Country-Specific Global Financial Cycle exposures and macroeconomic risk-return trade-off

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Country-Specific Global Financial Cycle exposures

and macroeconomic risk-return trade-off

University of Groningen

Faculty of Economics and Business

Msc Thesis

International Economics and Business

International monetary and financial economics

Student

Tizian Peukert

S2573865

Supervisor

Dr. Pieter IJtsma

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Abstract

The paper investigates individual country’s exposure to the Global Financial Cycle of 14 countries and relates it to their risk return trade-off. It implements the Common Factor Model to estimate a global price of risk from each country’s equity market index returns and 10-year sovereign bond returns. By using an iterative regression on individual countries’ output growth and output volatility, this study is able identify some countries, which exposure to the global price of risk significantly plays a role within the macroeconomic risk-return trade-off.

Key words: Global Financial Cycle, macroeconomic risk-return trade-off, exposure to global

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1. Introduction

Since the 1990s the international financial landscape has undergone a long-term trend of financial openness. Despite its changing landscape, according to Miranda and Rey (2015) the role of the United States as the epicentre of the international monetary system has mainly maintained its status. Along with that, emerging economies as well as developed economies have increasingly opened up with regard to financial flows (Rey, 2015). In turn, the degree to which capital flows furnish welfare gains or may injure the respective economy has expanded significantly since the 1990s. The transmission of exposure to the so called Global Financial Cycle into macroeconomic variables such as GDP per capita growth and GDP volatility is what motivates the relevance of this topic. As Adrian et al (2019) put it, integration into world capital markets may fuel growth, on the one hand, but may also lead to increased growth volatility since countries are increasingly exposed to fluctuations in the global price of risk. In other words, financial openness introduces the potential for a macroeconomic risk-return trade-off; the intensified financial integration might lead to both increased growth and risk (Adrian et al, 2019). Studies on the Global Financial Cycle (henceforth: GFC) have been growing since the after-math of the Global Financial Crises in 2008. Economists have - although not unanimously and even though hard to identify - proven the existence of the GFC. Nevertheless, the connection of the GFC with macroeconomic variables, has been an unoccupied terrain until the study of Adrian et al (2019).

This is why, this study aims to inspect the macroeconomic risk-return trade-off between output growth and output volatility and to combine it with county-specific exposure to the GFC. This leads to the following research question:

Does country-specific exposure to the Global Financial Cycle have an effect of GDP growth and GDP volatility and does it affect the macro-economic risk-return trade-off between GDP volatility and growth?

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relation between GDP growth and GDP volatility. In this regard, Adrian et al (2019) are pioneering to find a systematically positive relationship on a cross-sectional dataset. The true novelty, however, is that the authors present how cross-sectional exposure to the GFC into this macroeconomic risk-return trade-off (2019). That being said, other studies have also found theoretical proof for a positive macroeconomic risk-return relationship (Ranciere et al, 2008), however, excluding the connection with exposure to the global price of risk. In contrast, Ramey and Ramey (1995) and Ademoglu et al (2003) find evidence for a negative relationship between GDP growth and GDP volatility. These differences in findings stem from the selection of countries as well as time-period. Specifically, Adrian et al (2019) consider a set of developed countries and fairly advanced emerging markets, and a time period from 1995 onwards. Consequently, this study at hand aims validate the positive relation between GDP growth and GDP volatility and for which countries specifically, this is the case.

Secondly, this study tests if country-specific exposure to the Global Financial Cycle has an effect on GDP growth and GDP volatility. To do so, this research employs a Common Factor Analysis on monthly end-of-month equity market index returns of 14 countries, as well as 10-year sovereign bond returns of the same 18 countries.1_{These countries have been chosen, since} they represent the worldwide development of financial integration and are distributed across continents in the following way: Europe (9), Asia (2), North-America (2), Oceania (1). Furthermore, this sample of countries was chosen, since they are part of the Adrian’s et al (2019) sample. Via the Common Factor Analysis the underlying structure of country-specific asset returns2_{is extracted, which forms the so-called the global price of risk. The global factor} of risk is necessary to identify the country-specific asset return exposure to the GFC. In turn, this allows us to draw implications on the effect of country-specific asset return exposures on GDP growth and GDP volatility. This is why, this paper also identifies for which of the 14 countries the exposure to the GFC has an effect on GDP volatility and GDP growth.

