Discussion Papers In Economics
And Business

Implied Equity Duration: Lessons from the Japanese Financial
CrisesYuichi Fukuta, Akiko Yamane

Discussion Paper 24-08

July 2024

Graduate School of Economics
Osaka University, Toyonaka, Osaka 560-0043, JAPANImplied Equity Duration: Lessons from the Japanese Financial
Crises∗Yuichi Fukuta†

Akiko Yamane‡§

July 6, 2024

Abstract
We present novel insights into the Japanese equity return term structure by examining the reversals of risk-adjusted returns on duration-sorted portfolios, as were particularly observed during
the COVID-19 pandemic and are common during crises. Our analysis, conducted over the Japanesestock market from 1990 to 2022, reveals that market uncertainty significantly explains the returnsof the long-short duration portfolio. Additionally, we find that the countercyclicality of the equity
term structure can be attributed to differences in the response of returns to considerably large negative shocks. This study contributes to the understanding of the relationship between the timing of
cash flows and stock returns and offers valuable implications for studies on the cross-section of stock
returns.

Keywords: equity duration; cross-section of stock returns; market uncertainty; financial crisis; pandemic
JEL Classification: G12∗ We thank Kohei Aono and participants at the Asset Pricing Workshop and the 5th Fall Conference of the Nippon
Finance Association for their helpful comments. This work is supported by JSPS KAKENHI Grant Numbers 20H01515,
20K01745, and 23K01451.
† Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka 560-0043, Japan.
‡ Graduate School of Humanities and Social Sciences, Hiroshima University, 1-1-89 Higashisenda, Naka-ku, Hiroshima
730-0053, Japan.
§ Corresponding author: Akiko Yamane, E-mail: yamaneak@hiroshima-u.ac.jp.

1

Introduction

Recent research has actively explored the relationship between a firm’s cash flow timing and stock returns,
or the term structure of stock returns. The literature indicates higher returns for stocks generating nearfuture cash flows compared to those with distant-future cash flows. Additionally, several studies suggestthat the relationship between the timing of cash flows and stock returns may vary depending on thestate of the economy. For example, Gormsen (2021) suggests that returns on stocks with dividends inthe distant future increase in bad times. In addition, Gormsen (2021) states that the term structure ofstock returns is both downward sloping on average (i.e., stocks with cash flows in the near future havehigher returns on average) and countercyclical (i.e., stocks with cash flows in the distant future havehigher returns during bad times).
We provide more specific findings on the countercyclical nature of the equity term structure. Dechow
et al. (2021) find that portfolios that pay a large fraction of cash flows in the near future underperformed
during the early phase of the COVID-19 pandemic in U.S., which is consistent with Gormsen’s (2021)
claim that the equity term structure is countercyclical. However, considering that Dechow et al. (2021)
do not cover economic crises other than the pandemic, it is not clear whether their results are common
during crises or a pandemic-specific phenomenon. Countercyclicality of the equity term structure may becaused by the reverse relationship between the timing of cash flows and stock returns during the crises.
Regarding these previous studies, we use Japanese stock market data since 1990, which includes
three major economic downturns to specifically identify the negative shocks that may lead to changes in
the relationship between the timing of cash flows and stock returns. Using the implied equity duration
proposed by Dechow et al. (2004), a well-known measure of a firm’s cash flow timing, we analyze the crosssection of duration-sorted portfolio returns.1 We identify how the capital asset pricing model (CAPM)
alphas of portfolios with different equity durations relate to the state of the economy. In addition, we
examine the relationship between market uncertainty and the returns of the long-short duration portfolio.
The contributions of this paper can be summarized as follows: First, empirical evidence of thisstudy demonstrates that a large negative shock or increased market uncertainty may cause the reversalof risk-adjusted returns on duration-sorted portfolios. During more severe crises, such reversals may
contribute to the observed countercyclicality. Second, this study expands the literature on the equity
term structure by presenting a detailed relationship between equity duration and the cross-section ofstock returns using Japanese market data. Using data from the Japanese market allows us to include
three major economic shocks in our analysis. Moreover, short duration portfolios perform poorly in bad
times, indicating that a high premium for a short-duration portfolio is consistent with prevalent asset
pricing theory. Simultaneously, a long-duration portfolio may serve as a risk-hedging device against large
1 Implied equity duration proposed by Dechow et al. (2004) has been used in recent studies (e.g., Fukuta and Yamane(2015), Weber (2018), and Dechow et al. (2021)) and can be computed from a few financial variables, making it possible
to analyze historically.

1negative economic shocks. These findings may provide a useful clue in future research when considering
the cross-section of stock returns.
The remainder of the paper is organized as follows: Section 2 presents the related literature. Section
3 describes the data and the method used to create the duration measure. Section 4 presents theproperties of duration quintile portfolios in the Japanese market. Section 5 examines what leads to thecountercyclicality of the equity term structure. Section 6 presents the robustness of the analysis. Finally,
Section 7 concludes the paper.

2

Related LiteratureThis study is related to the literature on the timing of firms’ cash flows and the cross-section of stock
returns. Dechow et al. (2004) and other previous studies have used equity duration as a measure of thetiming of cash flows.2 Dechow et al. (2004) apply Macaulay duration to equities and analyze its relationship with equity returns. Weber (2018) uses Dechow et al.’s (2004) duration measure and demonstrates
that portfolios with longer duration are overvalued when sentiment is high in the previous month. Da(2009) uses a two-factor model of cash flow covariance and duration, and shows that it can potentiallyexplain the cross-section of stock returns. Schröder and Esterer (2016) measure duration using analyst
forecasts, and Chen (2022) uses changes in stock prices before and after the monetary policy announcements to obtain a duration measure. More recent studies have also shown that short-duration premiumis associated with premium for major risk factors such as profitability (Gonçalves (2021), Gormsen andLazarus (2023)).3
Most studies analyzing the relationship between equity duration and cross-section of stock returns
focus on the U.S. market, and non-U.S. analysis is limited. Fullana and Toscano (2014) calculate theimplied equity duration for firms listed on the Spanish stock market, and compare the results with thoseof Dechow et al. (2004) for the U.S. market. Fukuta and Yamane (2015) find that the duration risk factor
has similar information to the HM L factor for the Japanese market. Bae and Lee (2021) demonstratethat the duration factor may explain the momentum profits in the Korean market.
Studies that address the relationship of equity term structure to the business cycle include Gormsen(2021) and Bansal et al. (2021). Using data on dividend index futures, Gormsen (2021) reveals that theslope of the term structure of stock returns is both countercyclical and downward on average. Bansal
et al. (2021) also use data for dividend index futures and employ a regime-switching model to identify
the difference in the term structure during periods of economic expansion and recession.
Our study is also related to studies of cross-sectional returns on the timing of firms’ cash flows during
2 There are also studies that use dividend strip data calculated from dividend future prices or option prices to analyze
the term structure of equities; see van Binsbergen et al. (2012), van Binsbergen et al. (2013), van Binsbergen and Koijen(2017), Gormsen and Koijen (2020), Gormsen (2021) and Bansal et al. (2021).
3 Some studies, such as Lettau and Wachter (2007), have related the timing of firms’ cash flows to the value premium.
See Fukuta and Yamane (2015) for a literature review.

