ریسک و بازده
Tests of common real estate risk
premia in a time-varying expected
return framework
Tien Foo Sing and Leiting Deng
Department of Real Estate, National University of Singapore, Singapore, and
Hong Wang
School of Economics and Management, Tsinghua University, China
Abstract
Purpose – This paper aims to test the predictability of the three asset classes, namely direct
property, bond and property stocks in Singapore.
Design/methodology/approach – Using the generalized method of moment (GMM) estimation
methodology, the authors first estimate the excess returns of assets on five instrumental variables and
a constant term. Next the common risk factors are tested in three parts involving different portfolio of
sample assets.
Findings – The empirical results shows that there are at most three common risk factors that can be
used to predict the excess returns of six asset classes, that include four direct property assets, bonds
and property stocks. The results also indicate that there are separate common risk premia that are
priced in property stock and direct property markets, which indirectly reject the hypothesis that the
two property markets are integrated.
Practical implications – The empirical results that reject the market integration between property
and property stock markets imply that there are significant diversification benefits for holding both
assets in investors’ portfolios. The two property assets capture different risk premia in the markets.
Research limitations/implications – The GMM specifications that include five instrumental
variables may not fully capture all risk information. Omission of other variables is, however, traded-off
against the parsimony of the model specification. More independent variables could be included in the
future studies, and more asset classes could also be added to the tests.
Originality/value – The study provides alternative evidence to the test of market integration
between property and property stocks in Singapore. It also verifies the earlier study in the USA that
property and stock market effects could be separately priced by the market.
Keywords Real estate, Risk management, Return on investment, Singapore
Paper type Research paper
1. Introduction
In view of the trends in real estate securitization, investigating the integration between
real estate market and other capital markets has become increasingly important (Liu
et al., 1990). If there is no integration between the two markets, risk diversification can
be achieved through an efficient portfolio consisting of the two assets. Empirical tests
on market integration between real estate and other financial asset markets have been
conducted in the USA (see Liu and Mei, 1992, Mei and Lee, 1994, Ling and Naranjo,
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1463-578X.htm
The authors wish to thank the participants at the European Real Estate Society Conference in
Milan, Italy, 2004, for their comments.
Common real
estate risk
premia
359
Received December 2006
Accepted April 2007
Journal of Property Investment &
Finance
Vol. 25 No. 4, 2007
pp. 359-369
q Emerald Group Publishing Limited
1463-578X
DOI 10.1108/14635780710762508
1999), the UK (Lizieri and Satchell, 1997), Australia (Wilson et al., 1996) and Hong Kong
(Fu and Ng, 2001). The results were, however, mixed. Evidence of cross-country
integration of direct real estate markets and capital markets was found in studies by
Mei and Hu (2000), Liu and Mei (1998, 1999) and Bond et al. (2003).
Real estate investment trust (REIT) market in Singapore is at its infancy stage of
development. Publicly listed property stocks have been regarded as a close proxy for
securitized claims on real estate assets. The performance of securitized real estate is
expected to track closely the market values of the real estate assets held by the listed
companies, if the two markets are integrated. If this hypothesis is not rejected, it
implies that investors can efficiently price risk premiums embedded in direct real
estate market based on price information of property stocks. However, the results of
the empirical tests using Singapore data have been mixed (Ong, 1994, 1995; Liow, 1998,
2001; Sing and Sng, 2003, Sing, 2004).
This study aims to empirically re-examine the market integration between
securitized and direct real estate markets in Singapore using the multifactor
latent-variable model proposed by Mei and Lee (1994). It tests the existence of common
risk factors across different asset markets, which include property stock, government
bond, and four direct property sub-markets (industry, office, residential and retail). Our
results show that there are at most three common risk factors that explain the price
variations in direct property, property stocks and bond markets in Singapore. The
results imply that the two real estate markets are integrated.
The remainder of the paper is organized into five sections. Section 2 reviews the
literature on the market integration. Section 3 discusses the multi-factor latent variable
empirical methodology. Empirical data used and analyses of empirical results are
covered in Sections 4 and 5. Section 6 concludes the findings of the paper.