Thirdly, this papers aims to identify whether country-specific exposure to the Global Financial Cycle has an actual effect on risk-return trade-off that GDP growth and GDP volatility poses. To this end, interaction variable between GDP growth and country-specific exposure is constructed. Adrian et al (2012) has found that countries with higher exposure to the global price of risk tend to growth faster, which, however, comes at the cost of higher GDP volatility.

1_{List of countries enclosed in Appendix B}

2_{Asset returns = monthly end-of-month equity market index returns of 14 countries, as well as 10-year sovereign}

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Thus, this research intends to do this per country and therefore uses a part of the sample used by Adrian et al (2019).

The contribution of this research comprises thus an extension to the examination of country-specific risk-return trade-off, and thus how individual countries’ exposure to the GFC feeds into growth and volatility as well as the possible effect of country-specific exposure to the GFC. First, with regard to the risk-return trade-off, Adrian et al (2019) find a systematically positive relationship. The novelty, however, is that the authors present how cross-sectional exposure to the GFC into this macroeconomic risk-return trade-off. That being said, previous research has also found theoretical proof for a positive macroeconomic risk-return relationship (Ranciere et al, 2008), however, excluding the connection with exposure to the global price of risk (= exposure to the GFC). In contrast, Ramey and Ramey (1995) and Ademoglu et al (2003) find evidence for a negative relationship between GDP growth and GDP volatility. These differences in findings stem from the selection of countries as well as time-period. Specifically, Adrian et al (2019) consider a set of developed countries and fairly advanced emerging markets, and a time period from 1995 onwards. Secondly, and more importantly, Adrian et al (2019) form the only study that detects a significant risk-return trade-off; namely, countries with higher exposure to the global price of risk relates positively to macroeconomic risk and growth. What is not identified yet is for which of those countries specifically the exposure to the GFC plays into the macroeconomic risk-return trade-off. Therefore, this paper seeks to establish for which of those countries is the macroeconomic risk-return trade-off relatively high and how country-specific exposure to the global price of risk plays into the growth-risk trade-off individually. Since we have chosen the time period from 1999-2018, similarly positive relationship between output growth and volatility is expected as in Adrian et al (2019). Therefore, this paper at hand contributes to the existing literature on the GFC by connecting country-specific asset return exposures to the GFC with the relationship between GDP volatility and GDP growth

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2. Literature Review

This paper aims connect specific macroeconomic variables with country-specific variables of financial integration. More country-specifically, this study wishes to identify what effect does country-specific exposure to the Global Financial Cycle on the relationship between output growth and volatility. As a result, the relevant previous literature comprises on the one hand, the macroeconomic relationship between GDP growth and GDP volatility and, on the other hand, the study of the so-called Global Financial Cycle.

To begin with, previous research documents both a positive as well as negative relationship between GDP growth and GDP volatility, which appears to be dependent on time period and the set of countries under study. First, less recent studies such as from Ramey and Ramey (1995) as well as Acemoglu et al (2003) find evidence for a negative relation between volatility and growth. On the contrary, a group of more recent studies finds strong evidence for the positive relation between growth and volatility. These include: Acemoglu and Zilibotti (1997), Frankel and Romer (1999), Ranciere et al (2008), Giovanni and Lavchenko (2009), as well as Adrian et al (2019). For instance, Acemoglu and Zilibotti (1997), find evidence for a positive relationship between growth and volatility, since the completion of markets precede growth. This means, economic development is accompanied by financial development, which is guided by their theory of market incompleteness. To be specific, the authors show that higher income tends to go hand in hand with lower subsequent output volatility (Acemoglu and Zilibotti, 1997). Further, Frankel and Romer (1999) as well as Giovanni and Lavchenko (2009) indirectly find a positive relation between growth and volatility through trade openness. Particularly, Giovanni and Lavchenko (2009) provide evidence for a positive relationship between trade openness and volatility; sectors that are relatively more open to international

trade tend to be more volatile (Giovanni and Lavchenko, 2009). Similarly, Frankel and Romer

