What Goliaths and Davids among Swiss firms tell us about expected returns on Swiss asset markets

Haab, David R.; Nitschka, Thomas Article What Goliaths and Davids among Swiss firms tell us about expected returns on Swiss asset markets Swiss Journal of Economics and Statistics Provided in Cooperation with: Swiss Society of Economics and Statistics, Zurich Suggested Citation: Haab, David R.; Nitschka, Thomas (2019) : What Goliaths and Davids among Swiss firms tell us about expected returns on Swiss asset markets, Swiss Journal of Economics and Statistics, ISSN 2235-6282, Springer, Heidelberg, Vol. 155, Iss. 16, pp. 1-17, https://doi.org/10.1186/s41937-019-0045-3 This Version is available at: https://hdl.handle.net/10419/259741 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Swiss Journa l o f Economics and Statistics Haab and Nitschka Swiss Journal of Economics and Statistics (2019) 155:16 https://doi.org/10.1186/s41937-019-0045-3 ORIGINAL ARTICLE Open Access What Goliaths and Davids among Swiss firms tell us about expected returns on Swiss asset markets David R. Haab1and Thomas Nitschka2* Abstract Motivated by recent US evidence, we evaluate the predictive power of changes in the weight of large firms in the aggregate stock market (“Goliath vs David” (GVD)) for Swiss stock market returns and bond market returns. Previous research suggests that the asset return dynamics in the US and Switzerland differ markedly. Forecasting Swiss asset returns hence constitutes a challenging “out-of-sample” test for GVD. Over the sample period from January 1999 to December 2017, we find that the Swiss version of GVD exhibits predictive power for Swiss stock and bond market returns even in the presence of global predictors. However, Swiss bond market returns are best predicted by the US term spread. Keywords: Bond market, predictability, Risk premium, Stock market JEL: G15, G17 1 Introduction This paper examines a recently proposed predictor of the US bond and stock returns in a different country-specific context. Such international assessments help to shed light on the issue of whether conclusions drawn from empirical studies based on US data hold for other economies as well. For example, Cochrane (2008) shows that the US dividend-price ratio predicts US stock market returns but does not forecast dividends. However, international evidence provided by Engsted and Pedersen (2010)or Rangvid et al. (2014) suggests that dividend-price ratios predict dividend growth in various countries. Ourpaperfocusesonanintuitivepredictorofasset returns and the state of the economy proposed by Duarte and Kapadia (2017). Changes of large firms’ stock market capitalization relative to the changes in the aggregate stock market capitalization, “Goliath versus David” or GVD, forecast US stock and bond returns as well as macroeconomic variables. To the best of our knowledge, the in-sample and out-of-sample forecast ability for stock returns and bond returns makes it unique among *Correspondence: [email protected] 2Swiss National Bank, Börsenstrasse 15, 8022 Zürich, Switzerland Full list of author information is available at the end of the article predictors of US asset returns (Duarte and Kapadia 2017; Goyal and Welch 2008). Swiss asset markets provide an ideal “out-of-sample” test case for the predictive power of GVD. Rey (2004) and Nitschka (2014) highlight that the time variation in excess returns on both Swiss stock and Swiss bond markets predominantly reflects cash-flow news, i.e., dividend news in the case of stock market returns and long-term inflation news in the case of government bond returns. In this respect, Swiss stock markets appear to be representative of other European stock markets (Nitschka 2010). By contrast, time variation in the returns on the US stock and bond markets is primarily driven by discountrate/expected-return news (Campbell 1991;Campbelland Ammer 1993; Campbell and Vuolteenaho 2004). Duarte and Kapadia (2017) highlight that GVD is supposed to capture variation in discount rates. Against this background, it is not clear whether we can expect a Swiss version of GVD to predict returns on Swiss asset markets at all because cash-flow news appear to dominate their variation. Moreover,wehaveaccesstodataattheindividual stock level for all stocks that have ever been electronically traded on the Swiss stock exchange. This information © The author(s). 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Haab and Nitschka Swiss Journal of Economics and Statistics (2019) 155:16 Page 2 of 17 allows us to construct Swiss versions of GVD with data that matches the quality of the US data. To the best of our knowledge, our stock-level data is extraordinarily detailed compared with stock market data of other small, open economies. However, since electronic trading started only at the end of the 1990s, our empirical assessments of return predictability are restricted to the sample period from January 1999 to December 2017. We analyze the predictive power of a Swiss version of GVD for Swiss stock and bond markets. Similar to the US evidence, we find that a Swiss version of GVD forecasts Swiss stock market returns at time horizons of 6 to 12 months inand out-of-sample. Even though the outof-sample evidence is by far less pronounced than the in-sample evidence, our findings are qualitatively similar to the US evidence of this variable’s forecast power (Duarte and Kapadia 2017). However, we find that the distinction between the two components of GVD matters for its ability to forecast Swiss stock market returns. This is not the case in the US.1GVDnew (differences in net new equity issuances between large firms and the aggregate market) dominates variation in Swiss GVD. It is this component that exhibits the in-sample predictive power for Swiss stock market returns. GVDold (differences in the returns on existing