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研究生:林傳凱
研究生(外文):Chuan-Kai Lin
論文名稱:動態資產投資組合策略之比較-跳躍擴散模型之蒙地卡羅模擬研究
論文名稱(外文):A Comparison of Dynamic Assets Allocation Strategies-A Study by Using the Monte Carlo Simulation of Jump Diffusion Model
指導教授:洪子倫
指導教授(外文):Tzyy-Leng Horng
學位類別:碩士
校院名稱:逢甲大學
系所名稱:應用數學所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:中文
論文頁數:67
中文關鍵詞:投資組合策略後悔機率模擬卡羅法夏普比率風險值跳躍擴散模型
外文關鍵詞:VaRjump diffusion modelMonte Carlo simulation methodSharpe ratioregret ratioportfolio strategy
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本論文比較動態資產投資組合策略之績效,討論的策略為:買入持有(BH)策略、固定比例(CM)策略、固定比例投資組合保險(CPPI)策略與時間不變性投資組合保護(TIPP)策略。首先將資產分成風險性資產與無風險性資產,假設風險性資產服從擴散模型或跳躍擴散模型,且無風險資產為常數。模擬各投資組合策略之報酬率,觀察報酬率分配之樣本統計量:平均數、標準差、偏態與峰態,並利用夏普比率、風險值與後悔機率比較績效,判斷在多頭、空頭與盤整市場中各投資組合策略相對勝出之機率。結果顯示,CM策略最接近常態分配,CPPI策略與TIPP策略偏離最多。由夏普比率與一般化夏普比率可得知,BH策略與CM策略優於CPPI策略與TIPP策略,不過根據風險值可得知,CPPI策略與TIPP策略風險較低。一般來說,CM策略的後悔機率較低且在盤整市場較具優勢,CPPI策略與TIPP策略則在多頭與空頭市場較具優勢。
This thesis makes a simulation comparison of some dynamic strategies of asset allocation. The strategies are buy-and-hold (BH), constant mix (CM), constant proportion portfolio insurance (CPPI) and time invariant portfolio protection (TIPP). The portfolio under analysis is the combination of a risky asset and a risk-free asset. The risky asset price is assumed to be a diffusion process or a jump diffusion process, and the risk-free return is constant. For the simulated returns of each strategy, the mean, standard deviation, skewness and kurtosis are calculated. In addition, Sharpe ratio, the value at risk (VaR) and the regret ratio are computed for the comparison. Moreover, every pair of strategies is compared by the winning percentage under different market scenarios. The results show that the return of CM strategy is close to the normal distribution. However, the returns of CPPI and TIPP are quite different from normal. Under Sharpe ratio or generalized Sharpe ratio , BH and CM performs well by comparing with CPPI and TIPP. Nevertheless, by the risk measure VaR, CPPI and TIPP have the lowest risk. In general, CM has lower regret ratios, and good performance in flat markets. CPPI and TIPP dominate in bull and bear markets.
誌謝................................................................................................................................ i
中文摘要....................................................................................................................... ii
英文摘要...................................................................................................................... iii
目錄.............................................................................................................................. iv
第一章 緒論................................................................................................................. 1
1.1 研究動機與背景............................................................................................... 1
1.2 研究目的........................................................................................................... 2
1.3 研究架構........................................................................................................... 2
第二章 文獻探討......................................................................................................... 4
2.1 股價模型........................................................................................................... 4
2.1.1 布朗運動................................................................................................... 4
2.1.2 幾何布朗運動........................................................................................... 5
2.1.3 跳躍擴散模型........................................................................................... 5
2.2 投資組合策略................................................................................................... 7
2.2.1 買入持有................................................................................................... 7
2.2.2 固定比例................................................................................................... 8
2.2.3 固定比例投資組合保險........................................................................... 9
2.2.4 時間不變性投資組合保護..................................................................... 10
第三章 研究方法....................................................................................................... 11
3.1 蒙地卡羅模擬法............................................................................................. 11
3.2 績效衡量指標................................................................................................. 12
3.2.1 夏普比率................................................................................................. 12
3.2.2 風險值..................................................................................................... 13
3.2.3 後悔機率................................................................................................. 14
3.2.4 多頭、空頭及盤整市場勝出機率......................................................... 15
3.3 投資組合策略模擬......................................................................................... 15
第四章 研究結果與分析........................................................................................... 18
4.1 投資組合報酬率分配..................................................................................... 18
4.2 夏普比率......................................................................................................... 21
4.3 風險值............................................................................................................. 23
4.4 要保金額失守率............................................................................................. 25
4.5 後悔機率......................................................................................................... 26
4.6 多頭、空頭及盤整市場勝出機率................................................................. 27
第五章 結論............................................................................................................... 32
參考文獻..................................................................................................................... 34
附錄一 投資組合報酬率分配之樣本統計量詳細數據......................................... 36
附錄二 績效指標詳細數據..................................................................................... 42
附錄三 多頭、空頭及盤整市場勝出機率詳細數據............................................. 54
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