Risk-Return Trade-O¤ for European Stock Markets Nektarios Aslanidisy Universitat Rovira i Virgili, CREIP Charlotte Christiansenz CREATES, Aarhus University Christos S. Savvax Cyprus University of Technology February 20, 2014
Christiansen acknowledges support from CREATES funded by the Danish National Research Foundation (DNRF78) and from the Danish Council for Independent Research, Social Sciences. Aslanidis acknowledges support from the Spanish Ministry of Science and Innovation project grant (Reference No ECO2009-11055). The authors are grateful to an anonymous reviewer for helpful comments and suggestions. y Universitat Rovira i Virgili, Department d´Economia, CREIP, Avinguda Universitat 1, 43204 Reus, Catalonia, Spain. Email:
[email protected]. z CREATES, Department of Economics and Business, Aarhus University, Fuglesangs Alle 4, 8210 Aarhus V, Denmark. Email:
[email protected]. x Department of Commerce, Finance and Shipping, Cyprus University of Technology, P.O Box 50329, 3603 Limassol, Cyprus. Email:
[email protected].
1
Risk-Return Trade-O¤ for European Stock Markets Abstract: This paper adopts dynamic factor models with macro-…nance predictors to test the intertemporal risk-return relation for 13 European stock markets. We identify country speci…c, euro area, and global macro-…nance factors to determine the conditional moments of stock returns. The preferred combination of factors varies across countries with the risk-return trade-o¤ generally being negative. We document signi…cant time-variation in this trade-o¤ where the business cycle, stock market volatility, and dividend yields are important determinants of the relation. When economic conditions are weak the risk-return relation becomes less negative or positive. Keywords: Risk-return trade-o¤; Dynamic factor model; Macro-…nance predictors; European stock markets JEL Classi…cations: C22; G11; G12; G17
2
1
Introduction
The risk-return trade-o¤ is fundamental to many areas within …nancial economics such as optimal portfolio choice and risk analysis. Initially …nance theory postulates a positive risk-return relation, both across assets and over time. For instance, the Intertemporal Capital Asset Pricing Model (ICAPM) of Merton (1973) suggests that the conditional expected excess return on the stock market should vary positively with the market’s conditional volatility. However, the literature testing the intertemporal risk-return trade-o¤ documents that the relation is unstable and varies substantially over time; for recent contributions see, Ghysels, Santa-Clara, and Valkanov (2005), Ludvigson and Ng (2007), and Brandt and Wang (2010), among others. To explain the mixed results, earlier work by Abel (1988), Backus and Gregory (1993), and Gennotte and Marsh (1993) propose models in which a negative risk-return relation is theoretically plausible. For example, Backus and Gregory (1993), using a dynamic asset-pricing model, examine the relation in a series of numerical examples and show that it can be of virtually any shape; a negative relation is justi…ed when the autocorrelation of variables that describe the state of the economy is positive. Another theoretical framework that can generate a negative relation between …rst and second moments of returns is the model considered by Whitelaw (2000). He assumes that consumption growth follows a regime-switching process and shows that such a structure can generate a time-varying as well as a negative relation between expected returns and volatility.1 Thus, since theory supports both positive and negative risk-return trade-o¤ through time, 1
From an empirical point of view, there are several studies that document a negative relation; for example, Campbell (1987), Breen, Glosten, and Jagannathan (1989), Nelson (1991), Glosten, Jagannathan, and Runkle (1993), Whitelaw (2000), Harvey (2001), and Brandt and Kang (2004).
3
the intertemporal relationship is primarily an empirical question. We investigate the risk-return relation for 13 European stock markets, mainly old EU member states. So far, little attention has been given to Europe as most studies focus on the US stock market. Extending the US results to a European setting is a worthy exercise, given the importance of these countries and the process of integration of European …nancial markets. From a methodological point of view, our work is related to Stock and Watson (2002) who adopt dynamic factor models to summarize the information from a large number of economic variables by a relatively small number of estimated factors. Ludvigson and Ng (2007) use a dynamic factor approach to determine the risk-return relation for the US stock market. A similar approach is used by Goyal and Welch (2008) and Christiansen, Schmeling, and Schrimpf (2012) to predict asset returns and volatilities. In line with this approach, we estimate the conditional return and conditional variance of excess stock market returns using factor-augmented models. The factors are obtained as follows. First, we estimate country speci…c factors using a data set of macro-…nance variables for each country separately. Second, we use euro area macro-…nance variables to identify euro area factors. Third, we extract US factors from a US data base of macro-…nance variables. We estimate the linear risk-return trade-o¤ using the conditional return and conditional variance. Additionally, we take into account the effects from conditional skewness and kurtosis risk in the risk-return relation. Further, we allow the state of the economy to have an e¤ect on the relation by considering a time-varying risk-return trade-o¤ regression. More speci…cally, the coe¢ cients of the model are allowed to depend on commonly used market return predictors such as the short-term interest rate, the term spread, the dividend yield, the VIX volatility index as well as a business cy-
4
cle indicator. This analysis is in line with the conditional ICAPM where the state of the economy approximating investment opportunities is also important in asset pricing, cf. Merton (1973), Guo and Whitelaw (2006), Lustig and Verdelhan (2012), and Nyberg (2012). The empirical …ndings are as follows. We use monthly data from 1986 to 2012. For each country, the strength of the risk-return trade-o¤ varies according to which factors are used to estimate the conditional moments. Benchmark regression results show that, with the exception of the UK, the overall risk-return trade-o¤ is negative. Most importantly, we uncover significant time-variation in this trade-o¤ where the business cycle, stock market volatility, and dividend yields are all important determinants of the relation. The general message is that when economic conditions are weak the risk-return relation becomes less negative and in some cases it even turns positive. The structure of the remaining part of the paper is as follows. We introduce the data in Section 2 after which we explain the econometric framework in Section 3. The empirical results are found in Section 4 followed by the conclusion in Section 5. Various additional tables are delegated to the Appendix.
2
Data
We focus on the stock markets of 13 European economies, namely Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Spain, Switzerland, and the UK. The data frequency is monthly with the sample covering the period from 1986M 02 to 2012M 05 for most countries. The sample period begins later for Austria (1991M 8), Finland
5
(1987M 3), Greece (1994M 3), and Spain (1992M 2).
2.1
Realized Risk Measures
We use realized volatility to model return volatility, motivated by recent …ndings in the volatility modeling literature. Andersen, Bollerslev, Diebold, and Labys (2003) argue that realized volatility is free of tightly parametric functional form assumptions and provide a consistent estimate of ex-post return variability. To calculate the monthly realized volatility we use daily observations. The log-returns are obtained from the DataStream total return local currency stock indices. We use the 3-month interbank rates as risk free rates. These are calculated into daily rates by the money market convention (i.e. by dividing the yearly rate by 360). We calculate the end-of-month realized volatility for month t from daily excess returns, y t . V olt =
r Xnt
=1
y 2t
where nt is the number of days in month t and
(1) indicates the particular day
of that month ( = 1; ::; nt ). We use the corresponding realized skewness, Skt , and realized kurtosis, Kut , as additional risk measures.
2.2
Common Factors
We use a large number of explanatory variables to extract the common factors. The sample contains a number of country-speci…c variables for each country; Austria 110, Belgium 134, Denmark 130, Finland 134, France 152, Germany 147, Greece 125, Ireland 96, Italy 95, the Netherlands 146, Spain 155, Switzerland 152, and the UK 127. We also obtain aggregate data for the euro area (179 variables) and for the US (174 variables) to construct euro 6
area (regional) and US (global) factors, respectively. The series are selected to represent major categories of macro-…nance time series: foreign sector, output and income, sales, orders, purchases, employment, labour cost, money, prices, exchange rates, con…dence indicators, stock market indices, and interest rates and spreads. The variables are transformed to be stationary (taking logs and di¤erences where appropriate) and standardized. Further details about the data are available online. The choice of series is similar to Stock and Watson (2002) and others.
3
Econometric Methodology
3.1
Conditional Return and Conditional Risk
We estimate the conditional return and conditional volatility of excess stock market returns. The …rst stage of the modelling procedure is to estimate the common factors. Let Xtloc denote a large vector (Nloc
1) of country-speci…c
macro-…nance variables, XtEur is a large vector (NEur 1) of euro area macro…nance variables, and XtU S is a large vector (NU S
1) of US macro-…nance
variables. The macro-…nance variables are related to the unobserved common factors according to Xtj = where
j
is an Nj
j
Ftj + ejt ; for j = loc; Eur; U S
(2)
rj matrix of factor loadings and Ftj describes the rj
dimensional vector of unobserved common factors, where rj << Nj . The 1 vector ejt denotes the purely idiosyncratic errors that are allowed to
Nj
be serially correlated and weakly correlated across indicators.2 The above 2
This cross-correlation must vanish as N goes to in…nity. See Stock and Watson (2002) for a formal discussion of the required restrictions on the cross-correlation of the idiosyn-
7
equation re‡ects the fact that the elements of Ftj , which in general are correlated, represent pervasive forces that drive the common dynamics of Xtj . It is in principle not restrictive to assume that Xtj depends only on the current values of the factors, as Ftj can always capture arbitrary lags of some fundamental factors. We follow Stock and Watson (2002) and Ludvigson and Ng (2007) and split the analysis in two stages. At the …rst stage, we retrieve the principal component estimates, Fbtj . To determine the composition of Fbtj , we also use
j 2 the squared factors (Fbi;t ) (i = 1; :::; rj ). The dimension of the common factor
space, rj , is selected using the BIC criterion with the maximum order for rj
being set to 6. Let yt denote the excess stock market log-returns at month t:3 At the second stage, we predict the excess stock market return using a linear factor augmented regression
ybt = +
y
+
0y b U S 1 Ft 1
0y b loc 1 Ft 1
+
0y 2
where the symbol
+
0y 2
FbtU S1
Fbtloc1
Fbtloc1 +
FbtU S1 +
y
yt
1
0y b Eur 1 Ft 1
+
y
+
0y 2
FbtEur 1
FbtEur 1
(3)
Xt
indicates the Hadamard product. Xt includes a set of
conditioning variables, namely the term spread and the dividend yield for the return equation and the VIX volatility index for the volatility equation. The link between stock returns and dividend yields is well established among academics and practitioners. The fact that the term spread tracks timecratic errors. 3 With a slight misuse of notation letting yt denote monthly values in place of daily ones.
8
varying term premia in stock returns is …rst pointed by Fama and French (1989). Guo and Whitelaw (2006) show that implied volatility (as measured by VIX) is a very good predictor of the realized volatility of stock returns. The conditional volatility is estimated using a similar linear projection based upon the following factor augmented model by simply replacing ybt with
d V olt and the parameters are changed accordingly. Similarly, we estimate the c t - and the conditional kurtosis - Ku dt - regressions. conditional skewness - Sk
In the empirical analysis we select parsimonious speci…cations for eq.