capital between large firms and the aggregate market) exhibits some forecast ability for Swiss bond market returns, but its predictive power is by far less pronounced than for its US counterpart. Since financial markets are globally intertwined, we additionally evaluate whether the Swiss version of GVD adds additional predictive power for Swiss stock market returns in the presence of global (US) predictors of national stock market returns. Our results suggest that the US dividend yield is the best global predictor of Swiss stock market returns in our sample period. However, the predictive power of the Swiss GVDnew survives in the presence of the US dividend yield. On Swiss bond markets, the US term spread predicts Swiss government bond returns in-sample as well as out-of-sample and thus outperforms the Swiss GVDold . Lastly, we evaluate whether our findings have an impact on one of our motivations to examine a Swiss version of GVD, namely the different characteristics of Swiss and US asset return dynamics, i.e, whether cash-flow or discountrate news dominate the time variation in asset returns. Our results suggest that the general conclusions from earlier studies (Rey 2004; Nitschka 2014) qualitatively still hold. However, once we additionally take the US dividend yield and the US term spread explicitly into account, we attribute more of the variation in unexpected Swiss stock market returns to discount-rate news than in the earlier studies. The remainder of the paper is organized as follows. Section 2describes the data and their sources. Section 3 presents the baseline empirical results. Section 4assesses the implications of our main findings for decompositions of asset returns into news components. Finally, Section 5 concludes. The Appendix provides additional results and robustness checks. 2 Asset return predictability: data and descriptive statistics This paper assesses the predictability of Swiss asset returns over the sample period from January 1999 to December 2017. This sample period is restricted by the availability of data to construct GVD, the predictive variable that is the focus of our study. The data frequency is monthly. 2.1 Dependent variables This paper examines whether excess returns on Swiss stock and bond market indices are predictable. Excess returns are defined as log return on the Swiss stock or bond index, rt+1=ln(Pt+1 Pt), in excess of the risk-free rate, which we approximate by the 1-month Swiss franc (CHF) LIBOR rate. The source of the LIBOR rate is the Swiss National Bank (SNB). As a proxy of the Swiss stock market index, we use the MSCI Swiss total return index denominated in CHF. Total return indices assume that dividends are reinvested in the index. MSCI indices are widely used in academic studies and are publicly available on the MSCI website. As a proxy of the Swiss bond market index, we use the Citigroup World Bond Index Switzerland which is constructed under the assumption that coupon payments are reinvested in the index. In addition, it aggregates bonds across maturities. The source of this data is Thompson Reuters Datastream. 2.2 GVD Using stock-level data on the information about different components of changes in a stock’s market capitalization, we compile a Swiss version of a recently proposed predictor of the US asset returns and the state of the economy (Duarte and Kapadia 2017). Duarte and Kapadia (2017) argue that changes in large firms’ stock market capitalization relative to the changes in the aggregate stock market capitalization (“Goliath versus David” or GVD) areanaturalcandidateasapredictorofassetreturns. When the market capitalization of small firms falls relative to the market capitalization of the big firms, i.e., GVD increases, then this movement signals a bad economic state. This interpretation is based on work by Bernanke and Gertler (1989); Gertler and Gilchrist (1994); Kiyotaki and Moore (1997). These authors argue that small firms are more sensitive to the business cycle. Moreover, there is evidence that small US firms’ stocks exhibit greater variation in expected returns than large firms’ stocks during Haab and Nitschka Swiss Journal of Economics and Statistics (2019) 155:16 Page 3 of 17 expansions and recessions (Perez-Quiros and Timmermann 2000). In addition, changes in the market capitalization of large firms in the form of issuances of new equity might be less sensitive to the business cycle than equity issuances of small firms. Covas and Den Haan (2011)find equity issuances of small firms to be more pro-cyclical than equity issuances of large firms in a sample of US firms. We follow Duarte and Kapadia (2017) and define GVD as change in the weight of the Llargest firms in the aggregate Swiss stock market from t−tto t.Hence, GVD basically measures the total return of the Llargest firms relative to the total return on the market portfolio. This return difference can be decomposed into components that reflect the relative returns on existing capital, i.e., the relative ex-dividend returns (Rex t,t), and the relative growth rates due to the raising of (net) new capital (NNCt,t) GVDL t,t=Rex,L t,t−Rex,M t,t+NNCL t,t−NNCM t,t (1) The first term on the right-hand side of Eq. (1), (Rex,L t,t− Rex,M t,t), measures the changes in the prices of existing capital of the Llargest firms relative to the Mfirms that form the market portfolio. The second term on the right-hand side of Eq. (1), (NNCL t,t−NNCM t,t), measures changes in the market capitalization of the Llargest firms due to capital raising or capital decreasing activities relative to the M firms that form the market portfolio. NNC reflects the difference between corporate actions that increase and decrease market capitalization. Measures that increase the market capitalization are the issuance of new shares or new listings. Measures that decrease the market capitalization are