Cross-sectional seasonalities in international government bond returns

Accepted Manuscript

Cross-Sectional Seasonalities in International Government Bond Returns Adam Zaremba PII: DOI: Reference:

S0378-4266(18)30245-0 https://doi.org/10.1016/j.jbankfin.2018.11.004 JBF 5452

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Journal of Banking and Finance

Received date: Accepted date:

12 July 2018 3 November 2018

Please cite this article as: Adam Zaremba , Cross-Sectional Seasonalities in International Government Bond Returns, Journal of Banking and Finance (2018), doi: https://doi.org/10.1016/j.jbankfin.2018.11.004

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Adam Zaremba University of Dubai

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Cross-Sectional Seasonalities in International Government Bond Returns

Poznan University of Economics and Business

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[email protected]

Author’s Note

This paper is part of Project No. UMO-2015/19/B/HS4/00378 of the National Science Centre

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of Poland. Correspondence concerning this article should be addressed to Adam Zaremba, Dubai Business School, University of Dubai, Academic City, Emirates Road, Dubai, UAE, P.O. Box: 14143, e-mail: [email protected] (present address) or to Adam Zaremba, Poznan University of Economics and Business, al. Niepodleglosci 10, 61-875 Poznan, Poland, email: [email protected] (permanent address).

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ACCEPTED MANUSCRIPT This version: October 21, 2018

Cross-Sectional Seasonalities in International Government Bond Returns

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Abstract We are the first to document the cross-sectional return seasonality effect in international government bonds. Using a variety of tests, we examine fixed-income securities from 22 countries for the years 1980–2018. The bonds with high (low) returns in the same-calendar

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month in the past continue to overperform (underperform) in the future. The effect is robust to many considerations, including controlling for established predictors of bond returns. Our results support the behavioural story of the anomaly, demonstrating its highest profitability in

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the periods of elevated investor sentiment and in the market segments of strong limits to arbitrage. Nonetheless, investment application of bond seasonality might be challenging due

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to high trading costs and the required short holding periods.

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Keywords: return seasonalities, seasonal anomalies, calendar anomalies, government bonds,

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sovereign bonds, fixed-income securities, asset pricing, return predictability.

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JEL codes: G12, G14, G15.

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ACCEPTED MANUSCRIPT 1. Introduction Cross-sectional return seasonality is a tendency of assets with a high average samecalendar month returns to outperform the assets with the low mean same-calendar month returns. Described originally by Heston and Sadka (2008), it is one of the most pervasive anomalies ever discovered. It has been documented in U.S. and international equities, country

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and industry portfolio, commodities, or even equity anomalies and international factor strategies (Heston and Sadka 2008, 2010; Keloharju, Linnainmaa, and Nyberg 2016; Zaremba 2017). Nonetheless, one asset class has so far evaded the attention of academia: international government bonds. The major target of this study is to fill this gap.

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Taking into consideration the size and importance of the global government bond market, the lack of examination of return seasonality—one of the major cross-asset return patterns—in this asset class may be surprising. The central government bond securities

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outstanding worldwide at the end of 2017 exceeded 22 trillion U.S. dollars (BIS 2018), reaching the size of almost 30% of the global equity market (World Bank 2018). Also, the

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global bond funds account for more than 20% of the international mutual fund landscape

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(EFAMA 2018). Given the plethora of return patterns discovered in equities (Hou, Xue, and Zhang 2017), the international government bonds may appear clearly underresearched.

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This research undergirds a comprehensive examination of the cross-sectional seasonality effect in international government bonds. In particular, we aim to contribute to a

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fuller understanding of the phenomenon in in three ways. First, we are the first to verify the return seasonality anomaly in international bond markets. To this end, we investigate a sample of government bond portfolios from 22 countries for the years 1980–2018. Using cross-sectional and time-series tests, we uncover a strong return seasonality, which is not explained by established return predictors and risk factors in bond markets. The government bonds with high (low) average same-calendar month returns in the past tend to overperform

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ACCEPTED MANUSCRIPT (underperform) in the future. The zero-investment portfolio going long (short) for the bonds with high (low) same-calendar month returns produce statistically and economically significant raw and risk-adjusted returns. The cross-sectional seasonality is robust to many considerations, including alternative portfolio construction methods, weighting schemes, return conventions, and subsample and subperiod analysis, though it is particularly strong in

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portfolios of long-term bonds.

Second, we explore possible explanations for the return seasonality anomaly. In particular, using various tests we empirically examine five possible sources of the anomaly: 1) cross-sectional seasonality in a particular risk factor, 2) spillover from a different asset

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class, 3) manifestation of a return pattern in a single particular month, 4) macroeconomic conditions, and 5) behavioural phenomena. We find that the return seasonality in bond portfolios is not carried from a seasonality in a particular risk factor driven by a particular

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calendar month. It is also not linked to any seasonality in macroeconomic conditions or risks, and the seasonality profits do not exhibit material correlation with seasonalities in other asset

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classes. Our results are mostly aligned with the behavioural explanation for the return

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seasonality effect, arguing that a pattern results from cyclical swings in investors’ mood (Hirshleifer, Jiang, and Meng 2018). Consistent with the implications of this framework, we

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find that the anomaly is particularly pronounced in the periods of high investor sentiment and that it exhibits especially impressive profits in the market segments characterized by elevated

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limits to arbitrage.

Third, we are also interested in the investor’s perspective on the return seasonality

anomaly. Unfortunately, the implementation of the strategy might pose challenges, and there are at least three reasons for that. First, the incremental improvement in the Sharpe ratio of a diversified government bond investor or a portfolio manager already pursuing seasonality strategies in other asset classes is rather minuscule. Furthermore, the return seasonality

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ACCEPTED MANUSCRIPT portfolio is characterized by remarkable turnover, implying very high trading costs. Finally, the strategy performs poorly under extended holding periods that are longer than one month. Consequently, the detrimental impact of transaction costs might not be easy to mitigate. Summing up, the return seasonality does not appear to be a good candidate for a Holy Grail of quantitative strategies in sovereign bonds.

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Our study aims to add to two major strains of finance literature. First, we contribute to the growing research on cross-sectional seasonality in various asset classes (Heston and Sadka 2008, 2010; Keloharju, Linnainmaa, and Nyberg 2016; Zaremba 2017; Hirshleifer, Jiang, and Meng 2018). To the best of our knowledge, this effect has never been investigated

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in international government bond portfolios, and its potential explanations or practical applications have never been explored. Second, we extend the literature on the seasonal regularities in sovereign bonds (e.g., Schneeweis and Woolridge 1979; Smirlock 1985; Chang

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and Pinegar 1986; Clayton, Delozier, and Ehrhardt 1989; Clare and Thomas 1992; Chan and Wu 1993, 1995; de Vassal 1998; Lavin 2000; Chieffe, Cromwell, and Yoder 2000; Smith

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2002; Landon and Smith 2006; Zaremba and Schabek 2017). In general, the existing

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evidence on calendar patterns in sovereign bonds remains inconclusive. Some of the papers have documented seasonality effects in individual countries (e.g., Smith 2002; Landon and

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Smith 2006), yet the broader international examinations have provided mixed results (Clare and Thomas 1992) or pointed to lack of seasonality (Zaremba and Schabek 2017). Contrary

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to these studies, we look at seasonality from a different—cross-sectional—perspective and demonstrate convincing evidence of return seasonality in international government bonds. The remainder of the article proceeds as follows. Section 2 presents the data and

variables used in this study. Section 3 contains the baseline cross-sectional and time-series tests of the return seasonality in government bonds. Section 4 discusses and empirically verifies alternative explanations for the observed anomaly. Section 5 focuses on the

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ACCEPTED MANUSCRIPT investor’s perspective, testing the practical application of the return seasonality. Finally, section 6 concludes the paper.

2. Data and Variables We base our calculations on Thomson Reuters Datastream All Bond indices.1 The

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sample covers 22 developed and emerging markets: Australia, Austria, Belgium, Canada, China, Denmark, France, Germany, India, Ireland, Italy, Japan, South Korea, Mexico, the Netherlands, Portugal, South Africa, Spain, Sweden, Switzerland, the United Kingdom, and the United States. Each single-country universe is split into five maturity buckets: 1–3 years,

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3–5 years, 5–7 years, 7–10 years, and more than 10 years, generating 110 individual bond portfolios in total. The examination period for monthly returns runs from January 1980 to May 2018 and is motivated by data availability.

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To enable comparability, in our baseline approach, we follow the major international asset pricing studies, covering also government bonds (e.g., Asness, Moskowitz, and

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Pedersen 2013; Geczy and Samonov 2017) and express all the price and return data in a

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pooled sample in U.S. dollars. Importantly, the U.S. entities are the largest and most significant players in international bond markets (IMF 2018: Table 12), and the sentiment,

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risk, and monetary policy spill over from the United States to other developed and emerging markets (see, e.g., Bathia, Breding, and Nitzsche 2016; Ceylan 2017; Hofmann and Takáts

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2015; Srivastava, Lin, Premachandra, and Roberts 2016). The statistical properties of the basic research sample are reported in Table 1.

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[Insert Table 1 here]

We also replicate the calculations in the Datastream Tracker indices that exclude a small percentage of the

least liquid bonds, but provide somewhat lower historical coverage. The results demonstrate no qualitative difference.

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ACCEPTED MANUSCRIPT Significantly, for robustness and to better express the perspective of some investors in international markets, we also control for the FX variability and examine whether the documented relationship works within a sample of returns hedged to U.S. dollars. The monthly hedged returns are calculated as a sum of unhedged USD returns and the rate of return on a particular currency, adjusted with the monthly swap points, and based on the

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interest rate differential between 1-month Financial Times/Thomson Reuters deposit rates sourced from Datastream. The basic characteristics of the hedged returns are presented in Table A1 in the Online Appendix. We briefly discuss the result in the main paper and report them in the Online Appendix.

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Following Keloharju, Linnainmaa, and Nyberg (2016), we define the seasonality return predictive variable for month t (SAME) as the average local currency return in the same calendar month as t through the past 20 years, i.e., within the months t-240 to t-1, as

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available.2 On the other hand, other studies of the return seasonality anomaly (Heston and Sadka 2008, 2010; Li, Zhang, and Zheng 2017) relied sometimes on estimation periods as

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short as 5 years. We find that the longer windows improve the quality of the signal. However, our results do not hang on this particular choice (we confirm it in robustness checks in a

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further part of the paper).3

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Also, as in Keloharju, Linnainmaa, and Nyberg (2016), we test a ―benchmark‖ strategy that is based on other month returns, i.e., on all calendar months different than t. For

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instance, if the month t was January, the ―other-calendar month‖ return strategy would be

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The predictive signal based on local returns displays better quality than the U.S. dollar-denominated returns,

which is ―contaminated‖ by the FX variability. We demonstrate the performance of alternative signals in the robustness checks at a later stage of the paper. 3

As a robustness check, we have also examined the returns on alternative seasonality strategies with the

requirement of a minimum 60 months or 120 months of historical data. The outcomes were qualitatively consistent. However, not imposing this requirement allows for availability of longer time-series, thus, improving our statistical inferences.