(3) by following a general-to-speci…c search (deleting the least signi…cant regressor and re-estimating the regressions each time). The reported models are selected using the BIC and retaining only variables that are signi…cant at the 1% level of signi…cance. We investigate the e¤ects of using no factors i 1
( i 2
=
i 2
=
i 1
=
i 2
=
i 1
=
i 2
= 0), only local factors (
= 0), only local and euro area factors (
i 1
=
i 2
i 1
=
i 2
=
i 1
=
= 0), and all factors
simultaneously for the risk-return relation (i = y; v; s; k where y is the return regression, v is the volatility regression, s is the skewness regression, and k is the kurtosis regression).
3.2
Risk-Return Regressions
We consider the following risk-return relationship where the current conditional return is explained by its own lag and the current and lagged values of the conditional volatility. This is similar to Ludvigson and Ng (2007). As a novel feature, we allow for higher order risk e¤ects in the risk-return relation by adding the contemporaneous and lagged conditional skewness and conditional kurtosis. The linear risk-return regression reads:
9
ybt = c0 + c1 ybt
1
d d + c2 V olt + c3 V olt
c t + c5 Sk ct + c4 Sk
1
(4)
1
dt + c7 Ku dt + c6 Ku
1
+ et
Subsequently, we address the issue of time-variation in the risk-return relationship. A time-varying risk-return trade-o¤ can arise in many di¤erent settings such as when aggregate relative risk aversion (approximated by the volatility coe¢ cients) is countercyclical (e.g. Campbell and Cochrane (1999)), or when investment opportunities (the hedge component) are timevarying (Guo, Wang, and Yang (2013)), or during recessions as argued by Lustig and Verdelhan (2012). Following this line of research, we allow the coe¢ cients of the risk-return relation in eq. (4) to depend on commonly used market return predictors such as the business cycle indicator that equals one when the country is in recession (RECt ), the term spread (T St ), short-term interest rate (SRt ), the V IXt volatility index, and the dividend yield (DYt ).4 Then the time-varying risk-return trade-o¤ regression becomes
ybt = d0 + d1 ybt
1
d d + d2 V olt + d3 V olt
+ d4 RECt + d5 RECt ybt + d8 T St + d9 T St ybt
1
+ d12 SRt + d13 SRt ybt
1
4
1
1
1
1
d d + d14 SRt V olt + d15 SRt V olt
+ d16 V IXt + d17 V IXt ybt
+ d20 DYt + d21 DYt ybt
d d olt + d6 RECt V olt + d7 RECt V
d d + d10 T St V olt + d11 T St V olt 1
(5)
1
1
d d + d18 V IXt V olt + d19 V IXt V olt
d d + d22 DYt V olt + d23 DYt V olt
1
1
+ et
The business cycle data are taken from the Economic Cycle Research Institute (ECRI) following Schrimpf and Wang (2010). The other variables are from DataStream.
10
For readability, we do not include the conditional skewness and kurtosis e¤ects in the time-varying regression as the number of explanatory variables would become disproportionately large. Nevertheless, we estimate such a model and present the results in the Appendix. Since the variables in the risk-return regressions in eq. (4) and (5) stem from the …rst-step regressions in eq. (3), the standard errors are obtained by bootstrapping. 1; 000 samples are built by drawing with replacement.
4 4.1
Empirical Findings Factor Estimation
First we estimate a relatively large number of factors (10) for each country, the euro area, and the US. Second, we choose the most important factors using the Bai and Ng (2002) criterion. The number of factors that su¢ ciently describe the data set is 6 for all countries. The …rst factor explains the largest fraction of the total variation in the panel of data (which varies from 25% for Greece to 60% for Ireland), cf. Table A1 in the Appendix. The …rst six factors account for more than 81% of the variability in the data set of each country. Although there is variability in the persistence of the estimated factors as documented by the …rst order autocorrelation coe¢ cient for each factor, it is generally positive. These characteristics are similar to Ludvigson and Ng (2007).
4.2
Conditional Return and Conditional Risk
Table 1 displays the conditional return results for three countries, namely Germany, Spain, and the UK, while Table A2 (in the Appendix) displays
11
the results for the rest of the countries. We focus our attention on Germany as the largest euro area economy, Spain as the representative country from the troubled South, and the UK as the largest country outside the euro. We report results for the conditional return regression from eq. (3) using three speci…cations: with local factors, with local and euro area factors, and with local, euro area, and global factors. As we move from restricted to unrestricted regressions, there is generally an improvement in …t with the included regressors being similar which indicates that our speci…cation method is robust. For Germany, local factors are important determinants of the estimated excess returns along with a number of US factors and the term spread. As local and euro area factors may be highly correlated for Germany, this result is not unexpected. Excess returns for Spain are predicted mainly by local and euro area factors along with a US squared term. On the other hand, the UK is rather a¤ected by the US factors coupled with some squared local factors. The explanatory power of the factors is generally high with the adjusted R2 statistic being large for all countries except for the UK.5 Tables 2 and A3 show the factors that contain signi…cant information about the conditional volatility according to the volatility version of eq. (3). As in the case of conditional returns, local and US factors along with their squared terms are important predictors for future conditional volatility of Germany, while in the case of Spain local and euro area are the most important determinants of volatility. As for the UK, the conditional volatility is generally predicted by US and US squared factors along with a single euro area factor. The V IX is an important determinant of conditional volatility for all countries. This …nding corroborates the US results in Guo and Whitelaw (2006). The explanatory power of the factors for the volatility 5
Typically, the US studies …nd very modest R2 values of less than 5% when conditioning on a few predetermined instruments (e.g., dividend yield, term spread).
12
is fairly large with adjusted R2 values ranging from 47% to 69%. The explanatory power is much larger in the volatility equation than in the return equation, except for Germany where it is of about the same size. This …nding is not unexpected since …rst moments of returns are generally more di¢ cult to estimate than second moments, cf. Merton (1980). The corresponding regressions for the skewness and kurtosis are shown in Tables 3, 4, A4, and A5. Here, the explanatory power is much lower than for the return and volatility regressions. The conditional moments are standardized for the remaining analysis.
4.3
Choice of Factors
Tables 5 and A6 display the results of the linear risk-return trade-o¤ from eq. (4) as it appears when the return, volatility, skewness, and kurtosis are projected upon the di¤erent sets of factors. For the UK it is important to account for all factors when constructing the conditional moments because the explanatory power of the risk-return tradeo¤ regression is stronger the more factors are taken into account. Opposite for Spain where the best …t is achieved when local and euro area factors are only considered. Interestingly, for Germany the model with local factors only achieves the best goodness of …t. For all countries we build the further analysis on the speci…cations with the largest R2 values (indicated by boldface). In summary, for Germany and Italy it is based on local factors, for Belgium, Denmark, Finland, France, Ireland, and Spain it is based on local and euro area factors, and for Austria, Greece, the Netherlands, Switzerland, and the UK it is based on all factors.
13
4.4
Benchmark Risk-Return Results
The benchmark linear risk-return regressions from eq. (4) are summarized in Table 6 using the preferred factors from above. The explanatory power of the risk-return trade-o¤ equation di¤ers across the European stock markets. It is largest for Switzerland and Greece with adjusted R2 values higher than 60%, followed by Belgium (52%), Austria (50%), Germany (48%), Spain (48%), and Denmark (47%). For the rest of the countries the …t is a bit lower. Overall, the conditional risk variables have very large explanatory power for the conditional returns. For comparison, Ludvigson and Ng (2007) …nd an R2 value for the US of 41% using quarterly data. The autoregressive dynamics have a positive sign which is most reasonable at a monthly frequency. Further, the current conditional volatility generally has a negative e¤ect upon the conditional return with the lagged conditional volatility having a positive e¤ect. More importantly, the sign of the e¤ects is opposite to that of the US stock market documented in Ludvigson and Ng (2007). Nevertheless, summing up the coe¢ cients for the contemporaneous and lagged volatility the overall relation, although negative, is in line with some versions of the Ludvigson and Ng (2007) model. The negative riskreturn relation is in accordance with the previous literature, cf. the discussion of its sign in the Introduction. For the UK the overall risk-return relation is positive. The explanation is that the theoretical convention of treating the stock market as a claim to total consumption, or a proxy for the aggregate wealth of an economy, makes much more sense in a highly capitalized market such as the UK market. The contemporaneous conditional skewness generally has a small positive e¤ect on the conditional return, whereas the e¤ect from the conditional kur14
tosis is generally small and negative. Overall, the higher order moments only exert weak in‡uence on the risk-return trade-o¤.
4.5
Time-Varying Risk-Return Results
Table 7 shows the results from estimating the time-varying risk-return regression in eq. (5). We also report the Wald test of the joint signi…cance of each of the conditioning interaction variables. Our results can be summarized as follows. In the majority of cases, the recession indicator, the V IX, and the DY interaction terms pass the joint signi…cance test. In many cases, the same goes for the term spread and the short rate. Thus we conclude that the risk-return trade-o¤ is signi…cantly time-varying. Generally, the risk-return trade-o¤ for the European stock markets is signi…cantly di¤erent between recessions and expansions. In particular, for Germany, Denmark, and Ireland the relation becomes less negative in recessions compared to expansions. Moreover, for some countries it even turns positive: for the UK it is positive in expansions and becomes stronger in recessions, while for Italy and Greece it goes from insigni…cant in expansions to positive in recessions (though for Greece, recession dummies are not signi…cant overall). This …nding is consistent with Lustig and Verdelhan (2012) who …nd expected returns, adjusted for volatility, are higher in recessions than in expansions. Unlike us, Lustig and Verdelhan (2012) do not attempt to relate returns to any predictors but take a long-term perspective to the risk-return relationship. Stock market uncertainty (V IX) is another important determinant of the risk-return trade-o¤. For instance, high V IX periods are associated with a less negative trade-o¤ (e.g., Germany, Belgium, the Netherlands, Spain) compared to V IX periods. Actually, in the case of France the relation turns 15
positive. Since both risk aversion and stock market volatility show countercyclical variation, consistent with previous results in the literature such as Schwert (1989) and Campbell and Cochrane (1999), this …nding is expected. The dividend yield (DY ) variation is also informative about the strength of the risk-return trade-o¤. We …nd evidence that when dividend payouts are high, the trade-o¤ generally becomes more negative. This may be due to the fact that dividend yields are higher in expansions (Lustig and Verdelhan (2012)), during which the trade-o¤ is predominately negative. Although the term spread and the short rate appear to be signi…cant variables for the risk-return trade-o¤ (joint Wald test statistics are signi…cant in many cases), their interaction e¤ects upon the volatility - both contemporaneous and lagged ones - are generally insigni…cant. Table A7 shows the corresponding time-varying risk-return regression that also allows for skewness and kurtosis risk. The interaction e¤ects of the conditioning variables upon the conditional skewness and kurtosis are in most cases insigni…cant. This underscores that the skewness and kurtosis are not important determinants of the risk-return trade-o¤. Overall, the business cycle, stock market volatility, and dividend yields are important determinants of the risk-return trade-o¤. The general message is that when economic conditions are weak (e.g. the economy is in recession, there is high stock market uncertainty, or dividend payouts are low) the riskreturn relation becomes less negative or positive. This result emphasizes that investors become less willing to accept stock market risk during weak economic conditions.
