許多探討風險和超額報酬之間抵換關係的文獻多半著重於預期風險所造成的影 響，然而過去的文獻卻存在著該抵換關係正負不一致，甚至不顯著的結論。其中，負向 的抵換關係表示當資產的風險越低投資者反而會要求較高的風險貼水，此與 Merton (1973) 所提出的 ICAPM 有所矛盾。Nam and Krausz (2008) 則認為過去文獻之所以會得 到負向的關係是因為忽略了未預料到風險的影響，而導致犯了忽略重要變數 (Omitting Variables) 的問題。本研究則延伸 Nam and Krausz (2008) 做進一步的探討。
本研究主要目的在探討不僅僅只有預期風險會對超額報酬產生影響，同時前一期未 預料到的風險也會對於超額報酬有所影響，研究分別使用非線性的STAR model (Smooth Transition AutoRegression Model)，以及 ANST-GARCH-M 模型 (Asymmetric Nonlinear Smooth Transition GARCH in Mean)，做為估計模型的均數方程式和變異數方程式，並以 代表新訊息的前一期殘差做為轉換變數來探討新訊息分別對於預期波動和預期超額報 酬之不對稱的影響。與先前文章不同之處除了加入未預料到的風險外，而與 Nam and Krausz (2008)不同在於對於未預料到風險的處理並非以虛擬變數的方式來表示未預料 到風險的影響，而直接將未預料到的風險納入均數方程式中，如此可以看出前一期沒有 預料到的風險使投資者對於超額報酬修正的效果，此外，並考慮了新訊息在影響風險對 預期超額報酬不對稱的關係時存在門檻值，而非單以前一期股市價格的漲跌為好消息或 壞消息的依據。
然而，雖然研究結果無法判斷出忽略未預料到的風險是否會造成估計上的不正確，
但在非線性模型的估計結果下，正向與負向的抵換關係隨著不同的新訊息都有可能存 在，而在線性模型的估計下得到不顯著風險和超額報酬的抵換關係，表示估計的結果與 模型設定的設定有相當程度的關係。另一方面，對於未預料到風險的研究結果發現三個
國家的股市報酬未預料到風險確實會顯著地影響預期的超額報酬，並且呈現正向的關 係，亦即當投資者對於前一期波動的預期錯誤越高，將使得投資者修正對當期超額報酬 的預期，以至於使得所要求的超額報酬也將提高。而估計的結果門檻值皆顯著地大於 零，則可表示投資者對於好消息的定義更小，必須為意料之外的價格上漲至某一程度才 是為好消息。而不論預料到風險以及為預料到的風險都會因為不同的新訊息而有不對稱 的影響。
除此之外，研究也發現不但新訊息對於風險與報酬之間抵換關係有著不對稱的影 響，預料到的風險以及未預料到的風險也會隨著時間的進行而有著不同影響，其中日本 股市報酬的估計結果發現，在使用TV-STAR 模型後的估計下得到顯著的平滑結構性轉 變。此外，日本股市報酬的估計結果也顯示壞消息會得投資人增加所要求風險貼水，並 且有顯著的槓桿效果，即壞消息會使投資者提高對波動的預期。
參考文獻
Abel, A. B., 1988, Stock prices under time-varying dividend risk: an exact solution in an infinite-horizon general equilibrium model, Journal of Monetary Economics 22, 373-393.
Barsky, R. B., 1989, Why don’t the prices of stocks and bonds move together? American
Economic Review 79, 1132-1145.
Backus, D., and A. W. Gregory, 1993, Theoretical Relations between risk premiums and conditional variances, Journal of Business and Economic Statistics 11, 177-185.
Ball, R., and S. P. Kothari, 1989, Nonstationary Expected Returns: Implications for Tests of Market Efficiency and Serial Correlation in Returns, Journal of Financial Economics 25, 51-74.
Black, F., 1976, Studies in stock price volatility changes. Proceedings of the 1976 Business Meeting of the Business and Economics Section, American Statistical Association, pp.
177–181.
Brandt, M.W., and Kang, Q., 2004, On the relationship between the conditional mean and volatility of stock returns: a latent VAR approach. Journal Financial Economics 72, 217-257.
Campbell, J. Y., 1987, Stock returns and the term structure, Journal Financial Economics 18, 373-399.
Campbell, J. Y., and L. Hentschel, 1992, No news is good news: an asymmetric model of changing volatility in stock returns, Journal Financial Economics 31, 281-318.
Christie, A.A., 1982, The stochastic behavior of common stock variances—value, leverage and interest rate effects. Journal of Financial Economics 10, 407–432.
Enders, W., 2004, Applied econometric time series, John Wiley & Sons Inc.
Engle, R.F., and Ng, V.K., 1993, Measuring and testing the impact of news on volatility.
