行政院國家科學委員會專題研究計畫 成果報告
權益期限結構之估計與其結構性變化之研究
研究成果報告(精簡版)
計 畫 類 別 ： 個別型 計 畫 編 號 ： NSC 98-2410-H-004-060- 執 行 期 間 ： 98 年 08 月 01 日至 99 年 10 月 31 日 執 行 單 位 ： 國立政治大學國際貿易學系 計 畫 主 持 人 ： 郭維裕 計畫參與人員： 博士班研究生-兼任助理人員：李淯靖 處 理 方 式 ： 本計畫可公開查詢中 華 民 國 100 年 01 月 19 日
Empirical Equity Duration and Structural Change
Wei-Yu Kuo, Shinn-Juh Lin, and Yu-Ching Li
Department of International Business, National Chengchi University, Taiwan
December, 2010
Abstract
This paper studies the empirical equity duration by examining the sensitivity of stock returns to interest rate changes. In the regression framework, we control for three important asset-pricing factors, namely the market excess returns, and Fama and French’s (1993) two factors constructed on firm-size and book-to-market ratio. To account for possible biases generated from the collinearity between the market excess return and the interest rate change, this paper extends the work of Cornell (2000) by taking care of the collinearity problem with Fama and French’s orthogonalized market factor. This allows us to obtain a more viable estimate of the empirical equity duration. Furthermore, considering the time-varying nature of the empirical equity duration, we also test for the most recent break point of the regression relationship by the reversed ordered Cusum test (Pesaran and Timmermann, 2002), and propose a most up-to-date estimate of empirical equity duration, which is important for investors who view the empirical equity duration as important information in constructing their investment strategies.
Wei-Yu Kuo is an associate professor of the Department of International Business, National Chengchi
University. Shinn-Juh Lin is an associate professor of the Department of International Business, National Chengchi University. Yu-Ching Li is a PhD candidate of the Department of International Business, National Chengchi University. Kuo acknowledges financial support from the National Science Council of Taiwan (grant number: NSC-98-2410-H-004-060). Corresponding author: Wei-Yu Kuo. Email:[email protected]. Tel: 886-2-29393091 ext. 81244. Fax: 886-2-29387699. Address: Department of International Business, National Chengchi University, 64, Sec. 2, Tz-Nan Road, Taipei 116, Taiwan.
JEL Classification: C1; G1; G2.
Keywords: Empirical equity duration; Orthogonalized market factor; Reversed ordered Cusum test.
1. Introduction
Compared to the theoretical equity duration calculated on the basis of the
dividend discount model, the empirical equity duration measured by the sensitivity of
common stock returns to interest rate changes, is more appropriate and important for
fund managers and investors to assess the overall interest rate risk exposure of their
portfolios.
In its most primitive form, the empirical equity duration is typically estimated by
regressing stock returns on interest rate changes. However, as pointed out by Cornell
(2000), a simple univariate regression of stock returns on interest rate changes may
produce spurious results when other important explanatory variables are omitted from
the regression. To ensure model adequacy, previous studies also include in their
regression models other influential asset pricing factors as explanatory variables, such
as the market excess returns (Sweeney & Warga, 1986; Hevert, McLaughlin, &
Taggart, 1998; Cornell, 2000; and Reilly, Wright, & Johnson, 2007); and
Fama-French’s(1993) size and book-to-market (B/M) factors (Cornell, 2000). For example, Hevert, McLaughlin, and Taggart (1998, HMT hereafter) find that the
estimated duration switches from negative to positive for high growth (low
book-to-market) portfolios when the market return is added as an additional
explanatory variable. HMT conclude that growth opportunity leads to positive equity
duration. To examine more fully the impact of the specification of the regression
modelon empiricalestimatesofequity duration,Cornell(2000)extendsHMT’swork by dividing HMT’ssample into 25 size-B/M sorted portfolios, and demonstrating what HMT see as a book-to-market effect is a pure size effect. Cornell deduces that
HMT’sfinding isseen to bean artifactoffailing to includeFamaand French’s(1993) two factors constructed on firm-size (SMB) and book-to-market ratio (HML) in the
shows that none of the estimated equity durations is significantly different from 0, and
there is no longer any evidence of size, or B/M variation in equity durations. Since the
coefficient of the change in the interest rate is highly sensitive to the other explanatory
variable included in the regression, Cornell (2000) concludes that the relation between
stock returns and changes in interest rates depends critically on the conditioning
variables, especially the market factor.
Despite acknowledging the importance of controlling for the impact of the
market factor, past studies of empirical equity durations fail to account for the
possible collinearirty problem between market excess returns and interest rate changes,
which may contribute to biased parameter estimates in the regression framework.
Such a problem is not unusual, because existing common factors such as financial
distress risk often generate a certain degree of correlation between the stock market
and the bond market. For example, Fama and French (1993) find that, when the
interest rate factor is added as the fourth explanatory variable in their celebrated
three-factor model, the impact of interest rate factor tends to be absorbed by the
market factor, and causes insignificant parameter estimate on the interest rate factor.
What’s more interesting is that Fama and French (1993) also suggest to remedy the
problem by replacing the market excess returns with the orthogonalized market factor
to eliminate collinearity between the market excess returns and the interest rate
changes. Although the collinearity problem was also noted by Cornell (2000), no
attempt has been made to remedy the entailed statistical problem. Consequently, the
main aim of this paper is to extend the work of Cornell by taking care of the
collinearity problem with Fama and French’s orthogonalized market factor, which
allows us to obtain a more viable estimate of the empirical equity duration.
Empirical studies in the literature also reveal that the estimated equity durations
empirical investigation, and find evidence supporting that empirical equity durations
vary over time, which implies the relationship between stock-returns and interest rate
changes may exhibit structural breaks. From the historical perspective, it may be
interesting to detect and to date all of the structural break points. Nevertheless, since
mostinvestorsprobably caremoreabout“thenearest-future relationship between the stock returnsand theinterestratechanges”than about“how many timesthis relationship has broken so far”, we decide to focus on estimating the most up-to-date
empirical equity duration. To facilitate our analysis, we adopt the two-stage reversed
ordered Cusum test propsoed by Pesaran and Timmermann (2002), which allows
researchers to date the most recent break point.1 Compared with other popular
parameter-instability models, Pesaran and Timmermann find that the reversed ordered
Cusum test performs much better in predicting future changes in stock returns than
other models. In other words, even in the situation of multiple structural breaks, using
all available historical data to simultaneously estimate all the possible break points
and time-varying parameters does not help in correctly predicting future relationship
between the dependent variable and explanatory variables. Therefore, the second aim
of this paper is to propose an up-to-date empirical equity duration based on Pesaran
and Timmermann’stwo-stage reversed ordered Cusum test. This would be very helpful for investors who view the empirical equity duration as important information
in constructing their investment strategies.