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ACCEPTED MANUSCRIPT based on average returns in February–December periods. Hence, the OTHER signal is the average monthly return through all other-calendar months other than t from t-240 to t-13. The most recent 12 months are dropped to avoid an overlap with the momentum effect, for which we control separately. Besides the return seasonality variable, we also use a range of additional control

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variables. The duration (DUR) represents the value-weighted duration of the bond bucket. The credit rating (CRED) denotes the average quantified rating of the three agencies: Moody’s, S&P, and Fitch. Following Zaremba and Czapkiewicz (2017), we transform the ratings into numerical values by ranking them on a scale from 1 to 22, as illustrated in Table

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A2 in the Online Appendix. Following Asness, Moskowitz, and Pedersen (2013) and Geczy and Samonov (2017), we define the momentum signal (MOM) for month t as the total return on the bond index within months t-12 to t-1. Notably, we do not include the month t-12 in

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this calculation to avoid the overlap with the SAME variable. Also, contrary to Asness, Moskowitz, and Pedersen (2013), we do not skip the most recent month t-1. The reason is

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that we are not aware of any evidence of a short-run reversal in sovereign fixed-income

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securities, nor do we find it in our sample. In fact, even Asness, Moskowitz, and Pedersen (2013, 937) admit that skipping the last month is unnecessary. The long-run bond reversal

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(REV) signal is the cumulative 60-month return on the bond index with the 12 most recent months dropped, i.e., within the months t-60 to t-13. Eventually, to estimate carry yield

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(CAR), we loosely follow Asness, Ilmanen, Israel, and Moskowitz (2015), and compute as a yield-to-maturity minus the 1-month Financial Times/Thomson Reuters deposit rate sourced from Datastream, both expressed on a monthly basis. Importantly, we slightly depart from Asness, Ilmanen, Israel, and Moskowitz (2015) and, following the argumentation of Beekhuizen, Duybesteyn, Martens, and Zomerdijk (2016), we use the deposit rates instead of T-Bill rates, as the deposit rates seem more relevant for bond investors and provide better

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ACCEPTED MANUSCRIPT historical country coverage. All of the described signals come from existing finance literature. Thus, the studies of Ejsing, Grothe, and Grothe (2012), Luu and Yu (2012), Asness, Moskowitz, and Pedersen (2013), Asness, Ilmanen, Israel, and Moskowitz (2015), Hambush, Hong, and Webster (2015), Geczy and Samonov (2017), Zaremba and Czapkiewicz (2017), and Koijen, Moskowitz, Pedersen, and Vrugt (2018) argue that bonds

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with high duration, high credit risk, high short-term returns, low long-run returns, and high carry yield tend to outperform bonds with low duration, low credit risk, low short-term returns, high long-term returns, and low carry yield.

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3. Return Seasonality in Government Bonds

As suggested by Fama (2015), we examine the return seasonality in bond portfolios with both cross-sectional and time-series tests. Both types of tests provide unique

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perspectives and complement each other.

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3.1. Cross-Sectional Tests

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We start our tests with regressions in the style of Fama and MacBeth (1987), in which we regress the contemporaneous excess return Ri,t on a bond bucket i in month t on different

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return predictive variables Ki,t described in Section 2:4 ∑

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(1)

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The symbols β0,t and βj,t denote the estimated parameters, and εi,t is the error term. The

major aim of this exercise is to verify whether the return seasonality predicts future returns on international government bond portfolios, both as a stand-alone variable and after controlling for other return predictors.

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To remain consistent with the U.S. dollar approach, the excess returns are computed based on a 3-month T-Bill

rate sourced from French (2018). Replacing it with U.S. deposit rates has no major impact on the results.

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ACCEPTED MANUSCRIPT Table 1 reports the results of the cross-sectional Fama-MacBeth regressions. The SAME variable, representing the seasonality effect, is a strong and robust return predictor, significant both on a stand-alone basis (specification [1]), or after controlling for the other variables: DUR, CRED, MOM, REV, and CAR ([2]). On the other hand, the average return in the other calendar months (OTHER) plays no role for future returns—its coefficients are

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insignificant both in simple [3] and multiple [4] regressions. Furthermore, the return seasonality SAME remains significant also when we include both SAME and OTHER in the regressions, whereas the OTHER variables still demonstrate no predictive abilities (specifications [5] and [6]).

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[Insert Table 2 here]

As an additional confirmation of these results, we also examine the predictive abilities of the S-O variable, which is the difference between SAME and OTHER. In other words, S-O

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represents the difference between the average returns in the same and other calendar months. Again, the coefficients on this variable remain positive and significant, even when we control

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for DUR, CRED, MOM, REV, and CAR. This observation, once again, verifies positively the

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remarkable cross-sectional seasonality effect in international government bonds.5 Panel B of Table 1 presents a further robustness check, that is, an application of the

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Fama-MacBeth regressions to the hedged returns. The results are qualitatively consistent. In other words, even after controlling for the impact of currency movements on the bond

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returns, the SAME retains its forecasting abilities, whereas OTHER presents no important role for the cross-section of returns.

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Table A3 presents a further robustness check, that is, an application of the Fama-MacBeth regressions to the

hedged returns. The results are qualitatively consistent. In other words, even after controlling for the impact of currency movements on the bond returns, the SAME retains its forecasting abilities, whereas OTHER presents no important role for the cross-section of returns.

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ACCEPTED MANUSCRIPT The results reported in Table 1 holds also for other, shorter, SAME estimation periods. The regression coefficients are significant even when the window is as short as 5 years (see Figure A1 in the Online Appendix for details). Nonetheless, the use of longer series helps to mitigate the impact of noise in prices, resulting in better quality of return predictors and, thus,

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higher t-statistics.

3.2. Time-Series Tests

Having established the basic cross-sectional relationships, we now continue with time-series portfolio-based tests. To this end, each month we sort the bond buckets on SAME.

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Next, we determine 10%, 20%, or 30% cutoff points, and form equal-weighted portfolios of the bond buckets with the highest and lowest average same-calendar month return (SAME). We also form zero-investment portfolios that go long (short) for the bond buckets with the

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highest (lowest) SAME variable. For comparison, we also build identical strategies based on the average historical other month return, i.e., OTHER.

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We evaluate the strategies with the six-factor model based on the concepts of Asness,

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Moskowitz, and Pedersen (2013), Asness, Ilmanen, Israel, and Moskowitz (2015), Konstantinov (2016), and Zaremba and Czapkiewicz (2017), which control for the major risk

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and cross-sectional return patterns in international government bond markets:

.

(2)

where Ri,t is the excess return on the bond bucket i in month t, εi,t is the error term, αi the abnormal return—the so-called ―Jensen’s alpha‖—and βMKT,i, βDUR,i, βCRED,i, βMOM,i, βREV,i, and βCAR,i are measures of exposure to MKTt, DURt, CREDt, MOMt, REVt, and CARt factor returns. To ensure that the results are not driven by portfolio constructions, rebalancing frequencies, or weighting schemes, all of the factors’ payoffs are computed in a consistent

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ACCEPTED MANUSCRIPT way as the tested strategies, i.e., as the U.S. dollar returns on monthly-rebalanced equalweighted portfolios. MKTt is the market excess return, i.e., an equal-weighted excess return on all of the bond buckets in the sample. DURt, CREDt, MOMt, REVt, and CARt are longshort equal-weighted tertile portfolios from sorts on duration, credit risk, momentum, reversal, and carry. The portfolios go long (short) for the tertile of bond buckets with the

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highest (lowest) DUR, CRED, MOM, CAR, and the lowest (highest) REV. The statistical properties of the utilized factors are presented in Table A4 in the Online Appendix.

Panel A of Table 3 displays the performance of return seasonality strategies. The long-short portfolios from SAME produce positive mean monthly returns amounting to 0.07–

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0.30% per month. The average payoffs increase monotonically with the breadth between the breakpoints used to form the portfolio, so they are the highest for the deciles and the lowest for the tertiles. Most importantly, the abnormal returns remain positive and significant even

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after applying the six-factor model. The monthly alphas range from 0.09% to 0.42% with the corresponding t-statistics of 3.09 to 4.11. The R2 coefficients of the long-short portfolios are

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lower than 10%, implying that the considered factors do not capture well the behaviour of the

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return seasonality strategies.

[Insert Table 3 here]

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To provide a better overview of the return seasonality strategies from Panel A of Table 3, Figure 1 additionally presents their cumulative returns during our study period. The

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profitability appears quite stable through time. Most importantly, it does not display any dramatic decline in its effectiveness through recent years as was discovered for numerous equity market strategies (McLean and Pontiff 2015; Tobek and Hronec 2018). On the contrary, the bond return seasonality strategies have continued to produce consistent profits also during the last two decades.

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ACCEPTED MANUSCRIPT Panel B of Table 3 presents the payoffs of the strategies formed on the average othercalendar month returns. Notably, the long-short portfolios, in this case, demonstrate no significant raw or risk-adjusted returns. Clearly, only the same-month returns bear some predictive abilities for the cross-section of government bonds, whereas the other months play no important role. This observation also provides some insights into the sources of the return

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seasonality anomaly in government bonds. One of the possible explanations for the return seasonality in the government bonds could be the cross-sectional variation in long-term returns. An analogous hypothesis for momentum has been put forward by Conrad and Kaul (1998) and Bulkley and Nawosah (2009). In other words, the return seasonality strategy

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might simply pick bond buckets with the higher long-run expected returns due to, e.g., some additional underlying risk factors. Nevertheless, this cross-sectional variation would be also captured by the sorts on the average returns in other months. Our findings, however, do not

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support this view.

