3. 資料與實證結果
3.2 參數估計與效率前緣建構
在建構投資組合前，我們必須先對於參數進行估計，本研究採兩階段估計方式，
第一階段先利用報酬率超過三倍標準的方式來估計跳躍次數與共同跳躍次數，第 二階段為利用最大概似法估計方程式(5)中的漂移項、波動度、跳躍波動度與跳 躍幅度。根據表五與表六參數估計的結果，將其代入方程式(9)可計算出資產間 的共變異數，進一步可以計算 M-V 法則下的資產配置效率前緣。從圖三與圖四 可以看出次貸期間與次貸過後的效率前緣並沒有明顯的差異，雖然次貸期間的跳 躍與共同跳躍次數有些微增加，也因此增加了資產間的相關係數，但增加幅度不 足以影響到資產的配置情況。本文進一步分析，在次貸期間若提高共同跳躍的次 數，效率前緣則會有明顯的不同，如圖五。隨著共同跳躍次數愈高，效率前緣曲 線會躍趨近於一條直線，這顯示資產間的相關係數會因為共同跳躍的產生而提高 風險分散的效果遞減，且在共同跳躍次數增加到一定程度時，資產間的相關係數 趨近 1，此時，投資組合再也無法達到風險分散的效果，即當系統性風險發生時，
資產間的共同跳躍現象也會顯著的增加至一定的程度，此時，就會造成風險無法 分散而造成損失。
圖三 次貸期間平均數-變異數 效率前緣
註:此圖示利用次貸期間樣本所估計的參數，所畫出來的效率前緣。
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
0 0.2 0.4 0.6 0.8 1 1.2 1.4x 10-3
風險 (標準差)
預期報酬
平均數-變異數 效率前緣
次 貸 期 間
圖四 次貸後期間平均數-變異數 效率前緣
4. 結論
本文將 Markowitz 所提出的平均數-變異數法與本文所提出的多變量複合卜瓦 松跳躍擴散來描繪資產的動態過程結合，並探討共同跳躍現象對於投資組合效率 前緣的影響，並以道瓊三十檔成分股為研究標的。首先，研究結果發現次貸風暴 期間與次貸後期間成分股存在著跳躍與共同跳躍的現象，而這些現象在次貸風暴 期間更為顯著。此外，就投資組合的效率前緣而言，兩個樣本期間並無明顯的不 同，雖然次貸風暴期間跳躍與共同跳躍現象比次貸後期間明顯，但增加的幅度不 足以影響到投資組合的配置，然而，本文進一步分析，若在次貸期間持續增加共 同跳躍的頻率，則發現效率前緣會有明顯的不同，且共同跳躍頻率愈高則在一定 的風險(報酬的標準差)之下預期報酬率愈低，主要是因為共同跳躍頻率的增加，
將進一步增加資產間的相關係數，進而使得風險分善的效果遞減，且當共同跳躍 次數增加至某一程度時，資產間的相關係數將趨近於 1，此時，投資組合的建構 將無法達到風險分散的效果。
參考文獻
Andersen, T. G., Bollerslev, T. and Diebold, F. X. (2007) “Roughing it up: Including jump components in the measurement, modeling, and forecasting of return volatility,” The review of economics and statistics, Vol. 89, Issue 4, p.701-720.
Black, F. (1972) “Capital market equilibrium with restricted borrowing,” Journal of
Business, p. 444-455.
Brinson, G. P., Singer, B. D. and Beebower, G. L., (1991) “ Determinants of portfolio performance II: An updatem,” Financial Analysts Journal, Vol. 47, Issue 3, p.
40-48.
Chopra, V. K. and Ziemba, W. T. (1993) “The effect of errors in means, variances, and covariances on optimal portfolio choice,” The journal of portfolio
management, Vol. 19, Issue 2, p. 6-11.
De Roon, F. A., Nijman, T. E., and Werker, B. J. M. (2002) “Testing for Mean‐
Variance Spanning with Short Sales Constraints and Transaction Costs: The Case of Emerging Markets,” The Journal of Finance, Vol. 56, Issue 2, p.
721-742.
Dungey, M., McKenzie, M. and Smith, L., (2009) “News, no-news and jumps in the U.S. treasury market,” Journal of empirical finance, Vol. 16, p. 430-445.