The rest of the paper is organized as follows. In section 2, we lay out the
methodology adopted in this paper. Section 3 presents our empirical results. Section 4
concludes the paper.
1 WhatmotivatesPesaran and Timmermann’sreverseordered Cusum testisapracticalone.Thatis,
when facing with the possibility that model parameters might change over time, model users are often confronted with the problem in deciding how much historical data are adequate in correctly estimating the relationship between the dependent variable and the explanatory variables.
2. Methodology
2.1 Estimating the Empirical Equity Duration
As employed in the literature, there are three main types of regression models as
follows. t i t i i t i ED I R, , , (1) t i t m i t i i t i ED I R R, , , . (2) t i t hml i t smb i t m i t i i t i ED I R s R h R R, , , , , . (3)
whereRi,tdenotes excess returns on portfolio i; is the interest rate change;It
i
ED represents empirical equity duration of the portfolio considered; Rm,tis the
market excess return; Rsmb,t and Rhml,t are returns to the Fama-French mimicking
portfolios formed on size and book-to-market ratio, respectively.2
All three types of models try control for risk factor(s) to some extent in order to
examine the real impact of interest rate changes on stock returns.
2.2 Collinearity Problem
In this paper, we follow the literature in using regression models to estimate the
empirical equity duration. In addition to the interest rate changes, our regression
2 Fama and French construct the factor returns as follows. Each June, NYSE, Amex, and Nasdaq
stocks are allocated to two size groups, S and B, depending on whether the market equity is below or above the NYSE median. Stocks are also allocated to three book-to-market groups based on the bottom 30%, middle 40%, and top 30% break points for book-to-market ratio for NYSE stocks. Rsmb,t is the average monthly return on stocks in the three small-firm portfolios (one for each book-to-market ratio category) minus the average return on the three large-firm portfolios. Similarly, Rhml,t is the average monthly return on the two highest book-to-market portfolios (for both size groups) minus the average return on the two lowest book-to-market portfolios. Rm,t is the return on the value-weighted average
of all stocks that go into construction of the size and book-to-market portfolios, net of the one-month Treasury bill rate.
model also includes three important asset pricing factors, namely: market excess
returns, size factor, and book-to-market factor. In doing so, one needs to worry about
potential biases on the estimate caused by collinearity existing among interest rate
changes and the three asset pricing factors. Fama and French (1993) find statistical
significance of bond risk factor in explaining stock returns when the bond risk factor
is the sole explanatory variable. However, when other equity risk factors, such as the
market excess returns, are also included as explanatory variables, the significance on
the bond risk factor disappears. Fama and French (1993) deduce that such results
occur because stock markets are not completely isolated from the bond markets. In
particular, the two markets are very likely linked through a common risk factor. As a
result, when the bond risk factor is collinear with the equity risk factors, the impact of
the bond risk factor on stock returns are absorbed by the equity market factors,
particularly the market excess returns, which leads to insignificant coefficient estimate
on the bond risk factor. Similar problems also occur in Cornell (2000) and Reilly et
al.(2007). To resolve such a problem, Fama and French (1993) propose replacing the
market excess returns with the orthogonalized market factor to reduce interference on
the bond risk factor from the market factor. Specifically, regress the market excess
returns on other explanatory variables as follows,
t m t hml t smb t t m a I a R a R R , 1 2 , 3 , , . (4)
The estimated residuals from the above regression are defined as the orthogonalized
market factor (RMO , hereafter),t
t hml t smb t t m t m t R a I a R a R RMO ˆ, , ˆ1 ˆ2 , ˆ3 , . (5)
Intuitively, RMO represents the part of market excess returns which cannot bet
explained by interest rate changes, the size factor, or the book-to-market factor.
the regression model is modified as follows,
i
t i t i smbt i hmlt it i t i ED I RMO s R h R R, , , , . (6)This completes the description of the regression model adopted in this paper.
2.3 The Reversed Ordered Cusum Test
As demonstrated in Reilly et al. (2007), the empirical equity durations are
time-varying, which implies the relationship between stock-returns and interest rate
changes is not time-invariant, and may exhibit multiple structural break points. In the
literature, there exist many econometric models in estimating unstable parameters,
such as the recursive least squares model, the rolling least squares model, the
time-varying parameters model, and the multiple structural break model of Bai and
Perron (1998). Since most investors probably care more about “the nearest-future
relationship between thestock returnsand theinterestratechanges”than about“how many times this relationship has broken in thepast”, we decide to focus on the most recent structural break point, and estimate the most up-to-date empirical equity
duration based only on data after the break date. To facilitate our analysis, we adopt
the two-stage reversed ordered Cusum test propsoed by Pesaran and Timmermann
(2002).
In the following, we summarize Pesaran and Timmermann’s(2002) methodology.3 To begin with, the reversed ordered Cusum test reverses the order of the historical
data, i.e. treat the most recent observation as the first record, and the most distant
observation as the last record.
yT yT y y T , , , , ~ 1 1 , Y , T
xT,xT, ,x,x
~ 1 1 , X . (7)Then, the recursive least squares is applied to the order-reversed sample, which yield
the following parameter estimate
, , 1 , , ~ ~ ~ ~ ~ T T T T X X Y X , TT~,~1,,2,1. (8)where the shortened estimation period
T T~ 1
must be greater than the number of explanatory variables p, i.e.