The overperformance of the return seasonality strategy is robust to alternative

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portfolio construction and implementation methods. It also produces significant raw and risk-

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adjusted returns when implemented in value-weighted portfolios and after hedging out the currency risk, whereas the other-calendar month strategy does not deliver any significant

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payoffs in any of these settings (see Table A7 in the Online Appendix for details).6 Furthermore, whereas the strategy performs best when the SAME signals are derived from

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local currency returns, it qualitatively also holds for the SAME variables based on hedged or

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As we have already indicated, to assure that the results are not driven by the particular factor construction, the

factor portfolios are formed in an identical way as the tested portfolios, including weighting scheme and hedging approach. Tables A5 and A6 in the Online Appendix reveal statistical properties of the factors used to evaluate the alternatively implemented strategies presented in Table A7. Noticeably, in the hedged-returns approach, the MKTt and DURt factor returns display a significant positive correlation. Nonetheless, dropping either of the two factors has no qualitative influence on the results.

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ACCEPTED MANUSCRIPT unhedged U.S. dollar returns, with the long-short portfolios nearly always yielding significant positive alphas (for details, see Table A8 in the Online Appendix). We are also interested in whether the performance of the return seasonality strategies is particularly pronounced in some particular segment of the government bond market. Consequently, we implement it within various segments of the bond market. In particular, we

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test it in the five different maturity subsets—1–3 years, 3–5 years, 5–7 years, 7–10 years, and more than 10 years—as well as within high and low credit risk bond buckets, defined as the bond buckets with the above-median and below-median average quantified sovereign rating. The results for the quintile portfolios are reported in Table 4.7

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[Insert Table 4 here]

The effect is visibly the strongest among the long-term (more than 10 years) bond buckets, delivering the highest raw and risk-adjusted returns. In the segments of bond

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portfolios with the shorter maturity, namely, 1–10 years, the alphas are still significant, but the raw returns frequently do not depart significantly from zero. Clearly, it seems that the

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long-term bonds are the main source of the profitability of the return seasonality strategy.

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The influence of credit risk is lower. Although the strategy delivers abnormal payoffs in both high and low-risk fixed-income securities, the profits are marginally higher among the

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riskier bonds.

Importantly, the long-run and high-credit risk bonds are more volatile, frequently less

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liquid, and—in consequence—often more difficult to hedge. The more pronounced profits in the subset, which is more difficult to hedge, could be an argument supporting the behavioural story of the anomaly (see, e.g., Ali, Hwang, and Trombley 2013, Nagel 2005, or Gu, Kang, and Xu 2018). We will explore this aspect further in the Section 4 of the paper.

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The consistent results for the portfolios of 10% or 30% of bond buckets are presented in Table A9 in the

Online Appendix.

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ACCEPTED MANUSCRIPT 4. The Sources of the Seasonality Anomaly Having documented the strong return seasonality effect in the cross-section of government bond returns, we continue with an exploration of its possible explanations. In particular, we investigate five possible sources of the phenomenon: 1) return seasonality in some underlying risk factor, 2) spillover of the seasonality effect from a different asset class,

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3) manifestation of the seasonality in a particular calendar month, 4) unevenly accrued macroeconomic risk premia, and 5) behavioural anomaly. We discuss and verify the competing hypotheses one by one.

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4.1. Seasonality Effects in Underlying Risk Factors

Keloharju, Linnainmaa, and Nyberg (2016) demonstrate that the return seasonality effect is present not only in individual stocks but also in the risk factor. They show that the

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phenomenon is exhibited likewise in the portfolios from sorts on return predictive variables and equity anomalies. Zaremba (2017) extends this evidence to international factor strategies.

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Keloharju, Linnainmaa, and Nyberg (2016) argue that if the seasonality is observable in at

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least one risk factor, then, in consequence, it should be also present in the total returns. To check this, we follow the approach of these authors and examine the seasonality in one-way

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sorted portfolios.

To perform this test, in the first pass, we rank the bond buckets in our sample on the

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five return predictive variables considered in this study, namely, DUR, CRED, MOM, REV, and CAR. Next, we build equal-weighted decile portfolios sorted on these variables and implement the standard return seasonality strategies in these portfolio sets. In other words, we rank the decile portfolios on the average same-calendar month returns and form long-short strategies going long (short) for the deciles with the highest (lowest) returns. Once we test the seasonality effect in the portfolios, in the second pass, we regress the returns on the return

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ACCEPTED MANUSCRIPT seasonality strategies in individual bonds on the seasonality strategies in the decile portfolios. The aim of this task is to check whether the portfolio seasonality strategies explain the abnormal returns on the bond seasonality strategies. Table 5 reports the performance of return seasonality strategies implemented in the decile portfolios.8 Notably, the one-way sorted portfolios do not reveal any seasonality

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patterns in the cross-section. The average returns on long-short portfolios do not produce any significant profits in the cases of sorts on credit risk, momentum, reversal, and carry. The only exception is the duration. Nonetheless, in this particular case, the effect is clearly driven by the cross-sectional variation in expected returns.9

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[Insert Table 5 here]

Table 6 demonstrates the results of the regression of the bond seasonalities on the portfolio return seasonalities. In the main manuscript, we show the results for long-short

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quintile portfolios only, while the robustness checks regarding portfolios including 10% or 30% of assets are reported in Table A11 in the Online Appendix. Similarly, as in the equity

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research of Keloharju, Linnainmaa, and Nyberg (2016), the portfolio seasonalities are not

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able to explain the individual bond seasonalities. No matter whether we consider the strategies based on 10%, 20%, or 30% cutoff points, all of them continue to deliver positive

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and significant alphas. Although the regression coefficients on some of the portfolio seasonalities are significant—particularly in the cases of duration and credit risk-sorted

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portfolios—the R2 coefficients remain very low. The individual portfolio seasonalities explain no more than a few percent of the time-series variation of the individual bond seasonalities. Moreover, even if all of the portfolio seasonalities are considered jointly in one

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In the main manuscript, we report only the results for the portfolios including 20% (namely: 2) deciles, while

the robustness checks for the 10% and 30% of the assets are displayed in Table A10 in the Online Appendix. 9

Our additional calculations show that the effect is equally captured by the strategies formed on the average

other-calendar month returns. For brevity, we do not report these results.

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ACCEPTED MANUSCRIPT multiple regression (specification [6]), the explanatory power does not exceed 8.13%– 14.60%. As we also report in Table A12 in the Online Appendix, the picture does not change; even if we include all of the control variables from the six-factor model (2), all of the bond seasonality strategies continue to deliver significant alphas. To conclude, clearly, no single

government bond buckets. [Insert Table 6 here]

4.2. Spillover from Seasonality in Other Asset Classes

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risk factor seasonality is responsible for the development of the seasonality in individual

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Previous research has documented that the cross-sectional seasonality drives prices in numerous asset classes and security universes, including international stocks, equity indices, commodities, as well as equity anomalies and factor strategies (Heston and Sadka 2010;

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Keloharju, Linnainmaa, and Nyberg 2016; Zaremba 2017). Meanwhile, there is a growing literature showing that certain anomalies may spill over from one asset class to another; for

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instance, momentum may spill over from stocks to bonds (Gebhardt, Hvidkjaer, and

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Swaminathan 2005; Haesen, Houweling, and van Zundert 2017) or from credit derivatives to equities (Lee, Naranjo, and Sirmans 2014), and commodity and equity returns help to predict

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currency carry profits (Bakshi and Panayotov 2013; Lu and Jacobsen 2016). Consequently, we hypothesize that maybe the government bond return seasonality is also a manifestation of

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the seasonality in some other class. Admittedly, Keloharju, Linnainmaa, and Nyberg (2016) calculated correlations between seasonality profits in equities, indices, and commodities and found them very low or even negative; however, similar examinations for bonds have never been done. To verify this hypothesis, we first replicate our equal-weighted long-short seasonality strategies in alternative asset classes. We focus on five different security universes

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ACCEPTED MANUSCRIPT spotlighted in earlier research: 1) country equity indices, 2) industry equity indices, 3) double sorted global equity portfolios, 4) international equity factor portfolios, and 5) commodities. Country equity indices cover 51 developed, emerging, and frontier markets sourced from Datastream. The industry portfolios are based on the Industry Classification Benchmark into 19 supersectors within the sample of the 51 countries covered by our sample of industry

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indices. In total, the industry sample comprises 887 industry indices obtained from Datastream. The double-sorted equity portfolios are 100 global equity portfolios from twoway independent sorts on a) size and book-to-market ratio, b) size and momentum, c) size and profitability, and d) size and asset growth. This set covers 23 countries and is

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downloaded from French (2018). Next, the sample of returns on global factor portfolios includes 96 long-short global equity strategies based on four asset pricing factors—small minus big (SMB), high minus low (HML), up minus down (UMD), and betting against beta

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(BAB)—and is calculated by Frazzini and Pedersen (2018) within 24 individual equity markets. Finally, the commodity sample contains the historical data on 42 different

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commodities sourced from Bloomberg. Table A13 in the Online Appendix details the five

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samples representing alternative security universes. Having implemented the strategies in the five alternative asset classes, we examine

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their correlation with the respective bond strategies. Also, we regress the bond seasonality returns on the other classes’ seasonality returns. The aim of this exercise is to see to what

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extent the other class seasonality is able to explain the performance of their bond market counterpart.

In line with earlier evidence, the alternative asset classes exhibit a return seasonality

anomaly (see Table A14 in the Online Appendix for details). The effect is particularly strong in equity strategies and commodities. However, it is relatively weak in industries and insignificant in equity indices, which contradicts the findings of Keloharju, Linnainmaa, and

18

ACCEPTED MANUSCRIPT Nyberg (2016). It might suggest that these results were to some extent sample specific, as Keloharju, Linnainmaa, and Nyberg (2016) based their research on only 15 country portfolios. Table 7 reports the pair-wise correlation coefficients between the returns on longshort quintile government bond seasonality strategies and their counterparts in different asset

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classes.10 A quick overview of the results leads to a vivid conclusion: there is no strong crossasset relationship between the seasonality patterns. The correlations coefficients are very low and indistinguishable from zero in any case. [Insert Table 7 here]

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The results in Table 8 illustrate our considerations on cross-asset relationships further by presenting the regressions bond return seasonalities on return seasonalities in different asset classes. Similarly as in previous tests, in the main paper, we focus on the long-short

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quintile portfolios, while the supplementary tests for the portfolios based on 10%- and 30%cut-off points are demonstrated in Table A16 in Online Appendix. Again, the bond

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seasonality strategies are not explained by their other class counterparts. In all of the cases,

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they produce positive and significant abnormal returns that are not explained by the other asset portfolios. Even when we account for all five alternative strategies jointly

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(specifications [6]), the alphas still remain positive and significant. Furthermore, the coefficients on the other assets’ returns do not depart from zero in any case and, also, the R2

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coefficient points to no real explanatory power. Finally, the picture does not change even if we additionally control in the regressions for all of the six factors considered in the model (2) (see Table A17 in the Appendix for details). To sum up, clearly, the other asset classes’ seasonality patterns are not responsible for the seasonality of profits in international government bonds. 10

Analogous results for the long-short portfolios based on 10%- and 30%-cut-off points are presented in Table

A15 in the Online Appendix.