delistings of firms or share buybacks and dividend payments. As in Duarte and Kapadia (2017), we use the following abbreviations GVDL,old t,t=(Rex,L t,t−Rex,M t,t)and GVDL,new t,t= (NNCL t,t−NNCM t,t),suchthat GVDL t,t=GVDL,old t,t+GVDL,new t,t(2) Our main empirical results are obtained for L=50. We also follow Duarte and Kapadia (2017)andsettto 12 months in the baseline specification of GVD. The choice of L=50 as baseline case appears to be relatively high because these firms capture approximately 90% of the total market capitalization of all publicly traded shares as we highlight in the Appendix.Weoptedfor a relatively high number of firms to be included in the bucket of large companies in order to increase the range of industrial sectors in the computation of GVD. This limits theinfluenceoffew,bigfirmsontimevariationinGVD and thus on the empirical results. Three companies2make up between 40% and 50% of the total Swiss stock market capitalization in our sample period. Hence, the lower L, the higher the influence of these three firms on GVD and thus on the empirical results. We provide robustness checks (varying L)intheAppendix to illustrate this point. Panel A of Table (1) presents some descriptive statistics of GVD and its two components. The negative average value of GVD indicates that the market capitalization of the large firms grew less than the market capitalization of the smaller firms. This finding appears to be mainly driven by the evolution of net new capital because the average value of GVDnew explains most of the average value of GVD. The autocorrelation of GVD is relatively high with an autocorrelation coefficient of approximately 0.9. To get a sense of the main driver of the variation in total GVD (L=50 and setting tto 12 months), we perform a variance decomposition of the following form var(GVD)=var GVDold+var GVDnew +2cov GVDold,GVDnew(3) and 1= var GVDold var(GVD)+var GVDnew var(GVD)+2 cov GVDold,GVDnew var(GVD) (4) The results of this decomposition are displayed in panel B of Table 1and show that approximately 80% of the variationinGVDisdrivenbyGVDnew, i.e., changes in net new capital of large firms relative to changes in net new capital of the total Swiss stock market. The differences in the relative valuation of large and small firms in the Swiss stock market are hence primarily driven by differences in net new capital between large firms and the aggregate market. The correlation between the two components of GVD, GVDnew and GVDold, is close to zero (correlation coefficient – 0.03). 2.3 US predictors: data and correlation with Swiss GVD We assess whether GVD exhibits predictive power for Swiss asset market returns and compare it with the standard US predictors of stock and bond market returns. This comparison assumes that the US variables are a stand-in for global predictors of asset returns. We use the CRSP database to update the US version of GVD (GVDUS 250 ) based on the original data graciously provided to us by Haab and Nitschka Swiss Journal of Economics and Statistics (2019) 155:16 Page 4 of 17 Table 1 Descriptive statistics and variance decomposition: GVD and its components Panel A: Descriptive statistics Mean Std Dev Max Min Auto correlation GVD – 0.195 0.030 0.051 – 0.156 0.880 GVDnew – 0.173 0.027 0.035 – 0.130 0.838 GVDold – 0.022 0.013 0.055 – 0.045 0.906 Panel B: Variance decomposition var(GVDold) var(GVD) var(GVDnew) var(GVD)2cov(GVDold,GVDnew) var(GVD) Share explained 0.205 0.828 – 0.033 Notes: Panel A of this table presents descriptive statistics of GVD which is defined as the change in the weight of the Llargest firms in the aggregate Swiss stock market from t−tto t. Here, tis 12 months and L=50. GVDold measures that component of GVD that is due to changes in the prices of existing capital of the Llargest firms relative to the aggregate market from t−12 to t.GVD new measures that component of GVD that is due to changes in the market capitalization of the Llargest firms relative to the aggregate market from t−12 to tdue to capital raising or capital decreasing activities such as the issuance of new shares or share buybacks. Panel B presents the variance decomposition of GVD into the parts driven by GVDold,GVD new, and the covariance between GVDold and GVDnew. The sample period runs from January 1999 to December 2017 Nishad Kapadia. In addition, our assessment uses the Goyal and Welch (2008) dataset of standard US predictors of asset returns. These data are freely available on Amit Goyal’s website. We examine the forecast ability of the predictive variables for which data at the monthly frequency is available. These variables include different variants of ratios of dividends or earnings and prices of the S&P 500 index. These ratios are the dividend-price ratio (dp), the dividend yield (dy), the earnings-price ratio (ep), and the dividend payout ratio, which is defined as the difference between the log of dividends and the log of earnings (de). In addition, we assess the predictive power of stock market variance (svar), the net equity expansion (ntis), and two interest rate variables, i.e., the term spread (ts) and the default spread (ds). The stock market variance is the sum of squared daily returns on the S&P 500. Net equity expansion is the 12-month moving sum of net equity issues divided by the total market capitalization of stocks traded at the NYSE. Since our analysis is based on a shorter sample period than the analysis of Goyal and Welch (2008), we differ in the definition of interest rate-based predictors and define the term spread as the difference between a 10-year US government bond yield and the 1-month treasury bill rate. The default spread is the difference between yields on Baa-rated corporate bonds and the 10-year government bond yield. For a more detailed description of the data, we kindly refer the reader to Goyal and Welch (2008). Table 2displays the pairwise correlation coefficients between the components of Swiss GVD and the US predictors. The Swiss GVD components exhibit the strongest correlations with the dividend-price ratio, the dividend yield, and the term spread. The correlation coefficients with these variables range from approximately 0.3 to 0.5. The correlations with the US version of GVD are low. They range between 0.07 and 0.14. 