2the COVID-19 pandemic. Gormsen and Koijen (2020) demonstrate that when the stock-price decline
during the pandemic recovered, the dividend prices of the near future remained low while the dividend
prices of the distant future recovered. Dechow et al. (2021) obtain evidence that the average returns and
CAPM alphas are higher for the short-duration portfolio than for the long-duration portfolio before thepandemic, whereas the average returns and CAPM alphas for the short-duration portfolio are lower thanthose of the long-duration portfolio during the pandemic. Studies that examine the pandemic period canalso be related to the studies that consider the business cycle described above.

3

Data

We focus on firms listed on the first and second sections of the Tokyo Stock Exchange as of April 1,
2022. The sample period for the analysis of monthly returns is from February 1990 to June 2022, andthe sample period for daily returns begins on January 5, 1990. However, for calculating durations, we
use financial data spanning 1977 to 2022 to maximize the sample period for estimating future cash flow
parameters. Financial variables and daily stock prices of individual stocks are obtained from the Nikkei
NEEDS database, and monthly individual stock returns, daily and monthly market returns, and risk-freerates are obtained from Financial Data Solutions.4 We exclude firms whose identification for the industry
is not assigned, firms in the financial sector, non-surviving firms at the end of June 2022, and firms withan accounting period of less than 12 months.
Dechow et al. (2004) apply Macaulay duration to equities and propose implied equity duration.
Macaulay duration is expressed as follows:

D0M =

PT

B
B t
t=1 t(CFt /(1 + r ) )
,
B
P0

(1)

where CFtB denotes the cash flow at time t, rB denotes the yield to maturity, T denotes the maturity,
and P0B denotes the bond price at time 0. To apply this to equities, Dechow et al. (2004) assume thatcash flow payments continue for an infinite period, while predicted cash flows change to a certain period
T and remain constant after T + 1. Equation (1) can therefore be rearranged as follows:
P∞
D0 =

t
t=1 t(CFt /(1 + r) )

P0
P∞

PT
=

t
t=1 t(CFt /(1 + r) )+t
t=T +1 t(CFt /(1 + r) )

P0
P0
PT


t
t(CF
/(1
+
r)
)
1 + r (P0 − t=1 CFt /(1 + r)t )
t
t=1
+ T+
,
P0
r
P0

PT
=

(2)

4 The Nikkei NEEDS database is widely used in studies using financial data on Japanese firms. Financial Data Solutions
provides data on stock returns and is widely used in the analysis of the Japanese market. Kubota and Takehara (2018)
and Fukuta and Yamane (2015) also use these databases.

3

where CFt denotes the predicted net cash distribution to equity holders at time t, P0 denotes the market
capitalization of equity at time 0, r denotes the expected stock return, and T denotes the finite forecastinghorizon. In addition, given the clean surplus condition, the cash flow at time t can be expressed as

CFt = Et − (BEt − BEt−1 )(BEt − BEt−1 )Et−,= BEt−1 ×
BEt−1
BEt−1

(3)

where Et denotes the earnings at time t, BEt denotes the book equity at time t. Dechow et al. (2004)
assume that return on equity (ROE), Et /BEt−1 and growth in book equity, (BEt − BEt−1 )/BEt−1
follow the AR (1) process, respectively, and obtain the predicted values of cash flows up to t = T fromequation (3). They substitute the predicted values of cash flows into equation (2) and refer to it as
implied equity duration. The first line of equation (2) shows that implied equity duration is a weighted
average of the timing of cash flows with the weight being the ratio of the discounted present value ofcash flow in time t to the current market capitalization. Thus, the equity duration calculated with themethod by Dechow et al. (2004) provides a measure of the timing of cash flows.
In this study, we obtain the equity duration using the same method as in Dechow et al. (2004).
According to Weber (2018) and Dechow et al. (2021), the cash flow forecasting period T is set to 15
years, and the parameters for the autoregressive processes of ROE and book equity growth and r are
the same for all firms.5 In estimating the process of book equity growth, we obtain the autoregressive
coefficients estimated from sales growth as in Dechow et al. (2004), considering that the prediction fitsbetter with the parameters estimated using sales growth. The financial variables used in the calculationof the duration are book equity, earnings, sales growth, and market capitalization. We winsorize ROE
and sales growth at 1% and 99 % levels, respectively, and samples with negative book equity are excluded
from the analysis.
The autoregressive coefficients used to predict cash flows are the cross-sectional means of the estimatedfirst-order autoregressive coefficients of ROE and sales growth for each firm, weighted by the number ofsamples in the time series for each firm. Firms with a time series sample of less than 10 are excluded.
The autoregressive coefficient of ROE used in this study is 0.457, and the long-run average is 0.062,
which is the annualized value of the average TOPIX monthly return. The autoregressive coefficient of
the book equity growth rate is 0.166, and the long-run average is set to 0.044 using the long-run averageof the nominal GDP growth rate.6 These parameters are similar to those of Dechow et al. (2021) and5 Fukuta and Yamane (2015) use industry-specific parameters when calculating equity duration for the Japanese market,
although they note that the ranking of durations is not substantially different from those using the same parametersacross industries. Considering that we are using duration quintile portfolios in this study, the forecasting parameters being
identical for all firms should not significantly affect the results.
6 Although the forecasting model used in this study might be parsimonious, the correlation coefficient between realized
dividend payments and forecasted cash flows is around 0.8, which is considered to be sufficiently well predicted.

4Weber (2018) for the U.S. market, although the values are not the same.7
Table 1 presents the descriptive statistics for duration and financial variables. The statistics presented
in this table span 1990-2022, in line with subsequent analyses. Panel A shows the means and standard
deviations of the variables and the numbers of observations of firm × fiscal year, with a maximum numberof firms of 2409. Panel B shows the correlations across variables. Duration has a strong negative correlation with the book-to-market ratio, a negative correlation with ROE, and a weak positive correlation
with sales growth. Similar correlations between duration and firm characteristics are reported in Weber(2018) for the U.S. market. Note that the implied equity duration depends on the ratio of the present
value of the expected cash flows in the near future to the current market capitalization, which may have
similar information to the ratio of fundamentals to market capitalization, such as the book-to-market
ratio.
[Insert Table 1 here]