T T~1
p, to ensure the functionality of the least squares. The resulting recursive residual at periodis then defined as y 1x ~ ˆ , TT~,~1,,2,1. (9)
The corresponding standardized recursive residual at periodis
d ˆ ˆ , TT~,~1,,2,1. (10) where
1
1/2 1 , 1 , ~ ~ 1 x x d XTXT , TT~,~1,,2,1. (11) Based on the standardized recursive residual, the reversed ordered Cusum statistic isdefined as follows,
1 ~ 2 ~ 2 , ˆ ˆ T j j T j j T WW , 1, ,2,1 ~ , ~ TT . (12)According to Brown, Durbin, and Evans (1975), under the null of no structural change
on the model parameter, the confidence interval of the above reversed ordered Cusum
statistic can be specified as
c p T p c p T p c c p T p WW T , , , . (13) where p T i WW c p i p T i 1,max, 1 , i p p T i T p WW i c 1 , , 1max . (14)Furthermore, to control for the estimated parameter variance, Pesaran and
Timmermann (2002) suggest the shortest estimation period
T T~ 1
to be set to at least two to three times the number of parameters.3. Empirical Results
3.1 The Interference of the Market Factor
In order to clarify the influence of the market excess return on the interest rate
change, we need to see the difference between the results of regressions in which the
market factor is added or not. What we are going to do is exactly to compare the
results of Equation (1) with the ones of Equation (2) and (3). The sample period is
January 1966 through December 1998,thesameasCornell’s(2000).
Table 1, corresponding to Equation (1), shows that used alone as the explanatory
variable in the regression, the interest rate change does explain stock returns. We find
that the 25 stock portfolios formed on size and book-to-market ratio all produce
significantly negative equity durations ranging between 3.54 and 5.41. Exhibit 1
displays the estimated equity durations as a bar and the associated t-statistics as a line.
The 25 portfolios on the x-axis are arranged first by size and then by book-to-market
ratio. The quintile of the smallest firms is on the far left, and that of the largest is on
the far right. Within each size quintile, the portfolios run from low book-to-market to
high.From Exhibit 1, we recognize that there is a monotonic relationship between
equity duration and size or book-to-market ratio. The estimated equity durations
decrease when moving from small to large firms, and also when moving from low to
high book-to-market portfolios. But, on the other hand, the t-statistics have a different
pattern. As firm size or book-to-market ratio increases, the t-statistics rise. However,
the interest rate change does not explain much of stock returns. All of the 25 adjusted
R2value are merely below 0.14. And it means that there is a large part of stock returns not explained by the interest rate change.
【Insert Table 1 and Exhibit 1】
regress the 25 portfolios returns on three stock-pricing factors –the market, size, and
book-to-market factors to see influences of these factors. Table 2 presents that these
three stock risk factors explain much more stock returns than the interest rate change
does (see Table 1). All of the 25 adjusted R2value are above 0.82 and the coefficients of the three factors are almost reliably different from 0, except the hs of two portfolios
in the second book-to-market ratio quintile. From the results of Table 1 and 2, we
know that the interest rate change and the three stock risk factors all have significant
explanatory power on stock returns, but with different degrees.
【Insert Table 2】
Table 3, corresponding to Equation (2), indicate that adding the market factor to
the regressions has an interesting effect on the estimated equity durations. In
regressions of Table 3, six large-size portfolios in the middle-B/M quintile still have
significantly negative estimated equity durations. But the rest 19 portfolios’equity durations alter to be indistinguishable from 0 or significantly positive. From Exhibit 2,
we realize that equity durations are much smaller and seem to be periodically
insignificantly different from zero. Most important, there is a cross-sectional pattern
on size and book-to-market ratio. The estimated equity durations switch from positive
to negative when moving from small to large firms if we ignore ones in the lowest
book-to-market quintile. Furthermore, there is a decreasing tendency in equity
durations when moving from low to high book-to-market portfolios.
【Insert Table 3 and Exhibit 2】
In Table 4, corresponding to Equation (3), when all three stock risk factors are
added to the regression, the pattern of results changes once again. All the estimated
equity durations for the 25 portfolios are smaller, and most of them are indifferent
from 0 or reliably positive. Exhibit 3 reveals that there is a cross-sectional but
negative when moving from small to medium-size firms, but revert to positive for
large firms. Moreover, a decreasing trend also exists when moving from low to high
book-to-market portfolios, except in the largest-size quintile with a rise pattern. All of
theR’sfortheregressions are just a little bit higher than ones of the regressions in Table 2 where three stock risk factors are explanatory variables. Therefore, adding the
interest rate change into this three-factormodelhasno impacton model’sexplanatory power.
【Insert Table 4 and Exhibit 3】
As Cornell reports, there are substantial changes in the estimated equity
durations when progressing from a univariate regression to the model adding the
market return, and finally to the full three-factor model. He demonstrates that the
significant relation between the market factor and changes in interest rates causes
these results. The impact of interest rate changes on stock returns is transmitted
almost exclusively through the market factor. In our sample, the correlation
coefficients between the market excess return and the interest rate change is -0.3
showing that the market factor is highly correlated with the interest rate change.
However, the correlation coefficients of -0.02 and -0.04 between the interest rate
change and the size factor, the book-to-market factor showing that the interest rate
change is not highly related with the size and book-to-market factors. Therefore, we
also suggest that the collinearity existing between the interest rate change and the
market excess return causes this phenomenon. However, Cornell does not further deal
with such problem, but concludes that the relation between stock returns and changes
in interest rate depends critically on the conditioning variables, such as the
Fama-French’ssize and book-to-market factors. Here, to accommodate such a problem in estimating the empirical equity durations, we follow Fama and French
3.2 The Estimated Equity Durations on the Full Sample
After the orthogonalized market factor is used to replace the market excess return,
the results is shown in Table 5. Notice that the market βs in Table 4 and Table 5 are
almost the same, so are the adjusted R2values. Therefore, the explanatory power of this four-factor model is not influenced if we replace the market factor with the
orthogonalized one.
Compared to the results of Table 4, Table 5 reveals that changes in interest rate
can explain much more stock returns after the orthogonalized market factor is a
substitute for the market factor. The 25 stock portfolios all produce significantly
negative equity durations ranging from 3.41 to 5.35, like the results of Equation (1) in
Table 1. From Exhibit 4, we can see that the cross-sectional pattern on the size and
book-to-market ratio still exists. As firm size or book-to-market increases, the
estimated equity duration as well as the associated t-statistic decrease.
Exhibit 5 displays the estimated equity duration and the market βs. As we can see that there is a positive relationship between them. In each size quintile, themarketβs as well as the equity durations show a negative relation with the book-to-market ratio.
While the book-to-market ratio increases,themarketβ decreases, so does the equity duration. Therefore, we say that portfolios with low interest rate sensitivity tend to
face high market risk.
