第五章 結論
第二節 未來研究方向
本研究方法是假設投資組合的報酬是平穩的( stationary )，本研究所使用的 CUSUM 模型只考慮平均數的變動，並未考量變異數的變動，然而在實際情況中，
當有政策的發布或者發生金融危機時，資產的變異數應該是會增加的，礙於時間 考量，在此提供以上不足之處給後續研究者繼續探討。
35
參考文獻
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37
38
透過一次微分條件(first order condition, F.O.C.)即可導出權重估計式
⨂為 Kronecker product，定義如下：
若 A 為m × n的矩陣
39
40
附錄二 模擬研究圖
圖 4.1.2 模擬投資十年不再平衡、每兩期再平衡的兩期非條件投資組合報酬路徑
圖 4.1.3 模擬投資十年不再平衡、每兩期再平衡的兩期非條件投資組合報酬路徑
-0.002 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111 116
ucw(2,0) ucw(2,2)
-0.002 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111 116
ucw(3,0) ucw(3,3)
41
42
附錄三 實證分析表格
表 4.2.3 樣本資料 CUSUM 值與 Z 值(1999/09~2001/11)
date Sep-99 Oct-99 Nov-99 Dec-99 Jan-00 Feb-00 Mar-00 Apr-00 May-00 Z 值 0.4869 1.1195 0.5785 0.8290 0.9716 0.8734 1.2804 0.6164 0.245406
C 值 0 0 0 0 0 0 0 0 -0.14459
date Jun-00 Jul-00 Aug-00 Sep-00 Oct-00 Nov-00 Dec-00 Jan-01 Feb-01 Z 值 0.3430 -0.188 -0.7083 0.3963 -0.1791 -0.241 0.2969 0.6107 -0.0389 C 值 -0.1916 -0.7696 -1.8678 -1.8616 -2.4307 -3.0616 -3.1547 -2.9340 -3.3629 date Mar-01 Apr-01 May-01 Jun-01 Jul-01 Aug-01 Sep-01 Oct-01 Nov-01 Z 值 -0.525 0.3416 0.0898 -2.4311 -2.3245 1.8556 -1.1782 -3.2382 2.008 C 值 -4.2779 -4.3263 -4.6265 -7.4476 -10.1621 -8.6966 -10.2648 -13.893 -12.275
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表 4.2.4 投資期間 CUSUM 值與 Z 值(2007~2011)
date 2007/01 2007/02 2007/03 2007/04 2007/05 2007/06 2007/07 2007/08 2007/09 2007/10 2007/11 2007/12 Z 值 0.7730 0.5360 0.1835 1.1663 1.95834 4.36083 3.08904 -0.0127 -0.0426 2.4393 0.4696 -0.7797 C 值 0 0 -0.2066 0 0 0 0 -0.40272 -0.83535 0 0 -1.1697 date 2008/01 2008/02 2008/03 2008/04 2008/05 2008/06 2008/07 2008/08 2008/09 2008/10 2008/11 2008/12 Z 值 -0.23315 -0.48786 1.002462 1.180042 1.140419 1.911853 -0.17134 -0.14425 -2.93552 -1.89733 -4.20377 -3.83168 C 值 -1.79289 -2.67076 -2.0583 -1.26825 -0.51784 0 -0.56134 -1.09559 -4.42111 -6.70844 -11.3022 -15.5239 date 2009/01 2009/02 2009/03 2009/04 2009/05 2009/06 2009/07 2009/08 2009/09 2009/10 2009/11 2009/12 Z 值 0.281044 1.560574 1.056538 1.803606 2.743843 1.759077 -0.04455 -0.73793 0.533727 0.051869 1.715397 1.325154 C 值 -15.6328 -14.4623 -13.7957 -12.3821 -10.0283 -8.6592 -9.09375 -10.2217 -10.078 -10.4161 -9.09069 -8.15553 date 2010/01 2010/02 2010/03 2010/04 2010/05 2010/06 2010/07 2010/08 2010/09 2010/10 2010/11 2010/12 Z 值 1.411985 -0.62426 0.462231 1.097672 -0.37197 1.057132 0.199923 -1.52805 -0.57298 0.021681 3.874184 2.627812 C 值 -7.13355 -8.14781 -8.07558 -7.3679 -8.12988 -7.46275 -7.65282 -9.57087 -10.5339 -10.9022 -7.41799 -5.18018 date 2011/01 2011/02 2011/03 2011/04 2011/05 2011/06 2011/07 2011/08 2011/09 2011/10 2011/11 2011/12 Z 值 0.819644 -0.01656 -0.02434 0.126158 1.664377 1.461536 0.811704 -1.41482 -2.18918 0.77361 1.585226 0.249791 C 值 -4.75053 -5.1571 -5.57144 -5.83528 -4.5609 -3.48937 -3.06766 -4.87248 -7.45166 -7.06805 -5.87283 -6.01304