16
5
Conclusion
In this paper we contribute to the risk-return trade-o¤ literature in many ways. We broaden the existing literature by analyzing 13 large European stock markets instead of only considering the US stock market. We construct conditional returns and conditional risk measures using factors that are based upon a large number of macro-…nance variables. We consider the e¤ect of using local, regional, and global factors and show that the "optimal" choice varies across countries. We show that there is a strong relation between conditional returns and conditional volatilities. We add two new conditional risk measures, namely the conditional skewness and the conditional kurtosis, yet these risk measures are not overly important for the risk-return trade-o¤. The risk-return trade-o¤ is generally time-varying and di¤erent across economic variables. When economic conditions are weak the risk-return relation becomes less negative and in some cases it even turns positive. Our …ndings have substantial implications for international risk analysis and portfolio construction. Since economic conditions play an important role in the risk-return trade-o¤ of European markets, investors should consider economic conditions when constructing portfolios. An important question for future research arising from the present paper is whether economic models (e.g. Campbell and Cochrane (1999), consumption volatility model) can explain the time-series behavior of the empirical Sharpe ratio implied by our regressions.
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Stock, J. H., and M. W. Watson (2002): “Macroeconomic Forecasting Using Di¤usion Indexes,” Journal of Business and Economic Statistics, 20(2), 147–162. Whitelaw, R. (2000): “Stock Market Risk and Return: An Equilibrium Approach,”Review of Financial Studies, 13, 515–541.
A
Appendix
Additional Tables
21
Table 1: Return Regressions
constant Local Factor 1 Local Factor 2 Local Factor 3 Local Factor 4 Local Factor 5 Local Factor 6 Euro Factor 1 Euro Factor 2 Euro Factor 3 Euro Factor 4 Euro Factor 5 Euro Factor 6 US Factor 1 US Factor 2 US Factor 3 US Factor 4 US Factor 6 2 (Local Factor 2) (Local Factor 4)2 (Local Factor 6)2 (Euro Factor 5)2 2 (US Factor 3) (US Factor 4)2 Term Spread Dividend Yield yt-1 BIC 2 R
Local 0.008 -0.147 -0.244
Germany Euro Global 0.007 0.006 -0.253
-0.187
-0.407 -0.181 -0.933
-0.361 -0.112 -0.978
Local 0.003 -0.707 0.401
Spain Euro Global -0.025 0.005
Local 0.009 0.211
UK Euro Global 0.009 0.035 0.211
-0.214
-0.214
-0.421 -0.419 -0.210 -0.919
-0.124
-0.237 -0.298
-0.223 -0.343
0.612 -0.247 -0.697
-0.141 0.165
-0.305 0.569 -0.312 -0.617 -0.733 0.200
-0.304 -0.315
0.200 -0.248 -13.343 -13.343 -3.490 -3.490 -1.625
-1.547
-1.314
-0.006
-3.155 2.178 -0.006
-6.67 0.66
-0.122 -6.71 0.70
-4.286
-2.599 -3.044
-0.006 -0.106 -6.64 0.66
1.678
-5.71 0.10
0.011 -0.259 -6.01 0.41
-0.008 -6.07 0.43
-6.14 0.06
-6.14 0.06
-6.11 0.09
Notes: The table shows the coefficients from the return regression in eq. (3). The models are selected according to BIC. All coefficients are significant at the 1% level. For the remaining countries the results are available in the Appendix.
22
Table 2: Volatility Regressions
constant Local Factor 1 Local Factor 2 Local Factor 3 Local Factor 4 Local Factor 5 Local Factor 6 Euro Factor 1 Euro Factor 2 Euro Factor 4 Euro Factor 6 US Factor 1 US Factor 2 US Factor 6 (Local Factor 1)2 (Local Factor 2)2 (Local Factor 3)2 2 (Local Factor 4) 2 (Local Factor 6) 2 (Euro Factor 2) (Euro Factor 4)2 (US Factor 1)2 2 (US Factor 3) VIX RVt-1 BIC R2
Local 0.022
Germany Euro Global 0.018 0.020 0.050 0.083 -0.070 -0.095
Local 0.015
Spain Euro Global 0.018 0.015
Local 0.009 -0.087
-0.127
0.058 0.057 0.148
UK Euro Global 0.010 0.014 -1.659 1.594
0.145
0.173
0.065 0.075
0.074 0.081
-0.163 0.152
-0.152 0.153
-0.065
-0.053
-0.171 -0.110 0.079 1.107
1.421 1.220 2.245 -1.082
0.711 1.250 2.315 -0.945
0.143
0.150
-4.402 2.073 0.149
-8.08 0.64
-8.10 0.66
-8.12 0.69
2.289
6.134 -1.255 1.214 1.778
0.100 0.278 -7.85 0.49
1.272 1.015 1.368 0.082 0.209 -8.00 0.61
1.597 1.169 1.691 -12.442 0.109 0.184 -8.03 0.63
0.078 0.394 -8.00 0.47
-1.53 1.559 1.105
0.728
0.067 0.409 -7.94 0.48
-2.979 1.389 0.069 0.276 -7.95 0.52
Notes: The table shows the coefficients from the volatility regression in eq. (3). The models are selected according to BIC. All coefficients are significant at the 1% level. For the remaining countries the results are available in the Appendix.
23
Table 3: Skewness Regressions
constant Local Factor 2 US Factor 4 US Factor 5 US Factor 6 2 (Local Factor 2) 2 (Local Factor 6) 3 (Euro Factor 1) (Euro Factor 3)3 (US Factor 6)3 Term Spread Dividend Yield BIC R2
Local -0.176
26.186 24.046
1.14 0.05
Germany Euro Global -0.176 -0.176
26.186 24.046
1.14 0.05
Local -0.196
Spain Euro Global -0.147 0.024
Local -0.063 4.925
UK Euro Global -0.063 -0.066 4.925 4.423 -1.800 1.747 -1.578
26.186 24.046
-1.14 0.05
55.509 -54.978 -59.908 32.084 -0.075 0.049 0.057 -1.16 -1.15 -1.14 0.02 0.03 0.06
-1.23 0.02
-1.23 0.02
-1.22 0.05
Notes: The table shows the coefficients from the skewness regression in eq. (3). The models are selected according to BIC. All coefficients are significant at the 1% level. For the remaining countries the results are available in the Appendix.
24
Table 4: Kurtosis Regressions
constant Local Factor 2 Euro Factor 5 US Factor 1 US Factor 4 2 (Local Factor 3) 2 (Local Factor 6) 2 (Euro Factor 5) Term Spread BIC R2
Local 3.155
-0.184 0.59 0.03
Germany Euro Global 3.222 3.222 -5.516 -5.516 6.322 6.322
-65.770 -65.770 -0.187 -0.187 0.60 0.60 0.06 0.06
Local 2.867
0.01 0.02
Spain Euro Global 2.867 2.867
0.01 0.02
0.01 0.02
Local 2.705
UK Euro Global 2.701 2.673
-50.955 75.538
-5.266 3.213 -53.038 47.627 85.053
-0.10 0.04
-0.11 0.03
-0.09 0.06
Notes: The table shows the coefficients from the kurtosis regression in eq. (3). The models are selected according to BIC. All coefficients are significant at the 1% level. For the remaining countries the results are available in the Appendix.
25
Table 5: Linear Regressions Using Different Factors Germany Cons Ret(-1) Vol Vol(-1) Sk Sk(-1) Ku Ku(-1) Adj R2
Raw Data 0.00 0.01 -0.61 *** 0.31 *** 0.02 0.04 -0.03 -0.10 * 0.24
Local Factors 0.01 0.08 -1.11 *** 0.73 *** 0.27 *** -0.08 -0.06 -0.12 ** 0.48
Euro Factors 0.01 0.05 -1.01 *** 0.62 *** 0.25 *** -0.07 -0.04 -0.14 *** 0.41
Global Factors 0.01 0.05 -0.36 *** 0.16 -0.03 0.02 -0.09 -0.11 * 0.11
Spain Cons Ret(-1) Vol Vol(-1) Sk Sk(-1) Ku Ku(-1) Adj R2
Raw Data 0.04 ** -0.06 -1.92 *** 0.49 0.04 -0.02 0.08 ** -0.01 0.14
Local Factors 0.00 0.15 *** -0.35 *** 0.19 * -0.76 *** 0.71 *** 0.02 *** -0.01 * 0.46
Euro Factors 0.05 *** -0.13 ** -2.29 *** 0.46 ** 0.06 -0.01 0.12 *** -0.03 0.48
Global Factors 0.04 *** 0.09 -1.72 *** 0.58 *** 0.01 0.01 0.06 *** -0.02 0.36
UK Cons Ret(-1) Vol Vol(-1) Sk Sk(-1) Ku Ku(-1) Adj R2
Raw Data 0.00 0.03 -0.68 *** 0.45 *** 0.01 -0.06 -0.11 0.08 0.27
Local Factors -0.01 0.38 *** -0.70 *** 0.45 *** -0.01 0.00 0.22 *** -0.01 0.32
Euro Factors -0.01 0.38 -0.62 0.36 -0.01 -0.02 0.22 -0.02 0.34
Global Factors -0.01 0.51 *** -0.29 *** 0.33 *** 0.06 -0.04 -0.06 0.11 0.36
Notes: The table shows the results from the regressions in eq. (3) using various restrictions on the factors in eq. (2). */**/*** indicates that the parameter is significant at the 10%/5%/1% level (based on bootstrapped errors). For the remaining countries the results are available in the Appendix.
