預測性熵投資組合模型

傳統的投資組合的方法大多數都是藉由過去的歷史資料來追求未來的高報酬並將風險降低至一定的需求，但當投資市場呈現高波動或者是不穩定時，歷史數據並無法完全反應未來市場的不確定性。Leung et al. (2001) 說明了將預測未來的機制納入投資組合中能夠使投資組合在高波動的市場獲得更佳的績效。此外，Markowiz (1952) 所提出的投資組合均異模型也被明確的指出存在有過度集中投資的狀況。本研究的目的在於提出一個線性化的預測性熵投資組合模型：能夠有效分散風險避免集中投資以及能夠考量未來市場報酬的投資組合模型，在浮動需求報酬的機制之下考量了Yager (1995) 的熵作為分散化的機制與Ustun and Kasimbeyli (2012) 所提出投資組合結合預測技術的方式分別來處理風險的分散化與投資組合反應未來市場的不確定性，建構出Yager_Forecasting (Yager_F) 投資組合模型。因應不同時期會有不同的情境發生，本研究的需求報酬為浮動的需求報酬使預測機制更能夠反應市場，同時分析比較Yager模型、傳統均異模型 (MV) 以及平均分散投資各標的的投資組合 (1/N) 模型，觀察各投資組合的效益。在利用2007年9月25日到2014年10月20日的標準普爾500指數成份股及21支指數型基金、5支能源礦物型基金與1支不動產投資信託基金共27支基金標的作為兩組資料集，透過平均實際報酬、實際報酬標準差、平均投資標的數、夏普指數及歐米茄指數來進行績效的比較。本實驗可以發現在次級房貸風暴發生時或者是在長期投資時Yager_F能夠因為分散化而有效的降低投資風險並使損失降低使投資組合獲益。在景氣轉換的變動時也能夠及時的反應市場波動，使投資組合的市值績效能夠顯著的提升。

關鍵字

熵；投資組合；預測機制；多目標；再調整；放空；交易成本

並列摘要

In this research we present a forecasting entropy portfolio selection model, which have efficient diversification and consider uncertainty of future return. On the development of portfolio selection, Entropy is used as the measurement of risk to replace the variance in conventional Mean-Variance portfolio selection model to deal with the issue of non-diversification. Leung et al. (2001) illustrates the combined forecasts in portfolio optimization let the portfolio have better performance in the high volatility market. We consider the entropy model proposed by Yager (1995) and combine forecasts method proposed by Ustun and Kasimbeyli (2012) to construct a multi-objective Yager_Forecasting model (Yager_F) to deal with risk diversified and uncertainty of future return. To reflect the real transactions in the capital market, the proposed method allows short selling and considers transaction cost. In addition, we use two data sets: the constituent stocks in S&P 500 index (2007 to 2014) and Exchange Traded Funds (2007 to 2014) to compare with the 1/N model, MV model, Yager model and MV_Forecasting model (MV_F). The performance measures such as market value, realized return, Sharpe ratio, Omega ratio etc. are employed to evaluate each model under the floating required return and rebalancing mechanism. The results show that when the market is bearish like during Subprime mortgage crisis or long-term investment, Yager_F model can measure the uncertain returns and timely reflect to market volatility when Business Cycle converted, it make the market value of the portfolio can be outperform than other models.

並列關鍵字

Entropy ； Portfolio selection ； Forecasting ； Multi-Objective ； Rebalancing ； Short selling ； Transaction cost

參考文獻

Al-Sharhan, S., Karry, F., Gueaieb, W., and Basir, O. (2001) Fuzzy entropy: A brief survey. The 10th IEEE International Conference on Fuzzy Systems 3, 1135-1139, Melbourne, Australia.

Google Scholar

Bardong, F., Bartram, S. M., Yadav, P. K. (2008). Are short-sellers different? EFA 2008 Athens Meetings paper, Retrieved from http://ssrn.com/abstract=1101786.

Google Scholar

Bartlmae, K. (2009). Portfolio construction: using bootstrapping and portfolio weight resampling for construction of diversified portfolios. International Conference on Business Intelligence and Financial Engineering, Beijing.