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表 4.2.5 2007~2011 單期非條件投資組合動態再平衡每月投資報酬 Jan-07 0.052219 Sep-08 -0.07525 May-10 0.033458 Feb-07 -0.05164 Oct-08 0.234476 Jun-10 0.065001 Mar-07 -0.0433 Nov-08 0.052689 Jul-10 0.002002 Apr-07 0.030284 Dec-08 -0.12051 Aug-10 -0.01192 May-07 0.069396 Jan-09 0.024527 Sep-10 0.055836 Jun-07 0.091735 Feb-09 0.045694 Oct-10 0.00098 Jul-07 0.023792 Mar-09 -0.08743 Nov-10 0.035597 Aug-07 -0.05956 Apr-09 -0.1089 Dec-10 0.017739 Sep-07 -0.074 May-09 -0.10498 Jan-11 -0.00145 Oct-07 0.004463 Jun-09 0.027754 Feb-11 0.020703 Nov-07 -0.14237 Jul-09 0.001082 Mar-11 0.044242 Dec-07 -0.0766 Aug-09 0.008373 Apr-11 0.015658 Jan-08 -0.09323 Sep-09 -0.04547 May-11 0.032608 Feb-08 0.063288 Oct-09 -0.013 Jun-11 0.038308 Mar-08 0.037994 Nov-09 0.003943 Jul-11 0.047576 Apr-08 0.019556 Dec-09 -0.00991 Aug-11 0.10081 May-08 0.070144 Jan-10 0.007951 Sep-11 0.006362 Jun-08 0.102549 Feb-10 0.036663 Oct-11 -0.00262 Jul-08 0.046823 Mar-10 0.004204 Nov-11 -0.01149 Aug-08 -0.10817 Apr-10 -0.01342 Dec-11 0.015849
表 4.2.6 單期非條件投資組合動態再平衡投資平均報酬率 計算期間 平均報酬%
2007~2011 0.5618 2008~2009/06 0.1501
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附錄四 實證分析圖
圖 4.2.6 每季再平衡、動態再平衡非條件投資組合的報酬路徑
圖 4.2.7 樣本資料管制圖(1999/09~2001/11)
-0.25
Jan-07 Apr-07 Jul-07 Oct-07 Jan-08 Apr-08 Jul-08 Oct-08 Jan-09 Apr-09 Jul-09 Oct-09 Jan-10 Apr-10 Jul-10 Oct-10 Jan-11 Apr-11 Jul-11 Oct-11
ucw(1,3)
46
Jan-07 Apr-07 Jul-07 Oct-07 Jan-08 Apr-08 Jul-08 Oct-08 Jan-09 Apr-09 Jul-09 Oct-09 Jan-10 Apr-10 Jul-10 Oct-10 Jan-11 Apr-11 Jul-11 Oct-11
mw
Jan-07 Apr-07 Jul-07 Oct-07 Jan-08 Apr-08 Jul-08 Oct-08 Jan-09 Apr-09 Jul-09 Oct-09 Jan-10 Apr-10 Jul-10 Oct-10 Jan-11 Apr-11 Jul-11 Oct-11
cw(1,0)
47
圖 4.2.10 2007~2011 單期動態調整與兩期不調整投資報酬路徑
圖 4.2.11 2007~2011 單期動態調整、兩期非條件投資組合兩期調整投資報酬路徑
-0.25
Jan-07 Apr-07 Jul-07 Oct-07 Jan-08 Apr-08 Jul-08 Oct-08 Jan-09 Apr-09 Jul-09 Oct-09 Jan-10 Apr-10 Jul-10 Oct-10 Jan-11 Apr-11 Jul-11 Oct-11
ucw(2,0)
Jan-07 May-07 Sep-07 Jan-08 May-08 Sep-08 Jan-09 May-09 Sep-09 Jan-10 May-10 Sep-10 Jan-11 May-11 Sep-11
ucw(2,2) ucw(1,cusum)
48
Jan-07 Apr-07 Jul-07 Oct-07 Jan-08 Apr-08 Jul-08 Oct-08 Jan-09 Apr-09 Jul-09 Oct-09 Jan-10 Apr-10 Jul-10 Oct-10 Jan-11 Apr-11 Jul-11 Oct-11
mw
Jan-07 Apr-07 Jul-07 Oct-07 Jan-08 Apr-08 Jul-08 Oct-08 Jan-09 Apr-09 Jul-09 Oct-09 Jan-10 Apr-10 Jul-10 Oct-10 Jan-11 Apr-11 Jul-11 Oct-11
ucw(2,0) ucw(2,2) ucw(2,6) ucw(1,cusum)
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圖 4.2.14 2007~2011 兩期非條件投資組合、單期動態非條件投資組合報酬路徑
圖 4.2.15 2007~2011 單期條件投資組合報酬路徑
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
Jan-07 May-07 Sep-07 Jan-08 May-08 Sep-08 Jan-09 May-09 Sep-09 Jan-10 May-10 Sep-10 Jan-11 May-11 Sep-11
ucw(3,0) ucw(3,3) ucw(1,cusum)
-0.5 0 0.5 1 1.5 2 2.5
Jan-07 Apr-07 Jul-07 Oct-07 Jan-08 Apr-08 Jul-08 Oct-08 Jan-09 Apr-09 Jul-09 Oct-09 Jan-10 Apr-10 Jul-10 Oct-10 Jan-11 Apr-11 Jul-11 Oct-11
cw(1,0) cw(1,1) cw(1,cusum)