Dungey, M. and Hvozdyk, L. (2012) “Cojumping: evidence from the U.S. treasury bond and futures Markets,” Journal of Banking and Finance, Vol. 36, Issue 5, p.
1563-1575.
Fan, J., Zhang, J. and Yu, K. (2008) “Asset allocation and risk assessment with gross exposure constraints for vast portfolios,” The Annals of Statistics, Vol. 25, p.
1425–1432.
Fan, J., Li, Y. and Yu, K. (2012) “Vast volatility matrix estimation using high-frequency data for portfolio selection,” Journal of the American Statistical
Association, Vol. 107, Issue 497, p. 412-428.
Goldfarb, D. and Iyengar, G. (2003) “Robust portfolio selection problems,”
Mathematics of Operations Research, Vol. 28, Issue 1, p.1-38.
Jacod, J. and Shiryaev, A. N. (2003) “Limit theorems for stochastic processes” New York: Springer-Verlag.
Jagannathan, R., and Ma, T. (2003) “Risk reduction in large portfolios: Why imposing the wrong constraints helps,” The Journal of Finance, Vol. 58, Issue 4, p.1651-1684.
Koskosidis, Y. A. and Duarte, A. M. (1997), “A scenario-based approach to active asset allocation,” The journal of portfolio management, Vol.23, Issue 2, p.74-85.
Lai, T. L., Xing, H. and Chen, Z. (2011) “Mean–variance portfolio optimization when means and covariances are unknown,” The Annals of Applied Statistics, Vol. 5, Issue 2, p.798-823.
Lahaye, J., Laurent, S. and Neely C. J. (2011) “Jumps, cojumps and macro announcements,” Journal of Applied Econometrics, Vol. 26, Issue 6, p.893-921.
Laloux, L., Cizeau, P., Bouchaud, J. P. and Potters, M. (1999) “Noise dressing of financial correlation matrices,” Physical Review Letters, Vol. 83, Issue 7, p.1467-1470.
Ledoit, O. and Wolf, M. (2003) “Improved estimation of the covariance matrix of stock returns with an application to portfolio selection,” Journal of empirical
finance, Vol. 10, Issue 5, p. 603-621.
Ledoit, O. and Wolf, M. (2004) “A well-conditioned estimator for large-dimensional covariance matrices,” Journal of multivariate analysis, Vol. 88, Issue 2, p.365-411.
Lee, H. T. (2010) “Regime switching correlation hedging,” Journal of Banking &
Finance, Vol. 34, Issue 11, p.2728-2741.
Lien, D. and Tse, Y. K. (2002) “Some recent developments in futures hedging,”
Journal of Economic Surveys, Vol. 16, Issue 3, p.357-396.
Lintner, J. (1965) “The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets,” The review of economics and statistics, Vol. 47, Issue 1, p.13-37.
Markowitz, H. M. (1952) “Portfolio selection,” Journal of Finance, Vol. 7, p.77-91.
Markowitz, H. M. (1959) “Portfolio selection: E cient diversification of investments,”
Cowles Foundation Monograph.
Merton, R. C. (1973) “Theory of rational option pricing,” The Bell Journal of
Economics and Management Science, Vol. 4, Issue 1, p. 141-183.
Sharpe, W. F. (1964) “Capital asset prices: a theory of market equilibrium under Conditions of Risk,” Journal of Finance, Vol. 19, p. 425-442.
Stein, J. L. (1961) “The simultaneous determination of spot and futures prices,” The
American Economic Review, Vol. 51, Issue 5, p. 1012-1025.
Zhang, L., Mykland, P. A. and Aı̈t -Sahalia, Y. (2005) “A tale of two time scales,”
Journal of the American Statistical Association, Vol. 100, Issue 472, p.
1394-1411.