3 Predicting stock and bond market returns This section presents our baseline results. We start with the results from our assessments of in-sample predictability of Swiss stock and bond market returns. The second subsection provides the corresponding out-of-sample forecast results. 3.1 In-sample predictability Our in-sample predictability assessments are based on OLS regressions of log returns measured from tto t+hin excess of the risk-free rate on the predictive variables presented in Section 2. The regression has the following form rstock,bond t,t+h=α+βhxt+εt,t+h(5) in which the log excess return for time horizon t+his the sum of log one-period excess returns from tto t+hand xdenotes one of the predictors. The forecast horizons, h, that we consider are 1 month, 3 months, 6 months, and 12 months. The combination of long-horizon regressions over a relatively short sample period from January 1999 to December 2017 with overlapping returns and predictors that exhibit high autocorrelations leads to a number of wellknown econometric issues that will affect the inference from this regression (Ang and Bekaert 2007;Boudoukh et al. 2008;Fersonetal.2003;Hodrick1992;Stambaugh 1999). To mitigate these issues, we use a wild bootstrap to compute test statistics. We follow Rapach et al. (2016)and compute heteroskedasticity and autocorrelation robust tstatistics from a wild bootstrap procedure that tests the null hypothesis of ˆ βh=0 against the alternative that ˆ βh>0or ˆ βh<0 depending on the theoretical relation between the regressors and expected asset returns.3This one-sided test procedure follows the recommendation by Inoue and Kilian (2005). Following Rapach et al. (2016), we standardize all predictors to have a standard deviation of Haab and Nitschka Swiss Journal of Economics and Statistics (2019) 155:16 Page 5 of 17 Table 2 Pairwise correlations of CH GVD components with the US asset return predictors dp dy ep de svar ntis ts ds GVDUS 250 GVDnew GVDold dp 1 dy 0.98 1 ep – 0.05 – 0.05 1 de 0.51 0.50 – 0.89 1 svar 0.30 0.22 – 0.28 0.38 1 ntis – 0.56 – 0.55 0.07 – 0.32 – 0.26 1 ts 0.36 0.36 – 0.22 0.46 0.16 0.20 1 ds 0.68 0.60 – 0.52 0.74 0.62 – 0.45 0.32 1 GVDUS 250 0.43 0.43 – 0.07 0.25 0.10 – 0.51 – 0.13 0.31 1 GVDnew 0.46 0.48 0.16 0.08 – 0.05 – 0.12 0.32 0.08 0.07 1 GVDold 0.31 0.28 – 0.13 0.26 0.18 – 0.07 0.35 0.36 0.14 – 0.03 1 Notes: This table gives the pairwise correlations between the US predictors under study and the two components of GVD. The US variables are the dividend-price ratio (dp), the dividend yield (dy), the earnings-price ratio (ep), the dividend payout ratio (de), the stock market variance (svar), the net equity expansion (ntis), and two interest rate variables, i.e., the term spread (ts) and the default spread (ds). Moreover, we computed a US version of GVD (GVDUS 250). The sample period runs from January 1999 to December 2017 one to assess the relative importance of the different predictors. The pvalues of the t-statistics were obtained after 1000 bootstrap draws. Varying the number of draws from 1000 to 10000 has no material impact on the test statistics. 3.1.1 US GVD and the predictability of US and Swiss stock market returns over different sample periods InordertoconstructaSwissversionofGVD,werelyon data that is only available over a relatively short sample period. This observation immediately leads to two questions. First, is there any evidence suggesting that GVD could predict Swiss asset returns in such a short sample period at all? Second, do we need to construct a Swiss version of GVD? Given the international integration of stock markets, the original US version of GVD might provide a better prediction of Swiss asset market returns and it is available for a longer sample period. We address these two questions by running forecast regressions of the US and Swiss stock market returns on US GVD for different starting dates of the (in-sample) forecast sample period. Panel A of Table 3summarizes the outcome of these regressions. Keeping the end date of the sample fixed at December 2017, we find that the forecast ability of the US GVD for US stock market returns deteriorates somewhat with the shrinking sample period. However, even over the sample period from January 1999 to December 2017, there is some evidence of GVD’s predictive ability for future US stock market returns. Hence, assessing the predictive power of a Swiss version of GVD for Swiss asset returns is not a hopeless task. Related to the point above and the correlation coefficients presented in Section 2.3,panelBofTable3shows that the US GVD does not forecast Swiss stock market returns irrespective of the sample period. This finding further motivates an assessment of the predictive ability of a Swiss version of GVD. 3.1.2 Swiss GVD and its components This section presents the baseline results. It displays the main findings from evaluating whether the Swiss version of GVD exhibits in-sample predictive power for Swiss asset market returns. Table 4summarizes the results from the baseline regression of Swiss stock and bond market excess returns on GVD and its two components. Panel A of Table 4shows that GVD exhibits forecast power for Swiss stock market returns at all of the forecast horizons. GVD describes 1.6% of the variation in 1-month ahead stock market returns and almost 14% at the 12-month horizon. Judged by the bootstrapped pvalues, GVD’s predictive power is statistically significant at