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ACCEPTED MANUSCRIPT [Insert Table 8 here]

4.3. Influence of a Seasonal Pattern in a Particular Calendar Month By averaging historical same-calendar month returns, our seasonality frameworks aggregate all possible monthly anomalies. However, it is possible that the profits are driven

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by a strong pattern in only one month, reflecting, e.g., a bond counterpart of equity January effect (Haug and Hirschey 2006). Heston and Sadka (2008, 2010) and Keloharju, Linnainmaa, and Nyberg (2016) show that the equity return seasonality is robust enough to exclusion of the Januaries from the sample, but perhaps for bonds the main drive is a

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different calendar month. Indeed, certain studies have provided evidence of seasonal variation of government bonds resulting in abnormal returns in particular months in selected countries (Clare and Thomas 1992; Smith 2002; Landon and Smith 2006).

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To test the role of calendar variation, we start with a bird’s eye view on the performance seasonality strategy in different months. Figure 2 depicts average monthly

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returns on the long-short bond portfolios in various calendar months. Certainly, the payoffs

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are not stable through time. The profitability is lower in January and September and higher in the March–May and October–December periods. However, no single month clearly stands

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out as an unambiguous driver of the seasonality anomaly. To formalize the observations in Figure 2, we continue with regression-based tests in

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the style of Bouman and Jacobsen (2002) and Schabek and Castro (2017). Specifically, we estimate the parameters of the regression: ,

(3)

where Rt is the return on the seasonality strategy in month t, εt is the error term, and β0 and βM are regression parameters. Mt is a dummy variable taking the value of 1 in a selected calendar

20

ACCEPTED MANUSCRIPT month or 0 otherwise. Thus, βM could be interpreted as the average abnormal return linked to the investigated calendar month. The results of applying the regression formula (3) to long-short quintile are reported in Table 9.11 Indeed, we do observe significantly negative abnormal returns in September, which amount to −1.21%. However, no month exhibits significant and consistent positive

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returns that would be visible across all of the specifications.12 This corroborates the findings of Zaremba and Schabek (2017), who investigated selected monthly calendar patterns in international government bonds but found no convincing evidence to support them. Our findings suggest that the performance of the seasonality strategy is not driven by any

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particular strong calendar month seasonality, but rather aggregates a number of smaller seasonal patterns, which are too weak to exhibit significance on a stand-alone basis.

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[Insert Table 9 here]

4.4. Return Seasonalities and Time-Varying Macroeconomic Conditions

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Another explanation of the return seasonalities in government bonds might be a link

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with time-varying macroeconomic conditions. The risk premiums related to macroeconomic variables might not accrue evenly in all calendar months and might, therefore, be transferred

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to government bond performance. For instance, some measure of macroeconomic conditions might display some structural seasonality, which is, in turn, transferred into the government

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bond universe. If so, then we should expect to observe more pronounced bond seasonality profits in the periods of elevated readings of macroeconomic variables linked to risk premia in bond markets. Indeed, Keloharju, Linnainmaa, and Nyberg (2016), who examine this issue, 11

The robustness checks regarding the portfolios based on 10%- and 30%-breakpoints, that are reported in

Table A18 in the Online Appendix, yields consistent returns. 12

Admittedly, the average returns on the long-short quintile portfolios are markedly higher in April (0.59% per

month), but this is not confirmed by the tests based on portfolios including 10% or 30% of bond buckets in each leg (for details, see Table A18 in the Online Appendix).

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ACCEPTED MANUSCRIPT do not confirm such phenomenon in equities, but theoretically, the roots of the bond seasonality might be different. In order to verify this, we split the research sample into subperiods of different economic conditions and test performance of our strategy within them. We loosely follow Chordia and Shivakumar (2002) in the choice of macroeconomic variables. First, we examine the profitability of the strategy within the periods of global

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recessions of expansions as defined by Federal Reserve Bank of St. Louis (2018a). Second, we split the full research period into the subperiods of above-median and below-median termspread, credit spread, VIX volatility index, and TED spread. The results are reported in Table 10. For brevity, Table 10 contains only the results for the portfolios of 20% of bonds, while

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the results based on portfolios of 10% and 30% of bonds – which display no qualitative difference – are reported in Table A19 in the Online Appendix. [Insert Table 10 here]

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As in Keloharju, Linnainmaa, and Nyberg (2016), we find no difference between the average performance in various subperiods. Literally, no mean return and alpha are

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significantly higher in the subperiods of elevated macroeconomic risks compared to the other

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periods. Consequently, corroborating the findings of Keloharju, Linnainmaa, and Nyberg

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(2016), our results do not support the macroeconomic story of the return seasonality anomaly.

4.5. Behavioural Explanations

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Hirshleifer, Jiang, and Meng (2018) suggest that the cross-sectional seasonality might

be a behavioural phenomenon. They argue that the performance of the strategy might be driven by cyclical swings in investors’ mood that affects various groups of stocks differently. According to the behavioural finance literature, the anomalies are manifestations of investors’ behavioural biases that cannot be easily arbitraged away. This behavioural view on the return seasonality phenomenon yields two interesting testable implications. First, as

22

ACCEPTED MANUSCRIPT noticed by Stambaugh, Yu, and Yuan (2012), the anomalies tend to be stronger in the period following high investor sentiment when investors’ behavioural biases are particularly pronounced. Second, the effect should be particularly strong in the market segments when the arbitrage is more difficult. In this section, we test these two implications. Let us start with the time-varying investor sentiment.

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To test this the role of behavioural factors, we split the research sample using two separate approaches. First, we follow Jacobs (2015) and use certain sentiment indicators to divide the research period. Since we are not aware of any sentiment measure that would monitor investors’ moods in the international bond markets with sufficient time-series of

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historical observations, we use two distinct measures: the Baker and Wurgler (2006) sentiment index (BW) and the OECD Confidence Indicator (OECD) covering OECD member and nonmember economies.13 In our second approach, we follow the framework of Cooper, Gutierrez,

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and Hameed (2004). These authors argue that the investors’ behavioural biases (and overconfidence, in particular) should be particularly strong (weak) following bull (bear)

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markets. These authors empirically demonstrate that this relationship may influence the

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payoffs on certain anomalies, e.g., momentum and reversal. Thus, drawing on this argumentation, we examine the performance of the seasonality strategies in the periods

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following bull and bear markets. For robustness, we use three different definitions of the bull (bear) markets—we define a market state as bull (bear) if the total return during the preceding

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24, 36, and 48 months is positive (negative). Also, we consider the bull and bear markets in both government bonds—with the market portfolio proxied as the value-weighted return on all of the bonds in the sample—and in equities, where the market excess return is the payoff on the global equity portfolio sourced from Frazzini and Pedersen (2018).

13

The BW data is sourced from Wurgler (2018). OECD comes the Organization for Economic Co-operation and

Development (2018).

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ACCEPTED MANUSCRIPT Admittedly, each of our frameworks—based on BW, OECD, and past market returns as in Cooper, Gutierrez, and Hameed (2004)—has its soft spots. The BW index displays a pure measure of investor sentiment and it controls for the role of macroeconomic variables, but it is largely oriented on equities and focused on the United States. Although U.S. entities account for the largest stake of investment in global bond markets (IMF 2018: Table 12) and

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the American sentiment tends to spillover onto other developed markets (Bathia, Breding, and Nitzsche 2016), we may still end up losing some information on sentiment in other countries. Our second measure (OECD) overcomes some of the BW’s deficiencies, as it covers 39 different developed and emerging countries. Nonetheless, as it concentrates on

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consumer sentiment, it might be only partially related to financial markets. Finally, the approach based on past bull markets as in Cooper, Gutierrez, and Hameed (2004) provides a remedy for the outlined shortcomings, as it is derived directly from a broad range of

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international financial markets. Nonetheless, the aggregate asset returns are also influenced by various macroeconomic and non-macroeconomic risks, so this measure of investor

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sentiment may be ―contaminated‖ by other return drivers. In fact, this problem may apply

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also to the OECD-based test. Summing up, by using all three measures, we aim at obtaining a comprehensive view on the link between bond seasonality returns and investor sentiment.

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Finally, we are also aware that the mood swings in global bond markets may equally influence the foreign exchange returns. For instance, investors might be prone to move their

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investments into safe currencies, such as U.S. dollars or Swiss francs (Maggiori 2013; Cho, Choi, Kim, and Kim 2016; Leutert 2018). To control for this, we conduct the subperiod analysis for both regular unhedged returns and—for robustness—for the U.S. dollar hedged returns. We comment on the results for the hedged returns briefly here and report them in detail in Table A20 of the Online Appendix.

24

ACCEPTED MANUSCRIPT The results of these subperiod analyses are presented in Table 11. The two ―external‖ sentiment indicators—BW and OECD—do not appear to exert significant influence on the seasonality payoffs. Indeed, the return seasonality strategy displays positive and significant raw and risk-adjusted returns almost solely in periods of high OECD, but the differences between the performance in above-median and below-median subperiods are insignificant.

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Perhaps this mixed result is a consequence of the weaknesses of these sentiment measures that we have already outlined. In particular, Huang, Lehkonen, Pukthuanthong, and Zhou (2018) have shown that the sentiment in equities might not necessarily determine prices in different asset markets.

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[Insert Table 11 here]

However, the situation looks quite different when we consider the performance following bull and bond markets. In the majority of the considered approaches, the return

M

seasonality strategy is profitable only after the bull markets. Moreover, the difference in performance is usually positive and significant both in terms of average returns and alphas. In

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other words, the return seasonality strategy, in general, performs visibly better following the

PT

bull markets than the bear markets. This pattern is observable whether we consider the bull market in global bonds or in equities, regardless of the bull market estimation period—24, 36,

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or 48 months—and whether the returns are hedged or not to U.S. dollars (see Table A20 in the Online Appendix for details). This finding supports the behavioural story of momentum.

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One may wonder, how it is possible that both the equity and bond sentiment appears

to be driven by investor sentiment, but – as we have illustrated in Table 7 – there is no clear comovement between the seasonality returns in these two asset classes. In fact, there is no contradiction in these observations, since Huang, Lehkonen, Pukthuanthong, and Zhou (2018) have demonstrated that the equity sentiment does directly influence the government bond market.