表一 次貸期間敘述統計量 (2007/01/03~2010/12/31)
公司 AAPL AXP BA CAT CSCO CVX DD DIS GE GS HD IBM INTC JNJ JPM
觀察個數 1007 1007 1007 1007 1007 1007 1007 1007 1007 1007 1007 1007 1007 1007 1007 平均數 0.0013 -0.0003 -0.0003 0.0004 -0.0003 0.0002 0.0000 0.0001 -0.0007 -0.0002 -0.0002 0.0004 0.0000 -0.0001 -0.0001 標準差 0.0259 0.0356 0.0227 0.0261 0.0231 0.0219 0.0232 0.0222 0.0270 0.0344 0.0226 0.0167 0.0234 0.0121 0.0386 偏態系數 -0.4722 0.1139 0.2190 0.1042 -0.5512 0.2226 -0.2970 0.4203 0.0419 0.3477 0.4771 0.1621 -0.1334 0.6364 0.3347 峰態系數 8.2840 8.0644 6.6179 6.5683 9.7740 15.0810 6.9466 9.0235 9.3881 12.4291 6.3200 7.1467 6.5316 17.5827 10.7506
跳躍個數 6 12 8 10 5 7 7 10 10 10 7 7 6 6 14
公司 KO MCD MMM MRK MSFT NKE PFE PG TRV UNH UTX VZ WMT XOM
觀察個數 1007 1007 1007 1007 1007 1007 1007 1007 1007 1007 1007 1007 1007 1007 平均數 0.0003 0.0006 0.0001 -0.0002 -0.0001 -0.0001 -0.0004 0.0000 0.0000 -0.0004 0.0002 -0.0001 0.0001 0.0000 標準差 0.0147 0.0149 0.0174 0.0216 0.0216 0.0308 0.0179 0.0139 0.0260 0.0291 0.0190 0.0179 0.0148 0.0204 偏態系數 0.6942 0.0170 -0.0578 -0.4126 0.3527 -11.2710 -0.0830 -0.2150 0.3425 0.5451 0.4880 0.3348 0.2330 0.1371 峰態系數 14.2434 7.0405 7.4827 11.0434 10.6887 258.2040 8.0482 9.7230 17.5242 21.0881 8.7202 9.4760 9.7929 15.1223
跳躍個數 8 7 8 9 9 5 6 6 10 8 10 8 7 8
註:表一為次貸期間 2007/01/03~2010/12/31 道瓊三十檔成分股的敘述統計量，跳躍個數的計算是採用當個別分股的報酬率高於其報酬率的三倍標準差時，即定 義為跳躍。
表二 次貸後期間敘述統計量 (2011/01/03~2014/12/31)
公司 AAPL AXP BA CAT CSCO CVX DD DIS GE GS HD IBM INTC JNJ JPM
觀察個數 1005 1005 1005 1005 1005 1005 1005 1005 1005 1005 1005 1005 1005 1005 1005 平均數 -0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.001 0.000 0.001 0.001 0.000 標準差 0.063 0.014 0.015 0.017 0.017 0.013 0.014 0.014 0.013 0.017 0.013 0.012 0.014 0.009 0.018 偏態系數 -28.358 -0.307 -0.365 -0.271 -0.322 -0.471 -0.557 -0.544 -0.111 -0.193 0.011 -0.834 0.182 0.125 -0.199 峰態系數 866.201 6.811 5.917 5.986 23.574 6.481 8.233 7.670 6.303 6.994 5.428 9.796 6.310 5.334 7.163
跳躍個數 0 6 6 6 6 7 7 6 5 8 8 6 5 6 10
公司 KO MCD MMM MRK MSFT NKE PFE PG TRV UNH UTX VZ WMT XOM
