未來研究方向

第五章結論

5.2 未來研究方向

由於時間的關係，本研究在固定比例策略和投資組合保險策略上沒有給予理論值，再者，由實證分析部分可以知道真實股市的報酬大多不為常態，而本文模擬研究報酬皆假設常態，這些部分可以在未來研究上做調整，例如股價報酬大部分認為有厚尾的現象，因而可以建立符合厚尾分佈的模型，例如 T 分佈，或是可以用混合常態來更貼近真實市場的多峰狀態，進而讓本研究之結果更符合實際市場真實的情況。

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整工具。碩士論文。

Var(P_n) = Var(2X_n+ 2Y_n)

其中，固定持有投資組合 N 天 E(X) =∑^N_n=1E(X_n)

= ^X⁰^∑^Nⁿ⁼¹^[1+0.005(P_N ¹^−P²^)]ⁿ

_{= �}^X_N⁰_{� (}^c(c_c−1^N⁻¹⁾₎

E(Y) =∑^N_n=1E(Y_n) N

=^∑^Nⁿ⁼¹^Y⁰^(1+0.0001)_N ⁿ

= �^Y_N⁰� (^e�e_e−1^N^−1�) Var(X) =∑^N_n=1Var(X_n)

N =^∑^Nⁿ⁼¹_N(a−c^b[aⁿ^−c₂₎²ⁿ^]

=_N(a−c^b ₂₎[^a�a_a−1^N^−1�−^c²^(c_c₂^2N₋₁⁻¹⁾] =^X_N⁰²[^a�a_a−1^N^−1�−^c²^(c_c₂^2N₋₁⁻¹⁾

附錄二模擬研究表格與圖

(註：BAH 為買進並持有策略 CONSTM 為固定比例策略 CPPI 為固定比例投資組合保險策略)

表 1.景氣好各個策略不同持有期間的平均報酬-N=1 持有期間

(月)

6 12 30 60 90

BAH (0.99,0.01) (0.99,0.01) (0.99,0.01) (0.99,0.01) (0.99,0.01) Mean 0.0655421 0.1255506 0.3398450 0.7979358 1.4633460 CONSTM (0.99,0.01) (0.99,0.01) (0.99,0.01) (0.99,0.01) (0.99,0.01) Mean 0.0655249 0.1254954 0.3394176 0.7957867 1.4571380 CPPI(m=2) (0.99,0.01) (0.99,0.01) (0.99,0.01) (0.99,0.01) (0.99,0.01) Mean

0.0674509 0.1318386 0.3914543 1.0840269 2.3742628

表 2.景氣好各個策略不同持有期間的平均報酬-N=2 持有期間

(月)

6 12 30 60 90

BAH (0.2,0.7,0.1) (0.2,0.7,0.1) (0.2,0.7,0.1) (0.1,0.8,0.1) (0.1,0.8,0.1) Mean 0.0717732 0.1404450 0.3886169 0.9662310 1.7085047 CONSTM (0.2,0.7,0.1) (0.2,0.7,0.1) (0.2,0.7,0.1) (0.1,0.8,0.1) (0.1,0.8,0.1)

Mean 0.0714955 0.1393949 0.3820269 0.9332934 1.6148356 CPPI(m=2) (0.2,0.7,0.1) (0.2,0.7,0.1) (0.2,0.7,0.1) (0.1,0.8,0.1) (0.1,0.8,0.1)

Mean

0.0738881 0.1492936 0.4617378 1.4035625 3.0875597

表 3.景氣持平各個策略不同持有期間的平均報酬-N=1

持有期間 (月)

6 12 30 60 90

BAH (0.99,0.01) (0.9,0.1) (0.99,0.01) (0.99,0.01) (0.99,0.01)

Mean 0.0275570 0.0558382 0.1302574 0.2746025 0.4511878 CONSTM (0.99,0.01) (0.9,0.1) (0.99,0.01) (0.99,0.01) (0.99,0.01) Mean 0.0275562 0.0557500 0.1302097 0.2744030 0.4506729 CPPI(m=2) (0.99,0.01) (0.9,0.1) (0.99,0.01) (0.99,0.01) (0.99,0.01) Mean

0.0276779 0.0570747 0.1366150 0.3022646 0.5243077

表 4.景氣持平各個策略不同持有期間的平均報酬-N=2 持有期間

(月)