4

Duration Quintile Portfolios in the Japanese Market

4.1

Returns on duration quintile portfolios

We conduct the analysis using portfolio returns sorted by equity duration to clarify the differences in thevariation of returns across different values of equity duration. For each year in the sample, we obtain
the duration’s 20th, 40th, 60th, and 80th percentiles and create the quintile portfolios. Portfolios arerebalanced at the end of August each year and the daily and monthly value-weighted portfolio returns
are obtained.8
Panel A of Table 2 presents the average duration, book-to-market ratio, and market capitalizationof the duration quintile portfolios. The duration of the shortest-duration quintile portfolio averages 18.6
years, while the longest-duration portfolio averages 26.32 years. The book-to-market ratio is smaller for
longer durations, and the difference between the shortest- and longest-duration portfolios is significant.
Market capitalization tends to be larger for longer durations, and the difference between the portfolios
with the longest and shortest durations is also significant. Thus, the short-duration portfolio tends tocontain small and value stocks, and the long-duration portfolio tends to contain large and growth stocks.9
The top panel of Panel B in Table 2 lists the means and standard deviations of the monthly value-weighted
returns for the duration quintile portfolios. The Long-Short column presents the long-short portfolio,
which is the difference between the longest-duration portfolio return and the shortest-duration portfolio
7 For example, in Weber (2018), the autoregressive coefficient of ROE is assumed to be 0.41, with a long-run mean of
0.12, while the autoregressive coefficient of book equity growth is 0.24, with a long-run mean of 0.06.
8 When conducting portfolio-based analysis for the Japanese market, portfolios are often constructed at the end of
August, considering the fiscal year-end of companies (e.g., Kubota and Takehara (2018)).
9 This suggests that the difference in return behavior with duration may be owing to firm size and book-to-market ratio.
However, in Section 6, we show that the results of the subsequent analysis are robust even when controlling for size andbook-to-market ratio.

5

return. The average returns are significantly higher for the short-duration portfolio than those for the
long-duration portfolio. The bottom panel of Panel B lists the CAPM estimates for each duration
portfolio and the long-short portfolio. The estimation results indicate that CAPM alpha is higher for
short duration than for long duration, and beta is higher for long duration than for short duration. The
long-short differences are significant in both cases. These results are similar to what Weber (2018) has
shown for U.S. market data.
[Insert Table 2 here]

4.2

Findings of previous studies

In this subsection, we examine whether the portfolio return behavior presented in Dechow et al. (2021)
and the countercyclicality discussed in Gormsen (2021) can be observed using Japanese duration quintile
portfolio returns before moving on to the main analysis of this study.
First, Figure 1 depicts the cumulative daily returns of the duration quintile portfolios with a value of
1 on January 6, 2020, around the beginning of the COVID-19 pandemic. The shortest-duration portfolio
indicated by the blue dotted line experienced the largest price decline, and the longest-duration portfolio
indicated by the blue solid line experienced the smallest price decline during the large decline in thestock market from February to March 2020. Furthermore, the longest-duration portfolio recovered toits pre-decline level within about three months, whereas the shortest-duration portfolio took more than
one and a half years to recover. The observed difference in the degree of decline at the beginning of thepandemic across equity durations is similar to the result of Dechow et al. (2021) with U.S. data. The
faster recovery of stock prices in the long-duration portfolio is also consistent with Gormsen and Koijen(2020). They find that the distant future dividend strip prices recovered relatively faster using data on
dividend futures.
[Insert Figure 1 here]
Subsequently, we show whether similar findings are obtained in the Japanese market by using thepredictive regression that Gormsen (2021) uses to demonstrate the countercyclicality of the term structureof stock returns. The estimated equations are:ee
Ri,t,t+12= ai + b1,i Rm,t,t+12+ b2,i (dt − pt ) + i,t,t+12 ,(4)eRi,t,t+12= ai + b1.i (dt − pt ) + i,t,t+12 ,(5)ewhere Ri,t,t+12
denotes the one-year ahead return on duration-sorted portfolio i in excess of the risk-freeerate, dt − pt denotes a log of the monthly market’s dividend yield, and Rm,t,t+12
denotes the one-year

ahead excess market return. Both formulas indicate whether or not the dividend yield in the current
6period predicts the return one year ahead. As the market dividend yield takes large values at bad times,
the equity term structure is considered to be countercyclical if the coefficient of dt − pt for the long-shortduration portfolio is positive. We use the weighted average yield of the first section of the Tokyo Stock
Exchange as the market’s dividend yield.10 As these data are available from January 1998 at most, theestimation is for the sample period from 1998 onward. The d − p column in Table 3 summarizes thestatistics for the log of the market’s dividend yield.
[Insert Table 3 here]
Table 4 presents the results of the predictive regressions. Panel A lists the estimates from equation(4), and Panel B lists the estimates from equation (5). In both estimations, the longer the duration, thelarger the dt − pt loadings. The coefficient estimates of dt − pt for the long-short portfolio are positiveand significant at the 10% and 5% significance level for Panels A and B, respectively. Therefore, thecountercyclicality shown by Gormsen (2021) is also observed for the Japanese market.
[Insert Table 4 here]
We demonstrate the relationship between the long-short duration portfolio returns and the recession.
Figure 2 plots the 12-month moving average of the long-short return on duration-sorted portfolios andthe market return. The shadowed area represents the recession period, as stated by the Cabinet Office.
Although the discussion up to this point would lead us to expect that the long-short portfolio returnpresented by the black solid line would be positive during economic downturns, it is not always positive
during recessions. The correlation coefficient between the market return and the long-short portfolio
return is 0.29. The argument that the term structure of stock returns is countercyclical does not simply
mean that it is inversely correlated with a measure of economic fluctuations. Hence, we conduct further
investigations to examine the relationship between countercyclicality and economic conditions.
[Insert Figure 2 here]

5

Empirical Results

In this section, we examine the relationship between the returns on duration-sorted portfolios and market
uncertainty or the business cycle through regression analysis. Gormsen and Lazarus (2023) make CAPM
alphas the subject of their analysis when discussing the cross-section of equity returns. They discuss
whether returns are higher relative to conventional risk measures such as market betas. Similarly, we
analyze the CAPM alpha, or risk-adjusted return on each portfolio and identify the factors that cause
the countercyclical property of the term structure of stock returns by clarifying the variables that explain
the risk-adjusted returns.
10 This data is available on the website of the Japan Exchange Group https://www.jpx.co.jp/english/markets/statisticsequities/misc/03.html.

7

5.1

Time variation of CAPM alphaWe run the rolling regression of the CAPM on the daily returns of the shortest- and longest-duration
quintile portfolios to examine the behavior of the market-adjusted returns. The estimation window, set at
60 days, involves shifting it daily by one day to generate a time series of CAPM alphas after April 3, 1990.
Figure 3 shows the estimates and confidence intervals of CAPM alphas. The upper and lower panels
show alphas of the shortest- and longest-duration portfolios, respectively. For either figure, the solid lineis the estimate of CAPM alpha, the red dashed line is the 95% confidence interval, the blue-colored areas
show the period when the CAPM alpha is significantly negative, and the orange-colored areas show theperiod when the CAPM alpha is significantly positive. The Japanese banking crisis around 1997-1999
and the global financial crisis in 2008 are shown in the figures, in addition to the COVID-19 pandemic
in 2020 as events that would have had a significant impact on the market during the sample period.11
The shortest-duration portfolio tends to have positive CAPM alphas over the entire sample period,
whereas significantly negative alphas are observed during the two financial crises and the pandemic
that are mentioned above. Conversely, for the longest-duration portfolio, positive CAPM alphas areobserved at a time close to when the short-duration portfolio’s CAPM alphas are negative.12 Thus, therisk-adjusted return on the short-duration portfolio is higher in normal times, whereas the risk-adjusted
return on the long-duration portfolio is relatively high during the crisis.
[Insert Figure 3 here]