觀察個數 1005 1005 1005 1005 1005 1005 1005 1005 1005 1005 1005 1005 1005 1005 平均數 -0.0004 0.0002 0.0006 0.0005 0.0005 0.0001 0.0006 0.0003 0.0006 0.0010 0.0004 0.0002 0.0005 0.0002 標準差 0.0240 0.0089 0.0119 0.0117 0.0140 0.0273 0.0113 0.0089 0.0116 0.0147 0.0128 0.0105 0.0093 0.0115 偏態系數 -24.2256 -0.2648 -0.5774 -0.1376 -0.4174 -18.2240 -0.0533 -0.2585 -0.1416 -0.1240 -0.6311 -0.2309 -0.2628 -0.3442 峰態系數 702.1708 6.1756 7.3249 6.6150 9.9591 484.8927 5.5468 8.2200 8.5860 6.8717 7.8083 4.6235 6.8496 6.3467
跳躍個數 0 4 6 10 5 3 6 10 12 9 4 6 6 6
註:表二為次貸後期間 2011/01/03~2014/12/31 道瓊三十檔成分股的敘述統計量，跳躍個數的計算是採用當個別分股的報酬率高於其報酬率的三倍標準差時，即定 義為跳躍。
表三 次貸期間共同跳躍次數 (2007/01/03~2010/12/31)
Name AAPL AXP BA CAT CSCO CVX DD DIS GE GS HD IBM INTC JNJ JPM KO MCD MMM MRK MSFT NKE PFE PG TRV UNH UTX VZ WMT XOM
AAPL 6 2 2 1 3 2 2 2 3 2 3 2 2 2 2 2 2 2 2 2 1 2 2 1 3 2 2 3 2
AXP 2 12 3 5 4 2 4 3 3 5 3 3 2 1 5 1 1 3 1 4 0 1 2 2 2 4 1 1 2
BA 2 3 8 3 3 4 4 4 2 3 2 3 2 2 2 2 2 4 2 3 1 2 3 3 2 3 2 2 4
CAT 1 5 3 10 3 3 6 5 2 3 2 3 2 2 3 2 1 4 2 3 1 2 3 2 2 5 3 1 3
CSCO 3 4 3 3 5 2 4 3 3 3 3 3 3 2 2 2 2 3 2 3 1 2 2 1 3 3 2 2 2
CVX 2 2 4 3 2 7 4 6 3 2 3 3 2 4 1 5 3 6 4 4 3 4 5 4 3 5 5 2 7
DD 2 4 4 6 4 4 7 6 3 3 3 4 3 3 2 3 2 5 3 4 2 3 4 2 3 5 3 2 4
DIS 2 3 4 5 3 6 6 10 3 2 3 4 2 4 1 5 3 5 4 4 3 4 5 3 3 5 5 2 6
GE 3 3 2 2 3 3 3 3 10 3 2 3 3 2 6 2 1 4 3 5 2 3 4 3 3 5 2 1 3
GS 2 5 3 3 3 2 3 2 3 10 3 3 2 1 6 1 1 3 1 3 0 1 2 2 2 3 1 1 2
HD 3 3 2 2 3 3 3 3 2 3 7 3 2 3 1 3 3 3 3 2 2 3 3 2 4 3 3 2 3
IBM 2 3 3 3 3 3 4 4 3 3 3 7 1 2 3 2 1 3 2 2 2 2 3 1 3 3 2 1 3
INTC 2 2 2 2 3 2 3 2 3 2 2 1 6 2 2 2 2 3 2 4 1 2 3 2 3 4 2 2 2
JNJ 2 1 2 2 2 4 3 4 2 1 3 2 2 6 0 4 3 4 3 4 4 4 4 3 3 5 4 3 5
JPM 2 5 2 3 2 1 2 1 6 6 1 3 2 0 14 0 0 2 1 3 0 1 2 3 2 5 0 0 1
KO 2 1 2 2 2 5 3 5 2 1 3 2 2 4 0 8 3 4 4 3 3 4 4 3 3 4 5 2 5
MCD 2 1 2 1 2 3 2 3 1 1 3 1 2 3 0 3 7 2 3 3 2 2 2 1 2 3 3 3 4
MMM 2 3 4 4 3 6 5 5 4 3 3 3 3 4 2 4 2 8 3 5 3 4 5 4 3 6 4 2 6
MRK 2 1 2 2 2 4 3 4 3 1 3 2 2 3 1 4 3 3 9 2 2 4 3 3 3 3 4 2 4
MSFT 2 4 3 3 3 4 4 4 5 3 2 2 4 4 3 3 3 5 2 9 3 3 5 3 3 7 3 3 5
NKE 1 0 1 1 1 3 2 3 2 0 2 2 1 4 0 3 2 3 2 3 5 3 3 2 2 4 3 2 4
PFE 2 1 2 2 2 4 3 4 3 1 3 2 2 4 1 4 2 4 4 3 3 6 4 3 3 4 4 2 4
PG 2 2 3 3 2 5 4 5 4 2 3 3 3 4 2 4 2 5 3 5 3 4 6 4 4 6 4 2 5
TRV 1 2 3 2 1 4 2 3 3 2 2 1 2 3 3 3 1 4 3 3 2 3 4 10 3 4 3 2 4
UNH 3 2 2 2 3 3 3 3 3 2 4 3 3 3 2 3 2 3 3 3 2 3 4 3 8 4 3 2 3
UTX 2 4 3 5 3 5 5 5 5 3 3 3 4 5 5 4 3 6 3 7 4 4 6 4 4 10 4 3 6