26
Table 6: Benchmark Risk-Return Regressions Cons Ret(-1) Vol Vol(-1) Sk Sk(-1) Ku Ku(-1) Adj-R2 BIC
Austria 0.02 * 0.29 *** -1.39 *** 1.05 *** 0.02 *** -0.02 0.00 0.00 0.50 -0.43
Belgium 0.05 *** 0.32 *** -1.35 *** 0.94 *** 0.02 *** -0.01 -0.01 ** 0.00 0.52 -0.51
Denmark 0.03 * 0.24 *** -1.09 *** 0.44 *** 0.09 *** -0.04 *** -0.01 0.01 * 0.47 -0.44
Cons Ret(-1) Vol Vol(-1) Sk Sk(-1) Ku Ku(-1) Adj-R2 BIC
Ireland 0.06 ** 0.28 *** -1.33 *** 0.77 *** 0.03 *** 0.00 -0.01 0.00 0.42 -0.41
Italy Netherlands 0.01 0.14 *** 0.29 *** 0.22 *** -0.55 *** -1.27 *** 0.32 *** 0.91 *** 0.22 *** 0.05 *** 0.16 *** -0.02 0.00 -0.06 *** -0.06 0.02 * 0.45 0.35 -0.35 -0.32
Finland 0.13 *** 0.29 *** -0.39 *** 0.33 *** -0.18 *** 0.08 *** -0.01 -0.03 ** 0.25 -0.22
France 0.01 0.27 *** -0.63 *** 0.47 *** -0.14 0.00 -0.23 *** 0.08 0.34 -0.32
Germany 0.01 0.08 -1.11 *** 0.73 *** 0.27 *** -0.08 -0.06 -0.12 ** 0.48 -0.57
Spain Switzerland 0.05 *** 0.00 -0.13 ** 0.57 *** -2.29 *** -0.33 *** 0.46 ** 0.30 *** 0.06 -0.02 -0.01 0.00 0.12 *** 0.59 *** -0.03 -0.25 *** 0.48 0.62 -0.37 -0.86
UK -0.01 0.51 *** -0.29 *** 0.33 *** 0.06 -0.04 -0.06 0.11 0.36 -0.35
Greece 0.05 *** 0.19 ** -1.45 *** 0.73 *** -0.06 *** 0.03 -0.26 *** 0.07 ** 0.61 -0.85
Notes: The table shows the results from the regressions in eq. (3) and (4). */**/*** indicates that the parameter is significant at the 10%/5%/1% level (based on bootstrapped errors).
27
Table 7: Time-Varying Risk-Return Regressions with Interaction Variables Cons Ret(-1) Vol Vol(-1) REC REC*Ret(-1) REC*Vol REC*Vol(-1) TS TS*Ret(-1) TS*Vol TS*Vol(-1) SR SR*Ret(-1) SR*Vol SR*Vol(-1) VIX VIX*Ret(-1) VIX*Vol VIX*Vol(-1) DY DY*Ret(-1) DY*Vol DY*Vol(-1) Adj-R2 Wald test (REC) Wald test (TS) Wald test (SR) Wald test (VIX) Wald test (DY)
Austria 0.03 *** 0.20 -1.67 *** 1.06 *** -0.01 -0.17 * 0.38 -0.37 * -0.04 *** 0.26 *** -0.02 1.06 *** 0.03 *** -0.37 *** 0.13 -1.08 *** 0.01 -0.44 *** 0.48 ** -0.71 * 0.00 0.26 * -0.48 ** 0.44 0.60 3.4 *** 14.8 *** 7.1 *** 2.6 ** 2.5 **
Belgium 0.03 *** 0.32 *** -1.69 *** 0.53 ** 0.00 -0.01 -0.18 0.28 0.02 ** -0.32 *** -0.19 0.14 0.02 ** -0.14 0.00 -0.30 * -0.02 ** 0.16 * 0.29 0.47 ** -0.01 0.02 0.33 -0.19 0.57 1.1 7.8 *** 1.7 4.1 *** 0.5
Denmark 0.06 *** 0.13 -2.23 *** 0.70 -0.03 0.03 0.81 *** -0.22 -0.01 0.16 -0.03 0.36 0.01 -0.08 0.09 -0.41 0.02 -0.09 0.01 -0.27 -0.01 -0.25 ** 0.30 0.14 0.51 3.8 *** 2.5 ** 1.0 3.6 *** 4.8 ***
28
Finland 0.02 0.10 -0.72 * 0.56 0.00 0.02 0.80 -0.62 0.01 -0.13 0.20 -0.48 -0.01 0.25 ** -0.49 * 0.52 * -0.01 0.04 0.33 -0.33 0.00 0.11 0.48 -0.12 0.20 1.3 1.4 3.7 *** 1.1 3.8 ***
France Germany -0.01 -0.29 ** 0.25 * 0.09 -0.99 *** -1.56 *** 0.62 *** 0.43 ** 0.16 -0.02 0.03 -0.21 ** 0.33 ** 0.37 ** -0.35 ** -0.28 * 0.15 0.19 * -0.05 0.03 0.16 0.31 -0.19 0.14 -0.20 ** -0.01 0.07 -0.02 -0.18 0.14 0.12 -0.02 0.28 * 0.57 *** 0.08 -0.13 0.69 *** 0.32 * -0.05 -0.03 -0.48 *** -0.27 *** -0.24 ** 0.09 -0.34 * -0.06 -0.11 0.21 0.44 0.53 2.2 * 3.3 ** 1.1 2.3 * 1.8 0.5 3.9 *** 9.9 *** 7.2 *** 3.2 **
Greece 0.01 -0.21 -0.88 0.51 -0.10 ** 0.08 0.20 1.15 * 0.13 ** -0.24 -0.22 -1.16 0.04 0.39 ** -0.52 -0.02 0.00 0.07 -0.02 0.21 0.04 -0.08 -0.95 ** 0.25 0.32 1.4 1.5 2.8 ** 0.3 1.7
Cons Ret(-1) Vol Vol(-1) REC REC*Ret(-1) REC*Vol REC*Vol(-1) TS TS*Ret(-1) TS*Vol TS*Vol(-1) SR SR*Ret(-1) SR*Vol SR*Vol(-1) VIX VIX*Ret(-1) VIX*Vol VIX*Vol(-1) DY DY*Ret(-1) DY*Vol DY*Vol(-1) Adj-R2 Wald test (REC) Wald test (TS) Wald test (SR) Wald test (VIX) Wald test (DY)
Ireland 0.03 0.39 *** -1.83 *** 1.35 *** -0.01 -0.04 1.03 *** -0.81 ** 0.00 -0.12 -0.08 0.04 0.00 -0.04 0.34 -0.41 0.02 -0.16 0.40 -0.58 ** 0.01 0.05 -0.46 0.20 0.41 3.8 *** 0.5 1.4 2.4 ** 0.9
Italy Netherland Spain 0.69 *** 0.02 0.05 *** 0.10 0.86 *** 0.04 -0.14 -2.42 *** -1.68 *** 0.34 1.54 *** 0.43 -0.21 0.01 -0.01 0.24 * 0.21 0.18 -0.39 -0.83 *** 0.59 0.75 ** 0.41 * -0.10 -0.28 ** 0.01 -0.02 0.11 -0.04 0.05 -0.39 0.02 -0.18 0.05 0.11 0.63 * -0.03 0.02 ** 0.03 0.28 ** -0.47 *** -0.06 -0.58 * 0.16 0.11 0.10 -0.42 -0.09 -0.30 ** -0.01 -0.01 -0.08 -0.33 ** -0.12 -0.44 ** 1.34 *** 0.73 ** 0.08 -0.66 ** -0.07 -0.68 *** 0.01 0.05 ** -0.35 ** -0.59 *** -0.33 * 0.34 0.15 -0.99 ** -0.39 ** -0.29 -0.01 0.46 0.48 0.44 4.0 *** 4.6 *** 1.9 1.4 1.9 * 1.6 1.9 * 3.9 *** 1.6 2.2 ** 8.7 *** 8.8 *** 13.0 *** 4.2 *** 2.5 **
Switzerland 0.13 0.176 -0.447 * -0.094 -0.078 -0.033 0.101 -0.201 *** 0.136 0.269 ** -0.056 0.544 *** -0.225 ** 0.164 -0.076 0.056 0.016 -0.094 0.075 0.008 -0.299 *** 0.077 -0.244 * 0.238 ** 0.47 2.2 * 3.1 ** 2.2 * 0.3 4.2 ***
UK 0.13 0.54 *** -0.09 0.27 * 0.10 0.03 0.62 *** -0.37 *** 0.17 * 0.07 -0.18 * 0.03 -0.17 * -0.10 -0.20 -0.05 -0.15 -0.23 * -0.10 0.18 -0.30 *** 0.07 -0.34 0.10 0.38 2.3 * 2.2 * 1.7 1.6 4.0 ***
Notes: The table shows the risk-return regression including variaus interaction terms. */**/*** indicates that the parameter is significant at the 10%/5%/1% level (based on bootstrapped errors).
29
Table A1: Summary Statistics for Factors i 1 2 3 4 5 6
Austria AR1 %Acc 0.36 0.43 0.53 0.24 0.64 0.45 0.71 0.28 0.78 0.17 0.83 0.00
Belgium AR1 %Acc 0.39 0.44 0.55 0.25 0.64 -0.11 0.71 -0.03 0.78 -0.08 0.83 -0.02
Denmark AR1 %Acc 0.33 0.41 0.55 0.54 0.64 -0.25 0.71 -0.12 0.77 -0.23 0.82 0.06
Finland AR1 %Acc 0.40 0.35 0.56 0.62 0.64 0.05 0.71 -0.19 0.77 -0.16 0.83 0.00
France AR1 %Acc 0.20 0.38 0.74 0.54 0.13 0.62 0.13 0.69 -0.18 0.76 -0.07 0.82
Germany AR1 %Acc 0.37 0.32 0.48 0.46 0.11 0.57 -0.03 0.66 0.43 0.74 0.00 0.81
i 1 2 3 4 5 6
Greece AR1 %Acc 0.25 0.45 0.42 -0.09 0.55 0.15 0.65 0.02 0.74 0.19 0.81 -0.31
Ireland AR1 %Acc 0.60 -0.04 0.67 0.33 0.74 -0.55 0.79 -0.04 0.84 -0.41 0.87 -0.29
Italy AR1 %Acc 0.27 0.12 0.44 0.11 0.58 0.08 0.67 0.07 0.75 0.07 0.81 0.19
Netherlands AR1 %Acc 0.46 0.38 0.62 0.57 0.68 0.19 0.74 -0.09 0.80 -0.07 0.84 -0.01
Spain AR1 %Acc 0.38 0.28 0.51 0.32 0.62 -0.25 0.70 0.02 0.77 0.03 0.82 -0.10
Switzerland AR1 %Acc 0.33 0.80 0.50 0.38 0.61 0.28 0.70 0.32 0.77 0.04 0.82 0.14
i 1 2 3 4 5 6
UK AR1 %Acc 0.32 0.18 0.53 0.61 0.66 0.82 0.75 -0.09 0.80 0.43 0.84 0.07
Euro AR1 %Acc 0.40 0.22 0.55 0.87 0.66 0.10 0.74 0.21 0.80 0.03 0.85 -0.10
US AR1 %Acc 0.30 0.43 0.48 0.64 0.61 0.03 0.71 0.80 0.78 0.22 0.83 0.17
Notes: The table shows the summary statistics for the factors where AR1 is the first order autocorrelation coefficient and %Acc is the accumulated fraction of total variation in the data explained by factors.