【Insert Table 5, Exhibit 4 and 5】 3.3 Structural Changes of Equity Duration
Since we have confirmed the validity of model to estimate equity durations of
stock returns, we next conduct the reversed ordered Cusum test to examine the most
recent structural break point for our model. Before doing that,let’sfirst look at the estimated 36-month moving average equity durations to realize dynamic patterns of
equity durations over time.
Exhibit 6 shows that all 25 portfolios formed on size and book-to-market ratio
produce time-varying empirical equity durations, which implies the relationship
between stock returns and interest rates is not time-invariant. Most estimated equity
durations are negative before around 2002, but positive after 2002. Besides, it seems
that there are two structural changes during the period 1966-2008. One is about in
1981 and the other in 2002. Before 1981, equity durations for most portfolios are
more volatile but become stable after that. During the latter period of 2002-2008,
equity durations have ever risen sharply but finally declined.
【Insert Exhibit 6】
Table 6 presents the results of the reversed ordered Cusum test. Here, the sample
period is January 1990 to December 2008 because what we care about is the most
“up-to-date”empiricalequity duration.From Table 6, we can see that the most recent structural break for most portfolios happened in early 2000s. That is exactly when the
Internet bubble burst. In addition, it is worth to note that the detected most recent
structural break dates of some portfolios vary with different shortest estimation
windows. Pesaran and Timmermann (2002) do not specify rules of setting the shortest
estimation window; just roughly suggest to be set to at least two to three times the
number of parameters. Thus, we test by starting with the setting as 10, and choose the
one with the highest adjusted R2.
【Insert Table 6】
Table 7 presents the estimated results after the most recent break date. Notice
that all the 25 adjusted R2values are above 0.86, not lower than the full sample models. So it doesn’taffecttheadequacy ofregression ifconsidering the structural breaks. The relationship between stock returns and changes in interest rate has
equity durations, and other 4 having insignificant ones. From the panel (a) of Exhibit
7, we know that there is not a cross-sectional pattern on size any more. At a fist glance,
small firms seem to have lower equity durations than large firms. However, the
smallest growth firms have higher equity durations than most of the large firms.
Besides, there is either no cross-sectional pattern on book-to-market ratio from the
panel b of Exhibit 7.
【Insert Table 7 and Exhibit 7】
4. Conclusion
This paper studies the empirical equity duration by examining the sensitivity of stock
returns to interest rate changes in the regression framework that control for three
important asset-pricing factors, namely the market excess returns, and Fama and
French’s(1993)two factorsconstructed on firm-size and book-to-market ratio. Compared to the existing literature, the contribution of this paper is twofold. First of
all, although the collinearity problem was also noted by Cornell (2000), no attempt
has been made to remedy the entailed statistical problem. This paper takes care of the
collinearity problem with Fama and French’s orthogonalized market factor, which
allows us to obtain a more viable estimate of the empirical equity duration. Secondly,
considering the time-varying nature of the empirical equity duration, we also test for
the most recent break point of the regression relationship by the reversed ordered
Cusum test (Pesaran and Timmermann, 2002), and propose a most up-to-date estimate
of empirical equity duration, which is important for investors who view the empirical
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Table 1
Regressions on the interest rate changes
i
t it i t i ED I R, , Book-to-market ratio quintile Size quintile Small 2 3 4 Big α Low 0.125 0.38 0.445 0.476* 0.491** (0.326) (1.046) (1.34) (1.651) (2.058) 2 0.664** 0.624** 0.682** 0.43* 0.533** (1.995) (2.067) (2.505) (1.664) (2.346) 3 0.712** 0.841** 0.68** 0.67** 0.485** (2.363) (3.094) (2.795) (2.821) (2.288) 4 0.935** 0.949** 0.845** 0.745** 0.613** (3.298) (3.752) (3.693) (3.421) (3) High 1.031** 1** 0.93** 0.858** 0.696** (3.438) (3.557) (3.527) (3.332) (3.057) ED Low -3.538** -4.142** -4.317** -4.265** -3.709** (-3.044) (-3.765) (-4.296) (-4.88) (-5.135) 2 -3.706** -4.286** -4.65** -4.815** -4.147** (-3.679) (-4.69) (-5.64) (-6.149) (-6.026) 3 -3.893** -4.512** -4.922** -4.944** -4.132** (-4.27) (-5.482) (-6.683) (-6.872) (-6.442) 4 -3.779** -4.766** -4.804** -5.411** -4.084** (-4.402) (-6.223) (-6.934) (-8.202) (-6.598) High -3.653** -4.668** -4.797** -4.89** -3.868** (-4.023) (-5.483) (-6.008) (-6.275) (-5.612) Adj_R2 Low 0.02 0.032 0.042 0.055 0.06 2 0.031 0.05 0.072 0.085 0.082 3 0.042 0.069 0.1 0.105 0.093 4 0.044 0.087 0.106 0.144 0.097 High 0.037 0.069 0.082 0.089 0.0721. *, ** indicate significant at the 10% and 5% levels, respectively. 2. The t-statistics are in parentheses.