Journal of Finance 48, 1749–1778.
Fama, E. F., and French, K. R., 1993, Common risk factors in the returns on stock and bonds,
Journal of Financial Economics 33, 3-56.
Fama, E. F., and French, K. R., 2002, The equity premium. Journal of Finance 57(2), 637–659.
French, K. R., Schwert G. W., and Stambaugh, R. F., 1987, Expected stock returns and volatility, Journal of Financial Economics 19, 13-29.
Fornari, Fabio and Antonio Mele, (1997) , Sign-And Volatility-Switching ARCH Models:
Theory and Applications to International Stock Markets, Journal of Applied
Econometrics 12, 49-65.
Ghysel, E., P. Santa-Clara, and R. Valkanov, 2005, There is a risk-return trade-off after all,
Journal of Financial Economics 76, 509-548.
Glosten, L. R., R. Jagannathan, and D. E. Runkle, 1993, On the relation between the expected value and the volatility of the nominal excess return on stocks, Journal of Finance 48, 1779-1801.
Granger, C. and T. Teräsvirta (1993), Modeling Nonlinear Economic Relationships, Oxford University Press, Oxford.
Harvey, C., 1989, Time-varying conditional risk. Journal of Finance 46, 111-117.
Haugen, R. A., E. Talmor, and W. N. Torous, 1991, The effect of volatility changes on the level of stock prices and subsequent expected returns, Journal of Finance 46, 985-1007.
Kim, C. J., Morley, J. C., and Nelson, C. R., 2001, Does an intertemporal tradeoff between risk and return explain mean reversion in stock prices?, Journal of Empirical Finance 8, 403-426.
Koopman, S.J., and Uspensky, E.H., 2002, The stochastic volatility in mean model: empirical evidence from international stock markets. Journal of Applied Econometrics 17, 667–689.
Lin. C. F. and Teräsvirta, T. 1994, Testing the constancy of regression parameters against continuous structural change, Journal of Econometrics 62, 211-228.
Lucas, R. E. (1976).Economic policy evaluation: a critique. in Brunner, K. and Meltzer, A. H.
eds., The Phillips curve and labor market, 19-46. Amsterdam: North-Holland.
Lundbergh, S., Teräsvirta, T. and van Dijk, D. 2003, Time-varying smooth transition autoregressive models, Journal of Business and Economic Statistics 21, 104–121.
Ludvigson, S. C., and Ng, S., 2007, The empirical risk-return relation: a factor analysis approach, Journal of Financial Economics 83, 171-222.
Merton, R. C., 1973, An intertemporal capital asset pricing model, Econometrica: Journal of
the Econometric Society 41, 867-887.
Merton, R. C., 1980, On estimating the expected return on the market: An exploratory investigation, Journal of Financial Economics 8, 323-361.
Nam, K., C. S. Pyun, and A. C. Arize, 2002, Asymmetric return reversals and contrarian profits: ANST-GARCH approach, Journal of Empirical Finance 9, 475-608.
Nam, K., C. S. Pyun, and S. Avard, 2001, Asymmetric reverting behavior of short-horizon stock returns:an evidence of stock market overreaction, Journal of Banking and
Finance 25, 805-822.
Nam, K., and Krausz, J., 2008, Unexpected volatility shock, volatility feedback effect, and intertemporal risk-return relation, working paper.
Nelson, D. B., 1991, Conditional Heteroskedasticity in Asset Returns: A New Approach,
Econometrica 59, 347-370.
Scruggs, J. T., 1998, Resolving the puzzling intertemporal relation between the market risk premium and conditional market variance: a two-factor approach, Journal of Finance 52, 575-603.
Teräsvirta, T. 1994, Specification, estimation, and evaluation of smooth transition autoregressive models, Journal of the American Statistical Association 89, 208-218.
Tim Bollerslev, Hao Zhou, 2005, Volatility puzzles: a simple framework for gauging return-volatility regressions, Journal of Econometrics 131, 123-150.
Tong, H. (1990). Non-linear time series: a dynamical system approach, Oxford University Press, Oxford.
Turner, Christopher M., Richard Startz, and Charles R. Nelson, 1989, A Markov Model of Heteroskedasticity, Risk, and Learning in the Stock Market, Journal of Financial
Economics 25, 3-22.
Van Dijk, D., Teräsvirta, T., and Franses, P. H. 2002, Smooth transition autoregressive models:
a survey of recent developments. Econometric Reviews 21, 1-47.
Whitelaw, R. F., 1994, Time variations and covariations in the expectation and volatility of stock market returns, Journal of Finance 49, 515-541.
Whitelaw, R. F., 2000, Stock market risk and return: An equilibrium approach, Review of
Financial Studies 13, 521-547.
