本文以權益型REITs、抵押型REITs和台股指數對美元匯率之日資料分別組成兩個不同類型的國際投資組合，運用GARCH-BEKK模型來估計這些投資組合的風險值。首先利用 Kupiec(1995)的LRuc檢定和 Christoffersen(1998)的LRcc檢定，估算匯率影響這些國際投資組合風險值的準確度；其次再利用Lopez(1999)的市場風險損失函數和Hansen(2005)的SPA檢定，探討持有權益型REITs和抵押型REITs所需提列的市場風險資本有無顯著差異，藉以推論權益型REITs和抵押型 REITs之間是否具有替代性。
實證結果顯示：1. 無論在單一資產類型或兩資產類型的投資組合中，匯率變化對美元計價的REITs之風險值有其影響力。而且對於兩資產類型的投資組合，一旦增加較多的REITs權重，匯率對此投資組合的風險值影響更高，也就是滙率水準對不同權重的REITs有同方向的影響程度。2. 以單一資產組成的投資組合中，權益型REITs應提列的風險資本低於抵押型REITs應提列的部份。在此類型的投資組合下，機構法人欲增加一單位抵押型REITs部位，相較下必須負擔較多的機會成本。3. 在兩資產類型的資產組合中機構法人投資REITs權重超過50%時，權益型REITs應提列的風險資本低於抵押型REITs應提列的部份，兩者之間並沒有等比例增減的替代關係。

This thesis regards two types of international investment portfolio individually constructed with equity Real Estate Investment Trusts (EREITs), mortgage Real Estate Investment Trusts (MREITs) and Taiwan stock index against US Dollar as the research objects. And the GARCH-BEKK models are used in this study while evaluating the VaR estimates of these international portfolios. First, this study follows the LRuc test of Kupiec (1995) and the LRcc test of Christoffersen (1998), which can be viewed as accuracy evaluation of VaR models. Second, we employ the market risk capital loss function formalized by Lopez (1999) and Superior Predictive Ability (SPA) test proposed by Hansen (2005), to investigate the difference in market risk capital requirement between EREITs and MREITs is significant or not, and regard that, we can make a conclusion whether substitutability has been exited between EREITs and MREITs. 
The empirical result shows that：1. Exchange rate has influence on the VaR estimates of an international portfolio constructed by one-asset model or two-asset model. When the weight of REITs grows higher, the influence of exchange rate relatively goes bigger. That is, the influence on three different weights of EREITs and MREITs are positively related to exchange rate. 2. For the case of one-asset model, the required market risk capital of the EREITs investment is significantly below the holding level of the MREITs investment. The amount increased for MREITs investment will be adjusted to reflect the amount of opportunity cost held by financial institution, which is not less than that of EREITs. 3. While the weight of EREITs and MREITs of two-asset model exceed over 50%, the two types of REITs are neither substitutable nor to reflect the amount of market risk requirement on a proportionate basis.

TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS i
ABSTRACT IN CHINESE ii
ABSTRACT IN ENGLISH iv
LIST OF TABLES viii
LIST OF FIGURES ix

CHAPTER
1.Introduction 1
1.1 Motivations and objectives 1
1.2 The expatiation of REITs environment 3
1.2.1 REITs Basics 3
1.2.2 The Fundamentals of REITs 8
1.2.3 Return Delivered by REITs 9
1.3 The introduction of Value-at-Risk 13
1.4 Flow chart 15
2.Literature Review 16
2.1 Revenue side 16
2.2 VaR side 25
3.Econometric Methodology 29
3.1 The definition of Value-at-Risk 29
3.2 VaR for foreign-asset portfolio 31
3.3 Multivariate GARCH model 33
3.4 Accuracy and efficiency evaluation of VaR model 35
3.4.1 Accuracy evaluation 35
3.4.1.1 LR test for unconditional coverage (LRuc) 35
3.4.1.2 LR test for conditional coverage (LRcc) 36
3.4.2 Efficiency evaluation 37
3.5 Superior Predictive Ability (SPA) test 38
4.Empirical Results and Analysis 40
4.1 Data description 40
4.2 Analyzing predictive accuracy of GARCH - based VaRs
    with / without exchange rate for one-asset portfolio 42
4.3 Analyzing predictive accuracy of GARCH - based VaRs 
    with / without exchange rate for two-asset portfolio 48
4.4 Analyzing efficiency evaluation of GARCH-based VaRs
    with exchangte rate for an international portfolio   57
5.Conclusions and Suggestions 62
References 65

LIST OF TABLES
Table 1 Historical REIT industry market capitalization 5
Table 2 Descriptive statistics of daily returns using
        EREITs, MREITs, exchange rate  and Taiwan stock
        index data 42
Table 3 Summary and accuracy results of GARCH-based VaRs
        with/without exchange rate 47
Table 4 Summary and accuracy results of GARCH-based VaRs
        with two assets (Taiwan stock index weight: 75% &
        foreign asset weight: 25%) 52
Table 5 Summary and accuracy results of GARCH-based VaRs
        with two assets (Taiwan stock index weight: 50% &
        foreign asset weight: 50%) 53
Table 6 Summary and accuracy results of GARCH-based VaRs
        with two assets (Taiwan stock index weight: 25% &
        foreign asset weight: 75%) 54
Table 7 Summary and accuracy results of GARCH-based VaRs
        with two assets 55
Table 8 Summary of Superior Predictive Ability (SPA) test
        for market risk capital (MRC) 61

LIST OF FIGURES
Figure 1 REITs invest in all property types 4
Figure 2 Historical REIT industry market capitalization 7
Figure 3 Dividends of REITs 10
Figure 4 NAREIT equity REIT index 20 year of annual returns 12

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