conventional significance levels. Examining the two components of GVD separately, it becomes apparent that GVDnew drives the predictive power for stock market returns. At short forecast horizons it even outperforms total GVD, which might be due to the fact that GVDold doesnotforecaststockreturnsatall.The regression coefficient occasionally takes the wrong sign and is never significantly different from zero. ThispicturechangesfortheassessmentofGVD’spredictive power for Swiss bond market returns. The regression estimates presented in panel B of Table 4highlight that GVD does not forecast Swiss bond market returns at all. This finding is again driven by GVDnew - the dominant driver of variation in GVDwhich appears to be unrelated to future bond market returns. By contrast, GVDold forecasts bond market returns 1-month ahead with an R2statistic of 1.7%. However, it exhibits no Haab and Nitschka Swiss Journal of Economics and Statistics (2019) 155:16 Page 6 of 17 Table 3 In-sample predictability of US GVD for stock returns Panel A: Predictability of US stock market excess returns h=1 h=3 h=6 h=12 1980 ˆ βR2(%)ˆ βR2(%)ˆ βR2(%)ˆ βR2(%) 0.42** 0.94 0.52*** 4.15 0.43*** 5.13 0.35** 6.47 (pvalue) (0.02) (0.00) (0.01) (0.02) 1990 0.41** 1.00 0.46** 3.49 0.40*** 4.63 0.35** 6.41 (pvalue) (0.04) (0.01) (0.02) (0.04) 1999 0.31 0.52 0.37* 2.02 0.36* 3.20 0.37 5.84 (pvalue) (0.16) (0.08) (0.08) (0.12) Panel B: Predictability of Swiss stock market excess returns ˆ βR2(%)ˆ βR2(%)ˆ βR2(%)ˆ βR2(%) 1980 – 0.08 0.03 0.01 0.00 0.04 0.04 0.07 0.20 (pvalue) (0.62) (0.47) (0.25) (0.35) 1990 – 0.08 0.03 – 0.02 0.00 0.06 0.07 0.13 0.66 (pvalue) (0.57) (0.50) (0.37) (0.28) 1999 0.01 0.00 0.04 0.02 0.11 0.33 0.20 1.81 (pvalue) (0.49) (0.43) (0.33) (0.23) Notes: This table presents OLS estimates from univariate regressions of h-month ahead US (panel A) or Swiss (panel B) stock market returns on the US version of GVD over different sample periods that all end in December 2017. The starting points of the different sample periods are January 1980 (row “1980”), January 1990, and January 1999. The US GVD is z-standardized. We compute heteroskedasticity and autocorrelation robust pvalues (in parentheses below the estimates) from a wild bootstrap procedure that tests the null hypothesis of ˆ βh=0 against the alternative that ˆ βh>0 because high values of the US GVD predict high excess returns. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively Table 4 In-sample predictability of Swiss stock market and bond market excess returns using GVD or its components Panel A: Predictability of stock market excess returns h=1 h=3 h=6 h=12 Predictor ˆ βR2(%)ˆ βR2(%)ˆ βR2(%)ˆ βR2(%) GVD 0.50** 1.61 0.48** 3.46 0.59** 8.72 0.57** 13.88 (pvalue) (0.03) (0.02) (0.02) (0.02) GVDnew 0.55** 1.92 0.60** 5.33 0.61*** 9.44 0.55** 12.93 (pvalue) (0.03) (0.02) (0.00) (0.01) GVDold – 0.34 0.72 – 0.18 0.49 – 0.05 0.06 0.14 0.85 (pvalue) (0.84) (0.73) (0.53) (0.37) Panel B: Predictability of bond market excess returns Predictor ˆ βR2(%)ˆ βR2(%)ˆ βR2(%)ˆ βR2(%) GVD 0.02 0.05 0.03 0.35 0.04 0.88 0.04 1.56 (pvalue) (0.39) (0.33) (0.32) (0.35) GVDnew – 0.02 0.07 – 0.01 0.05 0.02 0.29 0.03 0.71 (pvalue) (0.67) (0.57) (0.38) (0.36) GVDold 0.12** 1.68 0.07 1.63 0.03 0.38 0.01 0.22 (pvalue) (0.01) (0.14) (0.35) (0.41) Notes: This table presents OLS estimates from univariate regressions of h-month ahead Swiss stock (panel A) and bond market (panel B) returns on GVD or one of its components (see Table 1for a description of the variables). All variables are z-standardized. The sample period runs from January 1999 to December 2017. We compute heteroskedasticity and autocorrelation robust pvalues (in parentheses below the estimates) from a wild bootstrap procedure that tests the null hypothesis of ˆ βh=0 against the alternative that ˆ βh>0 because the regressors are defined in such a way that high values predict high excess returns. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively Haab and Nitschka Swiss Journal of Economics and Statistics (2019) 155:16 Page 7 of 17 significant forecasting power at forecast horizons longer than 1 month. These results are unchanged if we run multivariate regressions, i.e., regressions in which GVDnew and GVDold are simultaneously used as regressors, because of the low correlation between the two components of GVD. The results of these regressions are not reported but available upon request. Taken together, these results suggest that the distinction between the two GVD components matters in the Swiss case. This finding stands in contrast to the US evidence which did not find significant differences between the forecast performances of GVD or its components. 3.1.3 Swiss GVD versus standard US predictors Does the predictive power of GVD survive in the presence of global predictors of asset market returns? This is a pertinent question because the Swiss stock market is dominated by firms that generate their earnings from worldwide activities (Rasch 2015) and Swiss government bonds tend to be viewed as safe assets which are in high demand during periods of international crises (Nitschka 2016). To assess this question, we run the in-sample forecast regression in Eq. (5)forexcessreturnsontheSwissstock market and use standard US predictors as stand-in for global predictive variables. The results of these regressions are summarized in Table 5.Notethatweperform only univariate regressions because of the high correlation between some of the US predictors (see Table 2). The main results of this assessment are easily summarized. At short forecast horizons of 1 month and 3 months, the US stock market variance (svar) appears to be the best US predictor. High svar predicts low future Swiss stock market returns, and the R2statistics reach 3% and 6% at the 1-month and the 3-month forecast horizon. At longer forecast horizons, the US dividend