考慮總體因素與關聯結構之最適資產配置

Optimal asset allocation with macroeconomic factors and dependence structure

陳竑廷(Hung-Ting Chen)

指導教授 ： 李美杏

國立臺北大學/商學院/統計學系/碩士(2011年)

摘要

建構投資組合時，關聯性大多利用線性關聯，忽略其他形式的關聯，很多實證顯示股票報酬並非常態分配，而是呈現左偏及厚尾的型態。若進行投資組合權重計算過程中，忽略了關聯結構的重要性以及假設資產報酬分配服從常態分配，可能會造成投資組合的不正確性，降低投資組合分散風險的效益。
本文採用Skewd-T-TGARCH 模型捕捉股票報酬左偏及厚尾現象，進行S&P500股票與美國十年期公債報酬的邊際分配模型估計；在資產間的關聯結構利用隨時間改變的動態Copula (Time-Varying Conditional Copula) 模型，並擴充加入總體經濟因素當作外生變數建構股票與債券的關聯結構。最後，在Copula-GARCH的架構下，利用美國股票與債券在近三十年來關聯性結構，考慮在不同程度的投資條件限制與投資者具有不同風險規避程度下，以CRRA(constant relative risk aversion) 效用函數當作投資者決策法則計算最適的投資權重。研究結果顯示，在總體變數方面，對S&P500股票影響較顯著的變數為公司債利率評等BAA級與AAA級利率差，兩者呈現負向關係，而對於美國十年期公債影響較顯著的變數為短期利率，考慮不同的投資情況與投資人不同的風險規避程度下，使用加入時間因子的Time-Varying copula模型建構S&P500與美國十年期公債的投資組合，在整體投資組合的效益會比起忽略關結構的二元常態固定關聯係數有較好的績效，另一方面，也發現當風險規避程度高的投資人利用Time-Varying Normal copula 模型，整體來說均有較好的績效表現。

關鍵字

關聯結構,Copula,Copula-GARCH,CRRA

並列摘要

In this study, an important issue is how dependence between equity returns and bond returns can be measured when equity returns are non-normal. We apply the skewed-T-TGARCH model for negatively skewed and fat tails returns, and we use the time-varying conditional Copula to measure conditional dependence in a GARCH context. The use of Copulas makes it possible to separate the dependence model from the marginal distributions.

This paper applies above methodology to the monthly returns of S&P500 stocks and U.S. 10-year bonds. We solve the optimal investment problem in the presence of asymmetric dependence and skewness for investors with constant relative risk aversion (CRRA) preferences. We consider both unconstrained and short sales constrained estimates of the optimal portfolio weight. For investors with unconstrained or short sales constrained, we find that the model capturing asymmetric dependence and skewness yield better portfolio performance than the bivariate normal model.

並列關鍵字

dependence structures, Copula, Copula-GARCH, CRRA

參考文獻

3.丁聖祐(2010)，「考慮關聯結構之最適投資組合」，國立台北大學統計學系研究

1. Andersen, T.G., Bollerslev, T., Diebold, F.X., and Vega, C., (2007). Real-time price discovery in stock, bond and foreign exchange markets. Journal of International Economics, 73, 251–277.

2. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31 (3) ,307-327.

3. Boyd, J.H., Jagannathan, R., and Hu, J., (2005) The stock market’s reaction to unemployment news：Why bad news is usually good for stocks. Journal of Finance 60, 649–672

4. Cappiello, L., Engle, R.F.,and Sheppard,K., (2006) Asymmetric dynamics in the correlations of global equity and bond returns .Journal of Financial Econometrics, 2006, 4(4), No. 4, 537–572