Table 2
Regressions on the market excess return and the mimicking returns for the size and book-to-market factors t i t hml i t smb i t m i i t i R s R h R R, , , , , Book-to-market ratio quintile Size quintile Small 2 3 4 Big α Low -0.495** -0.116 -0.027 0.089 0.233** (-5.008) (-1.527) (-0.352) (1.254) (3.604) 2 -0.057 -0.033 0.054 -0.176** 0.034 (-0.786) (-0.525) (0.758) (-2.191) (0.509) 3 -0.033 0.122** -0.023 -0.021 -0.061 (-0.553) (1.977) (-0.325) (-0.275) (-0.735) 4 0.155** 0.169** 0.096 -0.001 -0.071 (2.598) (2.855) (1.472) (-0.018) (-1.023) High 0.125* 0.071 0.017 -0.037 -0.123 (1.929) (1.1) (0.223) (-0.392) (-1.206) β Low 1.044** 1.093** 1.097** 1.053** 0.951** (42.95) (58.271) (58.596) (60.606) (59.722) 2 0.983** 1.022** 1.024** 1.083** 1.043** (55.081) (65.37) (58.137) (54.931) (63.326) 3 0.947** 0.971** 0.985** 1.058** 0.997** (63.688) (63.8) (56.611) (57.338) (48.482) 4 0.917** 0.976** 0.976** 1.017** 1.007** (62.304) (67.035) (60.678) (56.312) (58.764) High 0.962** 1.064** 1.07** 1.124** 1.032** (60.48) (67.235) (55.715) (47.913) (41.026) s Low 1.4** 1.037** 0.735** 0.319** -0.239** (40.193) (38.558) (27.379) (12.819) (-10.466) 2 1.27** 0.919** 0.624** 0.272** -0.197** (49.646) (41.005) (24.702) (9.621) (-8.325) 3 1.13** 0.841** 0.532** 0.236** -0.267** (53.028) (38.531) (21.303) (8.917) (-9.071) 4 1.061** 0.717** 0.444** 0.204** -0.186** (50.254) (34.332) (19.255) (7.862) (-7.559) High 1.154** 0.838** 0.613** 0.328** -0.022 (50.63) (36.919) (22.27) (9.748) (-0.604) h Low -0.283** -0.52** -0.474** -0.473** -0.463** (-7.125) (-16.929) (-15.483) (-16.645) (-17.779) 2 0.098** 0.02 0.054* 0.056* 0.014 (3.343) (0.786) (1.869) (1.749) (0.534) 3 0.256** 0.268** 0.326** 0.316** 0.217** (10.534) (10.762) (11.447) (10.479) (6.456) 4 0.407** 0.464** 0.487** 0.52** 0.522** (16.901) (19.47) (18.522) (17.598) (18.628) High 0.635** 0.683** 0.718** 0.713** 0.769** (24.419) (26.359) (22.837) (18.569) (18.688) Adj_R2 Low 0.939 0.96 0.952 0.946 0.935 2 0.956 0.96 0.939 0.917 0.925 3 0.964 0.954 0.928 0.916 0.867 4 0.96 0.953 0.931 0.908 0.901 High 0.958 0.954 0.924 0.882 0.823
1. *, ** indicate significant at the 10% and 5% levels, respectively. 2. The t-statistics are in parentheses.
Table 3
Regressions on the interest rate changes and the market excess return
i
t i mt it i t i ED I R R, , , Book-to-market ratio quintile Size quintile Small 2 3 4 Big α Low -0.609** -0.361** -0.255* -0.151 -0.02 (-2.793) (-2.088) (-1.846) (-1.508) (-0.218) 2 0.03 0.007 0.107 -0.133 0.033 (0.156) (0.048) (0.957) (-1.527) (0.47) 3 0.136 0.295** 0.175 0.16* 0.044 (0.796) (2.17) (1.616) (1.806) (0.472) 4 0.402** 0.443** 0.375** 0.292** 0.196** (2.414) (3.457) (3.538) (3.035) (2.024) High 0.49** 0.458** 0.417** 0.349** 0.274** (2.59) (2.925) (2.899) (2.587) (1.996) ED Low 2.517** 1.973** 1.454** 0.909** 0.506* (3.662) (3.619) (3.339) (2.887) (1.765) 2 1.526** 0.807* 0.094 -0.164 -0.022 (2.544) (1.797) (0.267) (-0.595) (-0.099) 3 0.856 -0.009 -0.757** -0.729** -0.497* (1.587) (-0.02) (-2.215) (-2.613) (-1.684) 4 0.62 -0.593 -0.925** -1.673** -0.638** (1.179) (-1.466) (-2.765) (-5.505) (-2.092) High 0.812 -0.195 -0.565 -0.695 -0.387 (1.361) (-0.394) (-1.245) (-1.631) (-0.894) β Low 1.463** 1.478** 1.395** 1.25** 1.019** (29.102) (37.049) (43.778) (54.259) (48.559) 2 1.265** 1.231** 1.147** 1.124** 0.997** (28.823) (37.485) (44.335) (55.791) (60.834) 3 1.148** 1.088** 1.007** 1.019** 0.878** (29.078) (34.643) (40.285) (49.951) (40.719) 4 1.063** 1.008** 0.937** 0.903** 0.833** (27.657) (34.062) (38.319) (40.62) (37.326) High 1.079** 1.081** 1.023** 1.014** 0.841** (24.716) (29.896) (30.775) (32.525) (26.535) Adj_R2 Low 0.689 0.784 0.837 0.888 0.865 2 0.688 0.792 0.845 0.897 0.912 3 0.695 0.77 0.824 0.878 0.826 4 0.675 0.768 0.811 0.835 0.801 High 0.622 0.715 0.73 0.752 0.6671. *, ** indicate significant at the 10% and 5% levels, respectively. 2. The t-statistics are in parentheses.