5.2

Market Uncertainty

As discussed in Section 4, the countercyclicality of equity term structure may not be caused by a negative
correlation with the business cycle. As illustrated in Figure 3, the risk-adjusted return of the shortduration portfolio tends to decline when a negative shock occurs, while the risk-adjusted return of thelong-duration portfolio tends to be zero or positive during the same period. That is, the risk-adjusted
return on the long-short portfolio tends to be larger under negative shocks, although it is negative on
average. Considering that the periods when the significant risk-adjusted returns observed for portfolio
returns in Figure 3 roughly correspond to the periods of large negative shocks such as the financial crisisand the COVID-19 pandemic, the countercyclical nature of the slope of the term structure may reflect
the difference in stock prices’ response to considerably large negative shocks. To confirm this conjecture,
we next examine the variables that explain the risk-adjusted returns on the duration-sorted portfolios.
11 In Japan, Yamaichi Securities, one of the country’s four major securities firms, and Hokkaido Takushoku Bank, thelargest commercial bank in the northern part of Japan, went bankrupt in November 1997. Thereafter, several financial
institutions failed, and the overall economic downturn continued. The global financial crisis of 2008 also had a major
impact on the Japanese economy, resulting in a rapid economic slowdown.
12 As there exist periods, such as 2019, when the CAPM alpha of the short-duration portfolio is significantly negative
and the CAPM alpha of the long-duration portfolio is significantly positive, it is possible that there are events other thanthe crises focused on in this paper that cause similar phenomena.

8

First, to clarify the relationship between the state of the market and CAPM alpha, we add intercept
dummy variables representing the state of the market to the CAPM. We use the following formulas:

e
e
Ri,t
= α0,i + α1,i DHret,t + α2,i DLret,t + βi Rm,t
+ i,t ,

(6)

e
e
Ri,t
= α0,i + α1,i DHsd,t + βi Rm,t
+ i,t ,(7)ewhere Ri,tdenotes the monthly return on duration-sorted portfolio i in excess of the risk-free rate atetime t, Rm,tdenotes the monthly excess market return at time t, DHret,t is an indicator that takes 1 if

the previous month’s market return is in the top 10% of monthly returns during the sample period and0 otherwise, DLret,t is an indicator that takes 1 if the previous month’s market return is in the bottom
10% of monthly returns during the sample period and 0 otherwise, and DHsd,t is an indicator that takes
1 if the standard deviation of the previous month’s market daily return is in the top 25% of the sample
period and 0 otherwise.13 If the ranking of risk-adjusted returns across portfolios reverses in the presenceof relatively large negative shocks, then the sign of the coefficient of the indicator that corresponds to anegative shock should be positive for the long-short portfolio.
Panel A of Table 5 presents the results of equation (6). CAPM alpha is higher for short-duration
portfolios than for long-duration portfolios, and CAPM beta is higher for long-duration portfolios thanfor short-duration portfolios. They are similar to the CAPM estimation results in Table 2. The coefficientof the indicator for high market return in the previous month is not significant for all five portfolios andthe long-short portfolio. The coefficients of the indicator for low market return in the previous monthtends to be larger for longer durations, although not monotonically, and is significantly positive for the
long-short portfolio. This result indicates that the responses of the risk-adjusted returns of durationsorted portfolios are asymmetric between times of extremely high and low market returns. Panel B
presents the results of equation (7). CAPM alpha and beta have a similar tendency as Panel A. Focusing
on the dummy variable that indicates a higher standard deviation of the previous month’s return, thecoefficient is monotonically larger for the long duration, and the coefficient is significantly positive forthe long-short portfolio. The results of Panels A and B indicate that the risk-adjusted return of thelong-short duration portfolio is positive when the market return is extremely low or when the market
return is highly volatile.
[Insert Table 5 here]
We explain the risk-adjusted returns on the duration-sorted portfolios using variables that capture
market uncertainty. Baker et al. (2016) quantify uncertainty about economic policy by picking the
13 When we use a threshold model to identify the conditions under which the risk-adjusted returns of each portfolio wouldchange, the thresholds vary considerably across portfolios. We use intercept dummy variables for clarity in Table 5. Notethat the values of market return and standard deviation used to define the dummy variables are close to the thresholdvalues obtained for some portfolios in the threshold model.

9number of terms about policy in major newspaper articles. They index them and describe their Economic
Policy Uncertainty Index as asymmetric in the sense that it spikes for large negative shocks and responds
less to small shocks. Based on the results in Figure 3 and Table 5, we expect that an uncertainty measurethat spikes in response to large negative shocks may explain the risk-adjusted returns on duration-sorted
portfolios.
The variables included in the analysis are the one-month standard deviation of daily market returns(SD) and the monthly average of the Volatility Index Japan (V XJ) in addition to the Japan Economic
Policy Uncertainty Index (EP U ). EP U for Japan is created by Arbatli-Saxegaard et al. (2022) basedon Baker et al. (2016).14 Although EP U measures economic policy uncertainty, Smales (2020) and
Arbatli-Saxegaard et al. (2022) find a strong relationship between financial market uncertainty and EP U
in the Japanese market. Simultaneously, Cascaldi-Garcia et al. (2023) state that news-based indices of
uncertainty such as EP U capture uncertainty in a broader sense than market-based uncertainty measures
such as the volatility index. V XJ is a volatility index for the Japanese market based on daily Nikkei 225
option prices.15 Note that all measures used here take higher values when market uncertainty increases.
Descriptive statistics for the measures of uncertainty are presented in Table 3. Owing to data availability,
the sample period for V XJ is from January 1998 onward.
To clarify whether these uncertainty measures explain risk-adjusted returns on duration-sorted portfolios, we use the following formula:

e
e
Ri,t
= αi + β1,i Rm,t
+ β2,i X + i,t ,(8)ewhere Ri,tdenotes the monthly return on duration-sorted portfolio i in excess of the risk-free rate at timeedenotes the monthly excess market return at time t, and X denotes the measures of uncertaintyt, Rm,tat time t or time t − 1. Table 6 presents the estimation results: Panel A summarizes the results when
the contemporaneous uncertainty measure is used as the explanatory variable; Panel B summarizes theresults when the one-period lag of the uncertainty measure is used as the explanatory variable. β1 denotes
the CAPM beta, and β2 denotes the coefficient of the uncertainty measure of interest. Regardless of thetiming of the uncertainty measure, the value of CAPM beta is higher for the long-duration portfolio thanfor the short-duration portfolio in all cases, a similar pattern to the CAPM estimation results in Table
2. Conversely, the coefficient of the uncertainty measure added to the CAPM is higher for long duration
than for short duration and the coefficient estimate for the long-short portfolio is significantly positive inSD (both contemporaneous and lagged) and EP U (contemporaneous); that is, the risk-adjusted returnsof the duration-sorted portfolios are affected significantly by the standard deviation of the market returns
14 TheJapan Economic Policy Uncertainty Index is available on the website of Economic Policy Uncertainty
https://www.policyuncertainty.com.
15 V XJ is available on the website of the Center for Mathematical Modeling and Data Science, Osaka University
https://www-mmds.sigmath.es.osaka-u.ac.jp/structure/activity/vxj.php (in Japanese).