2. Literature review
The notion of market integration is an important condition underlying many
well-accepted investment theories. If two asset markets are integrated, it would not be
possible for investors to arbitrage in one market by using information in another
market. Efficient diversification of risks can then be achieved by holding a portfolio of
assets across the markets Liu et al. (1990) tested the market integration between equity,
equity REITs and non-farm commercial real estate in the USA, and found that equity
REIT and stock markets were integrated. However, they rejected the hypothesis that
commercial real estate market and stock market are integrated.
If two markets were integrated, there should be no differential price premia
associated systematic risk factors in the markets. Ling and Naranjo (1999) empirically
tested the risk premiums of a set of pre-defined macro-economic factors in stock and
real estate markets. The fundamental variables include growth rate of industrial
production, consumer consumption, yield spread between long term and short term
government bonds, and unexpected inflation rate. They found evidence of market
integration between REIT and stock market, but no integration was found between
direct real estate and stock market. The results were consistent with those found in the
earlier study by Liu et al. (1990).
Liu and Mei (1992), Mei and Lee (1994) applied the generalized method of moments
(GMM) methodology to test common latent factors in asset markets. Liu and Mei (1992)
showed that the real estate return variations can be fully captured by the common risk
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factors in stock and bond markets. However, Mei and Lee (1994) subsequently found
that real estate market risk is independently priced as the third common factor in the
model. The results suggest that real estate asset should not be under-represented in
well-diversified portfolios of investors. Li and Wang (1995) using the same GMM
methodology, however, found that latent real estate factor was not significant in
predicting excess returns of REITs and other stocks.
The earlier tests of market integration in Singapore have produced mixed results.
Ong (1994) found a contemporaneous long-term relationship between property stock
return, direct real estate return and 3-month Treasury bills interest rate using a
structural vector autoregressive (VAR) model. The cointegration relationship
between securitized real estate and direct real estate was, however, rejected by Ong
(1995) and Liow (1998). Sing (2004) tested common risk premiums in the two real
estate markets, and found no evidence to support integration in the two real estate
markets. However, using Generalized Autoregressive Conditional Heteroscedasticity
in Mean (GARCH-M) model, Sing and Sng (2003) found that incremental information
in conditional volatility flowed uni-directionally from unsecuritized market to the
securitized property market. They then concluded that the two markets are partial
integrated.
3. Latent-variable asset pricing model framework
The latent factor asset pricing framework as applied by Liu and Mei (1992) to test
common risk factors in the US asset markets is summarized below. First, a k-factor
excess return function of asset i, ~ri;t1, is defined as:
~ri;t1 ¼ Et½~ri;t1_ X
K
k¼1
bik
~fk;t1 ~ 1i;t1 ً1ق
where Et½~ri;t1_ is the expected excess return on asset i conditional on information
known at the end of time t, bik is the time-invariant factor loading of the K-th factors,
and ~ 1i;t1 is the idiosyncratic error. The zero-beta return, Et½~ri;t1_, has the following
linear functional form:
Et½~ri;t1_ ¼X
K
k¼1
bik lkt ً2ق
where lkt is the “market price of risk” for the k-th factor at time t. For an information
set with a vector of L forecasting variables, Xnt, [n¼1. . .L], lkt is a linear function of
these variables:
lkt ¼X
L
n¼1
uknXnt ً3ق
and equation (2) can be represented as:
Et½~ri;t1_ ¼X
K
k¼1
bikX
L
n¼1
uknXnt ¼X
L
n¼1
ainXnt ً4ق
Common real
estate risk
premia
361
where ain is the risk premium for forecasting variable Xnt, which is subject to the
restrictions below:
aij ¼X
K
k¼1
bik ukn ً5ق
where bik and ukn are free parameters.
The model is normalized by setting the factor loadings for the first K assets as
follows: bij ¼ 1 (if j ¼ i) and bij ¼ 0 (if j – i) for 1 # i # K. The excess return matrix
is partitioned into, [R ¼ ًR1; R2ق], where R1 is a T £ K matrix of excess returns of K
assets, and R2 is a T £ ًN 2 Kق matrix of excess returns for the rest of the assets:
R1 ¼ X Q m1 ً6aق
R2 ¼ X a m2 ً6bق
where X is a T £ L matrix of the forecasting variables, Q is a matrix of uij, and a is a
matrix of aij.