6 12 30 60 90

BAH (0.8,0.1,0.1) (0.6,0.3,0.1) (0.6,0.3,0.1) (0.7,0.2,0.1) (0.8,0.1,0.1) Mean 0.0268763 0.0500995 0.1348059 0.2641176 0.4401678 CONSTM (0.8,0.1,0.1) (0.6,0.3,0.1) (0.6,0.3,0.1) (0.7,0.2,0.1) (0.8,0.1,0.1)

Mean 0.0268600 0.0499023 0.1342577 0.2619655 0.4350094 CPPI(m=2) (0.8,0.1,0.1) (0.6,0.3,0.1) (0.6,0.3,0.1) (0.7,0.2,0.1) (0.8,0.1,0.1)

Mean

0.0271359 0.0509360 0.1422666 0.2923038 0.5195654

表 5.景氣差各個策略不同持有期間的平均報酬-N=1

持有期間 (月)

6 12 30 60 90

BAH (0.99,0.01) (0.99,0.01) (0.99,0.01) (0.99,0.01) (0.99,0.01) Mean 0.0161444 0.0253890 0.0625236 0.1309179 0.2101976 CONSTM (0.99,0.01) (0.99,0.01) (0.99,0.01) (0.99,0.01) (0.99,0.01) Mean 0.0161438 0.0253883 0.0625167 0.1308967 0.2101441 CPPI(m=2) (0.99,0.01) (0.99,0.01) (0.99,0.01) (0.99,0.01) (0.99,0.01) Mean

0.0162321 0.0255482 0.0636093 0.1353135 0.2209996

表 6.景氣差各個策略不同持有期間的平均報酬-N=2

持有期間 6 12 30 60 90

(月)

BAH (0.2,0.7,0.1) (0.4,0.5,0.1) (0.2,0.7,0.1) (0.1,0.8,0.1) (0.1,0.8,0.1) Mean 0.0163947 0.0297525 0.0744002 0.1592312 0.2327419 CONSTM (0.2,0.7,0.1) (0.2,0.7,0.1) (0.2,0.7,0.1) (0.1,0.8,0.1) (0.1,0.8,0.1)

Mean 0.0163772 0.0296957 0.0742354 0.1587708 0.2314641 CPPI(m=2) (0.2,0.7,0.1) (0.2,0.7,0.1) (0.2,0.7,0.1) (0.1,0.8,0.1) (0.1,0.8,0.1)

Mean

0.0164706 0.0300122 0.0762741 0.1667082 0.2493467

表 7.景氣混合各個策略不同持有期間的平均報酬-N=1

持有期間 (月)

6 12 30 60 90

BAH (0.99,0.01) (0.9,0.1) (0.99,0.01) (0.99,0.01) (0.99,0.01) Mean 0.0375573 0.0746568 0.2277787 0.4773505 0.8093280 CONSTM (0.99,0.01) (0.9,0.1) (0.99,0.01) (0.99,0.01) (0.99,0.01) Mean 0.0375529 0.0744807 0.2275991 0.4766373 0.8074037 CPPI(m=2) (0.99,0.01) (0.9,0.1) (0.99,0.01) (0.99,0.01) (0.99,0.01) Mean

0.0380822 0.0768985 0.2499429 0.5704504 1.0730048

表 8.景氣混合各個策略不同持有期間的平均報酬-N=2 持有期間

(月)

6 12 30 60 90

BAH (0.3,0.6,0.1) (0.1,0.8,0.1) (0.3,0.6,0.1) (0.1,0.8,0.1) (0.2,0.7,0.1) Mean 0.0494638 0.0907609 0.2319202 0.5233716 0.8685383 CONSTM (0.3,0.6,0.1) (0.1,0.8,0.1) (0.3,0.6,0.1) (0.1,0.8,0.1) (0.2,0.7,0.1)

Mean 0.0494074 0.0903690 0.2289865 0.5141079 0.8435761 CPPI(m=2) (0.3,0.6,0.1) (0.1,0.8,0.1) (0.3,0.6,0.1) (0.1,0.8,0.1) (0.2,0.7,0.1)

Mean

0.0506418 0.0942454 0.2564078 0.6468451 1.2130962

表 9.景氣好各個策略不同持有期間的夏普指數-N=1 持有期間

(月)間(月) 6 12 30 60 90

BAH (0.5,0.5) (0.8,0.2) (0.2,0.8) (0.5,0.5) (0.01,0.99) Sharpe 1.2343610 1.7064828 2.4047556 3.0818882 3.2532253 CONSTM (0.5,0.5) (0.8,0.2) (0.2,0.8) (0.3,0.7) (0.01,0.99) Sharpe