10

or EP U . For V XJ, the estimated coefficients for the long-short portfolio are positive but not significant,which might be partly because of the shorter sample period than for SD and EP U estimation.16[Insert Table 6 here]
To validate that the results of the analysis thus far depend on the period of severe recession or timesof crisis, we estimate a threshold model that allows the coefficients of the uncertainty measures to varywith the degree of market uncertainty for equation (8). We use the EP U , which captures a broader
concept of uncertainty, as an indicator of the degree of market uncertainty. We assume that the regime
differs depending on the value of EP U . Table 7 presents the estimation results of the threshold modelfor the long-short duration portfolio. We use SD (contemporaneous and lagged) and contemporaneous
EP U as explanatory variables because the β2 estimates of these variables for the long-short portfolio are
significant in Table 6.
Panels A and B in Table 7 present the results of adding the SD (contemporaneous or lagged) to
the CAPM as an explanatory variable. Regime 1 corresponds to good times, and Regime 2 corresponds
to bad times. The evidence indicates that the coefficients of SD are not significant in good times. In
contrast, the coefficients of SD are positive and significant for bad times, suggesting that the resultspresented in Table 6 reflect the impact of crises with particularly high EP U . Panel C summarizes theresults when contemporaneous EP U is used as an explanatory variable. Considering that the coefficienton EP U is significantly positive regardless of the value of EP U , EP U has explanatory power for theduration premium.
[Insert Table 7 here]
The results thus far indicate that the countercyclicality of the equity term structure may arise fromthe differences in response to large negative shocks that increase market uncertainty.17 In addition, theshort-duration portfolio is risky; that is, it performs poorly during bad times, while the long-duration
portfolio may work as a risk-hedging device against negative shocks. While this paper does not discuss
investors’ preferences or risks reflected in stock prices, and therefore we cannot make a rigorous argument,these points may be consistent with the fact that the short-duration portfolio earns a higher premiumfrom the perspective of asset pricing theory.
16 As the Japanese market is known to be affected by changes in U.S. economic policy (e.g., Hausman and Wongswan(2011)), we also used the EP U for the U.S. and the ambiguity measure from Brenner and Izhakian (2018). However, theU.S. measures did not provide the expected results. We thank Yehuda Izhakian for sharing the data.
17 Our results are based on risk-adjusted returns using the CAPM as a benchmark. Although the Fama-French 3-factor
model or the 5-factor model could be used as a benchmark, the difference in Fama-French 3-factor model alpha between
long- and short-duration portfolios is insignificant for the Japanese market because the HM L factor is strongly related tothe duration premium. However, the analysis presented in Section 6 is sufficiently robust to book-to-market ratio or firmsize, and the correspondence with previous studies by Dechow et al. (2021) and Gormsen and Lazarus (2023) makes it
reasonable to use CAPM as a benchmark in this study.

11

6

Robustness Test

As mentioned in Section 3, the measure of duration used in this study has a high negative correlation withthe book-to-market ratio of the firms. Therefore, the results thus far may reflect the effect of differencesin firm characteristics such as book-to-market ratio or firm size on stock returns. In this section, we
demonstrate that the results remain unchanged even after controlling for size and book-to-market ratio.
First, Table 8 presents the results of the analysis controlling for firm size. All firms in the sample arecategorized as either large-cap or small-cap based on the median market capitalization of stocks listedon the first section of the Tokyo Stock Exchange. For each of the large-cap and small-cap stocks, wetake the 30th and 70th percentile points of duration and create three portfolios, making six portfolios.18
Panel A of Table 8 presents the monthly portfolio return statistics. The mean of short-duration portfolio
return exceeds the mean of long-duration portfolio return, although the statistical significance is slightly
weak for both large and small stocks. Panel B presents the results of the CAPM estimation based onequation (8) without uncertainty measures X and the estimation results for several variables from theanalyses in Tables 5 and 6 based on equation (8). For both large and small stocks, CAPM alpha is larger
for short duration than for long duration, and CAPM beta is larger for the long duration portfolio. In
the regression where the uncertainty measures are included, the coefficient estimates of the uncertainty
indicator for the long-short portfolio are positive in all cases and significant in several cases.
[Insert Table 8 here]
We analyze the case where we control for the book-to-market ratio in the same manner. First, we use
the median book-to-market ratio of stocks listed on the first section of the Tokyo Stock Exchange to sortthe firms into value and growth portfolios. We then classify each of them into three duration portfolios.
Panel A of Table 9 presents the monthly return statistics for the six portfolios, and Panel B presents
the CAPM estimates and the estimation results with variables indicating market uncertainty. Althoughless statistically significant, the average return and CAPM alpha are higher for the short duration and
CAPM beta is higher for the long duration. The coefficients of market uncertainty measures for the
long-short portfolio are generally positive and significant.
[Insert Table 9 here]
The above analysis confirms similar patterns as in Tables 2, 5, and 6, even when controlling for sizeand book-to-market ratio, although the results are weak in some cases. The result suggests that therisk-adjusted return of a long-short duration portfolio, which is negative on average, increases when the
18 The analysis in this section uses three portfolios sorted by the 30th and 70th percentiles, whereas up to Section 5, we
use quintile portfolios. Some of the weak results in this section regarding the difference between short and long duration
may be owing to the rough sorting of the duration portfolios. However, to ensure a sufficient number of firms per portfolio,
we sorted the portfolios into three, instead of quintile, portfolios.

12variable indicating market uncertainty increases. This evidence remains robust even after controlling forfirm characteristics.

7

Conclusion

We used the implied equity duration presented by Dechow et al. (2004) for the Japanese market andobserved a consistent finding with previous studies on the term structure of stock returns: the term
structure of equity returns is downward sloping on average and the slope is countercyclical. The increase
in returns on the long-short duration portfolio observed in the late 1990s, the late 2000s, and 2020 may
correspond to the two financial crises in Japan and the COVID-19 pandemic. Furthermore, long- andshort-duration portfolio returns tend to increase and decrease, respectively, when market returns are
extremely low or when the standard deviation of market returns is high. Economic uncertainty suchas the standard deviation of market returns, or EP U , may have explanatory power for the long-shortduration portfolio returns. The countercyclicality of stock return term structure may stem from different
responses to significantly large negative shocks, heightening market uncertainty.
We finally mention some topics that should be investigated in future studies. As discussed in Section
5, we indicated that portfolios with shorter durations underperform during serious economic downturns,
which could be a possible explanation for the duration premium. To understand these empirical results, amore formal discussion is needed. We have to develop a theoretical model compatible with the empiricalfindings of this study to better understand the duration premium and the cross-section of stock returns.
Second, the empirical model in this paper is related to the EP U , which has high explanatory power forthe long-short portfolio return. We have to consider what the EP U means.