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free rate for holding assets that increase their exposure to systematic market risk3_{(Adrian el al,} 2019). Moreover, their findings suggest that countries with higher exposure to the global price of risk tend to grow faster at the costs of more volatile GDP; this positive relation between growth and volatility has been addressed ‘risk-return trade-off’. This means, the study of Adrian

et al (2019) provides an adequate point of intersection between studies of the Global Financial

Cycle (henceforth GFC) and studies on the risk-return trade-off. Countries that tend to grow faster, do so at the cost of relatively more volatile GDP. As mentioned above differences in findings stem from different time periods the set of countries under study. In more recent periods the importance of international capital flows has increased, which subsequently, give countries the opportunity to grow faster, but at larger macroeconomic risk. Considering most recent literature, the time period in focus – 1999 to 2018, as well as the set of countries, this research aims to confirm the risk-return trade-off. This yields the following first hypothesis:

Hypothesis 1:there is a positive relation between GDP growth and volatility

The second part of relevant literature deals with the proof of existence and with the identification of the so-called Global Financial Cycle (GFC). The ambiguity of the GFC explains the need for proving its very existence. For instance, according to Certutti et al (2017) the global financial cycle is an intrinsically unobservable variable which complicates its identification and quantification. For the sake of clarity one need to define the concept of financial cycles before starting to define the GFC.

To begin with, in order to define the global aspect of financial cycles one first needs to look at the concept of financial cycles and how to understand them. Research on the financial cycle such as from Borio et al (2018) has identified two important features of it. Firstly, they point out that peaks of the financial cycle go along with financial stress or even banking crises. The self-reinforcing interaction of financing constraints, asset prices and risk-taking can lead to extensively large balance sheets, which make them more vulnerable to a subsequent financial contraction. Secondly, financial cycles tend to be longer than the business cycle (Borio et al, 2018).

After financial cycles, one needs to start defining the concept of the Global Financial Cycle, before comparing existing studies about it: There are two main characteristics about the

3_{Systematic risk refers to the risk that endogenous to the entire financial market. This kind of risk cannot be}

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Global Financial Cycle: (1) association with co-movements of asset prices, gross flows and leverage and (2) the transmission of US monetary policy across the globe. For instance, Rey (2015) argues that the global financial cycle is characterised by co-movements in asset prices, gross flows and credit flows, but also that this cycle relates to monetary conditions which are set in the epicentre monetary policy (namely the United States). The first characteristic, according to Rey (2015) is based on the pro-cyclicality of credit flows and asset prices. The latter characteristic functions via the credit channel as well as the risk-taking channel of monetary policy: Bernanke and Gretler (1995) define the credit channel in the following way:

“Expansionary monetary policy leads to an increase in the net-worth of borrowers, which in turn leads to an increase in lending.” Studies on the risk-taking channel (Borio and Zhu, 2012)

argue that loose monetary policy relaxes leverage constraints for financial intermediaries. According to Miranda-Agrippino (2015) and Rey (2015) channels reinforce each other. Similarly, Borio, Drehman and Xia (2018) refer to the “financial cycle” as the self-reinforcing interactions between perceptions of value and risk, risk-taking and financing constraints (also, Borio, 2014). This means, as credit increases rapidly, typically property and asset prices increase, which leads to increased collateral values and subsequent lending to the private sector. This process is argued to function in both directions. In short, what the majority of studies on the GFC agree upon is the strong association of pro-cyclical movements of asset prices and credit as well as the transmission mechanism of monetary policy in the centre country. Notably, these two characteristics of the GFC do not stand in contrast to each other, but they reinforce each other.

Even though inseparable, these two definitions of the GFC feed into two different methods examining its very existence on the one hand and its drivers on the other. Firstly, one stand of analysis, according to Cerutti et al (2017), captures a traditional ”push-pull” analysis. More concretely, this refers to the kind of studies which aims to explain capital flows with global “push” (origin country) and “pull” (recipient country) factors. Secondly, the other state of the art analysis is aimed at proving the existence of the Global Financial Cycle by examining the degree of commonality in global financial developments including capital flows, credit creation, and domestic asset prices, using factor models and structural time-series models.