1.2488698 1.7251121 2.7013703 3.6593765 4.4789584

CPPI(m=2) (0.5,0.5) (0.8,0.2) (0.1,0.9) (0.5,0.5) (0.01,0.99) Sharpe 1.2054539 1.6182471 2.1534220 2.4833478 2.5362829

表 10.景氣好各個策略不同持有期間的夏普指數-N=2 持有期間

(月) 6 12 30 60 90

BAH (0.5,0.4,0.1) (0.3,0.5,0.2) (0.4,0.4,0.2) (0.3,0.6,0.1) (0.3,0.2,0.5) Sharpe 1.9374659 2.5709443 3.7532041 4.5283152 5.2352679 CONSTM (0.5,0.4,0.1) (0.3,0.5,0.2) (0.1,0.1,0.8) (0.1,0.1,0.8) (0.1,0.1,0.8)

Sharpe

1.9471564 2.6115734 3.9227848 5.2210865 6.9283814

CPPI(m=2) (0.5,0.4,0.1) (0.3,0.5,0.2) (0.4,0.4,0.2) (0.3,0.6,0.1) (0.1,0.1,0.8)

Sharpe 1.8881990 2.4262719 3.2237965 3.6072206 3.7969322 表 11.景氣持平各個策略不同持有期間的夏普指數-N=1

持有期間

(月)間() 6 12 30 60 90

BAH (0.99,0.01) (0.6,0.4) (0.8,0.2) (0.5,0.5) (0.01,0.99) Sharpe 0.8408154 1.1767158 1.6961955 2.1331869 2.4842713 CONSTM (0.99,0.01) (0.6,0.4) (0.8,0.2) (0.1,0.9) (0.01,0.99) Sharpe

0.8408917 1.1902442 1.7112918 2.3151790 2.9503223

CPPI(m=2) (0.01,0.99) (0.6,0.4) (0.8,0.2) (0.1,0.9) (0.01,0.99) Sharpe 0.8340810 1.1426779 1.6210886 1.9396774 2.2277986

表 12.景氣持平各個策略不同持有期間的夏普指數-N=2 持有期間

(月) 6 12 30 60 90

BAH (0.3,0.3,0.4) (0.2,0.3,0.5) (0.4,0.5,0.1) (0.3,0.2,0.5) (0.1,0.3,0.6) Sharpe 1.4573041 1.7323377 2.2485846 2.9648167 3.6456167 CONSTM (0.3,0.3,0.4) (0.2,0.3,0.5) (0.4,0.5,0.1) (0.3,0.2,0.5) (0.1,0.3,0.6)

Sharpe

1.4631847 1.7541552 2.2518636 3.1387916 3.9246805

CPPI(m=2) (0.3,0.3,0.4) (0.2,0.3,0.5) (0.4,0.5,0.1) (0.3,0.2,0.5) (0.1,0.3,0.6)

Sharpe 1.4403693 1.6890643 2.1474760 2.7712058 3.2614969 表 13.景氣差各個策略不同持有期間的夏普指數-N=1

持有期間

(月)間() 6 12 30 60 90

BAH (0.99,0.01) (0.4,0.6) (0.01,0.99) (0.3,0.7) (0.1,0.9) Sharpe 0.5035781 0.6051070 0.8184432 1.2033430 1.5513779 CONSTM (0.99,0.01) (0.4,0.6) (0.01,0.99) (0.3,0.7) (0.1,0.9)

Sharpe

0.5035901 0.6081850 0.8374333 1.2368101 1.6572163

CPPI(m=2) (0.99,0.01) (0.4,0.6) (0.2,0.8) (0.3,0.7) (0.9,0.1)

Sharpe 0.5024537 0.6004363 0.8072537 1.1737823 1.3881604 表 14.景氣差各個策略不同持有期間的夏普指數-N=2

持有期間

(月) 6 12 30 60 90

BAH (0.4,0.4,0.2) (0.3,0.5,0.2) (0.4,0.4,0.2) (0.3,0.6,0.1) (0.3,0.2,0.5) Sharpe 0.7060418 0.8777337 1.3418093 1.8326994 2.3343119 CONSTM (0.4,0.4,0.2) (0.3,0.5,0.2) (0.4,0.4,0.2) (0.3,0.6,0.1) (0.3,0.2,0.5)