13References
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15

Table 1: Summary Statistics for Equity Duration and Financial Variables
Panel A: Means and standard deviations
Mean
Std
Obs

Duration

BE

ME

BE/M EROE

salesgr

22.8063.311
59534

112954.9475638.959534

176291.9
723991.7
59534

1.064
0.774
59534

0.058
0.119
59534

0.036
0.138
59534

Duration

BE

ME

BE/M EROE

salesgr

0.020

0.095
0.865

-0.741-0.047-0.133-0.2330.034
0.075-0.243

0.190
0.000
0.035
-0.2400.366

Panel B: Correlations

Duration
BE
ME
BE/M E
ROE

Notes. This table presents the descriptive statistics for firm characteristics and financial variables used
for forecasting firms’ cash flows. BE is book equity, M E is market equity, BE/M E is the book-tomarket ratio, ROE is return on equity, and salesgr is sales growth. BE and M E are in million yen.
Panel A shows means, standard deviations (Std), and numbers of observations of the variables (Obs).
Panel B shows their correlation coefficients. The sample period is from 1990 to 2022.

16

Table 2: Duration Quintile Portfolios
Panel A: Characteristics of duration quintile portfolios
Short Dur

2

3

4Long DurLong-Short

Duration

18.60

21.70

23.11

24.31

26.32

BE/M E

1.94

1.26

0.93

0.67

0.53

M E(million yen)

49698

99562

192151281607

258676

7.72(204.2)-1.41(-142.4)
208978(25.7)

Panel B: Monthly returns and CAPM coefficientsMonthly return
Mean
Std
CAPM
α

β

Short Dur

2

3

4Long DurLong-Short

0.672

0.578

0.359

0.311

0.066

-0.606

5.828

5.351

5.436

5.388

6.102

(-2.73)0.474(2.54)

0.381(2.72)

0.160(1.28)

0.110(1.35)-0.141(-1.24)-0.615(-2.38)0.912(23.5)

0.896(27.0)

0.936(25.9)

0.956(26.1)

1.067(32.4)

0.155(2.49)

Notes. This table presents the summary statistics for duration quintile portfolios. Panel A shows meansof the duration, book-to-market ratio and market equity of each portfolio. The Long-Short column
shows the difference between the portfolios with longest and shortest duration. Values in parentheses
indicate t-values. Notes on Table 1 are also referred. Panel B shows the monthly value-weighted
returns and CAPM coefficients for duration quintile portfolios. The top panel shows the means andstandard deviations (Std) of monthly returns on each portfolio (in %). The bottom panel shows theestimates of CAPM alpha and beta for each portfolio. The Long-Short column shows the result for the
longest-duration portfolio return minus the shortest-duration portfolio return. Values in parentheses
indicate t-values that are based on Newey and West (1987) standard errors corrected for 12 lags. The
sample period is from February 1990 to June 2022.

17

Table 3: Summary Statistics for Uncertainty and Cyclicality Variables
Panel A: Means and standard deviations
Mean
Std
Obs
Sample period

SD

EP U

V XJ

d−p

1.180
0.563
389
1990:02-2022:06

105.8
33.34
389
1990:02-2022:06

24.68
8.365
294
1998:01-2022:06

0.384
0.415
294
1998:01-2022:06

EP U

V XJ

d−p

0.403

0.796
0.508

0.025
0.350
0.102

Panel B: Correlation
SD
SD
EP U
V XJ

Notes. This table provides the summary statistics for uncertainty and cyclicality variables. Panel A
shows the means and standard deviations, and panel B shows the correlation coefficients. SD is themonthly standard deviation of daily market return, EP U is the Japan Economic Policy Uncertainty
Index, V XJ is the Volatility Index Japan, and d − p is the log of the market dividend-to-price ratio.
Correlation coefficients with V XJ and d − p are calculated on the sample from January 1998 to June
2022. Other correlation coefficients are calculated on the sample from February 1990 to June 2022.

Table 4: Predictive Regressions
Panel A: Controlling for the market and d − peRm,t,t+12

dt − pt
R¯2

Short Dur

2

3

4Long DurLong-Short

0.895(7.97)-14.13(-2.14)0.66

0.760(6.08)-6.987(-1.27)0.70

0.811(8.36)-5.980(-1.42)0.79

0.907(12.2)-0.829(-0.30)0.92

1.095(11.6)
3.520(0.86)
0.89

0.199(1.09)
17.65(1.81)
0.19

Short Dur

2

3

4Long DurLong-Short-1.765(-0.20)0.00

3.515(0.53)
0.01

5.225(0.80)
0.01

11.70(1.50)
0.05

18.64(1.96)
0.09

20.40(2.44)
0.15

Panel B: Controlling for d − p
dt − pt
R2

Notes. This table reports the results of the predictive regressions. Panel A shows the results of theestimation of equation (4), and Panel B shows the results of the estimation of equation (5). The LongShort column shows the results for the longest-duration portfolio return minus the shortest-duration
portfolio return. Values in parentheses indicate t-values and R¯2 denotes the adjusted R2 . The t-values
are based on Newey and West (1987) standard errors corrected for 18 lags. The sample period is fromJanuary 1998 to June 2022.

18

Table 5: Regression with Dummy Variables
Panel A: Dummy variables for market returns
α0
DHret
DLret
β
R¯2

Short Dur

2

3

4Long DurLong-Short

0.485(2.31)
0.653(1.16)-0.763(-1.23)0.906(24.1)

0.336(2.03)
0.200(0.69)
0.252(0.60)
0.895(27.2)

0.246(1.75)-0.353(-1.21)-0.506(-1.61)0.937(25.7)

0.102(1.09)-0.400(-1.31)0.477(1.03)
0.959(25.6)-0.263(-2.15)0.463(1.11)
0.759(2.45)
1.067(31.4)-0.749(-2.61)-0.190(-0.26)1.521(2.33)
0.161(2.61)

0.71

0.81

0.86

0.91

0.88

0.04

Panel B: Dummy variable for standard deviations of market returns
α0
DHsd
β
R¯2

Short Dur

2

3

4Long DurLong-Short

0.603(2.91)-0.515(-1.69)0.913(23.4)

0.399(2.50)-0.072(-0.28)0.896(27.0)

0.155(1.17)
0.017(0.07)
0.936(25.8)

0.090(0.90)
0.079(0.38)
0.956(26.2)-0.229(-1.78)0.348(1.37)
1.067(32.6)-0.832(-3.06)0.862(2.01)
0.154(2.47)

0.71

0.81

0.85

0.91

0.88

0.04

Notes. This table presents the results of the monthly CAPM with the addition of intercept dummy
variables representing the state of the market. Panel A shows the result of equation (6), and Panel B
shows the result of equation (7). The Long-Short column shows the results for the longest-duration
portfolio return minus the shortest-duration portfolio return. Values in parentheses indicate t-values
and R¯2 denotes the adjusted R2 . The t-values are based on Newey and West (1987) standard errors
corrected for 12 lags. The sample period is from February 1990 to June 2022.

