考慮行為股票之極值分布投資組合最佳化

現代化投資理論假設市場是有效率的且投資者都是理性的。但個人認知偏差或情緒化的決策會造成不理性的投資行為的發生，這些不理性的行為可能會造成股價的波動，而受不理性行為影響的股票我們稱為行為股票(B-stock)。一般假設股票報酬率呈現常態分配，但經過測試後，行為股票的報酬並不符合常態分配且大多數呈現厚尾的情形。因此本研究利用極值理論(EVT)來模擬行為股票(B-stock)的尾端分配。然而，股票報酬通常呈現非線性相關，利用Pair-Copula 可以更準確的估計股票報酬之間的相關性。此外，藉由給予不同情境的未來報酬進行機率分配，和Safety-first 模型來建構行為股票投資組合最佳化模式來產生最佳化投資組合。本研究將會比較利用歷史資料和由極值理論和Pair-Copula相關結構所模擬出來的未來報酬所產生的最佳化投資組合。從測試結果來看，利用極值理論和Pair-Copula相關結構來模擬行為股票(B-stock)的未來報酬可以產生顯著的利潤，且模擬產生的未來報酬比歷史資料資料有更好的報酬。

關鍵字

行為投資組合最佳化；極值理論； Pair-Copula相關性結構； Safety-first模型

並列摘要

Modern portfolio theory (MPT) assumes that the market is efficient and investors are rational. But each individual has their own cognitive and/or emotional bias that may lead to some irrational investment behaviors. Collectively, these irrationalities may have an effect on the stocks such that it can influence the price movements and returns. Stocks affected by these irrational behaviors are called behavioral stocks (B-stocks). The usual assumption on returns is that they follow normal distribution but upon testing the distributions of some B-stocks, it was observed that a lot of them have returns that are not normally distributed and they also have heavy tails on the downside risk. Accordingly, in this study the returns of B-stocks are modeled by extreme value theory (EVT) by doing so the underestimation of the downside risk is avoided. However, the downside risk of stocks is usually not linearly correlated so Pair-Copula must also be applied to have a more precise and symmetric estimate of the downside risk. Consequently, the simulated return scenarios utilizing EVT and Pair-Copula are compared to the historical return scenarios. From the back tests using the SF model, the results shows that portfolios of EVT and Pair Copula generated scenarios for B-stocks outperforms those portfolios of historical data scenarios. Moreover, comparing the portfolios with respect to their investment pools, the portfolios with B-stocks dominates all other portfolios without B-stocks. Furthermore, considering different representative parameters of individuals, the statistical test shows strong evidence that the portfolios of B-stocks using EVT and Pair-Copula can also outperform the market which indicates high potential of profiting.

並列關鍵字

Behavioral portfolio optimization ； Extreme value theory ； Pair-Copula dependence structure ； Safety-first model

參考文獻

[1] Aas, K., Czado, C., Frigessi, A., & Bakken, H. (2009). Pair-copula constructions of multiple dependence. Insurance: Mathematics and economics, 44(2), 182-198.

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[9] Ding, Y., & Zhang, B. (2009). Optimal portfolio of safety-first models. Journal of Statistical Planning and Inference, 139(9), 2952-2962.

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考慮行為股票之極值分布投資組合最佳化

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