yield (dy)appearsto perform best among the US predictors. It significantly predicts Swiss stock market returns at the 6-month and 12-months horizon with R2statistics of 7% and 13%, respectively. We use these results to evaluate the question of whether the predictive power of GVDnew survives in a multivariate forecast regression, i.e., in a regression in which we include the best US predictor for each forecast horizon (svar at 1-month and 3-month horizon and dy at 6-month and 12-month horizon) as an additional regressor to GVDnew.PanelBofTable5presents the results of this assessment. These results show that GVDnew exhibits predictive power for Swiss stock market returns that is Table 5 In-sample predictability of Swiss stock market excess returns: the US predictors versus GVD Panel A: Predictive power of US predictors h=1 h=3 h=6 h=12 Predictor ˆ βR2(%)ˆ βR2(%)ˆ βR2(%)ˆ βR2(%) dp 0.27 0.48 0.36 1.88 0.46 5.36 0.52* 11.52 (pvalue) (0.23) (0.19) (0.11) (0.06) dy 0.40 1.03 0.44 2.76 0.53* 6.92 0.55** 13.03 (pvalue) (0.12) (0.12) (0.06) (0.05) ep 0.23 0.34 0.13 0.26 0.08 0.16 0.16 1.07 (pvalue) (0.32) (0.42) (0.45) (0.38) de – 0.07 0.03 0.05 0.04 0.14 0.52 0.10 0.45 (pvalue) (0.52) (0.43) (0.35) (0.36) svar – 0.67*** 2.83 – 0.66*** 6.47 – 0.31 2.38 0.01 0.00 (pvalue) (0.00) (0.00) (0.25) (0.45) ntis 0.17 0.19 0.25 0.91 0.24 1.38 0.21 1.88 (pvalue) (0.35) (0.32) (0.36) (0.37) ts – 0.27 0.48 – 0.18 0.47 – 0.06 0.10 0.22 2.05 (pvalue) (0.83) (0.70) (0.55) (0.25) ds – 0.41 1.06 – 0.23 0.80 – 0.00 0.00 0.15 0.96 (pvalue) (0.78) (0.60) (0.48) (0.32) Panel B: marginal contribution of GVDnew in the presence of best US predictor at each forecast horizon ˆ βPartial R2(%)ˆ βPartial R2(%)ˆ βPartial R2(%)ˆ βPartial R2(%) GVDnew 0.54* 1.78 0.55** 4.58 0.51** 3.80 0.39* 4.31 (pvalue) (0.07) (0.04) (0.04) (0.10) Notes: Panel A of this table presents OLS estimates from univariate regressions of h-month ahead Swiss stock market returns on each potential US predictor variable described in Tables 1and 2with the exception of US GVD. Panel B gives OLS estimates from regressions of h-month ahead Swiss stock market returns on GVDnew and the best US predictor at each forecast horizon. These estimates show whether GVDnew adds predictive power in the presence of the best US predictor. The sample period runs from January 1999 to December 2017. We compute heteroskedasticity and autocorrelation robust t-statistics (in parentheses below the estimates) from a wild bootstrap procedure that tests the null hypothesis of ˆ βh=0 against the alternative that ˆ βh>0or ˆ βh<0 in the case of svar. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively Haab and Nitschka Swiss Journal of Economics and Statistics (2019) 155:16 Page 8 of 17 independent from the best US predictor. The regression coefficients of GVDnew are significant at all forecast horizons, and it additionally describes about 5% (according to the partial R2) of the return variation. We repeat this empirical analysis for Swiss bond market returns. The results of this assessment are summarized in Table 6. At the 1-month forecast horizon svar appears to predict Swiss bond returns best, but the forecast performance of the term spread is close. At longer forecast horizons, the US term spread clearly is the best and most significant predictor of Swiss bond market returns. The US term spread describes more than 30% of the variation in 12-month ahead returns on the Swiss bond market. GVDold exhibits forecast power for Swiss bond market returns at the 1-month horizon. Panel B of Table (6) shows that this forecast ability survives in the presence of svar. This finding also holds for the term spread as “control” variable in the regressions (not reported but available upon request). At longer forecast horizons, GVDold does not add forecast power to the US term spread. 3.2 Out-of-sample predictability Goyal and Welch (2008) argue that a predictor of asset returns should not only display in-sample predictive power but should also forecast asset returns out-ofsample. Many of the standard predictors of the US asset returns fail that test. There are notable exceptions. Short interest, loosely understood as an aggregate of the number of shares held short, explains the future US stock market returns significantly both in in-sample and in outof-sample forecast regressions (Rapach et al. 2016). The US version of GVD forecasts both stock market returns and bond market returns as well as variables that proxy the state of the economy in-sample and out-of-sample (Duarte and Kapadia 2017). This section provides the results from assessments of the out-of-sample forecast ability of the Swiss versions of GVD and the standard US predictors for stock market returns and bond market returns. We therefore run the regression in Eq. (5) over an evaluation period to obtain forecasts of the h-period ahead stock and bond market returns from the estimates of αand βforeachofthe predictor variables, i.e., ˆrstock,bond t,t+h=ˆα+ˆ βhxt(6) Then, we compute the out-of-sample R2statistic (R2 oos) proposed by (Campbell and Thompson 2008). This statistic obeys Table 6 In-sample predictability of Swiss bond market excess returns Panel A: Predictive power of US predictors h=1 h=3 h=6 h=12 Predictor ˆ βR2(%)ˆ βR2(%)ˆ βR2(%)ˆ βR2(%) dp 0.08* 0.87 0.06 1.39 0.05 1.32 0.03 0.95 (pvalue) (0.09) (0.18) (0.25) (0.34) dy 0.06 0.52 0.05 0.77 0.04 0.75 0.02 0.55 (pvalue) (0.16) (0.24) (0.31) (0.38) ep – 0.03 0.13 – 0.03 0.40 – 0.05 1.30 – 0.07 5.28 (pvalue) (0.70) (0.72) (0.78) (0.89) de 0.07 0.54 0.06 1.19 0.06 2.29 0.07 5.93 (pvalue) (0.17) (0.16) (0.13) (0.08) svar 0.19*** 4.72 0.13*** 5.45 0.07 2.96 0.05 2.90 (pvalue) (0.00) (0.00) (0.02) (0.07) ntis 0.01 0.03 0.02 0.20 0.01 0.03 -0.00 0.00 (pvalue) (0.43) (0.41) (0.48) (0.51) ts 0.18*** 3.95 0.19*** 12.18 0.21** 23.07 0.17** 33.22 (pvalue) (0.01) (0.01) (0.01) (0.01) ds 