Table 4
Regressions on the interest rate changes, the market excess return and the mimicking returns for the size and book-to-market factors
i
t i mt i smbt i hmlt it i t i ED I R sR hR R, , , , , Book-to-market ratio quintile Size quintile Small 2 3 4 Big α Low -0.518** -0.126* -0.032 0.089 0.232** (-5.298) (-1.656) (-0.414) (1.25) (3.568) 2 -0.072 -0.035 0.062 -0.168** 0.03 (-0.997) (-0.555) (0.869) (-2.097) (0.452) 3 -0.04 0.13** -0.006 -0.009 -0.062 (-0.665) (2.101) (-0.079) (-0.122) (-0.738) 4 0.148** 0.182** 0.111* 0.025 -0.077 (2.473) (3.094) (1.709) (0.354) (-1.099) High 0.107* 0.069 0.019 -0.038 -0.14 (1.682) (1.073) (0.245) (-0.396) (-1.369) ED Low 1.028** 0.43* 0.211 -0.003 0.065 (3.344) (1.793) (0.881) (-0.012) (0.319) 2 0.652** 0.089 -0.354 -0.321 0.164 (2.88) (0.445) (-1.571) (-1.27) (0.778) 3 0.301 -0.338* -0.772** -0.506** 0.021 (1.581) (-1.737) (-3.51) (-2.148) (0.08) 4 0.33* -0.561** -0.641** -1.17** 0.243 (1.753) (-3.038) (-3.146) (-5.224) (1.105) High 0.779** 0.066 -0.08 0.02 0.719** (3.889) (0.324) (-0.323) (0.067) (2.242) β Low 1.074** 1.106** 1.103** 1.053** 0.953** (41.842) (55.241) (55.051) (56.554) (55.855) 2 1.002** 1.024** 1.013** 1.073** 1.048** (52.971) (61.178) (53.865) (50.916) (59.419) 3 0.956** 0.961** 0.962** 1.043** 0.997** (60.187) (59.15) (52.406) (53.059) (45.273) 4 0.927** 0.959** 0.957** 0.982** 1.014** (58.995) (62.209) (56.217) (52.493) (55.318) High 0.985** 1.066** 1.068** 1.124** 1.053** (58.907) (62.869) (51.886) (44.738) (39.33) s Low 1.39** 1.033** 0.732** 0.319** -0.24** (40.225) (38.333) (27.171) (12.749) (-10.439) 2 1.263** 0.918** 0.627** 0.275** -0.198** (49.622) (40.744) (24.787) (9.705) (-8.357) 3 1.127** 0.844** 0.54** 0.241** -0.268** (52.752) (38.624) (21.841) (9.119) (-9.028) 4 1.057** 0.722** 0.451** 0.216** -0.188** (50.006) (34.823) (19.681) (8.572) (-7.631) High 1.146** 0.837** 0.614** 0.328** -0.029 (50.95) (36.687) (22.179) (9.687) (-0.812) h Low -0.259** -0.51** -0.469** -0.473** -0.462** (-6.499) (-16.38) (-15.069) (-16.356) (-17.412) 2 0.113** 0.022 0.046 0.049 0.018 (3.836) (0.852) (1.56) (1.494) (0.665) 3 0.263** 0.26** 0.308** 0.304** 0.218** (10.666) (10.302) (10.792) (9.97) (6.358) 4 0.415** 0.451** 0.472** 0.493** 0.528**Book-to-market ratio quintile Size quintile Small 2 3 4 Big (16.985) (18.809) (17.862) (16.946) (18.529) High 0.653** 0.684** 0.716** 0.713** 0.786** (25.149) (25.96) (22.383) (18.256) (18.881) Adj_R2 Low 0.94 0.96 0.952 0.946 0.934 2 0.957 0.96 0.94 0.917 0.925 3 0.964 0.955 0.93 0.917 0.866 4 0.96 0.954 0.933 0.914 0.901 High 0.959 0.954 0.924 0.882 0.825
1. *, ** indicate significant at the 10% and 5% levels, respectively. 2. The t-statistics are in parentheses.
Table 5
Regressions on the interest rate changes, the orthogonalized market factor and the mimicking returns for the size and the book-to-market factors
i
t i t i smbt i hmlt it i t i ED I RMO s R h R R, , , , Book-to-market ratio quintile Size quintile Small 2 3 4 Big α Low -0.518** -0.126* -0.032 0.089 0.232** (-5.298) (-1.656) (-0.414) (1.25) (3.568) 2 -0.072 -0.035 0.062 -0.168** 0.03 (-0.997) (-0.555) (0.869) (-2.097) (0.452) 3 -0.04 0.13** -0.006 -0.009 -0.062 (-0.665) (2.101) (-0.079) (-0.122) (-0.738) 4 0.148** 0.182** 0.111* 0.025 -0.077 (2.473) (3.094) (1.709) (0.354) (-1.099) High 0.107* 0.069 0.019 -0.038 -0.14 (1.682) (1.073) (0.245) (-0.396) (-1.369) ED Low -3.539** -4.271** -4.476** -4.479** -3.987** (-12.316) (-19.065) (-19.969) (-21.496) (-20.876) 2 -3.607** -4.265** -4.662** -4.883** -4.289** (-17.039) (-22.763) (-22.143) (-20.701) (-21.739) 3 -3.762** -4.424** -4.863** -4.937** -4.218** (-21.171) (-24.328) (-23.663) (-22.454) (-17.112) 4 -3.611** -4.638** -4.708** -5.345** -4.068** (-20.534) (-26.883) (-24.721) (-25.531) (-19.831) High -3.408** -4.467** -4.618** -4.759** -3.758** (-18.215) (-23.535) (-20.055) (-16.922) (-12.541) β Low 1.074** 1.106** 1.103** 1.053** 0.953** (41.842) (55.241) (55.051) (56.554) (55.855) 2 1.002** 1.024** 1.013** 1.073** 1.048** (52.971) (61.178) (53.865) (50.916) (59.419) 3 0.956** 0.961** 0.962** 1.043** 0.997** (60.187) (59.15) (52.406) (53.059) (45.273) 4 0.927** 0.959** 0.957** 0.982** 1.014** (58.995) (62.209) (56.217) (52.493) (55.318) High 0.985** 1.066** 1.068** 1.124** 1.053** (58.907) (62.869) (51.886) (44.738) (39.33) s Low 1.862** 1.519** 1.217** 0.783** 0.18** (56.777) (59.398) (47.576) (32.902) (8.238) 2 1.704** 1.369** 1.073** 0.747** 0.263** (70.507) (63.982) (44.657) (27.755) (11.658) 3 1.548** 1.267** 0.963** 0.7** 0.171** (76.289) (61.051) (41.051) (27.875) (6.08) 4 1.465** 1.144** 0.871** 0.648** 0.258** (72.986) (58.1) (40.088) (27.104) (11.011) High 1.579** 1.306** 1.084** 0.822** 0.434** (73.95) (60.291) (41.228) (25.609) (12.687) h Low -0.897** -1.166** -1.124** -1.098** -1.028** (-24.623) (-41.049) (-39.534) (-41.572) (-42.437) 2 -0.482** -0.586** -0.556** -0.588** -0.604** (-17.96) (-24.662) (-20.827) (-19.665) (-24.131) 3 -0.304** -0.31** -0.263** -0.315** -0.374** (-13.5) (-13.464) (-10.106) (-11.279) (-11.978) 4 -0.136** -0.119** -0.096** -0.09** -0.074**Book-to-market ratio quintile Size quintile Small 2 3 4 Big (-6.081) (-5.428) (-3.958) (-3.404) (-2.852) High 0.069** 0.051** 0.082** 0.046 0.16** (2.897) (2.127) (2.804) (1.276) (4.222) Adj_R2 Low 0.94 0.96 0.952 0.946 0.934 2 0.957 0.96 0.94 0.917 0.925 3 0.964 0.955 0.93 0.917 0.866 4 0.96 0.954 0.933 0.914 0.901 High 0.959 0.954 0.924 0.882 0.825
1. *, ** indicate significant at the 10% and 5% levels, respectively. 2. The t-statistics are in parentheses.