Sharpe

0.7066145 0.8830042 1.3421611 1.8538016 2.3956791

CPPI(m=2) (0.4,0.4,0.2) (0.3,0.5,0.2) (0.4,0.4,0.2) (0.3,0.6,0.1) (0.3,0.2,0.5)

Sharpe 0.7013538 0.8707157 1.3081216 1.7701607 2.2338557

表 15.景氣混合各個策略不同持有期間的夏普指數-N=1 持有期間

(月)間() 6 12 30 60 90

BAH (0.1,0.9) (0.7,0.3) (0.5,0.5) (0.9,0.1) (0.6,0.4) Sharpe 0.9223353 1.3836801 2.0744334 2.5721911 2.8439907 CONSTM (0.1,0.9) (0.7,0.3) (0.5,0.5) (0.01,0.99) (0.1,0.9)

Sharpe

0.9361111 1.3993972 2.1540949 2.9278686 3.5695289

CPPI(m=2) (0.1,0.9) (0.7,0.3) (0.5,0.5) (0.9,0.1) (0.5,0.5)

Sharpe 0.9103322 1.3319921 1.9196885 2.2203459 2.2880675 表 16.景氣混合各個策略不同持有期間的夏普指數-N=2

持有期間

(月) 6 12 30 60 90

BAH (0.4,0.3,0.3) (0.2,0.3,0.5) (0.3,0.4,0.3) (0.1,0.1,0.8) (0.4,0.3,0.3) Sharpe 1.5225411 2.0294197 2.7487033 3.7372690 3.9396372 CONSTM (0.4,0.3,0.3) (0.2,0.3,0.5) (0.3,0.4,0.3) (0.1,0.1,0.8) (0.1,0.1,0.8)

Sharpe

1.5253541 2.0724466 2.8346670 4.3520200 4.8414927

CPPI(m=2) (0.4,0.3,0.3) (0.2,0.3,0.5) (0.3,0.4,0.3) (0.1,0.1,0.8) (0.1,0.1,0.8)

Sharpe 1.4894468 1.9458218 2.5372439 3.1398888 3.2322940 總圖一.N=2 景氣情形不同且持有期間不同的夏普指數總圖

圖三同一市場變動下，投資組合持有兩年半，不同策略的效率前緣-景氣好

 以景氣好 N=2 為例，計算之絕對風險厭惡係數，其餘以此類推。

表 17. N=2，景氣好之絕對風險厭惡係數

6 期 U' U'' A(w)

BAH 2.05775 -1.35413 0.65807 Constm 2.05760 -1.37408

0.66781

CPPI(m=2) 2.00438 -1.32119 0.65915

12 期 U' U'' A(w)

BAH 2.69226 -1.46362 0.54364 Constm 2.70091 -1.52064

0.56301

CPPI(m=2) 2.53294 -1.37359 0.54229

30 期 U' U'' A(w)

BAH 3.88182 -2.38833

0.61526

Constm 3.78586 -2.04488 0.54014 CPPI(m=2) 3.31706 -1.89260 0.57057

60 期 U' U'' A(w)

BAH 4.65596 -3.09616 0.66499 Constm 4.70540 -3.15354

0.67020

CPPI(m=2) 3.76407 -2.51276 0.66756

90 期 U' U'' A(w)

BAH 5.49356 -1.95856 0.35652 Constm 6.00787 -2.37583

0.39545

CPPI(m=2) 3.78113 -1.28891 0.34088 圖六 N=2，景氣好，用過去資料預測未來之各個策略的夏普指數

圖七 N=2，景氣持平，用過去資料預測未來之各個策略的夏普指數

 以 N=1 為例，N=2 以此類推。

表 18.景氣好，用過去資料預測未來之各個策略的夏普指數

持有期間(月) 6 12 30 60 90

Markowitz(L=0.00001) 0.8248255

1.2819466

2.1834460 2.3765450 2.4470702 Markowitz(L=0.00005) 0.8804546 1.2714036 2.1978781 2.3926616 2.4411754 Markowitz(L=0.0001) 0.9369447 1.2688594 2.2086605 2.4034867 2.4436699 BAH 0.9919070 1.2291181 2.4479797 2.4015507 2.5938563 CONSTM