The significance of common forecasting variable, X, in predicting excess returns of
assets is a test of the rank restriction, [H0: a¼QB], where B is a matrix of bij elements.
The unrestricted conditional excess returns and the restricted conditional excess
returns are estimated using Hansen’s (1982) generalized method of moments (GMM)
methodology.
4. Empirical data
4.1. Data source and definition
Quarterly excess returns of property stock, long-term government bond, industry,
retail, office and residential properties in Singapore are computed for sample periods
from 1988Q2 to 2006Q2.
The Singapore Exchange (SGX) Property Sub-sector Index (PTYS) is used to
represent the performance of securitized real estate. The quarterly bond yield (rq;t) is a
compounded rate calculated from the annualized yield (ra;t ) of five-year government
bond (BOND) as: [rq;t ¼ ً1 ra;tق1=4 2 1]. The five-year government bond (BOND)
data are obtained from the Monetary Authority of Singapore (MAS) database.
Quarterly excess returns of industry (PPII), office (PPIO), residential (PPIR) and retail
(PPIS) properties are computed from the transaction price indices published by the
Urban Redevelopment Authority (URA) of Singapore.
The quarterly excess return of asset x, [ERx ], is computed by subtracting price
returns of indices, [Rx ], by the risk-free rate, [Rf ], which is denoted as [ERx¼Rx 2 Rf ].
The three-month Treasury bills rate published by the MAS is the proxy of the risk free
rate. The annualized three-month Treasury yield (Rf,a) is converted into the quarterly
risk-free rate (Rf,q) based on the same equation used to compute the quarterly five-year
bond yields.
Four instrumental variables are used in the models to control for systematic risks,
which include credit spread (CRDSD), excess equity market return (ESGXR), term
structure of government bonds (TERMS), unexpected inflation rate (UNINF), and yield
spread (YSPRD). CRDSD is defined as the difference between prime lending rate and
three-month inter-bank rate. ESGXR is the return of SGX-all share index over the risk
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free return. TERM is the term spread of annualized rates between five-year long term
government bond yield and two-year short term government bond yield. YSPRD is the
yield spread between three-month commercial bill and three-month T-bill. The
unexpected inflation (UNINF) is computed based on the interest rate model of Fama
and Gibbons (1984). Data on government bond yields are obtained from the MAS
database, and other data on economic variables are obtained from the Time Series
Retrieval and Dissemination (TREND) database by the Department of Statistics,
Singapore.
4.2. Descriptive statistics
Descriptive statistics of excess returns of six asset classes and four forecasting
variables are reported in Table I. During the sample period from 1988Q2 to 2006Q2,
property stock was the best performer among the asset classes in terms of excess
return with a mean excess quarterly return of 0.36 per cent. Property stock was also the
most volatile asset during the sample period with a standard deviation of 20.8 per cent.
Among the direct property assets, residential property has the highest average excess
return of 1.1 per cent. Shop has a negative return of 20.2 per cent over the sample
period, but it price changes were the least volatile among the direct property assets
with a standard deviation of 4.3 per cent. Bond was the safest investment with the
lowest volatility of 0.2 per cent.
Table II shows the correlation matrices between asset classes and fundamental
variables. Correlations between excess returns of two pairs of direct properties:
office and shop, and office and industry were reported at 0.77 and 0.73 respectively.
Property stock was more closely correlated with residential property (0.43) than
with other direct property assets. Pair-wise correlations between government bonds
and property stock and other direct properties were relatively low, which imply that
diversification benefits can be achieved by mixing bond and other asset classes in
portfolios.
Descriptive statistics and data source Symbol Data source Observation Mean
Std
dev.