Table 6
The most recent estimated breakpoint
Portfolios Breakpoint The Left observations The Shortest Estimation Window Small Low 2003/12 61 36 2 2001/7 90 10 3 2002/8 77 10 4 2003/12 61 14 High 2004/3 58 10 2 Low 2003/3 70 10 2 2003/12 61 10 3 2001/9 88 10 4 2003/11 62 10 High 2003/4 69 11 3 Low 2002/12 73 16 2 2001/8 89 10 3 2004/4 57 23 4 2001/7 90 10 High 2002/4 81 10 4 Low 2001/8 89 13 2 2002/7 78 10 3 2002/6 79 10 4 2001/8 89 13 High 2003/10 63 10 Big Low 2000/8 101 10 2 2001/6 91 12 3 2002/6 79 10 4 2002/6 79 10 High 2003/12 61 10
Table 7
After the most recent break, regressions on the interest rate changes, the orthogonalized market factor, and the mimicking returns for the size and the book-to-market factors
i
t i t i smbt i hmlt it i t i ED I RMO s R h R R, , , , Book-to-market ratio quintile Size quintile Small 2 3 4 Big α Low -0.643** -0.075 -0.023 0.06 -0.011 (-3.386) (-0.5) (-0.142) (0.515) (-0.122) 2 -0.131 0.226* 0.118 0.024 0.167 (-0.956) (1.846) (0.923) (0.179) (1.185) 3 -0.188 0.161 0.68** -0.194 -0.264* (-1.448) (1.361) (3.937) (-1.01) (-1.707) 4 -0.339** 0.121 0.065 0.14 -0.289** (-2.265) (0.833) (0.371) (0.783) (-2.207) High -0.284 0.038 0.314 -0.36** 0.447** (-1.647) (0.218) (1.388) (-2.073) (2.011) ED Low 3.093** 0.918 1.606** 4.038** 3.363** (3.863) (1.561) (2.512) (8.687) (8.896) 2 3.794** 1.957** 3.394** 1.695** 3.185** (6.871) (3.792) (6.639) (3.12) (5.584) 3 1.469** 2.428** 2.909** 2.967** 1.931** (2.814) (5.071) (4.074) (3.824) (3.09) 4 1.268** -0.217 4.402** 5.274** 2.366** (2.008) (-0.353) (6.263) (7.345) (4.486) High 2.798** 0.114 1.886** 1.035 1.862* (3.922) (0.166) (2.05) (1.397) (1.986) β Low 1.132** 1.055** 1.154** 1.073** 0.927** (22.575) (26.335) (26.999) (39.046) (42.804) 2 1.066** 0.948** 0.971** 1.081** 0.888** (32.676) (29.341) (32.11) (32.255) (26.544) 3 0.893** 0.878** 0.93** 1.174** 0.963** (27.69) (30.844) (20.218) (25.174) (25.66) 4 0.723** 0.934** 0.974** 1.06** 0.95** (18.281) (24.186) (23.465) (24.957) (29.969) High 1.002** 0.943** 1.023** 1.102** 1.082** (21.741) (20.172) (18.933) (23.913) (18.422) s Low 1.955** 1.823** 1.524** 1.012** 0.232** (23.092) (28.848) (22.208) (23.878) (7.094) 2 1.548** 1.576** 1.095** 1.07** 0.268** (31.247) (28.871) (23.469) (18.893) (5.374) 3 1.522** 1.386** 1.385** 0.993** 0.421** (27.373) (31.82) (17.845) (12.36) (6.508) 4 1.5** 1.588** 0.987** 0.952** 0.397** (22.473) (24.552) (15.654) (14.531) (7.263) High 1.716** 1.833** 1.08** 0.88** 0.684** (22.104) (24.857) (11.878) (11.444) (6.893) h Low -0.156 -0.139* -0.319** -0.602** -0.676** (-1.6) (-1.758) (-3.851) (-11.901) (-23.367) 2 -0.174** 0.106* -0.201** -0.14** -0.065 (-2.977) (1.69) (-3.615) (-2.148) (-1.085) 3 0.094 0.161** 0.06 -0.072 0.131* (1.483) (3.087) (0.682) (-0.766) (1.733) 4 0.551** 0.487** 0.254** 0.11 0.399**Book-to-market ratio quintile Size quintile Small 2 3 4 Big (7.169) (6.497) (3.413) (1.412) (6.276) High 0.753** 0.947** 0.269** 0.702** 0.466** (8.515) (10.196) (2.491) (7.807) (4.081) Adj_R2 Low 0.945 0.957 0.945 0.964 0.963 2 0.96 0.966 0.95 0.948 0.895 3 0.953 0.959 0.929 0.911 0.902 4 0.938 0.954 0.906 0.912 0.929 High 0.95 0.944 0.867 0.927 0.871
1. *, ** indicate significant at the 10% and 5% levels, respectively. 2. The t-statistics are in parentheses.
