臺灣博碩士論文加值系統

投資組合的選擇通常都是在不確定性下發生，在這種情況下有兩種方法常被用來選擇投資組合，第一種方法為隨機優勢，第二種方法為平均數-變異數分析。為了解決不確定性以及平均數-變異數分析的假設在實際應用上並不完善的情況，本研究在考慮三階隨機優勢及偏態下，建立投資組合最佳化模型，以此投資組合最佳化模型決定在期初個股購買的張數。我們的投資策略為在每個期貨交易月期初，買進股票之投資組合，如果目標函數是偏態，本研究利用整數變數來決定是否要在期初建構投資組合時放空一口期貨，如果目標函數是期望值，在期
初建構投資組合時同時放空一口期貨，除此之外，由於結算時間的不確定性，為了解決隨機出場的問題，本研究提出一個出場法則來尋找動態門檻值，做為決定出場日期的依據，在交易期間若報酬超過所預定之門檻值，則進行結算。為了衡量本研究提出的出場法則的表現，本研究設定一個固定的門檻值來做比較。

使用實際資料來測試本研究的投資組合最佳化模型，結果顯示與本研究的目標一致：本研究的投資組合的波動比大盤小，換言之，本研究所找到的投資組合表現比較穩定，風險低於大盤，並且獨立於大盤，投資組合的報酬率高於定存利率，最後，藉由本研究所提出的出場機制，可以避免投資組合持有時間過長或過短所造成的損失，進而獲得更高的報酬。

In this thesis, a portfolio optimization problem with the third-order stochasticdominance constraint and skewness or mean return objective function is utilized todetermine the asset assignment. If the objective function of the portfolio model isskewness, we will use an integer variable in the constraint to determine whetherthe short position of the index futures should be created in the beginning of the
portfolio construction. Otherwise, if the objective function is mean, we will take the
short position of index futures in the beginning. Consequently, the purchases of the
number of stocks under the transaction cost consideration will be decided.
The portfolio is constructed when the first date of index futures is issued. We willclose our portfolio whenever our profit exceeds the predetermined threshold duringthe investment period, otherwise, we will own the portfolio till the maturity date ofthe future. Furthemore, to deal with the uncertainty of the closing date of portfolios, astopping rule is proposed to determine the dynamic threshold in this research. Also,a fixed threshold, 46000, is given to make a contrast with the performance of the stopping rule.
The numerical testing results of our models are provided by using the real-world data. The results are consistent with what we expect. The return rates are more stable and higher than the savings, more profitable by using the stopping rule to decide the closing date of portfolio and independent of the market

1 Introduction ..............................................................1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Purpose . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Organization of The Thesis . . . . . . . . . . . . . . . . . . . . . . . 4
2 Literature Review .........................................................6
2.1 Stochastic Dominance . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Portfolio Optimization with Skewness . . . . . . . . . . . . . . . . . . 8
3 Portfolio Optimization Considering Stochastic Dominance and
Skewness ....................................................................12
3.1 Stochastic Dominance . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.1.1 Shortfall Function Representation of The Third-Order Stochastic
Dominance . . . . . . . . . . . . . . . . . . . . . . . . . . . .............13
3.1.2 Portfolio Problem with Third-order Dominated Constraint . . ...........15
3.2 Models Discription . . . . . . . . . . . . . .. . . . . . . . . . .......16
3.2.1 Computation Schemes for Skewness . . . . . . . . . . . . . . . ........17
3.2.2 Portfolio Optimization Models . . . . . . . . . . . . . . . . . . .....18
3.3 Stock Price Simulation . . . . . .. . . . . . . . . . . . . . . . . . . .22
4 Performances of Models ....................................................24
4.1 Data Description . . . . . . .. . . . . . . . . . . . . . . . ......... 24
4.2 Empirical esults . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5 Portfolio Optimization Models with Stoppong Rule ..........................29
5.1 Stopping rule . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . 29
5.2 Empirical Results . . . . . . .. . . . . . . . . . . . . . . . . . . . . 32
6 Conclusions ...............................................................40
Bibliography ................................................................42
Appendices ..................................................................47
A The Constituents of MSCI Taiwan Stock Index ...............................47
B The Profit of Model-1 with TX .............................................52
C The Profit of Model-2 with TX .............................................59
D The Profit of Model-3 .....................................................66
E The Profit of Model-4 .....................................................73
F The Profit of Model-5 .....................................................80
Vita ........................................................................87