25

ACCEPTED MANUSCRIPT The second implication of the behavioural story of seasonality is that it should be stronger in the market segments characterized by more difficult arbitrage conditions. In the equity universe, a similar pattern has been documented for, e.g., value effect (Ali, Hwang, and Trombley 2003), momentum anomaly (Nagel 2005), accrual anomaly (Mashruwala, Rajgopal, and Shevlin 2006), asset growth effect (Lam and Wei 2011), or low-risk

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phenomenon (Gu, Kang, and Xu 2018).

To verify the cross-sectionally varying limits on arbitrage, we utilize the method of Gu, Kang, and Xu (2018) and examine the performance of the seasonality strategy within the portfolios from two-way sorts dependent on sorts of proxies for limits to arbitrage and the

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average same-calendar month return in the past. To assure robustness of our results, we employ three different measures of limits to arbitrage motivated by the previous literature from the equity universe, which indicates that the anomalies are particularly pronounced

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within the securities characterized by small market value (Hong, Lim, and Stein 2000; Zhang 2006), high idiosyncratic volatility (Jiang, Lee, and Zhang 2015), and R2 coefficient (Hou,

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Xiong, and Peng 2006). To obtain these variables, we loosely transfer the equity-oriented

PT

approach to the government bond universe. Specifically, each month we rank the bond buckets on (a) total bond bucket capitalization in month t-1, (b) the idiosyncratic volatility

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from the one-factor model, controlling for the value-weighted portfolio of all government bond buckets in the sample based on a 60-month window, and (c) the R2 coefficient from the

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same one-factor model estimated during a trailing 60-month period. Eventually, we obtain nine portfolios from two-way sorts from the limits on arbitrage in the first pass, and from the average same-calendar month return in the second pass. The performance of the two-way sorted portfolios is displayed in Table 12. [Insert Table 12 here]

26

ACCEPTED MANUSCRIPT As we hypothesized, the profitability of the return seasonality strategy is indeed visibly higher in the segments of high limits to arbitrage. We observed the sorts on the market value. The mean return (alpha) on the long-short seasonality portfolio of small bond buckets amounts to 0.17% (0.24%), whereas for the large buckets the analogous number equals 0.05% (0.09%) and does not significantly depart from zero. The situation of idiosyncratic

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volatility is similar. The return seasonality strategy implemented in high-idiosyncratic risk produces a mean return (alpha) of 0.20% (0.26%), whereas in the low-idiosyncratic risk segment it delivers a −0.01% return (0.01%) alpha, again, not distinguishable from zero. Finally, the results for the R2 coefficients are also consistent, demonstrating superior

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performance in the low-R2 segment. These findings—along with the time-varying investor sentiment—provide additional support for the behavioural scenario of the return seasonality anomaly. Consequently, we agree with Hirshleifer, Jiang, and Meng (2018) that the swings of

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investors’ sentiments form currently the most likely explanation for the return seasonality in

ED

various asset classes, including also government bonds.

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5. Investment Considerations

Last but not least, we are also interested in the investment perspective of the return

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seasonality strategy in government bonds. Thus, following the ideas of Ball, Gerakos, Linnainmaa, and Nikolaev (2016) and Fama and French (2018), we estimate maximum ex-

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post Sharpe ratios attainable with different combinations of bond factors. In particular, we want to know two things. First, how much does the inclusion of the seasonality strategies add to the portfolio of the five factors: MKT, DUR, CRED, MOM, REV, and CAR? Second, does an investor pursuing the return seasonality strategy in other asset classes—namely, industry and country indices, commodities, and equity strategies— benefit from additional allocation

27

ACCEPTED MANUSCRIPT to the government bond return seasonality strategy? The answers to these questions are presented in Table 13. Panel A of Table 13 reports the results of portfolio allocation to various factor strategies in the government bond universe. The annualized Sharpe ratio of the combination of the six baseline factor portfolios amounts to 0.95. Once the seasonality strategy is added, a

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considerable share of the portfolio is allocated to it. In fact, no matter which type of seasonality strategy we follow—based on a 10%, 20%, or 30% breakpoint—it always becomes the largest position in the blended portfolio. Nonetheless, the overall benefit is not very big. Admittedly, the Sharpe ratio increases significantly (p-values equal from 4.82% to

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8.90%), but the total increase in the Sharpe ratio is rather moderate. It increases only to 1.06– 1.12, depending on the breakpoint of the seasonality strategy differential portfolio. Summing up, although the seasonality pattern in government bonds is quite strong and reliable, it might

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not be a game changer for quantitative investors with an international fixed-income mandate. [Insert Table 13 here].

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Panel B of Table 13 focuses on portfolio allocation to seasonality strategies in

PT

different asset classes. In this case, the results are even more disappointing. Although the optimal portfolios display roughly 20% of the allocation to the bond seasonality portfolios,

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the improvement in Sharpe ratios is marginal and insignificant. For different breakpoints in the spread portfolios, the Sharpe ratios increase from the range 1.66–1.84 for the strategies

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based on equities and commodities to 1.73–1.88. This marginal and insignificant improvement once again highlights the weakness of the government bond return seasonality strategy: although the anomaly is strong and robust, it is not the Holy Grail of asset allocation. Exploring the seasonality strategy from an investor’s angle, we find that it might exhibit two further pitfalls, limiting its usefulness for portfolio managers. The first challenge

28

ACCEPTED MANUSCRIPT is the trading cost. This aspect might be a remarkable practical problem, especially for the high-turnover strategies (Novy-Marx and Velikov 2016; Chen and Velikov 2017). To evaluate the potential impact of transaction costs, we begin by estimating the monthly turnover—following the formula of Chincarini and Kim (2006)—interpreted as the sum of the absolute values of all trades necessary to re-form the portfolio across all available bond

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buckets. The average turnover for the long-short equal-weighted portfolios displayed in Table 2 is relatively high. It amounts to 28%, 73%, and 88%, for the portfolios based on a 10%, 20%, and 30%-breakpoint, respectively. This characteristic makes it comparable to the top-turnover anomalies in the equity universe, such as short-run reversal (Novy-Marx and Velikov 2016).

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Interestingly, this high turnover is consistent with the evidence from the stock market— Keloharju, Linnainmaa, and Nyberg (2016) also observe a monthly turnover of nearly 100%—but, still, this particular aspect of the strategy might have a detrimental effect in its

M

real-life performance.

Table A21 in the Online Appendix illustrates the performance of return seasonality

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strategies assuming arbitrary cost levels ranging from 0.05% to 0.40% per one-way trade.

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The cost-adjusted performance is obtained simply as the difference between the raw returns and the transaction costs. Regrettably, the trading costs have a detrimental influence on the

CE

performance of the strategies. The profitability of all of the variants of the return seasonality portfolios quickly loses its significance. The least affected is the decile long-short portfolio, as

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in this case the mean returns remain significant even with the costs equaling 0.15% per trade, and do not go below zero even with the costs amounting to 0.40%. However, the situation of the portfolios based on 20% and 30% breakpoints is much worse. In particular, the 30%breakpoint portfolio began to produce significant losses as soon as the trading costs reached 0.15%.

29

ACCEPTED MANUSCRIPT Novy-Marx and Velikov (2013) and Zaremba and Andreu (2018) propose some cost mitigating techniques that could be potentially employed to regain the efficiency of the return seasonality strategy in government bonds. These include focusing on the most liquid-securities, the introduction of a buy/hold spread, and a reduced rebalancing frequency. And here we come to another Achilles’ heel of the return seasonality strategy. Although the first two approaches

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could be—at least theoretically—employed, the third one does not seem feasible. Due to its nature, the return seasonality strategy does not work well with the extended rebalancing periods. Table A22 in the Online Appendix depicts the performance of the long-short seasonality portfolios assuming different holding periods from one to six months.

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Unfortunately, extending the holding period proves almost lethal for the profitability of the strategy. Increasing it only from one to two months immediately results in the reduction of the average raw and risk-adjusted payoffs by more than a half. When the holding period equals

M

four months or more, the strategy no longer exhibits any significant mean return on alpha. To sum up, the excessive trading costs combined with the required high turnover might pose a

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serious challenge for a practical investment implementation of the return seasonality strategy in

6. Concluding Remarks

CE

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international government bond markets.

Our study examines comprehensively the return seasonality effect in government

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bond markets. We demonstrate a strong and robust return seasonality in international government bonds. The bond buckets with high (low) average same-calendar month returns in the past tend to outperform (underperform) in the past. The long-strategy going long (short) for the bond portfolios with the highest (lowest) same month return produces positive and significant raw and risk-adjusted returns. We also test a number of competing explanations of the bond cross-sectional bond seasonality, including spillover from different

30

ACCEPTED MANUSCRIPT asset classes, macroeconomic risk, manifesting seasonality in a particular factor or particular calendar month, and behavioural factors. Our findings most strongly support the behavioural explanation of the effect. In particular, the return seasonality is most pronounced in the periods of high investors’ sentiment and in the market segments characterized by high limits on arbitrage.

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Despite its reliability and robustness, in our opinion, the cross-sectional seasonality might be a poor candidate for a successful strategy in government bonds. First, its improvement in the Sharpe ratio, compared to an investor holding a diversified bond portfolio or already pursuing seasonality strategies in other asset classes, is marginal. Second, the

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strategy is characterized by high portfolio turnover, implying elevated trading costs. Third, the profitability of the strategy declines very quickly along with the extension of the holding period, making it difficult to mitigate the trading costs. Summing up, a successful practical

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implementation of the seasonality strategy might be challenging.

Our research provides new insights into asset pricing in international government

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bond markets. Future studies on the topics discussed in this paper could be further extended

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to examinations of the return seasonality in further asset classes, including, e.g., corporate

AC

CE

bonds, real estate, and alternative assets.

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ACCEPTED MANUSCRIPT Figures 160 140

Long-short portfolios of 10% of bonds

120

Long-short portfolios of 20% of bonds

100

Long-short portfolios of 30% of bonds

80 60 40

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0 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 -20 -40 -60

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Figure 1. Cumulative Payoffs on Long-Short Seasonality Portfolios

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Note. The figure presents the cumulative returns on the equal-weighted long-short portfolios from sorts on the average same-month return through the past 20 years. The portfolios go long (short) for 10%, 20%, or 30% of the bond buckets with the highest (lowest) average return. The returns are expressed as percentages and cumulative returns are estimated additively.

42

ACCEPTED MANUSCRIPT

1.00 0.80 0.60 0.40 0.20 0.00

-0.20 -0.60

Long-short portfolios of 10% of bonds

-0.80

Long-short portfolios of 20% of bonds

-1.00

Long-short portfolios of 30% of bonds

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-0.40

Figure 2. Average Return on Long-Short Seasonality Portfolios in Different Calendar Months

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Note. The figure presents the mean returns on the equal-weighted long-short portfolios from sorts on the average same-month return through the past 20 years. The portfolios go long (short) for 10%, 20%, or 30% of the bond buckets with the highest (lowest) average return.