30
Table A2: Return Regressions
constant Local Factor 1 Local Factor 2 Local Factor 3 Local Factor 4 Local Factor 5 Local Factor 6 Euro Factor 1 Euro Factor 2 Euro Factor 3 Euro Factor 4 Euro Factor 5 Euro Factor 6 US Factor 1 US Factor 2 US Factor 3 US Factor 4 US Factor 5 US Factor 6 (Local Factor 2)2 (Local Factor 3)2 (Local Factor 4)2 2 (Local Factor 6) 2 (Euro Factor 1) (Euro Factor 2)2 (Euro Factor 3)2 (Euro Factor 4)2 2 (Euro Factor 5) 2 (Euro Factor 6) 2 (US Factor 3) (US Factor 4)2 (US Factor 5)2 Term Spread Dividend Yield yt-1 BIC R2
Local 0.009
Austria Euro Global -0.014 -0.013
Local -0.004
Belgium Euro Global -0.005 -0.016
Local 0.008 0.340
Denmark Euro Global 0.003 -0.006
-0.391 0.404 -0.248 -0.264 0.200 -0.236 -0.455
-0.262
0.207
-0.328
-0.173 -0.304 0.277 -0.363 -0.386
-0.340 -0.395
0.152
-0.788 -0.260
-0.530
-0.603
0.322
0.296
0.285
0.359
0.430
-0.508
-0.509
-3.379
-3.202
-0.358 0.360 -0.361 -0.339 -0.737
0.155 -1.987 -2.504 -4.239
-2.936
-3.312
-1.677
-1.634
-1.656 4.202 -2.838
-2.017
0.006 -5.82 0.13
0.015
0.013
-5.89 0.30
-5.91 0.29
-6.02 0.08
31
0.005
0.007
-6.22 0.35
-6.25 0.36
0.005
0.010
1.797 0.009
-0.708 -5.92 0.21
-0.461 -6.13 0.36
-0.515 -6.12 0.38
constant Local Factor 1 Local Factor 2 Local Factor 3 Local Factor 4 Local Factor 5 Local Factor 6 Euro Factor 1 Euro Factor 2 Euro Factor 3 Euro Factor 4 Euro Factor 5 Euro Factor 6 US Factor 1 US Factor 2 US Factor 3 US Factor 4 US Factor 5 US Factor 6 (Local Factor 2)2 (Local Factor 3)2 (Local Factor 4)2 2 (Local Factor 6) 2 (Euro Factor 1) (Euro Factor 2)2 (Euro Factor 3)2 (Euro Factor 4)2 2 (Euro Factor 5) 2 (Euro Factor 6) 2 (US Factor 3) (US Factor 4)2 (US Factor 5)2 Term Spread Dividend Yield yt-1 BIC R2
Local -0.006
0.714 0.394 0.192
Finland Euro Global -0.007 -0.032 0.401
0.396
0.361 0.256
0.345 0.253
Local 0.007 -0.334 -0.267 0.546 -0.407 -0.509
France Euro Global 0.007 0.031 -0.334 -0.267 0.546 -0.407 -0.509
-0.206 0.542 -0.394 -0.495
Local -0.016 0.748 -0.743 -0.853 0.458
0.234
-0.226 0.558 -0.806
-0.545 0.577
0.494 -0.828
-2.426
-5.04 0.17
-2.941
-3.353
0.013
0.144 0.011
-5.17 0.31
-5.14 0.33
0.300 -0.424 -0.450
-0.488 -0.764
0.583 -0.668 -0.786
4.915
0.319 5.222
-0.624 0.561 -0.315
-0.276
0.008
Greece Euro Global -0.049 -0.038
-2.426
-2.108
-11.082 -13.139 -2.833 5.522 4.511
-0.271 -6.09 0.38
-0.271 -6.09 0.38
32
0.005 -0.010 -0.538 -6.18 0.47
-0.003 0.022 -0.406 -4.83 0.18
-0.003 0.021
0.014
-5.19 0.48
-5.21 0.49
constant Local Factor 1 Local Factor 2 Local Factor 3 Local Factor 4 Local Factor 5 Local Factor 6 Euro Factor 1 Euro Factor 2 Euro Factor 3 Euro Factor 4 Euro Factor 5 Euro Factor 6 US Factor 1 US Factor 2 US Factor 3 US Factor 4 US Factor 5 US Factor 6 (Local Factor 2)2 (Local Factor 3)2 (Local Factor 4)2 2 (Local Factor 6) 2 (Euro Factor 1) (Euro Factor 2)2 (Euro Factor 3)2 (Euro Factor 4)2 2 (Euro Factor 5) 2 (Euro Factor 6) 2 (US Factor 3) (US Factor 4)2 (US Factor 5)2 Term Spread Dividend Yield yt-1 BIC R2
Local 0.001
Ireland Euro Global 0.002 0.002
Local 0.014 0.206 -0.297
-0.374
Italy Euro Global -0.011 -0.016 -0.299
Netherlands Local Euro Global 0.009 -0.018 0.008 -0.207
-0.221
-0.410 -0.264 0.160
0.192
-0.204 -0.139 -0.413 0.419 -0.347 -0.498
-0.330 -0.870
-0.180 -0.188
-0.265
-0.213 -0.235 0.466 -0.493 -0.491
-0.427 0.470 -0.378 -0.491
-0.176 -0.313 0.503 -0.420 -0.572 -0.840
0.334 -0.437 -0.210
1.496
8.221 -2.720 4.468 1.618
6.968 -3.314 4.472 1.451
5.372
6.594
5.194 2.941 -2.410
-1.810
-2.016
8.262 -3.308 1.507 -2.901
-3.610 2.104
-0.008 -5.54 0.10
-5.77 0.37
-5.77 0.37
-5.48 0.10
-0.008 -0.126 -5.61 0.15
33
-0.009 -0.248 -5.49 0.20
0.008 -5.81 0.09
-6.18 0.44
-6.21 0.43
constant Local Factor 1 Local Factor 2 Local Factor 3 Local Factor 4 Local Factor 5 Local Factor 6 Euro Factor 1 Euro Factor 2 Euro Factor 3 Euro Factor 4 Euro Factor 5 Euro Factor 6 US Factor 1 US Factor 2 US Factor 3 US Factor 4 US Factor 5 US Factor 6 (Local Factor 2)2 (Local Factor 3)2 (Local Factor 4)2 2 (Local Factor 6) 2 (Euro Factor 1) (Euro Factor 2)2 (Euro Factor 3)2 (Euro Factor 4)2 2 (Euro Factor 5) 2 (Euro Factor 6) 2 (US Factor 3) (US Factor 4)2 (US Factor 5)2 Term Spread Dividend Yield yt-1 BIC R2
Switzerland Local Euro Global 0.037 0.040 0.039 0.268
0.329
-0.163 -0.373 -0.347 -0.147
-2.907
-3.082
-3.870
5.0313 -2.121
-1.434
1.107
-0.015 -0.0178
-0.014
-6.07 0.13
-6.13 0.16
-6.07 0.07
Notes: The table shows the coefficients from the return regression in eq. (2). The models are selected according to BIC. All coefficients are significant at the 1% level.
