結構轉換模型於風險值、資產配置決策、與貨幣回饋法則之運用

Value-at-Risk、Portfolio Allocation and Monetary Feedback Rule: Applications of the Multivariate Regime Switching Model

張光亮(Kuang-Liang Chang)

指導教授 ： 鍾經樊

共同指導教授 ： 陳南光

國立臺灣大學/社會科學院/經濟學研究所/博士(2004年)

https://doi.org/10.6342/NTU.2004.01661

摘要

本論文將狀態轉換模型 (regime-switching model) 運用到財務經濟學與總體經濟學，
其內容包含風險值 (Value at Risk) 之計算、
資產配置決策之制定、
與探討貨幣基數回饋法則。

第一章在於比較不同計量模型對於美法二國股票資產組合風險值 (Value at Risk, VaR) 的預測精確度，
比較的計量模型包含 GARCH 模型、 Hamilton and Susmel (1994) 的 Regime-Switching AR-ARCH (SWARCH) 模型、
與 Chung (2003) 的 Autoregressive Logit Regime-Switching (ALRS) 模型，
使用失敗率 (failure rate) 與 Kupiec (1995) 概似比檢定法 (likelihood ratio test) 來衡量預測精確度。
實證結果發現，
GARCH 模型的預測績效遠遠低於 SWRACH 與 ALRS 模型，
所以條件常態分配假設確實會忽略金融資產分配具有厚尾的現象，
造成 GAR-CH 模型估算之 VaR 無法反映真實的風險程度。
同屬於具有狀態轉換結構的 SWARCH 與 ALRS 模型，
將美國與法國股票市場結構轉換的特徵納入分析架構，
考量報酬率分配厚尾、 期望值和變異數隨狀態改變、 與波動叢聚現象 (SWACH 模型波動叢聚特性不明顯)，
資產組合報酬率 VaR 之預測能力較 GARCH 模型佳。
在投資損失超過風險值的可能性等於百分之一的情況下，
SWARCH 模型的預測能力較 ALRS 模型好；
在投資損失超過風險值的可能性等於百分之二點五、百分之五的情況下，
ALRS 模型的預測精確度較 SWARCH 模型好。

在美國與法國股票報酬率呈現狀態轉換的二元常態分配之假設下，
第二章研究極大化 CA-RA 效用函數 (constant absolute risk aversion utility)
與 CRRA 效用函數 (constant relative risk aversion utility) 所決定的資產配置決策是否與均數---變異數方法相同，
並且探討不同狀態轉換模型的資產配置績效。
實證結果有二個發現：
第一，
在允許資產報酬率出現狀態轉換的情況下，
極大化 CARA 效用函數與均數---變異數方法所決定的資產配置決策非常接近；
但是極大化 CRRA 效用函數與均數---變異數方法所決定的資產配置決策差距頗大。
第二，
不論資產配置決策方法與風險趨避度為何，
使用 Chung (2003) 的 Autoregressive Logit Regime Switching (ALRS)
模型來執行資產配置決策可以獲得最大的累積報酬，
ALRS 模型的資產配置績效比 Regime Switching AR-ARCH (SWARCH)、 GARCH 模型還要好。

文獻上常見的回饋法則存在二個缺點：
第一，
假設線性的回饋法則，
線性的設定方式無法反應 Bernanke and Mishkin (1992) 的貨幣管理當局危機意識行為 ---
當某一貨幣政策目標有危機時，
貨幣管理當局會提高該目標的重要性。
第二，
目標值事前就已經決定，
事先決定的目標值無法將決策時間落後 (time lags) 的問題納入考量。
第三章的目的即是在檢驗美國貨幣管理當局是否對產出和物價具有危機意識，
實證模型是一個根據貨幣基數成長法則的三變量三狀態馬可夫狀態轉換模型，
允許貨幣基數成長率、
實質產出成長率、
與物價成長率受到相同隨機變數的影響，
以內生決定狀態及其轉換的時間點，
並且在設定目標時將未來經濟情況納入考量。
實證結果發現，
在 1974 年第 1 季到 1975 年第 3 季、
與 1979 年第 1 季到 1980 年第 3 季 (低產出與高通膨狀態) 的時期，
產出成長率大幅下跌 (實際成長率低於目標值)，
產出缺口回饋係數的絕對值變大，
這個結果顯示在產出成長率下跌時，
貨幣管理當局對產出偏離目標所採取的因應措施較為強烈。
美國在上述二段期間出現通貨膨脹危機，
但是貨幣管理當局並未採取緊縮措施來抑制通貨膨脹，
此結論與 Clarida et al. (2000) 的看法相符---
在聯邦理事主席 Volcker 上任之前，
美國並未對通貨膨脹進行管制。
所以美國貨幣管理當局在上述期間對產出具有危機意識，
但是對物價並無明顯危機意識。