Excess return variables
Excess return of SGX property stock EPTYS Datastream 73 0.036 0.208
Excess return of five-year government bond EBOND MAS 73 0.004 0.002
Excess return of industry property EPPII URA 73 0.009 0.056
Excess return of office property EPPIO URA 73 0.002 0.060
Excess return of residential property EPPIR URA 73 0.011 0.049
Excess return of shop EPPIS URA 73 20.002 0.043
Forecasting variables
Credit spread between prime lending rate and
three-month inter-bank rate CRDSD Datastream 73 0.030 0.012
Excess return of SGX All-share index ESGXR Datastream 73 0.014 0.123
Yield spread between long and short term
government bonds TERMS Datastream 73 0.025 0.018
Unexpected inflation UNINF Datastream 72 0.009 0.007
Yield spread between three-month T-bill and
commercial bill rates YSPRD Datastream 73 0.008 0.012
Table I.
Summary statistics
Common real
estate risk
premia
363
5. Empirical results
5.1. Regressions for excess returns
Regression models for excess returns of six sample assets on five instrumental variables
and a constant term were estimated by a system of equations using the generalized
method of moments (GMM). The regression results were summarized in Table III. The
model of excess government bond return has the best fit estimation with an adjusted
R-square of 65.5 per cent. Variations in excess property stock returns were the least
predictable by the GMM model as reflected by the adjusted R-square of 1.1 per cent.
Durbin-Watson statistics were not significant for all the models except the excess
property stock return model. Persistence autocorrelations were expectedinthe models[1].
The market betas were negative in all models, but the coefficients were only
significant in the government bond, residential and office models at a 10 per cent
significance level. Credit spread, which measures the costs of external debt, was
negatively related in all direct property excess returns. Property investment and
development activities are in general highly leveraged. Therefore, increases in costs of
debt are expected to have negative effects on the performance in the returns of
properties. The same negative effects of commercial bill rate spread over the
three-month Treasury bill rate were also observed on the office and residential models.
The credit risks and spread in commercial bill rates, on the other hand, increase the
excess returns of government bonds.
In term of term structure of government bond yields, the positive result in the excess
government bond model is observed at a 5 per cent significance level. It is, however,
interesting to also note that excess returns of three of the four property submarkets
that include industry, residential and office, track the term structure positively. The
results also show that shop and residential properties were positive hedges against
unexpected inflation at a 10 per cent significance level.
In the excess return model for property stocks, only yield spread was significant but
negatively related to the variations in property stock excess returns at 5 per cent
significance level.
5.2. Tests of common latent risk factors
Based on the same GMM model specifications presented above in Section 5.1, which
include five instrumental variables and an intercept term, we device our tests of
common latent risk factors into three parts involving different portfolios of sample
Correlation
analysis EPTYS EBOND EPPII EPPIO EPPIR EPPIS CRDSD ESGXR TERMS UNINF
EBOND 20.064
EPPII 0.071 0.029
EPPIO 0.164 20.071 0.731
EPPIR 0.430 0.100 0.435 0.537
EPPIS 0.165 20.057 0.541 0.770 0.462
CRDSD 20.094 0.265 20.350 20.383 20.170 20.268
ESGXR 20.012 0.208 20.015 0.032 0.273 0.145 0.168
TERMS 0.053 0.241 0.483 0.348 0.357 0.236 20.555 0.037
UNINF 0.048 20.394 0.101 0.078 20.161 0.000 20.627 20.194 0.388
YSPRD 20.211 0.589 0.144 20.004 20.102 0.003 20.267 0.036 0.488 0.185
Table II.
Summary statistics
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Intercept
Credit
spread
Unexpected
inflation
Excess market
return
Term
structure
Spread of commercial
bills Adjusted
INT CRDSD UNINF ESGXR TERMS YSPRD R 2
Government
bond Coefficient 0.002 0.065 0.001 20.147 0.037 0.128 0.655
(EBOND) t-statistic 1.809 3.802 0.540 24.420 3.103 9.080
Prob. 0.071 0.000 0.589 0.000 0.002 0.000
Property stock Coefficient 0.096 21.840 0.020 20.609 1.899 25.729 0.011
(EPTYS) t-statistic 0.786 20.721 0.117 20.132 1.213 22.883
Prob. 0.432 0.471 0.907 0.895 0.226 0.004
Industry
property Coefficient 0.030 21.206 20.007 22.026 1.663 20.752 0.246
(EPPII) t-statistic 1.015 22.099 20.138 21.456 4.127 21.382
Prob. 0.311 0.036 0.890 0.146 0.000 0.168
Office Coefficient 0.078 22.316 0.034 22.604 1.184 21.390 0.226
(EPPIO) t-statistic 2.181 23.033 0.803 21.827 2.642 22.130
Prob. 0.030 0.003 0.423 0.069 0.009 0.034
Residential Coefficient 0.052 21.232 0.102 23.376 1.649 21.804 0.403
Property
(EPPIR) t-statistic 2.128 22.575 2.412 23.338 4.769 23.550
Prob. 0.034 0.010 0.016 0.001 0.000 0.000
Shop Coefficient 0.053 21.508 0.065 21.841 0.568 20.765 0.146
(EPPIS) t-statistic 1.479 22.029 1.870 21.620 1.391 21.635
Prob. 0.140 0.043 0.062 0.106 0.165 0.103
Table III.