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worsening in global risk conditions, typically measured by an increase in the VIX4_{, is} accompanied by lower capital flows. One example of this stand provides the publication of the ECB (Habib and Venditti, 2018), which identifies the drivers of the GFC and characterises them into transmission channels. The authors pinpoint US monetary policy as well as keenness of general risk aversion of market actors as the two main potential drivers of the GFC. Another example, poses the research of Miranda-Agrippino and Rey (2015), who find evidence for a global factor that explains up to a quarter of the variance of a large cross-section of risky returns. Spcifically, Miranda-Agrippino and Rey (2015) find proof for powerful financial spill-overs of the monetary policy of the hegemon to the rest of the world. In other words, US Federal reserve policy does not only affect the domestic business cycle, but also movements in international financial variables. In turn, this displays the powerful transmission channel of US monetary policy across borders via financial conditions that are reflected in asset prices, leverage of banks, risk premia and volatility. So, the authors conclude that the monetary policy of the hegemon influences aggregates risk appetite in international financial markets. However, as mentioned above, some studies regard the relevance of the global financial cycle as doubtful. Particularly, “How important is the global financial cycle? Evidence from Capital Flows” by Cerutti, Claessens and Rose (2017) use two approaches in order to quantify the GFC: Firstly, the VIX, similar to Rey so that time varying changes in volatility in the largest financial markets are included. In contrast to Rey’s research (2015), the authors only find limited evidence for the existence of the global financial cycle, since less than a quarter of the variation in observed cross-border flows can be explained by the global component. Therefore, the relevance of the GFC is in doubt at this point. Amiti et al (2019) while conducting a similar analysis, are able to draw a more distinct picture; the authors narrowed the focus to the global component in cross-border banking flows and find that the relevance of this global factor depends on the state of the global economy: While in good times, banks flows are well explained by the global factor, in crisis periods, namely the period following the global financial crisis, country and bank specific factor would dominate the global factor. Thus, the results remain ambiguous about the impact of the US monetary policy. On the one hand, capital flows are found to respond nonlinearly to US monetary policy such as found in Adrian et al (2019) between bond and equity flows. On the other hand, monetary variables are not always significant or do not have the consistently the same sign (e.g. Cerutti et al, 2017).

4_{VIX: represents the volatility of the United States’ stock market index, which is often being referred to as so}

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Secondly, the other, more recent method aiming to identify the existence of the Global Financial Cycle investigates co-movements in global financial developments such as capital flows, credit creation, asset price returns by utilising factor models or structural times-series models (which include variations of Vector Auto-regression). The most prominent examples of this second and more recently used method are the studies by Rey (2015) as well as Miranda-Agrippino and Rey (2015). Specifically, Rey (2015) finds negative correlations between different types of capital flows and the VIX. By implementing the principle component analysis, the author documents the presence of a large single common factor among various asset prices (850) of across the globe. The estimated first common factor delivers a relatively high negative correlation with the VIX (Rey, 2015). She then uses the Vector Autoregression (VAR) to illustrate the dynamic relationship between monetary policy of the US with the VIX, bank leverage, capital flows and credit. Her findings suggest that monetary policy in the centre country (USA) functions as important determinant of the Global Financial Cycle, since it affect leverage of global banks, credit flows and credit growth in the international financial system (Rey, 2015). Another study that considers the relevance of certain time period for the GFC is conducted by Jorda et al (2019), which argue that the co-movement in credit, house prices and equity price reached their historical heights in that past couple decades. The authors find strong evidence that co-movement in equity prices started exceeding real sector integration after 1990 and that the common market responses to US monetary policy drive this process. This research at hand, belongs thus to the latter stand of method, since it examines the underlying structure of the asset returns.

Lastly, up until recently is the connection between the GFC and macroeconomic variables: to that end, Adrian et al (2019) estimates of the global price of risk and connects it to country’s exposure to it with macroeconomic outcomes. They find that exposure to the global financial cycle bring a trade-off with it: higher exposure means higher output growth on the one hand, but also higher output volatility. Additionally they show that the transmission of the global price risk to macroeconomic outcomes can be reduced via stabilisation policies. This is why, the authors argue, macroeconomic policies should not be separated from policies that affect the stability of financial markets. Since the link between the Global Financial Cycle and macroeconomic outcomes has not been elaborately focussed on, except for the study by Adrian

et al (2019), this study seeks to intensify this corner of the Global financial Cycle. This is why

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13 Hypothesis 2: country-specific exposure to the GFC has an effect on GDP growth and GDP volatility