List of Tables
4.1 Return rates of Model-1, Model-2 and market . . . . . . . . . . . . . 27
4.2 Return rates of Model-3, Model-4, Model-5 and market . . . . . . . . 28
5.1 The value of k . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 31
5.2 Illustration of the stopping rule . . . . . . . . . . . . . . .. . . . . 32
5.3 Return rates of Model-1 with TX . . . . . . . . . . . . . . . . . . . . 35
5.4 Return rates of Model-2 with TX . . . . . . . . . . . . . . . . . . . . 36
5.5 Return rates ofModel-3 . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.6 Return rates ofModel-4 . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.7 Return rates ofModel-5 . . . . . . . . . . . . . . . . . . . . . . . . . 39
A.1 The Constituents of MSCI Taiwan Stock Index . . . . . . . . . . . ...... 48
B.1 The profit of Model-1 with TX from May 2004 to Auguest 2004 . . ........ 53
B.2 The profit of Model-1 with TX from September 2004 to December 2004 ......54
B.3 The profit of Model-1 with TX from January 2005 to April 2005 . . . .....55
B.4 The profit of Model-1 with TX from May 2005 to Auguest 2005 . . . .......56
B.5 The profit of Model-1 with TX from September 2005 to December 2005 ......57
B.6 The profit of Model-1 with TX from January 2006 to May 2006 . . ........ 58
C.1 The profit of Model-2 with TX from May 2004 to Auguest 2004 . . ........ 60
C.2 The profit of Model-2 with TX from September 2004 to December 2004 ......61
C.3 The profit of Model-2 with TX from January 2005 to April 2005 . . . .....62
C.4 The profit of Model-2 with TX from May 2005 to Auguest 2005 . . ........ 63
C.5 The profit of Model-2 with TX from September 2005 to December 2005 ......64
C.6 The profit of Model-2 with TX from January 2006 to May 2006 . . . .......65
D.1 The profit of Model-3 from May 2004 to Auguest 2004 . . . . . . . . .....67
D.2 The profit of Model-3 from September 2004 to December 2004 . . . . ......68
D.3 The profit of Model-3 from January 2005 to April 2005 . . . . . . . . ...69
D.4 The profit of Model-3 from May 2005 to Auguest 2005 . . . . . . . . .....70
D.5 The profit of Model-3 from September 2005 to December 2005 . . . . ......71
D.6 The profit of Model-3 from January 2006 to May 2006 . . . . . . . . .....72
E.1 The profit of Model-4 from May 2004 to Auguest 2004 . . . . . . . . .....74
E.2 The profit of Model-4 from September 2004 to December 2004 . . . . ......75
E.3 The profit of Model-4 from January 2005 to April 2005 . . . . . . . . ...76
E.4 The profit of Model-4 from May 2005 to Auguest 2005 . . . . . . . . .....77
E.5 The profit of Model-4 from September 2005 to December 2005 . . . . ......78
E.6 The profit of Model-4 from January 2006 to May 2006 . . . . . . . . .....79
F.1 The profit of Model-5 from May 2004 to Auguest 2004 . . . . . . . . .....81
F.2 The profit of Model-5 from September 2004 to December 2004 . . . . ......82
F.3 The profit of Model-5 from January 2005 to April 2005 . . . . . . . . ...83
F.4 The profit of Model-5 from May 2005 to Auguest 2005 . . . . . . . . .....84
F.5 The profit of Model-5 from September 2005 to December 2005 . . . . ......85
F.6 The profit of Model-5 from January 2006 to May 2006 . . . . . . . ...... 86

List of Figures
1.1 Illustration of positive skewness . . . . . . . . . . . . . . . . . . . . 2
4.1 Comparisons of the return rates among Model-1, Model-2 and market ......27
4.2 Comparisons of the return rates among Model-3, Model-4, Model-5
andmarket . . . . . . . .............. . . . . . . . . . . . . . . . . . . 28
5.1 Comparisons of the return rates of Model-1 with TX among stopping
rule, fixed threshold and market . . . . . . . . . . . . . . . . . . . . . 35
5.2 Comparisons of the return rates of Model-2 with TX among stopping
rule, fixed threshold and market . . . . . . . . . . . . . . . . . . . . . 36
5.3 Comparisons of the return rates of Model-3 among stopping rule, fixed
threshold and market . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.4 Comparisons of the return rates of Model-4 among stopping rule, fixed
threshold and market . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.5 Comparisons of the return rates of Model-5 among stopping rule, fixed
threshold and market . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

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