VZ 2 1 2 3 2 5 3 5 2 1 3 2 2 4 0 5 3 4 4 3 3 4 4 3 3 4 8 2 5
WMT 3 1 2 1 2 2 2 2 1 1 2 1 2 3 0 2 3 2 2 3 2 2 2 2 2 3 2 7 3
XOM 2 2 4 3 2 7 4 6 3 2 3 3 2 5 1 5 4 6 4 5 4 4 5 4 3 6 5 3 8
註:表三為次貸期間共同跳耀的統計，共同跳躍的定義為，當成分股 A 與成分股 B 在研究樣本第 i 天同時被定義為有跳躍現象時，即成分股 A 與成分股 B 在這第 i 天有共同跳躍的現象。
表四 次貸後期間共同跳躍次數 (2011/01/03~2014/12/31)
Name AAPL AXP BA CAT CSCO CVX DD DIS GE GS HD IBM INTC JNJ JPM KO MCD MMM MRK MSFT NKE PFE PG TRV UNH UTX VZ WMT XOM
AAPL 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
AXP 0 6 2 2 2 3 3 2 2 2 2 1 1 2 3 0 2 4 3 1 0 2 2 5 3 1 2 1 3
BA 0 2 6 2 1 1 2 2 1 2 1 1 1 1 2 0 1 2 2 1 0 1 1 2 2 1 1 1 1
CAT 0 2 2 6 1 2 3 2 2 2 2 1 1 1 3 0 1 3 2 1 0 2 1 2 2 2 1 1 1
CSCO 0 2 1 1 6 2 2 1 1 2 1 1 1 2 2 0 0 2 2 0 0 1 2 2 2 1 0 0 2
CVX 0 3 1 2 2 7 2 1 2 3 2 1 1 3 3 0 1 3 2 0 0 1 2 4 2 1 1 0 4
DD 0 3 2 3 2 2 7 2 2 3 2 1 1 2 5 0 1 4 3 1 0 2 2 3 3 2 1 1 2
DIS 0 2 2 2 1 1 2 6 1 1 1 1 1 1 2 0 1 2 2 1 0 1 1 2 2 1 1 1 1
GE 0 2 1 2 1 2 2 1 5 2 0 1 1 1 2 0 0 3 1 0 0 0 1 2 1 2 0 0 2
GS 0 2 2 2 2 3 3 1 2 8 1 1 1 2 5 0 0 3 2 0 0 1 2 3 2 2 0 0 2
HD 0 2 1 2 1 2 2 1 0 1 8 0 0 1 2 0 1 2 2 1 0 2 1 2 2 0 1 2 1
IBM 0 1 1 1 1 1 1 1 1 1 0 6 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 1
INTC 0 1 1 1 1 1 1 1 1 1 0 1 5 2 1 0 0 1 1 0 0 0 1 1 1 2 0 0 1
JNJ 0 2 1 1 2 3 2 1 1 2 1 1 2 6 2 0 0 2 2 0 0 1 2 2 2 2 1 0 3
JPM 0 3 2 3 2 3 5 2 2 5 2 1 1 2 10 0 1 4 3 1 0 2 2 4 3 2 1 1 2
KO 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
MCD 0 2 1 1 0 1 1 1 0 0 1 0 0 0 1 0 4 1 1 1 0 1 0 2 1 0 1 1 0
MMM 0 4 2 3 2 3 4 2 3 3 2 1 1 2 4 0 1 6 3 1 0 2 2 4 3 2 1 1 3
MRK 0 3 2 2 2 2 3 2 1 2 2 1 1 2 3 0 1 3 10 1 0 2 3 3 3 1 1 1 2
MSFT 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 1 1 5 0 1 0 1 1 0 1 1 0
NKE 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0
PFE 0 2 1 2 1 1 2 1 0 1 2 0 0 1 2 0 1 2 2 1 0 6 1 3 2 0 1 1 2
PG 0 2 1 1 2 2 2 1 1 2 1 1 1 2 2 0 0 2 3 0 0 1 10 2 2 1 0 0 2
TRV 0 5 2 2 2 4 3 2 2 3 2 1 1 2 4 0 2 4 3 1 0 3 2 12 4 1 1 1 3
UNH 0 3 2 2 2 2 3 2 1 2 2 1 1 2 3 0 1 3 3 1 0 2 2 4 9 1 1 1 2
UTX 0 1 1 2 1 1 2 1 2 2 0 1 2 2 2 0 0 2 1 0 0 0 1 1 1 4 0 0 1
VZ 0 2 1 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 6 1 1
WMT 0 1 1 1 0 0 1 1 0 0 2 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 1 6 0