34
Table A3: Volatility Regressions
constant Local Factor 1 Local Factor 2 Local Factor 3 Local Factor 4 Local Factor 5 Local Factor 6 Euro Factor 1 Euro Factor 2 Euro Factor 3 Euro Factor 4 Euro Factor 5 Euro Factor 6 US Factor 1 US Factor 2 US Factor 3 US Factor 5 US Factor 6 2 (Local Factor 1) (Local Factor 2)2 (Local Factor 3)2 (Local Factor 4)2 2 (Local Factor 5) (Local Factor 6)2 (Euro Factor 2)2 (Euro Factor 3)2 (Euro Factor 4)2 3 (Euro Factor 5) 2 (Euro Factor 6) 2 (US Factor 1) (US Factor 3)2 (US Factor 5)2 2 (US Factor 6) VIX RVt-1 BIC R2
Local 0.010
Austria Euro Global 0.016 0.021 -0.132 -0.127
Local 0.005 -0.170
Belgium Euro Global 0.009 0.006 -0.143
0.099
0.102
-0.099 0.094 0.053 0.085 -0.115 0.098 0.101
0.117 -0.132 0.103 0.092
-2.547
-2.921
-0.059 -3.206
-1.780
-2.275
-2.047
0.658
0.880
1.480
1.525
0.061 0.094 0.067 0.109
0.078 0.093 0.223
-0.120 2.833
1.245
2.287
0.971 0.796
-0.112
Local 0.021 0.078 -0.087
Denmark Euro Global 0.018 0.018
-0.085
-0.078
0.077 -0.099
0.112 -0.098
0.101
0.094 0.250
-0.099 0.109
-0.058
2.067
0.986 1.005
2.331 2.086
2.579
0.679 1.251 1.193 0.890 -0.663 0.412 -7.95 0.59
0.472 -7.96 0.63
0.281 -8.00 0.70
2.554 1.908
1.138 1.109
0.088 0.475 -7.92 0.52
0.069 0.409 -8.01 0.63
35
0.081 0.386 -8.01 0.64
0.085
0.093
0.080
-8.02 0.53
-8.06 0.57
-8.08 0.61
constant Local Factor 1 Local Factor 2 Local Factor 3 Local Factor 4 Local Factor 5 Local Factor 6 Euro Factor 1 Euro Factor 2 Euro Factor 3 Euro Factor 4 Euro Factor 5 Euro Factor 6 US Factor 1 US Factor 2 US Factor 3 US Factor 5 US Factor 6 2 (Local Factor 1) (Local Factor 2)2 (Local Factor 3)2 (Local Factor 4)2 2 (Local Factor 5) (Local Factor 6)2 (Euro Factor 2)2 (Euro Factor 3)2 (Euro Factor 4)2 3 (Euro Factor 5) 2 (Euro Factor 6) 2 (US Factor 1) (US Factor 3)2 (US Factor 5)2 2 (US Factor 6) VIX RVt-1 BIC R2
Local 0.018
Finland Euro Global 0.015 0.026
Local 0.015
France Euro Global 0.014 0.019 0.059
Local 0.043
Greece Euro Global 0.063 0.064
0.053 -0.109 0.094
-0.140 0.107
0.124 0.122
-0.147 0.051 0.121
-0.130 0.086 0.153
-0.091
0.107 0.145 -0.172
-0.131
0.088
0.122
-0.107 -0.127 0.163 -0.124
-0.114 -0.127 0.209 -0.107
-0.193 0.207
-0.223 0.248 -0.176
1.534
1.569
2.451
2.669
1.035
0.991
-0.116 0.129 -0.113 -0.055
0.095 -1.994
-2.281
-1.874
0.976
1.053
1.604 0.676
1.559 0.685
1.876
-1.261
1.397 0.565
-0.579 2.621
1.698 -2.590 2.023 0.120 0.615 -7.21 0.62
0.133 0.593 -7.23 0.66
0.110 0.565 -7.23 0.66
0.085 0.246 -7.96 0.57
0.090 0.260 -7.94 0.58
36
0.086 0.176 -8.00 0.61
0.130 0.300 -7.07 0.46
0.088 0.247 -7.052 0.55
0.092 0.169 -7.10 0.60
constant Local Factor 1 Local Factor 2 Local Factor 3 Local Factor 4 Local Factor 5 Local Factor 6 Euro Factor 1 Euro Factor 2 Euro Factor 3 Euro Factor 4 Euro Factor 5 Euro Factor 6 US Factor 1 US Factor 2 US Factor 3 US Factor 5 US Factor 6 2 (Local Factor 1) (Local Factor 2)2 (Local Factor 3)2 (Local Factor 4)2 2 (Local Factor 5) (Local Factor 6)2 (Euro Factor 2)2 (Euro Factor 3)2 (Euro Factor 4)2 3 (Euro Factor 5) 2 (Euro Factor 6) 2 (US Factor 1) (US Factor 3)2 (US Factor 5)2 2 (US Factor 6) VIX RVt-1 BIC R2
Local 0.011
Ireland Euro Global 0.014 0.016
Local 0.019 0.098
Italy Euro Global 0.019 0.029 0.098 0.080 1.558
0.080
Netherlands Local Euro Global 0.005 0.018 0.018 0.130
0.093
-0.096
-0.112
-0.057
0.078
0.100
0.079 0.081
0.079 0.081
0.097 -0.119 0.108 0.098
0.144 -0.111 0.105 0.096
0.103 -0.143 0.151 0.098
0.103 -0.143 0.151 0.098
1.241
1.241
0.075 0.423 -7.98 0.71
0.075 0.423 -7.98 0.71
-0.095 -0.092 3.555 0.843 1.558 0.863
1.610
-1.521
0.916 0.697
0.966 0.068 0.506 -7.47 0.43
0.070 0.407 -7.485 0.51
0.067 0.293 -7.50 0.54
1.887 0.058 0.398 -7.56 0.40
0.058 0.398 -7.56 0.40
37
0.388 -7.59 0.42
0.101 0.429 -7.86 0.64
constant Local Factor 1 Local Factor 2 Local Factor 3 Local Factor 4 Local Factor 5 Local Factor 6 Euro Factor 1 Euro Factor 2 Euro Factor 3 Euro Factor 4 Euro Factor 5 Euro Factor 6 US Factor 1 US Factor 2 US Factor 3 US Factor 5 US Factor 6 2 (Local Factor 1) (Local Factor 2)2 (Local Factor 3)2 (Local Factor 4)2 2 (Local Factor 5) (Local Factor 6)2 (Euro Factor 2)2 (Euro Factor 3)2 (Euro Factor 4)2 3 (Euro Factor 5) 2 (Euro Factor 6) 2 (US Factor 1) (US Factor 3)2 (US Factor 5)2 2 (US Factor 6) VIX RVt-1 BIC R2
Switzerland Local Euro Global 0.006 0.012 0.017
-0.066
-0.158
1.767
1.780
-1.281 1.179
-2.180 1.442
-1.702 1.108
1.039
2.468 0.114 0.218 -7.67 0.37
0.084 0.221 -7.76 0.37
0.102 -7.78 0.43
Notes: The table shows the coefficients from the volatility regression in eq. (2). The models are selected according to BIC. All coefficients are significant at the 1% level.
38
Table A4: Skewness Regressions
constant Local Factor 1 Local Factor 2 Local Factor 6 Euro Factor 1 Euro Factor 4 Euro Factor 5 Euro Factor 6 US Factor 1 US Factor 2 US Factor 3 US Factor 4 US Factor 5 US Factor 6 (Local Factor 1)2 (Local Factor 2)2 (Local Factor 3)2 2 (Local Factor 4) 2 (Local Factor 5) (Local Factor 6)2 (Euro Factor 1)3 (Euro Factor 3)3 3 (Euro Factor 4) (Euro Factor 5)3 (Euro Factor 6)3 (US Factor 1)2 (US Factor 3)2 2 (US Factor 4) 2 (US Factor 5) (US Factor 6)3 Term Spread Dividend Yield VIX Skt-1 BIC R2
Local -0.110 2.613
Austria Euro Global -0.110 -0.151 2.613
2.261
Local -0.271
Belgium Euro Global -0.082 -0.082
4.783 -1.804
4.026 -2.229 2.531
Local -0.321
Denmark Euro Global 0.234 -0.139
4.026 -2.229 2.531 2.144 -3.131
-3.173
-2.606 38.035 55.716
48.265
48.265
29.720 28.326 0.878 -1.01 0.03
-1.01 0.03
-1.00 0.06
-0.88 0.10
-0.88 0.11
39
-0.88 0.11
1.065
-0.325 0.928
-0.91 0.04
-0.90 0.08
-0.93 0.06
constant Local Factor 1 Local Factor 2 Local Factor 6 Euro Factor 1 Euro Factor 4 Euro Factor 5 Euro Factor 6 US Factor 1 US Factor 2 US Factor 3 US Factor 4 US Factor 5 US Factor 6 (Local Factor 1)2 (Local Factor 2)2 (Local Factor 3)2 2 (Local Factor 4) 2 (Local Factor 5) (Local Factor 6)2 (Euro Factor 1)3 (Euro Factor 3)3 3 (Euro Factor 4) (Euro Factor 5)3 (Euro Factor 6)3 (US Factor 1)2 (US Factor 3)2 2 (US Factor 4) 2 (US Factor 5) (US Factor 6)3 Term Spread Dividend Yield VIX Skt-1 BIC R2
Local -0.020
France Euro Global -0.020 -0.020
Local -0.072
Finland Euro Global -0.070 -0.069
Local 0.091
Greece Euro Global 0.091 0.117
1.823 2.552 1.562 26.125
26.125
26.125
-28.888 -28.888 -27.956
-26.485 -26.485 -26.485
-26.989
-1.22 0.03
-1.22 0.03
-1.22 0.03
-0.78 0.01
40
-0.78 0.01
0.227 -0.98 0.08
0.227 -0.98 0.08
0.234 -0.96 0.12
constant Local Factor 1 Local Factor 2 Local Factor 6 Euro Factor 1 Euro Factor 4 Euro Factor 5 Euro Factor 6 US Factor 1 US Factor 2 US Factor 3 US Factor 4 US Factor 5 US Factor 6 (Local Factor 1)2 (Local Factor 2)2 (Local Factor 3)2 2 (Local Factor 4) 2 (Local Factor 5) (Local Factor 6)2 (Euro Factor 1)3 (Euro Factor 3)3 3 (Euro Factor 4) (Euro Factor 5)3 (Euro Factor 6)3 (US Factor 1)2 (US Factor 3)2 2 (US Factor 4) 2 (US Factor 5) (US Factor 6)3 Term Spread Dividend Yield VIX Skt-1 BIC R2
Local -0.074
Ireland Euro Global -0.499 -0.499
Local 0.015
Italy Euro Global -0.044 0.147
Netherlands Local Euro Global -0.288 -0.288 -0.140
2.357 -1.249 -3.170
-1.283
-3.170 -2.243 -2.891
101.985
23.712
43.015
43.015
51.565
51.565 17.775
-0.66 0.02
0.118
0.118
-0.047
-0.68 0.09
-0.68 0.09
-1.10 0.01
-0.061 -1.10 0.01
41
-1.08 0.04
1.037 -1.29 0.03
1.037 -1.29 0.03
-1.28 0.06
constant Local Factor 1 Local Factor 2 Local Factor 6 Euro Factor 1 Euro Factor 4 Euro Factor 5 Euro Factor 6 US Factor 1 US Factor 2 US Factor 3 US Factor 4 US Factor 5 US Factor 6 (Local Factor 1)2 (Local Factor 2)2 (Local Factor 3)2 2 (Local Factor 4) 2 (Local Factor 5) (Local Factor 6)2 (Euro Factor 1)3 (Euro Factor 3)3 3 (Euro Factor 4) (Euro Factor 5)3 (Euro Factor 6)3 (US Factor 1)2 (US Factor 3)2 2 (US Factor 4) 2 (US Factor 5) (US Factor 6)3 Term Spread Dividend Yield VIX Skt-1 BIC R2
Switzerland Local Euro Global -0.413 -0.413 -0.243 1.966
118.996
32.307
32.307
118.996 47.364 -24.996 0.051 1.003
1.003
-1.14 0.03
-1.14 0.03
-1.11 0.05
Notes: The table shows the coefficients from the skewness regression in eq. (2). The models are selected according to BIC. All coefficients are significant at the 1% level.