43

Tables Table 1 The Statistical Properties of the Basic Research Sample R

5-7 year maturity Vol N 0.54 3.46 375 0.44 3.16 401 0.51 3.28 401 0.35 2.53 401 0.43 1.22 131 0.53 3.3 401 0.49 3.18 401 0.24 3.48 461 0.27 3.03 131 0.69 3.62 280 0.41 3.59 335 0.27 3.63 437 0.37 2.52 74 0.21 4.23 95 0.26 3.47 461 0.45 4.5 263 0.58 5.75 211 0.39 3.44 302 0.43 3.29 400 0.18 3.53 450 0.28 3.35 461 0.27 1.75 461

R

7-10 year maturity Vol N 0.58 3.61 375 0.49 3.24 401 0.47 3.24 384 0.4 2.7 401 0.44 1.31 131 0.62 3.47 401 0.56 3.31 401 0.27 3.63 461 0.25 3.27 131 0.66 4.11 401 0.49 3.79 326 0.33 3.82 437 0.43 2.67 74 0.38 4.72 95 0.3 3.61 461 0.58 4.34 298 0.62 6.05 213 0.44 3.72 330 0.39 3.41 376 0.23 3.59 450 0.34 3.57 461 0.3 2.15 461

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3-5 year maturity Vol N 0.49 3.35 375 0.38 3.1 401 0.44 3.19 401 0.29 2.39 401 0.4 1.04 131 0.45 3.2 401 0.41 3.07 401 0.17 3.37 461 0.26 2.82 131 0.53 3.63 401 0.35 3.35 353 0.2 3.49 437 0.35 2.42 74 0.18 3.97 95 0.2 3.36 461 0.42 3.83 305 0.5 5.43 213 0.36 3.27 345 0.38 3.22 401 0.15 3.49 450 0.23 3.16 461 0.22 1.29 461

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R

R

10+ year maturity Vol N 0.64 3.86 375 0.52 3.46 251 0.53 3.47 325 0.52 3.09 401 0.52 1.89 131 0.57 3.38 316 0.66 3.69 401 0.47 3.69 385 0.32 3.76 131 0.72 4.5 401 0.63 4.15 294 0.35 4.07 375 0.52 3.19 74 0.36 5.48 95 0.55 3.42 323 0.43 5.06 205 0.7 6.71 213 0.53 4.03 293 0.48 3.77 347 0.28 3.79 450 0.42 3.98 461 0.41 3.15 461

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Australia Austria Belgium Canada China Denmark France Germany India Ireland Italy Japan Korea Mexico Netherlands Portugal South Africa Spain Sweden Switzerland United Kingdom United States

1-3 year maturity Vol N 0.4 3.28 375 0.3 3.08 401 0.35 3.14 401 0.22 2.25 401 0.36 0.87 131 0.37 3.14 401 0.31 3.05 401 0.1 3.25 461 0.23 2.64 131 0.42 3.27 401 0.24 3.12 353 0.12 3.37 437 0.3 2.36 74 0.18 3.62 95 0.09 3.18 461 0.33 3.2 305 0.45 5.12 213 0.24 3.12 353 0.27 3.16 390 0.08 3.43 450 0.15 3.03 461 0.13 0.71 461

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R

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Note. This exhibit displays the statistical properties of the returns on government bond buckets of different countries and maturities: the mean monthly excess return (R), the standard deviation of monthly excess returns (Vol), and the number of monthly observations (N).

44

ACCEPTED MANUSCRIPT Table 2 Results of Cross-Sectional Fama-MacBeth Regressions

(3) (4) (5) (6) (7)

CRED

0.00* (1.96)

-0.08 (-0.67)

MOM

REV

0.10 (1.21)

-0.20 (-1.05)

CAR

0.41 (0.68)

R2 10.94 62.94 12.83

0.00** (2.26)

0.18 (1.27)

0.06 (0.73)

-0.20 (-1.12)

0.26 (0.51)

64.28 22.44

0.00** (2.11) 0.15** (2.32) 0.13** (2.08)

(8)

DUR

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(2)

S-O

-0.48 (-1.07)

0.00 (-0.02)

-0.81 (-1.53)

0.64 (1.18)

67.45 10.34

0.00** (2.49)

-0.05 (-0.40)

0.10 (1.29)

-0.18 (-0.97)

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(1)

SAME OTHER 0.17*** (2.77) 0.15** (2.11) 0.12 (0.65) 0.15 (0.69) 0.18*** 0.10 (2.70) (0.53) 0.19** 0.60 (2.25) (1.23)

0.22 (0.38)

62.64

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Note. The table presents the slope coefficients from the monthly cross-sectional regressions in the style of Fama and MacBeth (1973) applied to excess returns unhedged returns on buckets of international government bonds: ∑ , where Ri,t is the contemporaneous excess return on the bond bucket i in month t; β0,t and βj,t are regression parameters; and Ki,t are various predictors of bond returns: the average return in the same-calendar month through the months t-240 to t-1 (SAME), the average other-calendar return in months t-240 to t-13 (OTHER), the difference between the average same and other month returns, i.e., the difference between the SAME and OTHER variables (S-O), the duration (DUR), the quantified average credit rating (CRED), the total return in months t-11 to t-1 (MOM), the total return in months t-60 to t-13 (REV), and the carry yield (CAR). R2 denotes the average cross-sectional coefficient of determination (expressed in %). The numbers in brackets are NeweyWest (1987) adjusted t-statistics. Asterisks *, **, and *** indicate values significantly different from zero at the 10%, 5%, and 1% levels, respectively.

45

Table 3 Performance of Portfolios from One-Way Sorts on Average Past Returns Panel A: Sorts on the same-month average return 10% of bond buckets 20% of bond buckets 30% of bond buckets Low High H-L Low High H-L Low High H-L

βMKT βDUR βCRED βMOM βREV βCAR R2

0.30** (2.03) 2.78 0.37 -0.30 1.49

0.28** (2.17) 2.78 0.35 0.08 0.29

0.50*** (4.00) 3.01 0.58 0.06 1.09

0.22** (1.97) 2.13 0.36 -0.40 1.89

0.28** (2.35) 2.68 0.36 0.13 0.37

-0.17*** (-2.64) 0.92*** (22.94) 0.11** (2.27) 0.04 (1.33) 0.03 (1.44) 0.10*** (3.47) 0.00 (-0.04) 75.72

0.25*** (3.35) 0.86*** (15.76) 0.19*** (3.33) 0.23*** (4.49) -0.01 (-0.43) -0.05 (-1.01) -0.09* (-1.75) 71.96

0.42*** (4.11) -0.06 (-0.71) 0.08 (0.98) 0.19*** (2.64) -0.05 (-0.98) -0.15** (-2.22) -0.09 (-1.22) 8.34

-0.11** (-2.45) 0.97*** (36.62) 0.08** (2.08) 0.00 (0.03) 0.01 (0.92) 0.06*** (2.80) 0.00 (-0.12) 86.77

0.18*** (3.41) 0.92*** (23.80) 0.11*** (2.69) 0.12*** (3.34) -0.02 (-0.92) -0.05 (-1.57) -0.03 (-0.84) 83.17

0.29*** (3.63) -0.05 (-0.82) 0.03 (0.43) 0.12** (2.20) -0.04 (-1.00) -0.11** (-2.21) -0.02 (-0.48) 5.61

-0.06*** (-3.23) 1.03*** (84.09) -0.03** (-2.28) -0.04*** (-3.48) 0.01 (1.47) 0.02* (1.73) 0.01 (0.80) 97.67

Panel B: Sorts on the other-month average return 10% of bond buckets 20% of bond buckets 30% of bond buckets Low High H-L Low High H-L Low High H-L

Basic statistical properties 0.35*** 0.07* 0.29** (3.05) (1.70) (2.44) 2.71 0.78 3.05 0.45 0.31 0.33 0.13 -0.50 0.36 0.68 3.21 0.96

0.37** (2.32) 3.59 0.36 -0.02 1.39

0.08 (0.46) 3.02 0.09 -0.60 2.31

0.30** (2.54) 2.92 0.36 0.34 1.01

0.36*** (2.61) 3.14 0.40 0.00 1.17

0.07 (0.50) 2.35 0.10 -0.64 2.74

0.37*** (3.22) 2.63 0.49 0.15 0.55

0.40*** (3.44) 2.61 0.53 -0.02 0.76

0.03 (0.73) 0.85 0.12 -0.71 3.27

0.11 (0.88) -0.04 (-0.39) 0.14 (1.16) 0.25*** (2.66) -0.09 (-1.01) -0.22** (-2.17) -0.06 (-0.69) 12.30

-0.12** (-2.23) 1.06*** (24.58) -0.02 (-0.52) -0.06 (-1.64) 0.02 (0.72) 0.09** (2.09) -0.01 (-0.49) 85.93

-0.02 (-0.36) 0.98*** (19.47) 0.20*** (4.03) 0.10** (2.16) -0.04 (-1.12) -0.07 (-1.62) -0.06 (-1.52) 81.68

0.10 (0.94) -0.08 (-0.92) 0.23*** (2.61) 0.16** (2.07) -0.07 (-1.01) -0.16* (-1.95) -0.05 (-0.77) 10.97

-0.01 (-0.47) 1.03*** (57.06) -0.06*** (-3.24) -0.06*** (-4.00) 0.01 (0.75) 0.02 (1.38) 0.02 (1.62) 97.06

0.03 (1.40) 0.99*** (58.64) 0.03** (2.15) -0.01 (-0.47) -0.02 (-1.33) -0.03 (-1.55) 0.00 (-0.30) 96.95

0.04 (1.03) -0.04 (-1.33) 0.09*** (3.11) 0.05* (1.71) -0.03 (-1.14) -0.05 (-1.56) -0.02 (-1.04) 10.04

AN US

α

0.58*** (4.31) 3.34 0.60 0.24 1.75

Evaluation with the five-factor model 0.03* 0.09*** -0.15** -0.04 (1.82) (3.09) (-2.10) (-0.51) 1.01*** -0.01 1.04*** 0.99*** (110.43) (-0.55) (19.29) (13.62) -0.02 0.02 0.07 0.21*** (-1.40) (0.69) (1.23) (2.67) -0.01 0.03* -0.06 0.20*** (-0.81) (1.82) (-1.37) (3.03) -0.01 -0.02 0.03 -0.05 (-1.08) (-1.37) (0.83) (-0.98) -0.02** -0.03* 0.14*** -0.08 (-2.04) (-1.93) (2.67) (-1.37) 0.00 -0.01 -0.03 -0.08 (-0.32) (-0.63) (-0.73) (-1.36) 98.21 4.85 78.73 71.12

M

Vol SR Skew Kurt

0.29** (2.07) 2.96 0.34 0.04 0.47

ED

R

CR IP T

ACCEPTED MANUSCRIPT

AC

CE

PT

Note. This table reports the returns on portfolios from sorts on average same-calendar month returns (Panel A) and the average other-calendar month returns (Panel B). The High (Low) portfolios equally weight 10%, 20%, or 30% of the bond buckets considered with the highest (lowest) average return. H-L is the long-short portfolio going long (short) for the High (Low) portfolio. R is the average monthly excess return, Vol is the standard deviation, SR is the annualized Sharpe ratio, Skew is the skewness, and Kurt is the kurtosis. α denotes the abnormal return, i.e., the intercept from the six-factor model, and βMKT, βDUR, βCRED, βMOM, βREV, and βCAR are measures of exposure to market portfolio (MKT), duration (DUR), credit risk (CRED), momentum (MOM), reversal (REV), and carry (CAR) risk factors. R2 is the time-series coefficient of determination. R, Vol, α, and R2 are expressed in percentage. The numbers in parentheses are NeweyWest (1987) adjusted (for regression coefficients) and bootstrap (for R) t-statistic, and *, **, and *** indicate statistical significance at 10%, 5%, and 1% levels, respectively.

