在避險原則下,投資組合數理規劃模式之研究

投資組合之選擇與風險管理近年來在現代財務之研究領域已成為重要的一環.由於資產(例如有價證券)在其獲利能力與價格波動上都是屬於不確定性的,所以投資者面臨了越來越多複雜的投資決策問題.在本論文中,修正了MAD (Mean-Absolute-Deviation) Model並加入交易費用與證交稅之考量而成為Amount-MAD Model,再以此Amount-MAD Model來選擇出低風險的投資組合與作出正確的投資決策.然而由實驗的結果發現,雖然Amount-MAD Model所選擇的投資組合獲利績效很好,但是其投資組合還是具有風險性.為了避免證券市場波動對投資組合造成價格上的損失,本研究加入了台指期貨作為避險工具並且設計了幾個避險策略與數學模式來趨避市場上不可消除的風險.在本論文裡所研究的避險策略,最主要是以MAD與LPM0 (Lower Partial Moment 0)的概念為基礎所發展出來的.再以價差與報酬率兩者不同的考量分別產生了策略I與策略II,並且以實際的歷史資料展現此避險策略的績效. 在第二章與第三章後半節,分別節錄了Amount-MAD Model與避險策略I與避險策略II之投資績效.在Amount-MAD Model的部分,以1996年至2000年的歷史資料來獲得實驗之結果.而避險策略的部分則以1998年至2001年的歷史資料來取得績效之評量,並且與傳統的Minimum-Variance Model作比較.從績效結果可以發現,避險策略的績效比Minimum-Variance Model來得出色,這也是此論文的成果之一.

關鍵字

投資組合；避險部位；風險管理；避險策略；台指期貨

並列摘要

Portfolio selection and risk management had been the most important research fields in modern finance recently. Since the values (price) and risk (deviation) of assets of investors in the future are all uncertainty, investors will face more complex investment problems than usual. In this thesis, the modified Amount-MAD model was applied to select riskless portfolio and make correct investment decisions. Although the modified Amount-MAD model performs well, the portfolio that selected by it is still risky. To avoid the fluctuated risk, we formulate our Hedging Strategies that based on LPM0 and MAD concepts to solve the problem. At the end of this study, we evaluated our Hedging Strategies by using real historical data and compare that with conventional minimum-variance method. It demonstrates that our Hedging Strategies can provide a sophisticate investment tool for the investor or fund manager in the world.

並列關鍵字

MAD Model ； Hedging ratio ； Amount-MAD Model ； Minimum-Variance ； LPM

參考文獻

[2] Bawa, V. S. (1975): “Optimal Rules for Ordering Uncertain Prospects,”

Journal of Financial Economics, 2: 95-121

[3] Bawa, V. S. (1978): “Safety-First, Stochastic Dominance and Optimal

[4] Bawa, V. S. and Lindenberg, E. B. (1977): “Capital Market Equilibrium in a

Futures Market under Price Uncertainty,” Economics Letters, 13: 141-145.

國際替代計量

在避險原則下,投資組合數理規劃模式之研究

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