Exhibit 1
Equity durations in regressions of interest rate changes
i
t it i t i ED I R, , -6 -5 -4 -3 -2 -1 0Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High
E qu it y D ur at io n 0 1 2 3 4 5 6 7 8 9 t-st at is ti c ED t
Small firms Large firms
Exhibit 2
Equity durations in regressions of
the interest rate change and the market excess return
i
t i mt it i t i ED I R R, , , -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High
E qu it y D ur at io n -4 -3 -2 -1 0 1 2 3 4 5 6 t-st at is ti c ED t
Exhibit 3
Equity durations in regressions of
the interest rate change, the market excess return, the size and book-to-market factors
i
t i mt i smbt i hmlt it i t i ED I R s R h R R, , , , , -1.5 -1 -0.5 0 0.5 1 1.5Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High
E qu it y D ur at io n -6 -4 -2 0 2 4 6 t-st at is ti c ED t
Small firms Large firms
Exhibit 4
Equity durations in regressions of
the interest rate change, the orthogonalized market factor, the size and book-to-market factors
i
t i t i smbt i hmlt it i t i ED I RMO s R h R R, , , , -6 -5 -4 -3 -2 -1 0Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High
E qu it y D ur at io n 0 5 10 15 20 25 30 t-st at is ti c ED t
Exhibit 5
The estimated equity durationsand themarketβsin regressionsincluding theorthogonalized market factor -6 -5 -4 -3 -2 -1 0
Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High
E qu it y D ur at io n 0 0.2 0.4 0.6 0.8 1 1.2 B et a ED Beta
Small firms Large firms
Exhibit 6
The 36-month Moving Average Equity Duration of 25 stock portfolios formed on size and B/M Small-size and lowest-B/M
0 50 100 150 200 250 300 350 400 450 -10 -5 0 5 10 15 ED 5%~10% 5% 10% Small-size and 2nd-B/M 0 50 100 150 200 250 300 350 400 450 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 ED 5%~10% 5% 10%
0 50 100 150 200 250 300 350 400 450 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 ED 5%~10% 5% 10% 0 50 100 150 200 250 300 350 400 450 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 ED 5%~10% 5% 10%
Small-size and highest-B/M
0 50 100 150 200 250 300 350 400 450 -10 -5 0 5 10 ED 5%~10% 5% 10%
Second-size and lowest-B/M
0 50 100 150 200 250 300 350 400 450 -15 -10 -5 0 5 10 ED 5%~10% 5% 10% Second-size and 2nd-B/M 0 50 100 150 200 250 300 350 400 450 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 ED 5%~10% 5% 10% Second-size and 3rd-B/M 0 50 100 150 200 250 300 350 400 450 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 ED 5%~10% 5% 10%
0 50 100 150 200 250 300 350 400 450 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 ED 5%~10% 5% 10% 0 50 100 150 200 250 300 350 400 450 -15 -10 -5 0 5 10 ED5%~10% 5%10%
Third-size and lowest-B/M
0 50 100 150 200 250 300 350 400 450 -15 -10 -5 0 5 10 ED5%~10% 5% 10% Third-size and 2nd-B/M 0 50 100 150 200 250 300 350 400 450 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 ED 5%~10% 5% 10% Third-size and 3rd-B/M 0 50 100 150 200 250 300 350 400 450 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 ED 5%~10% 5% 10% Third-size and 4th-B/M 0 50 100 150 200 250 300 350 400 450 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 ED 5%~10% 5% 10%
0 50 100 150 200 250 300 350 400 450 -10 -5 0 5 10 ED 5%~10% 5% 10% 0 50 100 150 200 250 300 350 400 450 -15 -10 -5 0 5 10 ED 5%~10% 5% 10% Fourth-size and 2nd-B/M 0 50 100 150 200 250 300 350 400 450 -15 -10 -5 0 5 10 ED 5%~10% 5% 10% Fourth-size and 3rd-B/M 0 50 100 150 200 250 300 350 400 450 -15 -10 -5 0 5 10 ED 5%~10% 5% 10% Fourth-size and 4th-B/M 0 50 100 150 200 250 300 350 400 450 -15 -10 -5 0 5 10 ED 5%~10% 5% 10%
Fourth-size and highest-B/M
0 50 100 150 200 250 300 350 400 450 -10 -5 0 5 10 ED 5%~10% 5% 10%
0 50 100 150 200 250 300 350 400 450 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 ED 5%~10% 5% 10% 0 50 100 150 200 250 300 350 400 450 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 ED 5%~10% 5% 10% Largest-size and 3rd-B/M 0 50 100 150 200 250 300 350 400 450 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 ED 5%~10% 5% 10% Largest-size and 4th-B/M 0 50 100 150 200 250 300 350 400 450 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 ED 5%~10% 5% 10%
Largest-size and highest-B/M
0 50 100 150 200 250 300 350 400 450 -10 -5 0 5 10 ED 5%~10% 5% 10%
Exhibit 7
Equity durations in regressions of
the interest rate change, the orthogonalized market factor, the size and book-to-market factors
-2 0 2 4 6 8 10
Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High Low 2 3 4 High
E qu it y D ur at io n -2 0 2 4 6 8 10 t-st at is ti c ED t
Small firms Large firms
(a) arranged first by size and then by book-to-market ratio.
-2 0 2 4 6 8 10 Small 2 3 4 Big Small 2 3 4 Big Small 2 3 4 Big Small 2 3 4 Big Small 2 3 4 Big E qu it y D ur at io n -2 0 2 4 6 8 10 t-st at is ti c ED t
Growth firms Value firms
國科會補助計畫衍生研發成果推廣資料表
日期:2011/01/19國科會補助計畫
計畫名稱: 權益期限結構之估計與其結構性變化之研究 計畫主持人: 郭維裕 計畫編號: 98-2410-H-004-060- 學門領域: 財務無研發成果推廣資料
98 年度專題研究計畫研究成果彙整表
計畫主持人：郭維裕 計畫編號： 98-2410-H-004-060-計畫名稱：權益期限結構之估計與其結構性變化之研究 量化 成果項目 實際已達成 數（被接受 或已發表） 預期總達成 數(含實際已 達成數) 本計畫實 際貢獻百 分比 單位 備 註 （ 質 化 說 明：如 數 個 計 畫 共 同 成 果、成 果 列 為 該 期 刊 之 封 面 故 事 ... 等） 期刊論文 0 0 100% 研究報告/技術報告 1 1 100% 研討會論文 1 1 100% 篇 本 研 究 之 論 文 初 稿 已 於 去 年 的 台 灣 財 務 金 融 學 會 年會報告過。目前 正持續修改中，近 期 內 將 投 稿 至 國 外學術期刊。 論文著作 專書 0 0 100% 申請中件數 0 0 100% 專利 已獲得件數 0 0 100% 件 件數 0 0 100% 件 技術移轉 權利金 0 0 100% 千元 碩士生 0 0 100% 博士生 1 1 100% 博士後研究員 0 0 100% 國內 參與計畫人力 （本國籍） 專任助理 0 0 100% 人次 期刊論文 0 0 100% 研究報告/技術報告 1 1 100% 研討會論文 1 1 100% 篇 論文著作 專書 0 0 100% 章/本 申請中件數 0 0 100% 專利 已獲得件數 0 0 100% 件 件數 0 0 100% 件 技術移轉 權利金 0 0 100% 千元 碩士生 0 0 100% 博士生 1 1 100% 博士後研究員 0 0 100% 國外 參與計畫人力 （外國籍） 專任助理 0 0 100% 人次其他成果