46

ACCEPTED MANUSCRIPT Table 4 Performance of Long-Short Seasonality Portfolios within Different Maturity and Credit Risk Subsamples

CR IP T

Long-short portfolios of 20% of the bond buckets Return t-statR Alpha t-stata Panel A: Different maturity classes 1-3 year maturity bonds 0.10 (0.81) 0.20** (2.34) 3-5 year maturity bonds 0.11 (0.89) 0.20** (2.28) 5-7 year maturity bonds 0.12 (0.98) 0.23*** (2.61) 7-10 year maturity bonds 0.17 (1.36) 0.28*** (2.79) 10+ year maturity bonds 0.44*** (2.94) 0.45*** (3.96) Panel B: Different credit risk classes High credit risk bonds 0.22 (1.51) 0.28** (2.06) Low credit risk bonds 0.14 (1.26) 0.17* (1.92)

AC

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Note. This table reports the mean returns (Return) and the six-factor model alphas (Alpha) on equal-weighted long-short portfolios from sorts on average same-calendar month returns. The portfolios go long (short) for 10%, 20%, or 30% of the bond buckets considered with the highest (lowest) average return. Panel A presents the results within the subsamples of different maturity buckets; Panel B reports the results for the bonds with the above-median (High credit risk) and below-median (Low credit risk) average quantified sovereign rating. The numbers in parentheses are Newey-West (1987) adjusted (for Alpha) and bootstrap (for Return) t-statistic, and *, **, and *** indicate statistical significance at 10%, 5%, and 1% levels, respectively.

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ACCEPTED MANUSCRIPT Table 5 Seasonality Effects in Portfolio Returns

Vol SR R Vol SR R Vol SR R Vol SR

CR IP T

R

AN US

Vol SR

M

R

Low High H-L Panel A: Duration-sorted portfolios 0.25** 0.43*** 0.17*** (2.47) (3.76) (3.30) 2.47 2.55 1.45 0.35 0.58 0.41 Panel B: Credit risk-sorted portfolios 0.31*** 0.26** -0.05 (2.77) (2.37) (-0.59) 2.71 2.56 1.80 0.40 0.35 -0.10 Panel C: Momentum-sorted portfolios 0.42*** 0.37*** -0.05 (3.93) (3.39) (-0.33) 2.40 2.57 2.25 0.61 0.50 -0.08 Panel D: Reversal-sorted portfolios 0.24* 0.29** 0.05 (1.95) (2.57) (0.69) 2.45 2.62 1.91 0.34 0.38 0.09 Panel E: Carry-sorted portfolios 0.23** 0.40*** 0.16 (2.05) (3.60) (1.34) 2.55 2.77 2.63 0.31 0.50 0.21

AC

CE

PT

ED

Note. This table reports the returns on portfolios of test assets from sorts on average same-calendar month returns. The test assets are equal-weighted decile portfolios ranked on duration (Panel A), sovereign risk (Panel B), momentum (Panel C), reversal (Panel D), and carry (Panel E). The High (Low) portfolios equally weight 20% (2) of the deciles with the highest (lowest) average same-month return. H-L is the long-short portfolio going long (short) for the High (Low) portfolio. R is the average monthly excess return, Vol is the standard deviation, and SR is the annualized Sharpe ratio. R and Vol are expressed in percentage. The numbers in parentheses are bootstrap t-statistic, and *, **, and *** indicate statistical significance at 10%, 5%, and 1% levels, respectively.

48

ACCEPTED MANUSCRIPT Table 6 Regressions of Individual Bond Bucket Return Seasonalities on Portfolio Return Seasonalities DUR 0.31*** (3.21)

CRED

MOM

(1)

0.16* (1.90)

(2)

0.23***

0.29***

(2.71) 0.22*** (2.73) 0.27*** (2.93) 0.21** (2.53) 0.18** (2.41)

(3.88)

(3) (4) (5)

CAR

4.29 5.73 -0.04 (-0.70)

-0.06

-0.15** (-2.03)

0.42*** (6.19)

R2

0.19*** (3.05)

-0.05 (-0.96)

-0.15** (-2.55)

1.98

0.04 (0.94) -0.01 (-0.30)

0.04

14.60

AN US

(6)

REV

CR IP T

α

AC

CE

PT

ED

M

Note. The table reports the regression coefficient of time-series regressions in which the dependent variable is the return on the long-short equal-weighted seasonality strategy that trades individual bond buckets and the explanatory variables are return on long-short equal-weighted seasonality strategies that trade one-way sorted portfolios formed on duration (DUR), sovereign risk (CRED), momentum (MOM), reversal (REV), and carry (CAR). α denotes the intercept, R2 is the coefficient of determination, both expressed in percentage. The numbers in parentheses are Newey-West (1987) adjusted t-statistic, and *, **, and *** indicate statistical significance at 10%, 5%, and 1% levels, respectively.

49

ACCEPTED MANUSCRIPT Table 7 Correlation Coefficients between Seasonality Strategy Returns in Different Asset Classes Correlation coefficient with government bond seasonality 0.04 Country equity indices 0.03 Industry equity indices -0.07 Double-sorted global equity portfolios -0.03 International equity factor portfolios 0.01 Commodities

t-statistics (0.77) (0.71) (-1.32) (-0.57) (0.20)

CR IP T

Asset class

AC

CE

PT

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Note. The table reports the Pearson’s product momentum correlation coefficients along with the corresponding t-statistics between the returns on bond seasonality strategies and the returns on seasonality strategies implemented in different asset classes. The strategies go long (short) for an equal-weighted portfolio of 20% of assets with the highest (lowest) average return in the same-calendar month return in the past. The different asset class universes are described in Table A13 in the Online Appendix.

50

ACCEPTED MANUSCRIPT Table 8 Regressions of Bond Return Seasonalities on Return Seasonalities in Different Asset Classes Double-sorted International Country Industry global equity equity factor Commodities equity indices equity indices portfolios portfolios 0.22** 0.02 (2.37) (0.81) 0.21** 0.02 (2.36) (0.60) 0.24** -0.08 (2.50) (-1.33) 0.25*** -0.03 (2.65) (-0.49) 0.20** 0.00 (2.45) (0.20) 0.21* -0.01 -0.01 -0.09 0.01 0.02 (1.89) (-0.22) (-0.11) (-1.44) (0.25) (1.30)

(1) (2) (3) (4) (5) (6)

R2 -0.09 -0.11 0.23

CR IP T

α

-0.18 -0.22 -0.49

AC

CE

PT

ED

M

AN US

Note. The table reports the regression coefficient of time-series regressions in which the dependent variable is the return on the long-short equal-weighted seasonality strategy that trades bond buckets and the explanatory variables are returns on long-short equal-weighted seasonality strategies that are implemented in different asset classes, as described in Table A13 in the Online Appendix. α denotes the intercept, R2 is the coefficient of determination, both expressed in percentage. The numbers in parentheses are Newey-West (1987) adjusted tstatistic, and *, **, and *** indicate statistical significance at 10%, 5%, and 1% levels, respectively.

51

ACCEPTED MANUSCRIPT Table 9 Performance of Bond Seasonality Strategies in Different Calendar Months Month January February March April

Coef. -0.47 -0.22 0.51 0.59**

t-stat (-1.21) (-0.80) (1.60) (1.99)

Month May June July August

Coef. 0.30 -0.26 0.15 -0.23

t-stat (0.82) (-0.63) (0.39) (-0.79)

Month September October November December

Coef. -1.21*** 0.33 0.29 0.21

t-stat (-3.10) (0.86) (0.70) (0.60)

AC

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CR IP T

Note. The table reports the β1 regression coefficients from the simple time-series regression: , where Rt is the return on a given seasonality strategy in month t, Mt is the dummy variable taking the value of 1 in a considered calendar month and 0 otherwise, β0 and βM are regression parameters, and εt is the error term. The numbers in brackets are t-statistics. The seasonality strategies are zero-investment portfolios of bonds going long (short) for 20% of the bond buckets with the highest (lowest) average return in the same calendar month as t in the past.