0.9920713

1.2295132

2.4511271 2.4072120 2.6025270

CPPI 0.9756090 1.1864096 2.1603425 1.9197023 1.9020487 表 19.景氣持平，用過去資料預測未來之各個策略的夏普指數

持有期間(月) 6 12 30 60 90

Markowitz(L=0.00001) 0.5678086 0.8518931 1.3133834 1.6818361 2.2607006 Markowitz(L=0.00005) 0.5908635 0.8472576 1.3045065 1.6869149 2.2601491 Markowitz(L=0.0001)

0.6028125

0.8468350 1.3077166 1.6983388 2.2568671 BAH 0.5953347 0.8527328 1.3664964 1.7571964 2.3433144 CONSTM 0.5954067

0.8528599 1.3669319 1.7588156 2.3464197

CPPI 0.5865057 0.8416360 1.3152256 1.5995465 2.0582917

表 20.景氣差，用過去資料預測未來之各個策略的夏普指數

持有期間(月) 6 12 30 60 90

Markowitz(L=0.00001) 0.4276095 0.4772427 0.4857556 0.7515665 1.0968281 Markowitz(L=0.00005) 0.4395190 0.4870165

0.4871323

0.7550375 1.0936294 Markowitz(L=0.0001) 0.4464490 0.4961164 0.4858581 0.7718916 1.1003060 BAH 0.4507806 0.4986976 0.4858864 0.7722537 1.1003060 CONSTM

0.4507920 0.4987530

0.4859592

0.7723854 1.1008434

CPPI 0.4504509 0.4944781 0.4866650 0.7636068 1.0429417 表 21.景氣混合，用過去資料預測未來之各個策略的夏普指數

持有期間(月) 6 12 30 60 90

Markowitz(L=0.00001) 0.5811741 0.8148826 1.6923230

2.3912894

2.0901300 Markowitz(L=0.00005) 0.6332450 0.8140427 1.6955368 2.3687129 2.1003879 Markowitz(L=0.0001) 0.6754694 0.8114407 1.6952136 2.3706481 2.1038466 BAH

0.7501720

0.8817951 1.7730384 2.3189038 2.2259317 CONSTM 0.7501234

0.8819775 1.7742517

2.3218000

2.2323118

CPPI 0.7457282 0.8582450 1.6548418 2.0199152 1.6865383

在文檔中最佳動態投資策略及其效用函數之分析與比較 (頁 44-61)

第五章 結論

5.2 未來研究方向

參考文獻

Financial Analysts Journal , 48, 5,pp. 28.

Journal of Finance, pp.283-299.

ALBERTO NOTEBOOKS, Working Paper ,108.

Portfolio Management 1987.14.1, pp. 48-51.

Econometrica, 32, 1-2.

附錄二模擬研究表格與圖

0.0674509 0.1318386 0.3914543 1.0840269 2.3742628

0.0738881 0.1492936 0.4617378 1.4035625 3.0875597

0.0276779 0.0570747 0.1366150 0.3022646 0.5243077

0.0271359 0.0509360 0.1422666 0.2923038 0.5195654

0.0162321 0.0255482 0.0636093 0.1353135 0.2209996

0.0164706 0.0300122 0.0762741 0.1667082 0.2493467

0.0380822 0.0768985 0.2499429 0.5704504 1.0730048

0.0506418 0.0942454 0.2564078 0.6468451 1.2130962

1.2488698 1.7251121 2.7013703 3.6593765 4.4789584

1.9471564 2.6115734 3.9227848 5.2210865 6.9283814

0.8408917 1.1902442 1.7112918 2.3151790 2.9503223

1.4631847 1.7541552 2.2518636 3.1387916 3.9246805

0.5035901 0.6081850 0.8374333 1.2368101 1.6572163

0.7066145 0.8830042 1.3421611 1.8538016 2.3956791

0.9361111 1.3993972 2.1540949 2.9278686 3.5695289

1.5253541 2.0724466 2.8346670 4.3520200 4.8414927

0.66781

0.56301

0.61526

0.67020

0.39545

1.2819466

0.9920713

2.4511271 2.4072120 2.6025270

0.6028125

0.8528599 1.3669319 1.7588156 2.3464197

0.4871323

0.4507920 0.4987530

0.7723854 1.1008434

2.3912894

0.7501720

0.8819775 1.7742517

2.2323118

第五章結論