Hypothesis 3:country-specific exposure to the GFC has a alter the relationship between GDP growth and GDP volatility

3. Data Analysis

3.1 Data

The sample comprises a dataset of 14 countries and their monthly end-of-the month market index returns of 14 countries and 10-sovereign bond returns, which yields a total of 28 asset returns. All stock and bond returns are converted into USD and extracted from

investing.com and yahoo-finance.com and fred.stlouisfed.org. When an index is to be found

from multiple sources, then the one with longer historical data. This way, for all the 14 countries during the period from the beginning of 1999 to the end of 2018 the sample is with the exception of a few bond returns5_{. The list of countries and their equity market indices is enclosed in} Appendix B. Secondly, in order to connect this with macroeconomic outcomes, GDP growth (expenditure product) are collected from OECD for 14 countries. This growth rate is seasonally adjusted and expresses growth rate compared to previous quarter. Consequently, since the asset returns are monthly recorded and GDP growth and the standard deviation (GDP volatility) comprise quarterly data, GDP growth and GDP volatility are aggregated across months.

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3.2 Data Analysis

In this section we want to take a closer look at the data collected in order to access the adequacy of the data for the regression and principle component analysis. Firstly, the asset returns which comprise monthly end-of-the month market index returns of 14 countries and 10-sovereign bond returns, which yields a total of 28 asset returns are examined. Specifically, this part inspects how these asset returns move over time during the last two decades and how they correlate with one another. Secondly, Scatter matrices in Appendix D indicate in how far the suggested regression is plausible and whether the data is suitable for the respective regression. To start off, the collected data with respect to asset returns (equity and bond returns) indicate a first glance on some common movements as well as correlation. When we look at Figure 3a, which presents the country-specific equity returns over the period of 1999 to 2018, considerably high co-movements of the different market indices can be observed. For instance, major (negative) peaks are clearly illustrated by all the market indices. This is especially the case for the Global Financial crisis in 2008, but also after the burst of the dot-com bubble after 2002. A similar but much less volatile picture is being painted by the behaviour of bond returns in figure 3b. Striking are the outliers of Hong Kong and Australia.

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15 Figure 1b: Country-Specific 10-year sovereign bond returns over 1999-2018

Additionally, in order to validate a possible common factor in asset price movements and also in order to set the stage for the Principle Component Analysis one needs to examine the correlations between all of those asset returns. This is important since the PCA uses unities in the diagonal of the correlation matrix, which computationally implies that all the variance is common. The correlation matrix (enclosed in Appendix C) displays considerably significant correlations between asset price returns display significant correlations between the equity and bond returns. This is especially the case for equity returns. For instance, the first difference of the DAX (the German equity market index) correlates 81% with the S&P 500 (Equity market index of the US) and the FTSE100 (Equity market index of the UK). Considering that the GFC is characterised by co-movements in asset prices, these significant correlations as well as the similarities in movements of these asset prices provide promising illustration of an underlying structure. Following then the same method employed by Rey (2015), this underlying structure will be estimated using the Principle Component Analysis and the Common Factor Analysis.

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variable GDP volatility for each of the 14 countries in the sample. One can observe a positive relation between output growth and output volatility for nearly all the countries, since high (low) values of GDP growth are associated with high (low) values of GDP volatility. The exceptions are Hong Kong (China), Sweden and United States, where the relationship is less clearly visualised. Still, this shows the adequacy of the data for testing the relationship between GDP volatility and GDP growth.

4. Methodology

4.2. Risk exposure and Risk-Return Trade-off

This model examines the relationship between individual country´s macroeconomic risk-return trade-off and checks whether adding each countries exposure to the GFC changes this relationship. Since this regression has been previously performed by Adrian et al (2019) on a cross-sectional dataset, the method performed per country follows a similar regression. The authors regress GDP volatility against GDP growth and each country´s exposure to the global price of risk across sections.