Regression results of
unrestricted excess
returns of sample assets
Common real
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365
assets. The first set of the tests involves only all direct property excess returns. We
then add government bond and property stocks in the two subsequent tests. The
incremental approach could allow us to separate the common property market effects
from the bond and equity market effects. The results of the tests of existence of
common latent factors were summarized in Table IV.
The chi-square statistics, which were computed from J-statistics in the GMM model,
were used to test the restriction in equation (5). In Panel (A) of Table IV, the regression
results do not reject the null hypothesis, Ho: [K ¼ 1], which implies that there is at most
one latent systematic risk factor that explains variations in excess returns of the four
direct property assets. Next, we add government bond into the sample portfolio in the
second stage tests. The results in Panel (B) shows that when bond is used as the reference
asset, the chi-square statistic of 49.405 rejected the null hypothesis for [K ¼ 1] latent
factor. However, the chi-square test (x2 ¼ 12:576) failed to reject the hypothesis for
[K ¼ 2] when industry property excess return (EPPII) was included as the second
common reference factor. The results implies that there are at most two common latent
risk factors, which include a common bond market factor and a common direct property
market factor, that are sufficient to predict the excess returns of the sample assets.
In stage three (Table IV – Panel C), property stock was added to the five asset
sample portfolio consisting of four direct property assets and government bond. The
chi-square statistics rejected the null hypotheses for [K ¼ 1] and [K ¼ 2] at 10 per cent
significance level when EBOND and EPTYS were used as reference assets
respectively. The null hypothesis for [K ¼ 3] when EPPII was added as the third
reference asset was not rejected at 5 per cent significance level. The results collectively
imply that three common latent factors that include government bond, property stock
and direct property could predict the variations in the excess returns of the six sample
assets. The results were not different from those in Mei and Lee (1994) in term of
number of common risk factors found in the US markets. However, in Mei and Lee
(1994), they showed that bond, stock (equity) and equity REITs latent factors were the
three significant latent risk factors. Whereas in our model, equity market excess return
is used as an instrumental variable to control for systematic market risks. The three
common factors in our model include bond, property stocks (a close proxy of equity
REITs in the US market) and direct property latent variables.
The above results offer further empirical evidence to reject that property stock
(securitized) and direct property markets were integrated in Singapore markets. At
least, the two property market risk factors were priced significantly different in the
multi-factor latent risk models. The finding that rejects the market integration
hypothesis for the two property markets in Singapore was consistent with the earlier
results of Ong (1995), Liow (1998), Sing and Sng (2003) and Sing (2004). The results
suggest that there was no dilution of diversification efficiency if investors include both
direct property and property stocks in the same portfolio. These two assets capture
significantly different risk premiums in the markets, and variations in excess returns
could be incrementally explained by common latent factors in bond, property stocks
and direct property markets.