42
Table A5: Kurtosis Regressions
constant Local Factor 1 Local Factor 2 Local Factor 5 Euro Factor 2 Euro Factor 3 Euro Factor 4 Euro Factor 5 Euro Factor 6 US Factor 1 US Factor 4 US Factor 5 US Factor 6 (Local Factor 2)2 2 (Local Factor 3) (Local Factor 4)2 2 (Local Factor 5) (Local Factor 6)2 (Euro Factor 1)2 (Euro Factor 2)2 (Euro Factor 5)2 (Euro Factor 6)2 2 (US Factor 2) 2 (US Factor 3) VIX Term Spread Dividend Yield BIC 2 R
Local 3.274
Austria Euro Global 3.274 3.274
Belgium Local Euro Global 3.606 3.256 3.594 -20.044 -19.920 -19.307
Local 2.944
Denmark Euro Global 2.944 2.920
4.151 289.020 289.020 285.468
62.560 113.734 -38.012
93.196 55.126 -49.772
-0.166
-0.166
-0.166
-2.214 -0.172
0.44 0.02
0.44 0.02
0.44 0.02
0.59 0.11
43
-0.198
-2.114 -0.209
0.58 0.12
0.59 0.13
0.56 0.04
0.56 0.04
0.58 0.07
constant Local Factor 1 Local Factor 2 Local Factor 5 Euro Factor 2 Euro Factor 3 Euro Factor 4 Euro Factor 5 Euro Factor 6 US Factor 1 US Factor 4 US Factor 5 US Factor 6 (Local Factor 2)2 2 (Local Factor 3) (Local Factor 4)2 2 (Local Factor 5) (Local Factor 6)2 (Euro Factor 1)2 (Euro Factor 2)2 (Euro Factor 5)2 (Euro Factor 6)2 2 (US Factor 2) 2 (US Factor 3) VIX Term Spread Dividend Yield BIC 2 R
Local 3.057
France Euro Global 3.057 3.057
Local 3.230
Finland Euro Global
6.238
Local 3.305
Greece Euro Global 2.464 2.464
6.238 -5.075 6.410
-5.075 6.410
-65.612 -59.951 -59.951 #### #### #### -44.514 -44.514 -44.514
-0.122
-0.122
-0.122
0.13 0.02
0.13 0.02
0.13 0.02
0.87 0.01
0.86 0.04
44
0.86 0.04
2.695
3.237
3.237
-0.244 0.42 0.05
0.42 0.07
0.42 0.07
constant Local Factor 1 Local Factor 2 Local Factor 5 Euro Factor 2 Euro Factor 3 Euro Factor 4 Euro Factor 5 Euro Factor 6 US Factor 1 US Factor 4 US Factor 5 US Factor 6 (Local Factor 2)2 2 (Local Factor 3) (Local Factor 4)2 2 (Local Factor 5) (Local Factor 6)2 (Euro Factor 1)2 (Euro Factor 2)2 (Euro Factor 5)2 (Euro Factor 6)2 2 (US Factor 2) 2 (US Factor 3) VIX Term Spread Dividend Yield BIC 2 R
Local 3.373
Ireland Euro 3.380
4.716
5.214
6.061 -4.299
-4.482
-7.385
Global 3.169
Local 2.905 -6.372
Italy Euro Global 2.904 2.904 -6.380 -6.380
2.873
Netherlands Local Euro Global 2.346 2.346 2.982
2.873 3.436
-2.869
64.57
66.221
66.221
73.961 47.367 -0.076 0.98 0.03
-0.084 0.99 0.05
-0.087 1.01 0.08
-0.123 0.40 0.03
45
0.40 0.04
0.40 0.04
0.159 -0.04 0.03
0.159 -0.04 0.03
-0.02 0.05
constant Local Factor 1 Local Factor 2 Local Factor 5 Euro Factor 2 Euro Factor 3 Euro Factor 4 Euro Factor 5 Euro Factor 6 US Factor 1 US Factor 4 US Factor 5 US Factor 6 (Local Factor 2)2 2 (Local Factor 3) (Local Factor 4)2 2 (Local Factor 5) (Local Factor 6)2 (Euro Factor 1)2 (Euro Factor 2)2 (Euro Factor 5)2 (Euro Factor 6)2 2 (US Factor 2) 2 (US Factor 3) VIX Term Spread Dividend Yield BIC 2 R
Switzerland Local Euro Global 2.894 2.894 2.974
-8.642
57.967
57.967
0.52 0.01
0.52 0.01
0.52 0.02
Notes: The table shows the coefficients from the kurtosis regression in eq. (2). The models are selected according to BIC. All coefficients are significant at the 1% level.
46
Table A6: Benchmark Regressions Using Different Factors Austria Cons Ret(-1) Vol Vol(-1) Sk Sk(-1) Ku Ku(-1) 2 Adj R
Raw Data 0.02 * 0.12 -1.26 *** 0.77 *** 0.04 -0.03 0.02 0.01 0.15
Local Factors 0.05 ** 0.21 *** -0.79 *** 0.58 *** 0.00 -0.01 -0.03 0.01 0.41
Euro Factors 0.08 * 0.24 *** -1.07 *** 0.75 *** 0.00 0.00 -0.03 0.01 0.39
Global Factors 0.02 * 0.29 *** -1.39 *** 1.05 *** 0.02 *** -0.02 0.00 0.00 0.50
Belgium Cons Ret(-1) Vol Vol(-1) Sk Sk(-1) Ku Ku(-1) 2 Adj R
Raw Data 0.07 0.09 -1.41 0.85 0.00 0.02 -0.01 0.00 0.20
Local Factors 0.03 *** 0.33 *** -0.22 ** 0.16 * -0.01 ** 0.00 0.00 -0.01 *** 0.32
Euro Factors 0.05 *** 0.32 *** -1.35 *** 0.94 *** 0.02 *** -0.01 -0.01 ** 0.00 0.52
Global Factors 0.03 ** 0.33 *** -1.17 *** 0.86 *** 0.01 0.00 -0.01 * 0.00 0.39
Denmark Cons Ret(-1) Vol Vol(-1) Sk Sk(-1) Ku Ku(-1) Adj R2
Raw Data 0.06 0.04 -1.31 *** 0.68 *** 0.07 *** -0.02 -0.02 0.01 0.18
Local Factors 0.09 *** -0.07 -0.68 *** -0.08 0.00 0.00 -0.01 -0.01 * 0.32
Euro Factors 0.03 * 0.24 *** -1.09 *** 0.44 *** 0.09 *** -0.04 *** -0.01 0.01 * 0.47
Global Factors 0.05 ** 0.17 ** -1.12 *** 0.46 *** 0.08 *** -0.03 * -0.01 0.00 0.42
*** *** *** *
47
Finland Cons Ret(-1) Vol Vol(-1) Sk Sk(-1) Ku Ku(-1) Adj R2
Raw Data 0.21 *** 0.19 *** -0.13 0.02 0.02 -0.05 -0.01 -0.05 * 0.09
Local Factors -0.01 0.33 *** -0.06 0.04 -0.05 0.03 0.01 -0.01 0.10
Euro Factors 0.13 *** 0.29 *** -0.39 *** 0.33 *** -0.18 *** 0.08 *** -0.01 -0.03 ** 0.25
Global Factors 0.11 *** 0.30 *** -0.48 *** 0.49 *** -0.08 ** -0.03 -0.01 -0.03 ** 0.23
France Cons Ret(-1) Vol Vol(-1) Sk Sk(-1) Ku Ku(-1) Adj R2
Raw Data 0.00 0.00 -0.64 *** 0.38 *** -0.05 -0.12 * 0.05 -0.14 0.24
Local Factors 0.01 0.24 *** -0.56 *** 0.42 *** -0.15 -0.01 -0.27 *** 0.09 0.29
Euro Factors 0.01 0.27 *** -0.63 *** 0.47 *** -0.14 0.00 -0.23 *** 0.08 0.34
Global Factors 0.01 0.23 *** -0.67 *** 0.49 *** -0.11 -0.03 -0.14 0.00 0.34
Greece Cons Ret(-1) Vol Vol(-1) Sk Sk(-1) Ku Ku(-1) Adj R2
Raw Data 0.06 0.04 -1.60 0.69 -0.07 0.00 -0.22 0.01 0.30
Local Factors 0.06 0.18 ** -0.92 *** 0.24 -0.01 -0.02 -0.02 0.02 0.42
Euro Factors 0.19 *** 0.08 -1.52 *** 0.93 *** -0.04 0.00 -0.07 *** 0.02 0.35
Global Factors 0.05 *** 0.19 ** -1.45 *** 0.73 *** -0.06 *** 0.03 -0.26 *** 0.07 ** 0.61
*** *** ** ** ***
48
Ireland Cons Ret(-1) Vol Vol(-1) Sk Sk(-1) Ku Ku(-1) Adj R2
Raw Data 0.07 0.07 -1.47 0.74 0.04 0.03 -0.01 0.00 0.16
Italy Cons Ret(-1) Vol Vol(-1) Sk Sk(-1) Ku Ku(-1) Adj R2
Raw Data 0.00 0.10 -0.47 0.31 0.17 -0.08 0.04 -0.13 0.15
Netherlands Cons Ret(-1) Vol Vol(-1) Sk Sk(-1) Ku Ku(-1) Adj R2
Raw Data 0.18 -0.04 -1.71 1.22 0.03 -0.03 -0.05 0.00 0.25
* *** *** *
*** *** ** **
*** *** *** **
Local Factors 0.02 * 0.25 *** -0.53 *** 0.33 *** 0.02 0.00 0.00 0.00 0.20
Euro Factors 0.06 ** 0.28 *** -1.33 *** 0.77 *** 0.03 *** 0.00 -0.01 0.00 0.42
Global Factors 0.07 *** 0.24 *** -1.26 *** 0.73 *** 0.05 *** 0.00 -0.01 0.00 0.35
Local Factors 0.01 0.29 *** -0.55 *** 0.32 *** 0.22 *** 0.16 *** 0.00 -0.06 0.35
Euro Factors 0.00 0.35 *** -0.35 *** 0.21 * 0.02 0.26 *** 0.07 -0.01 0.31
Global Factors 0.00 0.31 *** -0.30 *** 0.08 0.03 0.19 *** 0.10 -0.08 0.24
Local Factors 0.06 *** 0.00 -0.25 ** 0.04 -0.02 0.03 -0.16 *** 0.14 *** 0.43
Euro Factors 0.06 0.16 * -1.52 *** 0.78 *** 0.17 *** -0.04 -0.06 0.06 0.39