關鍵字

均數-變異數方法 ； 資產配置績效 ； 極大化效用函數方法 ； Autoregressive Logit Regime Switching (ALRS) 模型 ； 三變量三狀態馬可夫狀態轉換模型 ； 貨幣基數回饋法則 ； GARCH 模型 ； Regime Switching AR-ARCH (SWARCH) 模型 ； 風險值 ； 回饋係數 ； 時間落後

並列摘要

This dissertation analyses the applications of the multivariate regime switching model to
estimate the Value-at-Risk (VaR)，
the portfolio allocation, and the monetary feedback rule。

In Chapter 1, we analyse the application of a switching volatility model
to forecast the distribution of returns and to estimate the VaR of a portfolio of sotcks.
The calculated VaR values are also compared with the generalized autoregressive
conditional heteroscedasticity (GARCH) model,
and the Regime Switching AR-ARCH (SWARCH) model (Hamilton and Susmel, 1994),
and the Autoregressive Logit Regime Switching (ALRS) model (Chung, 2003).
Using a portfolio composed of two stocks, the US stock and French stock,
we evaluate the forecasting performance of VaR obtained from the above approaches by
computing Kupiec's (1995) likelihood ratio tests on the empirical failure rates.
The empirical results show that the VaR values calculated from the bivariate SWARCH and ALRS models
outperform the GARCH model.
We show that the GARCH model based on conditional normal distribution assumption is at odds
with reality and often results in misleading estimates of VaR.
At the 1 \% level,
the SWARCH model significantly outperforms the ALRS model.
In contrast,
the ALRS model outperforms the SWARCH model with 2.5\% and 5\% tail probabilities.

It is frequently asserted that mean-variance analysis applies exactly only when distributions
are normal or utility functions are quadratic,
suggesting that it gives almost optimum results only when distributions are apporximately normal
or utility functions look almost like a parabola.
On the other hand,
the mean-variance approximation (a second-order Taylor expansion of the utility function around the mean
of portfolio return) is equivalent to the utility maximization.
Regime-switching models have been successfully used to model many financial time series.
Based on regime switching models,
in Chapter 2 we examine whether investors with exponential and power utility functions
choose mean-variance efficient portfolio when returns are state-dependent bivariate normal distribution.
We illustrate the use of regime switching models (SWARCH, ALRS) in portfoilio choice problems and
compare the performances of regime switching models.
The results show that the portfolios of exponential utility investors plot very closely to the MV-efficient
frontier.
However, portfolio allocations are marked differences between
utility maximization and mean-variance approximation.
We also find that, compared to GARCH and SWARCH frameworks,
the portfolio choices resulting from ALRS model lead to higher investment performances.

Many monetary feedback rules are assumed to be linear,
i.e. the feedback coefficients of target variables are constants.
Linear rules have difficulty in capturing the discretionary actions taken by monetary authorities,
especially when monetary authorities encounter unexpected or drastic changes in economic situations.
Furthermore, the object targets do not include current information and ignore the problem of time lags.
The empirical model we propose is a trivariate three-state Markov
regime-switching model that is originated from McCallum's (1987) monetary base growth rule.
The three macro variables we consider are the monetary base growth,
the real GDP growth, and the inflation rate.
It is assumed that these three variables are subject to the same
Markov regime-switching variable in determining their three states.
The feedback coefficients and the weighted coefficients are governed by a state variable.
Our empirical
results using US's quarterly data suggest a low growth-high inflation state,
and a high growth-medium inflation state,
and a medium growth-low inflation state :
the former includes 1974Q1 -- 1975Q3,
and 1979Q1 -- 1980Q3.
The main finding of this chapter is that
the behavior of the Feds does exhibit some features of crisis mentality in real GDP growth,
but not in inflation rate.

並列關鍵字

time lags ； SWARCH ； ALRS ； utility maximization ； mean-variance ； portfolio allocation performance ； feedback coefficient ； monetary feedback rule ； Value-at-Risk ； GARCH ； trivariate three-state Markov regime-switching model

參考文獻

Shen, C. H. and S. C. Hsu (2000), Discretionary Monetary Feedback Rule : The Taiwan Case,Academia Economic Papers, 4, 339-364.

Clark, R. G. and H. D. Silva (1998), State-Dependent Assest Allocation,The Journal of Portfolio Management, 57-64.

French, K. R. and J. M. Poterba (1991), Investor Diversification and International Equity Markets,

Ang, Andrew and G. Bekaert (2000a), International Assest Allocation with Regime Shifts, The Review of Financial Studies, 15, 1137-1187.

Ang, Andrew and G. Bekaert (2000b), How do Regimes Affect Asset Allocation ?,working paper.