股市的長期風險管理與總體經濟基要

LONG-RUN RISK AND MACROECONOMIC FUNDAMENTALS

本文以Engle and Rangel（2008）提出的spline-GARCH為基礎，建構納入總體經濟基要變數的長期波動度新模型與預測長期風險的方式。我們利用Empirical Mode Decomposition（EMD）方法拆解GDP與CPI季資料得到去除長期趨勢後數個不同頻率且互相正交的數列，檢驗長期下股票市場風險與總體經濟環境的關聯，以及總體景氣狀態變數在股市風險結構轉換中所扮演的角色。我們的實證結果顯示，利用這些總體市場基要成分建立的模型使得財務市場的總風險（波動度）得以自然地隨著總體經濟狀況作結構性轉換調整而無需依賴特定門檻效果或者馬可夫轉換等機制，本文之模型結構轉換的觸發取決於總體經濟環境的改變。我們進一步利用此架構預測金融海嘯後2008與2009年為期兩年的樣本外99%信心水準下的風險值期限結構，結果顯示適度地納入長期總體經濟環境的資訊於風險模型中不僅有助於降低極端損失風險，而且同時加入實質面與名目面的資訊內涵對長期風險危機預警會更有效。

Generalizing the component GARCH by Engle and Rangel (2008), this paper pro-poses a new modeling and forecasting strategy for systemic risk both in the short term and long-run. Utilizing the orthogonally decomposed stationary regularity series from real quarterly GDP and CPI by EMD (Empirical Mode Decomposition), an empirical adaptive decomposition method that aims to entertain nonlinear and nonstationary time series, we demonstrate the close coupling relationship between long-run stock market volatility and the business cycle fluctuations. As these component series preserve the most primary in-formation in the macroeconomic state variables sampled at lower frequencies, the long-run component volatility is capable of generating regime shift behaviors in daily volatility with-out resorting to Markov switching or other regime switching mechanisms. Moreover, the prediction of future volatility at various horizons is easy within the framework by taking advantage of the decomposed stable cyclical pattern of these macroeconomic series. By further examining the relative contribution of 3 factors (namely long-term, medium-term and short-term) comprising the long-run risk to the overall volatility, we find that the median frequency factor in long-run volatility explains the turbulent market variations during periods of recession. Our empirical applications in hedging and evaluating VaR reveal that incorporating information from lower frequency macroeconomic fundamentals did provide incremental value toward the modeling of long-run risks.