To begin with, the method of the paper at hand also tests the relationship between GDP volatility and GDP growth, and connects each country’s exposure to the global price of risk to this relationship. This way, one can infer on the effect of global risk exposure on growth and GDP volatility per country. In addition, this model also tests whether adding exposure to bond and equity affects the risk-return trade-off that GDP growth and volatility poses. To do so, two interaction variables are included which consisting of:

1) Country-specific GDP growth and exposure of equity return to the GFC 2) GDP growth and exposure of bond return to the GFC

3)

Therefore, the subsequent regression subject to this research yields:

𝑦𝑐,𝑡= 𝛼0+ 𝛽1𝛥𝐺𝐷𝑃𝑐,𝑡+ 𝛽2𝑒𝑥𝑝𝑐,𝑡𝑒𝑞𝑢𝑖𝑡𝑦+ 𝛽3𝑒𝑥𝑝𝑐,𝑡𝑏𝑜𝑛𝑑+ 𝛽4𝛥𝐺𝐷𝑃𝐸𝑋𝑃𝑐,𝑡𝑒𝑞𝑢𝑖𝑡𝑦+ 𝛽4𝛥𝐺𝐷𝑃𝐸𝑋𝑃𝑐,𝑡𝑏𝑜𝑛𝑑+ 𝜀𝑐,𝑡. (3.1)

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a measure of macroeconomic risk in this model. Second, 𝛥𝐺𝐷𝑃𝑐,𝑡 refers to the logged GDP growth rate of country c during time t (quarterly over 1999-2018, and monthly aggregated), which represents the measure of macroeconomic return. Consequently, GDP volatility and GDP growth represent the macroeconomic risk-return trade-off that built the basis for this model. This model was employed by Adrian et al (2019) to identify the positive relation between GDP volatility and GDP growth.

Thirdly, 𝑒𝑥𝑝_𝑐,𝑡𝑒𝑞𝑢𝑖𝑡𝑦 denotes the exposure of equity market return of each country c to the GFC during time t, and fourth, 𝑒𝑥𝑝_𝑐,𝑡𝑏𝑜𝑛𝑑_{is the exposure of bond returns of each country c to} the GFC during time t (monthly, 1991 – 2018). These two measures are added to the equation to examine the effects of exposure on GDP growth and GDP volatility, and are constructed as

𝑒𝑥𝑝_𝑐,𝑡𝑒𝑞𝑢𝑖𝑡𝑦 = 𝑓_1,𝑡∗ 𝑒𝑞𝑢𝑖𝑡𝑦_𝑐,𝑡 (3.2) 𝑒𝑥𝑝_𝑐,𝑡𝑏𝑜𝑛𝑑_{= 𝑓}

1,𝑡∗ 𝑏𝑜𝑛𝑑𝑐,𝑡, (3.3)

where 𝑒𝑥𝑝_𝑐,𝑡𝑒𝑞𝑢𝑖𝑡𝑦 is the product of each country´s equity market index return and the global price of risk (𝑓_1,𝑡), and 𝑒𝑥𝑝_𝑐,𝑡𝑏𝑜𝑛𝑑_{is the product of each country´s 10-year sovereign bond return} and the global price of risk factor (𝑓1,𝑡). The global price of risk is estimated via the Common Factor Model, which is elaborated in section 3.2. Adding the bond and equity exposure indicates the effect on GDP growth and volatility.

Lastly, the interaction terms 𝛥𝐺𝐷𝑃𝐸𝑋𝑃_𝑐,𝑡𝑒𝑞𝑢𝑖𝑡𝑦 and 𝛥𝐺𝐷𝑃𝐸𝑋𝑃_𝑐,𝑡𝑏𝑜𝑛𝑑_{of GDP growth with} country specific equity and bond exposure may indicate an indicate a possible effect on the risk return trade-off.

𝛥𝐺𝐷𝑃𝐸𝑋𝑃𝑐,𝑡𝑒𝑞𝑢𝑖𝑡𝑦= 𝛥𝐺𝐷𝑃𝑐,𝑡∗ 𝑒𝑥𝑝_𝑐,𝑡𝑒𝑞𝑢𝑖𝑡𝑦 (3.4)

𝛥𝐺𝐷𝑃𝐸𝑋𝑃_𝑐,𝑡𝑏𝑜𝑛𝑑 ₌_{𝛥𝐺𝐷𝑃}

𝑐,𝑡∗ 𝑒𝑥𝑝𝑐,𝑡𝑏𝑜𝑛𝑑 (3.5) The two interaction terms are constructed as a product of their respective country specific exposure to the global price of risk and the (logged) GDP growth rate. Here it is important to mention that the asset returns contain monthly data, whereas output growth consists of quarterly data. Therefore, the growth rate is aggregated across months (such that 1 quarter growth rate equals 3 months).