0.11* 1.59 0.09* 2.42 0.06 2.20 0.05 2.96 (pvalue) (0.06) (0.09) (0.16) (0.13) Panel B: marginal contribution of GVDold in the presence of the best US predictor at each forecast horizon ˆ βPartial R2(%)ˆ βPartial R2(%)ˆ βPartial R2(%)ˆ βPartial R2(%) GVDold 0.10** 1.49 0.06 1.55 0.01 0.64 0.01 0.43 (pvalue) (0.03) (0.23) (0.46) (0.50) Notes: This table presents OLS estimates from univariate regressions of h-month ahead Swiss stock market returns on each potential predictor variable described in Tables 1 and 2with the exception of US GVD. Panel B gives OLS estimates from regressions of h-month ahead Swiss bond market returns on GVDold and the best US predictor at each forecast horizon. These estimates show whether GVDold adds predictive power in the presence of the best US predictor. The sample period runs from January 1999 to December 2017. We compute heteroskedasticity and autocorrelation robust t-statistics (in parentheses below the estimates) from a wild bootstrap procedure that tests the null hypothesis of ˆ βh=0 against the alternative that ˆ βh>0or ˆ βh<0 in the case of svar. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively Haab and Nitschka Swiss Journal of Economics and Statistics (2019) 155:16 Page 15 of 17 is linearized. This weight is slightly lower than unity. A representation of unexpected stock return movements can be obtained from rearranging Eq. (9) for the stock price, pt≈k+ρpt+1+(1−ρ)dt+1−rt+1and then expanding this equation to the infinite horizon. This expansion relies on imposing the condition that discounted stock prices cannot grow forever, lim j→∞ρjpt+j=0, and taking expectations on both sides of the equation such that pt=k 1−ρ+Et⎡ ⎣ ∞  j=0 ρj((1−ρ)dt+1+j−rt+1+j)⎤ ⎦(10) with Ethe expectation operator conditional on information at time t. Substituting Eq. (10)intoEq.(9), Campbell (1991) highlights that unexpected changes of stock returns either reflect news (revisions in expectations) of dividend growth or future discount rates, i.e., rt+1−Etrt+1=(Et+1−Et) ∞  j=0 ρjdt+1+j−(Et+1−Et) ∞  j=0 ρjrt+1+j (11) Campbell and Ammer (1993) study excess returns, i.e., stock returns in excess of a short-term debt rate. In addition, they assume that the discount rate, r,isthesumof short-term real interest rates, rr, and a risk premium term, rx. Unexpected stock excess returns then obey rxt+1−Etrxt+1=(Et+1−Et) ⎧ ⎨ ⎩ ∞  j=0 ρjdt+1+j− ∞  j=0 ρjrrt+1+j− ∞  j=1 ρjrxt+1+j⎫ ⎬ ⎭(12) For notational convenience, Eq. (12)canberewrittenas NRt+1=NCFt+1−NRRt+1−NRXt+1(13) with NRt+1≡rxt+1−Etrxt+1, the unexpected stock market excess return; NCFt+1≡(Et+1− Et)∞ j=0ρjdt+1+j, the news of future cash-flows (dividends); NRRt+1≡(Et+1−Et)∞ j=0ρjrrt+1+j,thenews of the real interest rate; and finally, NRXt+1≡(Et+1− Et)∞ j=1ρjrxt+1+j, the news of future excess returns which can be interpreted as proxy of expected risk premia. Following from this accounting identity a positive surprise movement in the excess stock market return is associated with positive dividend news, lower than expected real interest rates or lower than expected future excess returns or an arbitrary combination. A similar decomposition as the one for stock excess returns applies to bond excess returns. Define the real, log bond return in excess of the short-term rate as brxN t+1≡bN t+1−πt+1−rrt+1(14) in which bN t+1≡pN−1 t+1−pN tis the log nominal oneperiod holding return on a N-period zero-coupon bond with nominal price, p. Inflation is denoted by πand rr represents the short-term real rate. Campbell and Ammer (1993) show that the unexpected bond excess return for a bond with maturity Nheld from tto t+1 (at which it becomes a N-1 period bond) obeys brxN t+1−EtbrxN t+1=(Et+1−Et) − N−1  i=1 πt+1+i− N−1  i=1 rrt+1+i− N−1  i=1 brxN−1 t+1+i(15) or in more compact notation NBRt+1=−NBCFt+1−NBRRt+1−NBRXt+1(16) with NBRt+1≡brxN t+1−EtbrxN t+1,theunexpected excess return on the n-period, zero-coupon bond; NBCFt+1≡(Et+1−Et)N−1 i=1πt+1+i, the cash-flow, i.e., inflation, news component; NBRRt+1≡(Et+1− Et)N−1 i=1rrt+1+i, the real interest rate news over the lifetime of the bond; and NBRXt+1≡(Et+1− Et)N−1 i=1brxN−1 t+1+i, the news about bond excess returns. A positive, unexpected bond excess return hence reflects an unexpected decline in inflation over the maturity of the bond, lower than the expected real interest rates or lower than the expected bond excess returns. Inflation corresponds to cash-flows because the bond price at the maturity date is fixed in nominal terms. Even when expected real interest rates or excess returns stay constant, the expected real payoff of the bond could vary because of changes in inflation over the lifetime of the bond. VAR-based decomposition of unexpected asset returns The state vector of the VAR contains the stock excess return as its first element and then follows the short-term, ex post measured, real interest rate, the change in the short-term nominal interest rate, and the spread between a long-term government bond yield and the short-term interest rate. These four elements are necessary to back out the different stock and bond excess return news components. Other elements should be able to predict future returns. The state vector should also include one variable that could predict both future returns or future cash-flows on the stock market because stocks’ cash-flow news are obtained as residual from the other directly estimated news components (Engsted et al. 2012). Its importance could thus be overstated if the VAR system includes relatively poor predictors of future stock returns. For notational convenience, consider a first-order VAR: zt+1=Γzt+ut+1(17) Haab and Nitschka Swiss Journal of Economics and Statistics (2019) 155:16 Page 16 of 17 in which is the matrix of VAR coefficients and udenotes the error terms. Further define the vectors e1 to e4 to pick out different elements of the state