Global Factors 0.14 *** 0.22 *** -1.27 *** 0.91 *** 0.05 *** -0.02 -0.06 *** 0.02 * 0.45
49
Switzerland Cons Ret(-1) Vol Vol(-1) Sk Sk(-1) Ku Ku(-1) Adj R2
Raw Data 0.00 0.02 -0.62 0.24 -0.08 0.23 0.19 -0.07 0.35
*** *** *** **
Local Factors 0.02 0.68 *** -0.29 *** 0.21 *** -0.09 * 0.15 *** -0.09 -0.05 0.54
Euro Factors 0.01 0.54 *** -0.56 *** 0.32 *** -0.08 0.16 *** -0.02 -0.06 0.54
50
Global Factors 0.00 0.57 *** -0.33 *** 0.30 *** -0.02 0.00 0.59 *** -0.25 *** 0.62
Table A7: Time-Varying Risk-Return Regressions with Skewness, Kurtosis, and Interaction Variables Cons Ret(-1) Vol Vol(-1) Sk Sk(-1) Ku Ku(-1) Rec Rec*Ret(-1) Rec*Vol Rec*Vol(-1) Rec*Sk Rec*Sk(-1) Rec*Ku Rec*Ku(-1) Term Term*Ret(-1) Term*Vol Term*Vol(-1) Term*Sk Term*Sk(-1) Term*Ku Term*Ku(-1) Short Short*Ret(-1) Short*Vol Short*Vol(-1) Short*Sk Short*Sk(-1) Short*Ku Short*Ku(-1) Vix Vix*Ret(-1) Vix*Vol Vix*Vol(-1) Vix*Sk Vix*Sk(-1) Vix*Ku Vix*Ku(-1) DY DY*Ret(-1) DY*Vol DY*Vol(-1) DY*Sk DY*Sk(-1) DY*Ku DY*Ku(-1) Adj-R2 Wald test Wald test Wald test Wald test Wald test
(Recession) (Term) (Short Term) (Vix) (DY)
UK 0.10 0.59 *** -0.25 0.34 ** -0.02 -0.13 0.51 ** 0.03 0.05 0.09 0.27 ** -0.14 0.21 -0.15 0.61 *** -0.27 0.16 0.07 -0.03 -0.04 0.10 0.11 -0.55 *** -0.08 -0.11 -0.12 -0.26 * -0.04 0.02 0.10 0.38 ** -0.29 * -0.15 -0.25 * 0.00 0.12 0.09 -0.08 -0.45 *** -0.15 -0.27 *** 0.04 -0.09 0.00 -0.05 0.08 -0.62 ** 0.48 ** 0.41 7.80 2.86 2.16 4.98 3.34
*** *** ** *** ***
Austria 0.05 *** 0.03 -1.78 *** 0.92 ** 0.01 0.04 * 0.03 -0.02 -0.02 * -0.04 0.62 ** -0.39 0.03 -0.05 0.02 -0.01 -0.04 *** 0.30 *** -0.16 1.36 *** 0.02 0.00 0.00 0.00 0.02 *** -0.19 0.16 -0.92 *** 0.00 -0.04 ** -0.02 0.02 0.00 -0.30 * 0.61 *** -0.61 0.01 -0.01 -0.03 0.01 0.01 0.18 -0.60 ** 0.30 -0.01 -0.02 -0.02 -0.05 ** 0.63 2.05 5.31 6.40 2.64 1.95
** *** *** *** *
Belgium 0.02 0.35 *** -1.99 *** 0.78 *** 0.04 * 0.00 0.00 0.00 0.03 -0.12 -0.06 0.06 -0.02 0.01 0.01 -0.02 * 0.02 -0.17 -0.26 0.25 0.02 -0.01 0.00 0.00 -0.01 -0.09 0.08 -0.21 0.01 -0.01 0.00 0.00 0.05 0.05 0.55 ** 0.06 -0.02 0.01 -0.01 *** -0.01 0.00 -0.06 0.43 * -0.30 -0.03 ** 0.01 0.00 0.00 0.58 1.61 3.71 *** 0.84 3.33 *** 1.11
51
Denmark 0.12 ** 0.20 * -1.79 *** 0.71 ** 0.11 ** -0.06 0.00 -0.03 ** -0.10 -0.06 0.74 *** -0.09 0.09 ** 0.00 -0.01 0.03 -0.06 0.13 0.14 -0.13 0.03 -0.03 0.00 0.02 -0.04 -0.05 -0.11 -0.02 -0.05 ** 0.00 0.00 0.01 0.09 ** -0.19 * -0.33 -0.79 * -0.01 0.03 -0.01 0.00 -0.03 -0.28 ** 0.13 -0.03 0.02 0.03 0.01 0.01 0.64 4.03 2.89 1.68 2.88 6.16
*** *** *** ***
Finland 0.27 *** -0.05 -0.89 ** 0.70 * 0.06 0.05 -0.03 -0.04 * 0.04 -0.12 1.17 ** -0.73 -0.13 -0.26 * -0.03 0.01 -0.13 * 0.07 0.43 -0.41 0.02 0.08 0.09 *** -0.05 ** -0.06 -0.12 0.36 *** -0.26 0.23 -0.19 *** 0.03 0.00 0.03 0.07 0.31 -0.26 -0.15 ** -0.02 0.01 0.00 -0.02 0.16 0.45 -0.13 -0.03 0.01 -0.04 * 0.05 ** 0.34 1.38 1.60 2.00 ** 0.80 1.79 *
France -0.08 0.22 -1.22 0.63 0.04 0.10 -0.25 0.15 0.14 -0.02 0.35 -0.56 -0.10 0.35 0.12 0.07 0.18 -0.09 0.14 -0.23 -0.06 0.27 -0.01 0.23 -0.17 0.09 -0.09 0.23 0.03 -0.17 0.14 0.04 0.34 0.05 0.63 -0.34 0.05 0.20 0.21 -0.33 -0.43 -0.15 -0.14 -0.09 -0.28 0.03 0.25 -0.21 0.55 3.81 2.66 1.60 9.18 3.77
*** *** *** *
*** *** ** * ** * ** *
*** *** ** ** *** ***
* * ** *** *** *** ***
Germany -0.37 *** 0.10 -1.32 *** 0.28 -0.09 0.06 0.14 0.06 -0.09 -0.26 ** 0.30 * -0.24 0.08 0.05 0.08 -0.12 0.34 *** 0.04 -0.26 0.44 *** 0.84 *** -0.17 -0.23 ** 0.02 0.01 0.04 -0.15 0.18 0.17 0.04 -0.16 * -0.06 0.54 *** -0.13 0.28 0.07 -0.11 -0.16 -0.01 -0.12 -0.29 *** 0.08 -0.10 0.24 * 0.09 -0.07 0.27 *** -0.02 0.64 3.38 6.98 1.57 6.67 4.69
*** *** *** ***
Cons Ret(-1) Vol Vol(-1) Sk Sk(-1) Ku Ku(-1) Rec Rec*Ret(-1) Rec*Vol Rec*Vol(-1) Rec*Sk Rec*Sk(-1) Rec*Ku Rec*Ku(-1) Term Term*Ret(-1) Term*Vol Term*Vol(-1) Term*Sk Term*Sk(-1) Term*Ku Term*Ku(-1) Short Short*Ret(-1) Short*Vol Short*Vol(-1) Short*Sk Short*Sk(-1) Short*Ku Short*Ku(-1) Vix Vix*Ret(-1) Vix*Vol Vix*Vol(-1) Vix*Sk Vix*Sk(-1) Vix*Ku Vix*Ku(-1) DY DY*Ret(-1) DY*Vol DY*Vol(-1) DY*Sk DY*Sk(-1) DY*Ku DY*Ku(-1) Adj-R2 Wald test Wald test Wald test Wald test Wald test
(Recession) (Term) (Short Term) (Vix) (DY)
Greece 0.02 0.22 -1.40 *** 1.13 ** 0.07 -0.08 -0.16 * 0.05 -0.04 0.59 ** 0.39 0.02 -0.01 0.05 -0.05 0.28 *** 0.18 *** -0.47 ** -0.54 -1.52 *** 0.01 0.02 0.08 0.00 0.05 -0.07 -0.03 -0.64 -0.08 0.07 -0.12 -0.04 0.00 -0.26 * 0.36 -0.30 -0.09 *** 0.09 *** -0.14 *** -0.03 -0.01 0.20 -0.35 0.33 -0.01 -0.02 0.02 -0.01 0.69 4.95 *** 9.45 *** 1.39 4.11 *** 1.03
Ireland 0.07 0.38 *** -1.47 *** 1.23 *** 0.10 *** 0.01 -0.01 0.00 -0.02 -0.11 1.33 *** -1.00 *** 0.04 0.01 0.00 0.00 -0.08 -0.16 -0.14 0.13 -0.04 * -0.01 0.02 ** 0.00 0.03 -0.04 0.11 -0.33 -0.04 -0.03 ** -0.01 0.00 0.05 -0.07 0.35 -0.46 * 0.03 0.02 -0.01 0.00 -0.04 0.00 -0.67 ** -0.04 -0.05 *** 0.02 0.01 0.01 0.49 4.05 1.86 2.45 1.79 2.42
*** * ** * **
Italy Netherland Spain Switzerland 0.44 *** -0.03 0.03 * 0.17 0.05 0.95 *** 0.01 0.31 ** -0.24 -2.31 *** -1.48 *** -0.13 0.04 1.69 *** 0.25 -0.25 * 0.02 0.07 * -0.07 0.04 0.12 -0.04 0.02 0.13 0.00 -0.02 0.01 0.74 *** -0.35 ** 0.03 0.04 -0.38 *** -0.38 ** 0.07 0.05 ** -0.07 -0.02 0.18 -0.02 -0.13 * -0.61 -0.48 ** 1.03 ** -0.09 0.77 ** 0.32 -0.98 0.01 0.31 -0.03 -0.24 *** -0.04 0.07 0.01 0.12 0.08 -0.15 0.01 -0.10 0.01 -0.50 *** -0.03 -0.02 -0.11 -0.26 ** 0.12 0.00 0.11 0.28 * -0.03 -0.01 0.16 -0.20 -0.08 -0.72 ** 0.07 0.11 0.02 0.09 0.26 ** -0.08 0.02 0.39 *** 0.06 -0.08 0.03 -0.27 *** -0.02 0.03 -0.01 0.06 0.13 -0.15 -0.03 -0.02 -0.03 0.06 0.12 ** 0.03 ** -0.08 0.16 -0.48 *** -0.16 0.31 ** 0.04 0.07 -0.93 *** -0.05 0.28 -0.31 -0.55 * 0.30 *** 0.06 -0.02 -0.05 0.11 0.05 -0.01 0.07 -0.03 -0.18 -0.01 0.06 * -0.26 ** 0.48 *** -0.02 0.01 0.09 -0.06 0.04 0.00 -0.15 0.04 -0.32 *** -0.10 -0.04 -0.48 *** 1.39 *** 0.21 0.00 0.32 ** -0.67 ** -0.23 0.16 0.14 -0.03 0.22 ** -0.23 *** -0.09 -0.01 -0.06 -0.10 0.05 -0.04 * 0.04 0.11 0.22 * 0.02 -0.01 0.04 -0.51 *** 0.04 0.00 -0.32 *** -0.22 -0.55 *** -0.04 0.02 0.39 * -0.01 -1.30 *** -0.10 -0.29 -0.22 1.53 ** 0.18 ** -0.13 0.02 0.14 -0.03 -0.02 0.03 0.01 -0.25 *** 0.15 -0.01 0.09 -0.06 0.18 0.00 -0.06 0.30 ** 0.54 4.13 1.29 3.52 2.53 5.67
*** *** ** ***
52
0.55 2.11 0.94 2.54 4.37 3.21
** ** *** ***
0.59 2.67 3.21 2.48 4.50 4.89
*** *** ** *** ***
0.67 0.69 1.28 2.75 *** 2.29 ** 4.64 ***