附圖
0.0 0.2 0.4 0.6 0.8 1.0
-1200 -800 -400 0 400 800 RES_MEAN(-1)
G_DOT
圖 2-1：美國股市-均數方程式轉換函數
G
( , ,γ
gc ε
t−1)對應轉換變數ε
t−1之關係圖.0 .1 .2 .3 .4 .5 .6 .7 .8
50 100 150 200 250 300 350 400 G_DOT
圖 2-2：美國股市-均數方程式轉換函數
G
( , ,γ
gc ε
t−1)隨時間經過而變化之關係圖0.0 0.2 0.4 0.6 0.8 1.0
-1200 -800 -400 0 400 800 RES_MEAN(-1)
F_DOT
圖 2-3：美國股市-變異數方程式轉換函數
F
( ,γ ε
f t−1)對應轉換變數ε
t−1之關係圖0.0 0.2 0.4 0.6 0.8 1.0
50 100 150 200 250 300 350 400 F_DOT
圖 2-4：美國股市-變異數方程式轉換函數
F
( ,γ ε
f t−1)隨時間經過變化之關係圖0.0 0.2 0.4 0.6 0.8 1.0
-400 -300 -200 -100 0 100 200 RES_MEAN(-1)
G_DOT
圖 3-1：日本股市-均數方程式轉換函數
G
( , ,γ
gc ε
t−1)對應轉換變數ε
t−1之關係圖0.0 0.2 0.4 0.6 0.8 1.0
100 200 300 400 500 G_DOT
圖 3-2：日本股市-均數方程式轉換函數
G
( , ,γ
gc ε
t−1)隨時間經過而變化之關係圖0.0 0.2 0.4 0.6 0.8 1.0
-400 -300 -200 -100 0 100 200 RES_MEAN(-1)
F_DOT
圖 3-3：日本股市-變異數方程式轉換函數
F
( ,γ ε
f t−1)對應轉換變數ε
t−1之關係圖0.0 0.2 0.4 0.6 0.8 1.0
100 200 300 400 500 F_DOT
圖 3-4：日本股市-變異數方程式轉換函數
F
( ,γ ε
f t−1)對應轉換變數ε
t−1之關係圖0.0 0.2 0.4 0.6 0.8 1.0
-1600 -1200 -800 -400 0 400 800 RES_MEAN(-1)
G_DOT
圖 4-1：英國股市-均數方程式轉換函數
G
( , ,γ
gc ε
t−1)對應轉換變數ε
t−1之關係圖0.0 0.2 0.4 0.6 0.8 1.0
250 500 750 1000
G_DOT
圖 4-2：英國股市-均數方程式轉換函數
G
( , ,γ
gc ε
t−1)隨時間經過而變化之關係圖0.0 0.2 0.4 0.6 0.8 1.0
-1600 -1200 -800 -400 0 400 800 RES_MEAN(-1)
F_DOT
圖 4-3：英國股市-變異數方程式轉換函數
F
( ,γ ε
f t−1)對應轉換變數ε
t−1之關係圖0.0 0.2 0.4 0.6 0.8 1.0
250 500 750 1000
F_DOT
圖 4-4：日本股市-變異數方程式轉換函數
F
( ,γ ε
f t−1)隨時間經過而變化之關係圖0.0 0.2 0.4 0.6 0.8 1.0
-400 -300 -200 -100 0 100 200 RES_MEAN(-1)
G_DOT
圖 5-1：日本股市- TVSTAR 均數方程式轉換函數
G
( , ,γ
gc
gε
t−1)對應ε
t−1之關係圖0.0 0.2 0.4 0.6 0.8 1.0
100 200 300 400 500 G_DOT
圖 5-2：日本股市- TVSTAR 均數方程式轉換函數
G
( , ,γ
gc
gε
t−1)對應時間之關係圖0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0 T
H_DOT
圖 5-3：日本股市- TVSTAR 均數方程式轉換函數
H
( , , )γ
hc t
h * 對應t 之關係圖
*0.0 0.2 0.4 0.6 0.8 1.0
100 200 300 400 500 GH_DOT
圖 5-4：日本股市- TVSTAR 均數方程式轉換函數 ( ) ( )
G
⋅H
⋅ 對應t 之關係圖
*0.0 0.2 0.4 0.6 0.8 1.0
-400 -300 -200 -100 0 100 200 RES_MEAN(-1)
F_DOT
圖 5-5：日本股市- TVSTAR 變異數方程式轉換函數
F
( ,γ ε
f t−1)對應ε
t−1之關係圖0.0 0.2 0.4 0.6 0.8 1.0
100 200 300 400 500 F_DOT
圖 5-6：日本股市- TVSTAR 變異數方程式轉換函數