vector. The first element in e1 is one and all other elements are zero, and the second element in e2 is one and all other elements zero and analogously for the other vectors e3 and e4.Thenews of the stock excess return can be directly obtained from Eq. (17)asNR t+1=e1ut+1because the stock excess return is the first element of the state vector. News of the bond excess return can be derived from news of the short-term interest rate and news of the yield spread, i.e., NBRt+1=−(n−1)(e3+e4)ut+1, thus exploiting that excess return news can equivalently be written as news of future bond yields. This latter news can again be written as the sum of news of changes in the short rate and the term yield spread because the lagged short-term interest rate is known at time t. Innovations in the change of the short-term interest rate thus reflect innovations in the level of the short-term interest rate (Campbell and Ammer 1993). The other news components are derived from (17) by using the VAR estimates to compute revisions in (longhorizon) expectations as (Et+1−Et)zt+1+j=jut+1.In both stock and bond excess return decompositions two of the three different news components can be directly computed from the VAR estimates such that the third component has to be obtained as a residual. The three news components of the stock market excess return are obtained in the following way. News of future expected stock market excess returns can be directly derived from the VAR estimates as NRXt+1=e1 ∞  j=1 ρjjut+1=e1ρ(I−ρ)−1ut+1 and news of future real interest rates obey NRRt+1=e2 ∞  j=0 ρjjut+1=e2(I−ρ)−1ut+1 The news of future cash-flows of the stock market excess return is then obtained as residual, i.e., NCFt+1=NRt+1+NRXt+1+NRRt+1 The VAR estimates allow us to extract news components for bond excess returns too. From the VAR estimates, we can directly derive the news about real interest rates over the lifetime of the bond as NBRRt+1=e2 n−1  i=1 jut+1=e2(I−)−1(−n)ut+1 (16) and cash-flow news (inflation news) as NBCFt+1=−NBRR +e3(I−)−1[(n−1)I +(I−)−1(n−ut+1 (17) such that news of future bond excess returns is obtained as the residual: NBRXt+1=−NBRt+1−NBRRt+1−NBCFt+1 Since directly estimating the excess return news would require to take the shrinking maturity of the bond into account, we have to obtain that news component as the residual (Campbell and Ammer 1993;Engstedetal.2012). Endnotes 1Slegers (2014) examined the forecast ability of GVD (and its components) for France, Germany, Italy, and UK but did not find any sign of predictive ability. However, Slegers (2014) has to employ a short cut to calculate GVDnew. By contrast, we have high quality and detailed information about the data that is necessary to compute GVDnew. This difference in the data quality is the most likely explanation of the differences in our assessments of GVD’s forecast performance, because the results in Nitschka (2010) suggest that the stock markets of Germany and also France and Italy are primarily driven by cash-flow news and thus similar to the Swiss stock market that we examine. 2Nestlé, Novartis, and Roche 3We are grateful to David Rapach for making the MATLABcodeforthesetestsavailableonhiswebsite. 4The yield is just a convenient way to think of bond prices. The log yield of a bond with maturity N (yN)is defined as yN=− 1 NpNin which pdenotes the log of the bond price. Bond returns (loosely speaking: changes in bond prices) are thus closely linked to yields. 5There are two broad categories of shares that grant voting rights to shareholders. Among these shares, one can distinguish shares that inform the firm about the name of the shareholder (in German: “Namensaktien”) and shares that inform the firm only about the depository institutions at which the shares are held (in German: “Inhaberaktien”). In addition, we take into account “Partizipationsscheine,” which are shares that do not grant any voting rights to shareholders. Many firms in our sample use at least two of the three different types of shares at the same time. Haab and Nitschka Swiss Journal of Economics and Statistics (2019) 155:16 Page 17 of 17 Abbreviations CHF: Swiss franc exchange rate; de: Logarithmic payout ratio; dp: Logarithmic dividend-price ratio; ds: Default spread; dy: Dividend yield; ep: Logarithmic earnings-price ratio; GVD: Changes of large firms’ stock market capitalization relative to the changes in the aggregate stock market capitalization (“Goliath versus David”); NNC: Net new capital; ntis: Net equity expansion; SNB: Swiss National Bank; svar: Stock market variance; ts: Term spread Acknowledgements Substantial parts of this paper were written when David R. Haab was at the Swiss National Bank. The paper benefited from comments and suggestions by Cedric Tille (the editor), two anonymous referees of this journal, two anonymous referees of the SNB working paper series, Tjeerd M. Boonman, Richard Stehle, Adrien Verdelhan, and participants at the SSES Annual Meeting 2017 (Lausanne), the EEFS Annual Conference 2017 (Ljubljana), and the SNB Brown Bag workshop. Earlier versions of this paper circulated under the titles “Predicting returns on asset markets of a small, open economy and the influence of global risks” (SNB Working Paper 2017-14) and “What Goliaths and Davids among Swiss firms tell us about expected asset returns and the state of the economy.” Moreover, we gratefully acknowledge that David Rapach made his MATLAB code for various tests of stock return predictability publicly available and that Nishad Kapadia provided us with the original US GVD data. Any errors and omissions are our own. The views, opinions, findings, and conclusions or recommendations expressed in this paper are strictly those of the authors. They do not necessarily reflect the views of the Swiss National Bank or the University of Zurich. 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