19

Table 6: Regression with Market Uncertainty Indicators
Panel A: Contemporaneous variables
X
SDt

α
β1
β2
R¯2

EP Ut

α
β1
β2
R¯2

V XJt

α
β1
β2

R¯2
Panel B: Lagged variables
X
SDt−1

α
β1
β2
R¯2

EP Ut−1

α
β1
β2
R¯2

V XJt−1

α
β1
β2
R¯2

Short Dur

2

3

4Long DurLong-Short

1.068(2.44)
0.897(23.4)-0.503(-1.51)0.71

0.688(2.72)
0.888(26.3)-0.260(-1.40)0.81

0.432(1.71)
0.929(25.7)-0.230(-1.22)0.86

0.018(0.07)
0.958(22.9)
0.078(0.34)
0.91-0.758(-3.01)
1.083(34.2)
0.522(2.71)
0.88-1.825(-3.55)0.186(3.13)
1.025(2.63)
0.05

1.506(2.62)
0.904(24.7)-0.010(-1.77)0.71

0.639(1.79)
0.894(27.5)-0.002(-0.75)0.81

0.449(1.38)
0.934(25.7)-0.003(-0.91)0.85-0.085(-0.32)0.957(25.6)
0.002(0.84)
0.91-1.419(-3.49)1.077(34.5)
0.012(3.09)
0.89-2.924(-3.62)0.173(3.02)
0.022(2.68)
0.06

0.908(1.45)
0.941(19.2)-0.012(-0.56)0.68

0.426(1.22)
0.856(17.7)- 0.000(-0.04)0.73

0.375(0.80)
0.894(20.5)-0.005(-0.25)0.80

0.473(2.10)
0.911(38.4)-0.014(-1.83)0.91-0.694(-1.64)1.051(28.3)
0.027(1.60)
0.85-1.602(-1.78)0.110(1.47)
0.039(1.16)
0.01

Short Dur

2

3

4Long DurLong-Short

1.038(3.09)
0.911(23.2)-0.478(-1.98)0.71

0.300(1.32)
0.896(27.0)
0.069(0.39)
0.81

0.389(1.87)
0.935(26.0)-0.194(-1.07)0.86

0.042(0.26)
0.956(26.0)
0.058(0.49)
0.91-0.514(-2.42)
1.068(32.4)
0.316(2.09)
0.88-1.552(-3.63)0.157(2.50)
0.795(2.57)
0.04

1.041(1.71)
0.912(23.6)-0.005(-1.00)0.71

0.311(0.85)
0.896(27.0)
0.001(0.23)
0.81

0.364(1.12)
0.936(25.8)-0.002(-0.72)0.85

0.049(0.23)
0.956(26.1)
0.001(0.38)
0.91-0.681(-2.20)1.067(32.7)
0.005(1.78)
0.88-1.722(-2.30)0.155(2.50)
0.010(1.50)
0.04

0.844(1.35)
0.935(20.5)-0.011(-0.57)0.68

0.025(0.07)
0.855(17.6)
0.016(1.47)
0.73

0.026(0.07)
0.894(20.3)
0.009(0.58)
0.80

0.184(0.77)
0.921(43.0)-0.002(-0.27)0.91-0.293(-0.92)1.039(29.0)
0.011(0.95)
0.85-1.137(-1.38)0.105(1.46)
0.022(0.82)
0.01

Notes. This table reports the results of the monthly regressions of equation (8). Panel A shows theresults with the contemporaneous variable as X and Panel B shows the results with the lagged variable
as X. The Long-Short column shows the results for the longest-duration portfolio return minus theshortest-duration portfolio return. Values in parentheses indicate t-values, and R¯2 denotes the adjusted
R2 . The t-values are based on Newey and West (1987) standard errors corrected for 12 lags. The sample
period for SD and EP U is from February 1990 to June 2022, and for V XJ is from January 1998 toJune 2022.

20

Table 7: Regression with Market Uncertainty Indicators in Two Regimes
Panel A: SDt as independent variable
α
β1

β2

-1.262(-2.46)0.179(4.24)
Regime 1: EP U ≤ 111.72
0.165(0.31)

Regime 2: EP U > 111.72
1.120(2.82)

Panel B: SDt−1 as independent variable
α
β1

β2

-1.178(-2.61)
0.158(3.82)
Regime 1: EP U ≤ 111.72
0.182(0.40)

Regime 2: EP U > 111.72
0.934(2.55)

Panel C: EP Ut as independent variable
α
β1

β2

-4.754(-3.94)0.172(4.16)
Regime 1: EP U ≤ 124.85
0.043(3.40)

Regime 2: EP U > 124.85
0.030(3.26)

Notes. This table provides the results of the threshold model for equation (8). The dependent variable
is the long-short duration portfolio return. The coefficients of uncertainty measures (described as β2 inequation (8)) are allowed to vary with the value of the EP U . Values in parentheses indicate t-values
that are based on Newey and West (1987) standard errors corrected for 12 lags. The sample period isfrom February 1990 to June 2022.

21

Table 8: Controlling for the Size
Panel A: Monthly returns

Mean
Std

small stocks
3

1

2

0.591
6.006

0.439
5.879

0.445
6.751

large stocks
3

Long-Short

1

2-0.146(-1.10)

0.483
5.219

0.336
5.314

1

2

0.288
(2.11)
0.872(23.8)

0.136(1.94)
0.954(35.9)-0.075(-0.68)1.042(29.6)-0.363(-1.58)0.169(2.66)

0.317(2.14)
0.869(25.8)-0.293(-0.67)0.154(1.99)
0.952(32.0)-0.175(-0.45)-0.173(-1.36)1.054(29.3)
0.962(2.69)-0.490(-1.95)0.185(3.06)
1.255(2.09)

0.652(2.23)
0.863(25.7)-0.308(-1.28)0.171(0.81)
0.953(31.6)-0.029(-0.16)-0.650(-2.49)1.056(28.9)
0.486(2.56)-1.302(-2.98)0.193(3.22)
0.795(2.43)

0.895(2.46)
0.868(25.0)-0.006(-1.73)0.229(0.95)
0.953(35.1)-0.001(-0.40)-0.963(-2.84)
1.049(30.4)
0.008(2.76)-1.858(-3.11)
0.181(3.02)
0.014(2.61)

0.130
5.939

Long-Short-0.353(-1.83)

Panel B: CAPM and market uncertainty indicators
1

2

small stocks
3

Long-Short

CAPM
α

0.392
0.240
0.239
-0.153(1.88)(1.47)(1.21)(-1.02)
β
0.929
0.937
1.052
0.123
(24.0)(21.0)(22.2)(3.83)
Regression with a dummy variable
α
0.449
0.268
0.267
-0.182(2.01)(1.48)(1.25)(-1.19)
β
0.922
0.933
1.049
0.126
(23.7)(21.1)(23.3)(3.95)
DHsd -0.564 -0.277 -0.282
0.282(-0.89) (-0.42) (-0.39)(0.63)
Regression with uncertainty indicators: SDt
α
1.034
0.552
0.500
-0.534(1.84)(1.05)(0.94)(-1.93)
β1
0.913
0.929
1.046
0.133
(24.0)(22.1)(22.4)(3.90)
β2-0.543 -0.264 -0.221
0.322(-1.22) (-0.61) (-0.52)(1.29)
Regression with uncertainty indicators: EP Ut
α0.543-0.365 -0.672-1.215(0.86) (-0.74) (-1.02)(-2.53)
β1
0.928
0.941
1.059
0.131
(25.0)(22.1)(23.0)(4.05)
β2-0.001
0.006
0.009
0.010
(-0.26) (1.25)(1.51)(2.18)

large stocks
3

Long-Short

Notes. This table presents the results when controlling for firm size. Panel A shows means and standard
deviations of size × duration portfolios. The Long-Short column shows the difference between the longest
duration portfolio (labeled as 3) and the shortest duration portfolio (labeled as 1). Panel B presents theresults of CAPM and several analyses from those in Tables 5 and 6. DHsd is an intercept dummy variable
that takes 1 when the standard deviation of the previous month’s daily market return is in the top 10% of
the sample period and 0 otherwise. Values in parentheses indicate t-values that are based on Newey and West
(1987) standard errors corrected for 12 lags. The sample period is from February 1990 to June 2022.