52

ACCEPTED MANUSCRIPT Table 10 Performance of Bond Seasonality Strategies in Different Macroeconomic Conditions

Return

Return

Return

Difference -0.03 (-0.36) Difference 0.03 (0.37)

CR IP T

Return

AN US

Return

Pane A: Recessions vs. expansions Recessions Expansions Difference Recessions Expansions 0.18 0.25** -0.04 Alpha 0.35*** 0.31** (0.95) (2.12) (-0.07) (2.66) (2.57) Panel B: High vs. low term spread High Term Low Term Difference High Term Low Term 0.21 0.22 -0.01 Alpha 0.26** 0.28** (1.30) (1.54) (0.13) (2.05) (2.36) Panel C: High vs. low credit spread High BAA Low BAA Difference High BAA Low BAA 0.26* 0.17 0.05 Alpha 0.35*** 0.21* (1.79) (0.99) (0.75) (3.00) (1.70) Pamel D: High vs. low VIX volatility index High VIX Low VIX Difference High VIX Low VIX 0.17 0.36*** -0.10 Alpha 0.21* 0.36*** (1.35) (2.71) (-1.13) (1.80) (3.05) Panel E: High vs. low TED spread High TED Low TED Difference High TED Low TED 0.35*** 0.18 0.09 Alpha 0.42*** 0.12 (2.67) (1.21) (0.78) (3.22) (1.05)

Difference 0.08 (0.87) Difference -0.10 (-1.03) Difference 0.12 (1.19)

AC

CE

PT

ED

M

Note. The table reports the performance of long-short equal-weighted portfolios of government bonds in different macroeconomic conditions. The zero-investment portfolios go long (short) in 20% of the bonds with the highest (lowest) average return in the same calendar month as t in the past. Return is the mean return on a portfolio and Alpha is the monthly abnormal return from the six-factor model (2). Recessions and expansions are based on the OECD Recession Indicators for OECD and Non-member Economies from the Peak through the Trough. VIX is the VIX volatility index, BAA is the BAA credit spread, TED is the TED spread, and Term is the term spread. High (Low) refers to the months with the above-median (below-median) readings at the end of the preceding month. Difference represents the performance of the strategy going long (short) in the first-row (second-row) subperiod. The numbers in parentheses, denoted t-statR and t-statα, boostrap and ewey-West (1987) adjusted t-statistic for Return and Alpha, respectively. The symbols *, **, and *** indicate statistical significance at 10%, 5%, and 1% levels, respectively.

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ACCEPTED MANUSCRIPT Table 11 Performance of Bond Seasonality Strategies in Subperiods of Different Investor Sentiment t-statR

Alpha

t-statα

Return

t-statR

Alpha

t-statα

High vs. low OECD Economic Sentiment Indicator 0.24* (1.89) 0.29** (2.52) Hich OECD 0.18 (1.05) 0.30** (2.36) Low OECD 0.07 (0.31) 0.03 (0.15) Difference Bull vs. bear market in global government bonds (36 m.) 0.33** (2.49) 0.36*** (3.48) Bull bond (36 m.) -0.06 (-0.55) 0.11 (0.82) Bear bond (36 m.) 0.25** (2.48) 0.27*** (3.23) Difference Bull vs. bear market in global equities (24 m.) 0.34*** (3.26) Bull equity (24 m.) 0.30*** (2.66) -0.04 (-0.21) 0.21** (2.02) Bear equity (24 m.) 0.24** (2.56) 0.25*** (2.82) Difference Bull vs. bear market in global equities (48 m.) 0.18 (1.41) 0.31*** (3.29) Bull equity (48 m.) 0.30 (1.55) 0.19 (1.41) Bear equity (48 m.) 0.03 (0.22) 0.08 (0.87) Difference

AN US

CR IP T

Return

High vs. low Baker's and Wurgler's (2006) index 0.12 (0.56) 0.23** (2.18) High BW 0.34*** (2.69) 0.39*** (3.01) Low BW -0.14 (-0.97) -0.07 (-0.47) Difference Bull vs. bear market in global government bonds (24 m.) 0.24* (1.78) 0.34*** (3.26) Bull bond (24 m.) 0.17 (0.74) 0.21** (2.02) Bear bond (24 m.) 0.11 (1.20) 0.18** (2.20) Difference Bull vs. bear market in global government bonds (48 m.) 0.27** (2.43) 0.31*** (3.29) Bull bond (48 m.) 0.03 (-0.11) 0.19 (1.41) Bear bond (48 m.) 0.21** (2.30) 0.23*** (2.84) Difference Bull vs. bear market in global equities (36 m.) 0.36*** (3.48) Bull equity (36 m.) 0.26** (2.23) 0.09 (0.45) 0.11 (0.82) Bear equity (36 m.) 0.16* (1.68) 0.13 (1.48) Difference

AC

CE

PT

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M

Note. The table reports the performance of long-short equal-weighted portfolios of government bonds in subperiods of different investor sentiment. The zero-investment portfolios go long (short) for 20% of the bonds with the highest (lowest) average return in the same calendar month as t in the past. Return is the mean return on a portfolio and Alpha is the monthly abnormal return from the six-factor model (2). BW denotes the Baker and Wurgler (2006) sentiment index, and OECD is the OECD Confidence Indicator. High (Low) refers to the months with the above-median (below-median) readings at the end of the preceding month. Bull mkt. (Bear mkt.) indicates the months following the 24-month or 36-month periods of positive (negative) cumulative excess return on the international equity or government bond market. Difference represents the performance of the strategy going long (short) in the first-row (second-row) subperiod. The numbers in parentheses, denoted t-statR and t-statα, boostrap and ewey-West (1987) adjusted t-statistic for Return and Alpha, respectively. The symbols *, **, and *** indicate statistical significance at 10%, 5%, and 1% levels, respectively.

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ACCEPTED MANUSCRIPT Table 12 Performance within Subsamples and the Role of Limits to Arbitrage

Medium Low

Sorts on idiosyncratic volatility

High Medium Low

Medium Low

0.09 (0.97) 0.16** (2.20) 0.24** (2.26) 0.26** (2.10) 0.09 (1.29) 0.01 (0.06)

-0.03 (-0.51) 0.14* (1.87) 0.36*** (3.02)

M

Sorts on R2

High

H-L

CR IP T

High

Alpha Sorts on same-month average return Low Medium High H-L Low Medium High Panel A: The sorts within tertiles of market value 0.29*** 0.34*** 0.34*** 0.05 -0.07 -0.02 0.03 (2.58) (3.29) (2.97) (0.40) (-1.12) (-0.43) (0.50) 0.28** 0.29** 0.40*** 0.11 -0.08** 0.01 0.08* (2.01) (2.21) (3.20) (1.25) (-2.09) (0.20) (1.66) 0.28* 0.26** 0.45*** 0.17* -0.11** -0.06 0.13* (1.85) (1.96) (3.14) (1.73) (-2.03) (-1.40) (1.73) Panel B: The sorts within tertiles of idiosyncratic volatility 0.46*** 0.50*** 0.66*** 0.20* -0.09 0.03 0.17** (3.01) (3.40) (3.89) (1.69) (-1.29) (0.48) (2.14) 0.34** 0.37** 0.44*** 0.09 -0.17*** -0.12** -0.08* (2.30) (2.53) (3.00) (1.25) (-3.18) (-2.14) (-1.74) 0.33*** 0.34*** 0.32*** -0.01 -0.04 0.00 -0.03 (2.60) (2.91) (2.61) (-0.13) (-0.71) (-0.06) (-0.62) Panel C: The sorts within tertiles of R2 0.42*** 0.41*** 0.43*** 0.00 -0.04 -0.06 -0.07 (2.87) (2.86) (2.78) (0.05) (-0.72) (-1.43) (-1.63) 0.31** 0.39*** 0.50*** 0.18** -0.19*** -0.10* -0.04 (2.22) (2.89) (3.35) (2.19) (-3.68) (-1.95) (-0.76) 0.41*** 0.43*** 0.72*** 0.30** -0.02 0.08 0.34*** (3.37) (3.50) (5.52) (2.47) (-0.22) (1.34) (4.18)

AN US

Sorts on market value

Return

AC

CE

PT

ED

Note. The table reports the performance of the equal-weighted tertile portfolios of bonds from two-way dependent sorts on the average same-calendar month return in the past and on additional variables representing limits to arbitrage. Return is the mean excess return on a portfolio and Alpha is the monthly abnormal return from the six-factor model (2). The bonds are first sorted into tertiles based on total market value (Panel A), idiosyncratic volatility (Panel B), an R2 coefficient, and subsequently on the average same-calendar month return. The H-L portfolio goes long (short) for the High (Low) portfolio. The left section of the table reports the mean excess returns (Return), whereas the right section reports the six-factor model alphas (Alpha) from the model (2). The symbols *, **, and *** indicate statistical significance at 10%, 5%, and 1% levels, respectively, and values in brackets indicate bootstrap (Newey-West adjusted) t-statistics for R (α).

55

ACCEPTED MANUSCRIPT Table 13 Maximum Ex-Post Sharpe Ratios Based on Government Bond Factor Strategies Panel A: Government Bond Factor Strategies

Panel B: Return Seasonality Strategies in Different Asset Classes

(1) (2)

7.75 5.82

(1) (2)

3.57 2.93

(1) (2)

8.10 6.78

Portfolio weights Double-sorted International Industry Government global equity equity factor Commodities equity indices bonds portfolios portfolios Long-short portfolios of 10% of assets -17.61 57.74 46.36 5.76 -12.94 45.30 36.15 4.21 21.46 Long-short portfolios of 20% of assets -15.43 47.52 53.90 10.43 -11.71 38.34 43.13 8.16 19.15 Long-short portfolios of 30% of assets -19.28 40.78 60.88 9.51 -15.14 33.42 49.07 7.60 18.28

AN US

Country equity indices

SRSEAS > SRNO-SEAS

SR 0.95 1.12 1.10 1.06

4.82* 6.37* 8.90*

CR IP T

(1) (2) (3) (4)

Portfolio weights MKT DUR CREDIT MOM REV CAR SEAS10% SEAS20% SEAS30% 19.8 28.7 16.5 12.5 17.3 5.2 16.3 19.8 8.1 10.6 16.4 5.9 23.0 15.5 19.7 8.6 9.9 15.3 4.3 26.7 10.6 13.9 6.7 7.3 10.4 3.1 48.0

SR

SRBOND > SRNO-BOND

1.66 1.73

24.00

1.84 1.88

26.02

1.83 1.86

27.77

AC

CE

PT

ED

M

Note. This table presents the maximum ex-post Sharpe ratios that can be attained by using different combinations of factor portfolios and the weights on each factor necessary to achieve the maximum Sharpe ratio. Panel A reports the Sharpe ratios attainable within the government bond markets. The six baseline factors portfolios are the market portfolio (MKT) and five long-short equal-weighted strategies based on duration (DUR), credit risk (CRED), momentum (MOM), reversal (REV), and carry (CAR). SEAS10%, SEAS20%, and SEAS30% are long-short equal-weighted seasonality strategies, that go long (short) for 10%, 20%, and 30%, respectively, of the bonds with the highest (lowest) average same-calendar month return. Panel B Sharpe ratios are attainable with the return seasonality strategies implemented in different asset classes. The strategies in Panel B are zero-investment portfolios going long (short) for the 10%, 20%, or 30% of the assets with the highest (lowest) average same-calendar month return in the past. The maximum Sharpe ratios (SR) are reported on an annualized basis. The last column reports the p-values from the test verifying the equality of the Sharpe ratios of the portfolios including and excluding the government bond seasonality strategies. Portfolio weights and p-values are expressed in percentage.

56