XOM 0 3 1 1 2 4 2 1 2 2 1 1 1 3 2 0 0 3 2 0 0 2 2 3 2 1 1 0 6
註:表四為次貸後期間共同跳耀的統計，共同跳躍的定義為，當成分股 A 與成分股 B 在研究樣本第 i 天同時被定義為有跳躍現象時，即成分股 A 與成分股 B 在這 第 i 天有共同跳躍的現象。
表五 次貸期間參數估計 (2007/01/03~2010/12/31)
公司名稱 u
公司名稱 u
AAPL 0.0015 0.0235 -0.0163 0.0980 0.0060 KO 0.0001 0.0122 0.0117 0.0615 0.0079 (0.0008) (0.0006) (0.0224) (0.032) (0.077) (0.0004) (0.0004) (0.0115) (0.016) (0.0889) AXP -0.0005 0.0287 0.0061 0.1183 0.0119 MCD 0.0005 0.0132 0.0022 0.0538 0.0070
(0.001) (0.0009) (0.0164) (0.0235) (0.1086) (0.0005) (0.0004) (0.0103) (0.0151) (0.0832) BA -0.0008 0.0208 0.0321 0.0684 0.0079 MMM 0.0002 0.0147 -0.0039 0.0616 0.0079
(0.0008) (0.0006) (0.0167) (0.0282) (0.0889) (0.0005) (0.0004) (0.01) (0.0143) (0.0889) CAT 0.0001 0.0228 0.0143 0.0857 0.0099 MRK 0.0002 0.0165 -0.0129 0.0782 0.0089
(0.0008) (0.0006) (0.0148) (0.0214) (0.0993) (0.0006) (0.0005) (0.0108) (0.0153) (0.0942) CSCO 0.0002 0.0200 -0.0345 0.0891 0.0050 MSFT 0.0000 0.0178 -0.0020 0.0798 0.0089
(0.0007) (0.0005) (0.018) (0.0262) (0.0704) (0.0006) (0.0005) (0.0128) (0.0182) (0.0942) CVX 0.0003 0.0171 -0.0043 0.0978 0.0070 NKE 0.0000 0.0183 -0.0085 0.1789 0.0050
(0.0006) (0.0005) (0.0168) (0.023) (0.0832) (0.0006) (0.0005) (0.0328) (0.0422) (0.0704) DD 0.0004 0.0203 -0.0187 0.0787 0.0070 PFE -0.0003 0.0155 -0.0096 0.0704 0.0060
(0.0007) (0.0006) (0.0144) (0.021) (0.0832) (0.0006) (0.0004) (0.0138) (0.0193) (0.077) DIS -0.0001 0.0182 0.0070 0.0792 0.0099 PG 0.0002 0.0117 -0.0124 0.0534 0.0060 (0.0007) (0.0005) (0.0123) (0.0174) (0.0993) (0.0004) (0.0004) (0.0097) (0.0138) (0.077) GE -0.0001 0.0206 -0.0164 0.0906 0.0099 TRV -0.0001 0.0192 0.0065 0.1059 0.0099 (0.0007) (0.0007) (0.0117) (0.0164) (0.0993) (0.0007) (0.0006) (0.0156) (0.0214) (0.0993) GS -0.0001 0.0252 -0.0014 0.1319 0.0099 UNH -0.0002 0.0213 -0.0053 0.1172 0.0079
(0.0009) (0.0007) (0.018) (0.0247) (0.0993) (0.0008) (0.0007) (0.0168) (0.0234) (0.0889) HD -0.0009 0.0209 0.0900 0.0167 0.0070 UTX 0.0000 0.0161 0.0090 0.0653 0.0099
(0.0007) (0.0005) (0.014) (0.014) (0.0832) (0.0006) (0.0005) (0.0107) (0.0156) (0.0993) IBM 0.0004 0.0150 -0.0013 0.0571 0.0070 VZ -0.0002 0.0151 0.0063 0.0659 0.0079