22

Table 9: Controlling for the Book-to-Market Ratio
Panel A: Monthly returns
1
Mean
Std

0.376
5.378

growth stocks
2
3Long-Short
0.258
5.450

0.062
6.187

-0.314(-1.57)

value stocks
3

1

2

0.661
5.853

0.532
5.306

1

2

0.463
(2.41)
0.912(22.3)

0.336(2.39)
0.881(27.5)

0.321(2.46)
1.007(29.9)-0.142(-1.12)0.095(2.85)

0.527(2.61)
0.904(22.8)-0.639(-1.17)0.308(1.99)
0.884(28.8)
0.279(0.69)

0.291(1.96)
1.011(29.3)
0.301(0.68)-0.236(-1.85)0.106(3.30)
0.940(1.94)

1.151(2.76)
0.895(22.2)-0.582(-1.83)0.432(1.56)
0.879(27.6)-0.081(-0.37)0.373(1.40)
1.006(28.2)-0.044(-0.21)-0.777(-2.28)0.111(3.47)
0.538(2.00)

1.551(2.59)
0.904(23.5)-0.010(-1.77)0.519(1.44)
0.880(28.3)-0.002(-0.49)0.836(2.24)
1.003(30.1)-0.005(-1.33)-0.715(-1.71)
0.099(3.07)
0.005(1.44)

0.524
5.918

Long-Short-0.136(-1.05)

Panel B: CAPM and market uncertainty indicators
1

growth stocks
2
3Long-Short

CAPM
α

0.178
0.056
-0.144-0.322(1.28)(0.79) (-1.03)(-1.26)
β
0.915
0.971
1.055
0.139
(21.9)(27.7)(25.8)(2.20)
Regression with a dummy variable
α
0.245
0.034
-0.237-0.481(1.56)(0.39) (-1.57)(-1.73)
β
0.907
0.974
1.066
0.158
(22.7)(24.6)(26.4)(2.78)
DHsd -0.663
0.222
0.918
1.582
(-1.33) (0.43)(2.49)(2.17)
Regression with uncertainty indicators: SDt
α0.652-0.239 -0.677-1.329(1.97) (-0.81) (-2.48)(-2.60)
β1
0.903
0.978
1.068
0.165
(22.5)(24.3)(26.8)(2.91)
β2-0.401
0.250
0.451
0.852
(-1.47) (1.01)(2.22)(2.12)
Regression with uncertainty indicators: EP Ut
α0.326-0.412 -1.308-1.634(0.86) (-1.44) (-3.19)(-2.33)
β1
0.914
0.975
1.064
0.150
(21.9)(27.4)(27.2)(2.46)
β2-0.001
0.004
0.011
0.012
(-0.44) (1.75)(2.90)(2.01)

value stocks
3

Long-Short

Notes. This table presents the results when controlling for the book-to-market ratio. Panel A shows means
and standard deviations of book-to-market ratio × duration portfolios. The Long-Short column shows thedifference between the longest duration portfolio (labeled as 3) and the shortest duration portfolio (labeledas 1). Panel B presents the results of CAPM and several analyses from those in Tables 5 and 6. DHsd isan intercept dummy variable that takes 1 when the standard deviation of the previous month’s daily market
return is in the top 10% of the sample period and 0 otherwise. Values in parentheses indicate t-values that are
based on Newey and West (1987) standard errors corrected for 12 lags. The sample period is from February
1990 to June 2022.

23

1.5

1.4

1.3

1.2

1.1

1

0.9

0.8

0.7

0.6

Dur_1

Dur_2

Dur_3

Dur_4

Dur_5

Figure 1: Cumulative Daily Returns on Duration Quintile Portfolios
Notes. This figure illustrates the cumulative daily returns on duration quintile portfolios with a value of 1 on
January 6, 2020. Dur 1 indicates the shortest duration portfolio and Dur 5 is the longest duration portfolio.

24

6

4

2

0

-2

-4

-6

recession

Rm

Dur_51Figure 2: Moving Average Returns of the Duration Long-Short Portfolio and the Market
Notes. This figure depicts the 12-month moving average of the long-short duration portfolio return (Dur 51) andthe market return (Rm). The shadowed area represents the recession period as stated by the Cabinet Office.

25

A. Short Duration Portfolio
0.008

Nov.1997 Collapse of Yamaichi Securities
and Hokkaido Takushoku Bank

0.006

Mar.2020
declaration ofpandemic

Sep.2008 Collapse of
Lehman Brothers

0.004
0.002
0

-0.002-0.004-0.00620141217

20150813

20160411

20161206

20170731

20180327

20181115

20190719

20200318

2020111320210709

20220308

20160411

20161206

20170731

20180327

20181115

20190719

20200318

2020111320210709

20220308

20140424

20130827

20130104

20120514

20110914

20110124

20100531

upper_ci

20150813

alpha20090930

20090204

20080610

20071012

20070220

20060627

20051101

20050309

20040713

20031117

20030327

positive alpha20141217

negative alpha20020730

20011203

20010412

20000817

19991224

19990430

19980903

19980114

19970521

19960920

19960201

19950612

19941017

19940223

19930701

19921104

19920316

19910719

19901121

19900403-0.008lower_ci

B. Long Duration Portfolio
0.006
0.004
0.002
0
-0.002-0.004-0.006

negative alphapositive alphaalphaupper_ci

20140424

20130827

20130104

20120514

20110914

20110124

20100531

20090930

20090204

20080610

20071012

20070220

20060627

20051101

20050309

20040713

20031117

20030327

20020730

20011203

20010412

20000817

19991224

19990430

19980903

19980114

19970521

19960920

19960201

19950612

19941017

19940223

19930701

19921104

19920316

19910719

19901121-0.00819900403

26

0.008

lower_ci

Figure 3: CAPM Alphas
Notes. This figure shows the estimates of the CAPM alpha for the shortest and longest-duration portfolio returns. The red dashed line is the 95% confidence interval; theblue and orange areas show the period when the alpha is significantly negative and positive, respectively. The standard errors are based on Newey and West (1987) with 5
lags. The initial rolling regression was on April 3, 1990, and the last was on June 30, 2022.