6. Conclusion
In this paper, the multi-factor latent variable model was used to test the predictability
of the five asset markets and the significance of common risk premia in bond, property
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Number of latent
factor (K)
Reference
asset
Excess
return
Property stock
(EPTYS)
Industry
property (EPPII)
Office property
(EPPIO)
Residential
property (EPPIR)
Shop
(EPPIS) Chi-square
Degree of
freedom Probability
Panel (A): All direct property asset (EPPII, EPPIO, EPPIR, EPPIS)
K¼1 EPPII bi 1.043 1.130 0.542 18.607 15 0.232
t-statistic 6.942 6.191 4.239
Prob. 0.000 0.000 0.000
Panel (B): All direct property assets (EPPII, EPPIO, EPPIR, EPPIS) Government Bond (EBOND)
K¼1 EBOND bi 11.583 13.947 14.866 7.472 49.405 20 0.000
t-statistic 3.720 3.580 4.507 2.859
Prob. 0.000 0.000 0.000 0.005
K¼2 EBOND bi 23.005 20.216 20.732 12.576 8 0.127
t-statistic 22.925 20.141 20.877
Prob. 0.004 0.888 0.381
EPPII bi 1.254 1.420 0.635
t-statistic 6.297 5.186 3.652
Prob. 0.000 0.000 0.000
Panel (C): All direct property assets (EPPII, EPPIO, EPPIR, EPPIS) Government Bond (EBOND) Property Stock (EPTYS)
K¼1 EBOND bi 24.298 9.520 11.203 13.458 5.066 44.315 25 0.010
t-statistic 2.514 4.202 3.727 4.795 2.436
Prob. 0.012 0.000 0.000 0.000 0.015
K¼2 EBOND bi 4.210 2.212 4.528 1.863 25.241 16 0.066
t-statistic 1.916 0.882 1.847 1.330
Prob. 0.056 0.378 0.065 0.184
EPTYS Coefficient 0.561 0.704 0.721 0.311
t-statistic 2.222 2.384 2.381 2.363
Prob. 0.027 0.018 0.018 0.019
K¼3 EBOND bi 21.858 0.628 20.593 12.730 9 0.175
t-statistic 21.810 0.470 20.720
Prob. 0.071 0.639 0.472
EPTYS bi 0.113 0.053 20.014
t-statistic 1.875 0.626 20.240
Prob. 0.062 0.532 0.810
EPPII bi 0.915 1.194 0.725
t-statistic 5.116 5.141 4.116
Prob. 0.000 0.000 0.000
Notes: Et ½~ri;t1_ ¼X
K
k¼1
bikX
L
n¼1
uknXnt ¼X
L
n¼1
ainXnt (4)
aij ¼X
K
k¼1
bik ukn (5)
Empty cells indicate that either the excess returns of the assets were not included in the sample or they were used as reference assets in the latent variable tests
Table IV.
Estimation results for
multi-factor latent
variable models
Common real
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premia
367
stock and four property markets in Singapore. Compared with the results in Mei and
Lee (1994) study, who found bond, stock and equity REIT as three significant common
latent risk factors in the US asset markets, our results show that securitized property
stock (a close proxy of equity REITs) and direct property captured different risk
premia, in addition to common bond risk premium in the model. The results imply that
risk premium in securitized property market could not be replicated by holding direct
property and vice versa. In other words, the two property markets were not perfectly
integrated. They were not perfect substitutes from the portfolio diversification
perspective.
In our GMM framework, five instrumental variables that include credit risk spread,
excess stock market return, unexpected inflation, terms structure between two
government bonds of different terms, and the spread between commercial and
Treasury bill rates. The explanatory variations in the significance of the estimated
coefficients of instrumental variables also pointed to the evidence there was no single
common risk factor that can fully capture the risk premiums in bond, property stocks
and direct property markets. One technical caveat in the empirical specification is that
it is difficult to fully capture all risk information as represented by the GMM model
with five instrumental variables. The omission of other variables is, however,
traded-off against the parsimony of the model specification in this study.
Note
1. Ferson (1990, footnote 18) explained that residual autocorrelations in the GMM estimation
could be caused by the omission of “market” information that is not captured by the
instruments. The results do not imply mis-specification of the conditional means in the
model, and therefore, the model structure does not affect our tests of significance of latent
risk factors for the sample assets in the next section.
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Corresponding author
Tien Foo Sing can be contacted at: rststf@nus.edu.sg
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سلام , این وبلاگ رو در اصل به منظور موضوعات مالی و فاینانس ایجاد کردم ولی گاهی اوقات از مطالب و تصاویری که شخصاَ بهشون علاقمند هستم استفاده می کنم.مرسی از بازدیدتون.