(0.0006) (0.0005) (0.0111) (0.0175) (0.0832) (0.0005) (0.0005) (0.0113) (0.0161) (0.0889) INTC 0.0002 0.0211 -0.0095 0.0828 0.0060 WMT 0.0001 0.0125 -0.0002 0.0586 0.0070
(0.0007) (0.0006) (0.0171) (0.0252) (0.077) (0.0005) (0.0004) (0.0107) (0.015) (0.0832) JNJ 0.0000 0.0094 -0.0046 0.0513 0.0060 XOM -0.0001 0.0157 0.0022 0.0899 0.0079
(0.0004) (0.0003) (0.0084) (0.0117) (0.077) (0.0006) (0.0004) (0.0151) (0.0206) (0.0889) JPM -0.0010 0.0276 0.0207 0.1285 0.0139
(0.001) (0.0009) (0.0152) (0.0211) (0.1172)
表六 次貸後期間參數估計 (20011/01/03~2014/12/31)
公司名稱 公司名稱
AAPL -0.0011 0.0632 -0.0086 0.0521 0.0000 KO -0.0005 0.0240 -0.0035 0.0197 0.0000 (0.002) (0.0015) (443.4051) (443.4051) (0) (0.0008) (0.0006) (443.4051) (443.4051) (0) AXP 0.0008 0.0130 -0.0031 0.0519 0.0060 MCD 0.0004 0.0081 -0.0085 0.0326 0.0040
(0.0005) (0.0004) (0.0128) (0.0188) (0.0771) (0.0003) (0.0003) (0.0074) (0.0105) (0.063) BA 0.0010 0.0135 -0.0229 0.0449 0.0060 MMM 0.0012 0.0101 -0.0212 0.0368 0.0060 (0.0005) (0.0004) (0.0118) (0.0179) (0.0771) (0.0004) (0.0003) (0.0064) (0.0091) (0.0771) CAT 0.0003 0.0155 -0.0232 0.0526 0.0060 MRK 0.0005 0.0105 0.0001 0.0389 0.0100
(0.0006) (0.0004) (0.0132) (0.0199) (0.0771) (0.0004) (0.0003) (0.0072) (0.0106) (0.0994) CSCO 0.0005 0.0124 -0.0085 0.0806 0.0060 MSFT 0.0006 0.0128 -0.0049 0.0580 0.0050
(0.0005) (0.0004) (0.0139) (0.0191) (0.0771) (0.0005) (0.0004) (0.0148) (0.0209) (0.0704) CVX 0.0006 0.0115 -0.0231 0.0368 0.0070 NKE 0.0008 0.0127 -0.0558 0.2142 0.0030
(0.0004) (0.0004) (0.0093) (0.0138) (0.0833) (0.0005) (0.0004) (0.047) (0.0631) (0.0546) DD 0.0005 0.0119 -0.0063 0.0522 0.0070 PFE 0.0007 0.0105 -0.0049 0.0381 0.0060
(0.0004) (0.0003) (0.0101) (0.0142) (0.0833) (0.0004) (0.0003) (0.0084) (0.0124) (0.0771) DIS 0.0012 0.0122 -0.0128 0.0502 0.0060 PG 0.0004 0.0078 0.0013 0.0306 0.0100
(0.0004) (0.0004) (0.0099) (0.0142) (0.0771) (0.0003) (0.0003) (0.0054) (0.0077) (0.0994) GE 0.0005 0.0122 -0.0079 0.0495 0.0050 TRV 0.0007 0.0095 0.0012 0.0399 0.0120
(0.0004) (0.0003) (0.0112) (0.0158) (0.0704) (0.0004) (0.0003) (0.0058) (0.0082) (0.1087) GS 0.0002 0.0154 -0.0031 0.0606 0.0080 UNH 0.0011 0.0131 -0.0004 0.0512 0.0090
(0.0006) (0.0005) (0.0116) (0.0169) (0.089) (0.0005) (0.0004) (0.0097) (0.0139) (0.0943) HD 0.0010 0.0117 0.0074 0.0399 0.0080 UTX 0.0008 0.0118 -0.0610 0.0118 0.0040
