market
value of each property owned by a REIT, often visiting larger properties. They use these NAV estimates to advise their
large institutional clients on selecting REITs as investments. Finally, Green Street released NAV at the end of each
month beginning in 1994.
1
2 Datastream also includes real estate developers and related companies in their classification. Thus our sample is not
a completely clean “real estate investment” sample. As property developers / traders are usually associated with a
NAV “premium”, our NAVDISC results have to be interpreted with this shortcoming in mind. Whilst we try our best to
check that the sample only includes property firms that are primarily investment companies, this is definitely one
possible source of error in our results.
Stationarity refers to a case where a time-series has a constant mean and constant variance. On the contrary, if a
series must be differenced once before becoming stationary, then it contains one unit root and is said to be integrated
of order 1, denoted as I(1). One important property of I (1) variables is that linear combinations of these variables can
be I (0), that is, stationary. If this is so then these variables are said to be cointegrated.
3
Please refer to Pindyck and Rubinfield (1991) for the mathematical formulations used in the Granger causality test.
We use E-view 5.0 to execute the test.
4
36