(0.0004) (0.0003) (0.0085) (0.0127) (0.089) (0.0004) (0.0003) (0.0082) (0.0087) (0.063) IBM 0.0006 0.0101 -0.0247 0.0394 0.0060 VZ 0.0006 0.0101 -0.0362 0.0029 0.0060 (0.0004) (0.0003) (0.0076) (0.0111) (0.0771) (0.0004) (0.0003) (0.0131) (0.0053) (0.0771) INTC 0.0005 0.0134 0.0125 0.0535 0.0050 WMT 0.0006 0.0082 -0.0083 0.0334 0.0060
(0.0005) (0.0004) (0.0135) (0.0199) (0.0704) (0.0003) (0.0003) (0.0062) (0.0088) (0.0771) JNJ 0.0005 0.0084 0.0113 0.0252 0.0060 XOM -0.0005 -0.0004 -0.0135 -0.0199 -0.0704
(0.0003) (0.0003) (0.0084) (0.0138) (0.0771) (0.0005) (0.0084) (0.0113) (0.0252) (0.006) JPM 0.0004 0.0151 0.0004 0.0588 0.0100
(0.0006) (0.0005) (0.0095) (0.0139) (0.0994)
圖二 道瓊三十檔成分股報酬率圖
2007 2008 2009 2010 2011 2012 2013 2014 -1.5-1
-0.50
AAPL
Year
Return
2007 2008 2009 2010 2011 2012 2013 2014 -0.2
2007 2008 2009 2010 2011 2012 2013 2014 -0.1
2007 2008 2009 2010 2011 2012 2013 2014 -0.1
2007 2008 2009 2010 2011 2012 2013 2014 -0.10.10
CSCO
Year
Return
2007 2008 2009 2010 2011 2012 2013 2014 -0.10.10
0.2
CVX
Year
Return
2007 2008 2009 2010 2011 2012 2013 2014 -0.1
2007 2008 2009 2010 2011 2012 2013 2014 -0.1
2007 2008 2009 2010 2011 2012 2013 2014 -0.1
2007 2008 2009 2010 2011 2012 2013 2014 -0.2
2007 2008 2009 2010 2011 2012 2013 2014 -0.1
2007 2008 2009 2010 2011 2012 2013 2014 -0.1
2007 2008 2009 2010 2011 2012 2013 2014 -0.1
2007 2008 2009 2010 2011 2012 2013 2014 -0.050.050.10
JNJ
Year
Return
2007 2008 2009 2010 2011 2012 2013 2014 -0.2
2007 2008 2009 2010 2011 2012 2013 2014
2007 2008 2009 2010 2011 2012 2013 2014 -0.1
2007 2008 2009 2010 2011 2012 2013 2014 -0.1
2007 2008 2009 2010 2011 2012 2013 2014 -0.1
2007 2008 2009 2010 2011 2012 2013 2014 -0.10
0.1
MSFT
Year
Return
2007 2008 2009 2010 2011 2012 2013 2014 -0.6-0.4
-0.20
NKE
Year
Return
2007 2008 2009 2010 2011 2012 2013 2014 -0.1
2007 2008 2009 2010 2011 2012 2013 2014 -0.1
2007 2008 2009 2010 2011 2012 2013 2014 -0.2
2007 2008 2009 2010 2011 2012 2013 2014 -0.2
2007 2008 2009 2010 2011 2012 2013 2014 -0.1
2007 2008 2009 2010 2011 2012 2013 2014 -0.1
2007 2008 2009 2010 2011 2012 2013 2014 -0.1
2007 2008 2009 2010 2011 2012 2013 2014 -0.10.10
XOM
Year
Return