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4.3 Common Factor Model for country-specific market returns

The GFC is often being described as ´global price of risk´ (Adrian et al, 2019) or ´global

factor of risk´ (Miranda-Agrippino and Rey, 2015). The literature investigating this issue has

hitherto used Dynamic Factor Model aimed at identifying the underlying structure of asset price movements allowing different global, regional and, in some specification, sector specific factors. The rationale behind this econometric approach is to both define and quantify a single global factor capable of explaining a significant portion of the common variation in asset price movements. For instance, Miranda-Agrippino and Rey (2015) find one global or common factor that explains a large part of the common variation among risky asset prices traded around the global. This study at hand employs the Common Factor Model, since the it is aimed to identify one common factor that explains the underlying structure the asset returns of the 14 countries in the sample (list of countries and their equity market indices enclosed in Appendix B). We thus define the common factor, also referred to as “global price of risk”, which explains a large proportion of the variation of the asset returns. Using a similar methodology employed Miranda-Agrippino and Rey (2015) the same line of reasoning is applied to the present research. Our method to produce n common factors is finalised to identify one global factor that explains the underlying structure of asset returns and can be described as follows: in order to estimate the ´global´ factor of the collected asset returns a Principle Component Analysis (PCA) is conducted on the first differences on the country-specific asset returns at first, which secondly leads the way to the Common Factor Analysis.

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to be conducted correctly, a number of assumptions need to be fulfilled regarding the size of the sample, which comprise: the correlation of the variables, their linearity of the variables and the outlier’s sensitivity. First, regarding the size of the sample it exceeds the requirement by of at least 150 cases, since this sample includes 18 countries over 20 years (monthly) which yields 4320 cases. Secondly, the correlation matrix enclosed in Appendix C indicates several significant correlations between country-specific equity and bond returns. This is important since the PCA uses unities in the diagonal of the correlation matrix, which computationally implies that all the variance is common (Jolliffe, 2002). Thirdly, it is assumed that the relationships between the variables are linearly related. In this regard, the scatter matrices on (Appendix D, Figure 1 and Figure 2) illustrate linear relationships, the equity returns more so than bond returns. Lastly, that load below .15 are excluded from the sample due to the sensitivity of PCA for outliers. In turn, the data on asset returns fulfils the assumptions to perform a PCA. The respective Principle Component Analysis employed under the example of Rey (2015) extract the underlying structure of asset return movements assuming that common variance takes up all the variance, this models asset returns as a function of a global factor,:

𝑝_𝑐,𝑡 = 𝜆_𝑐,𝑔𝑓_𝑡𝑔 + 𝜀_𝑐,𝑡. (3.6) So, for an country-specific asset return c at date i there is a vector of global factors 𝑓_𝑡𝑔 at time t, which capture common sources among asset returns and are loaded through the coefficient 𝜆. The error term 𝜀𝑐,𝑡, represents idiosyncratic shocks that captures measurement errors.

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is represented by the so-called factor loadings. These two components yield loadings to be observed in Figure 2. We can observe that the majority of equity returns and bond returns tend to be loaded with component one, while bond returns are also loaded with component two. Through the remainder of this factor analysis asset returns that are loaded with less than .15 to component one, will be treated as outliers, due to the PCA’s sensitivity to outliers.6_{Figure 2a} displays the component loadings without the above identified outliers.

Figure 2: Component Loadings of the PCA

6_{The dropped outliers for the Priniple Component Analysis are: fraquity, prtequity, prtbond,}

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21 Figure 2a: Component Loadings of the PCA excluding outliers

The next step to arrive at the common factor among the country-specific asset price returns is the so-called Common Factor Analysis (CFA). Other than the PCA, the CFA assumes that that that total variance can be partitioned into common and unique variance. Within the context of asset returns and following the model of Rey (2015) this translates into the following: asset returns are modelled such that each country-specific asset price is a function of a global factor, a regional factor and an idiosyncratic term.

𝑝_𝑐,𝑡 = 𝜆_𝑐,𝑔𝑓_𝑡𝑔 + 𝜆_𝑐,𝑚𝑓_𝑡𝑚_{+ 𝜀}

𝑖,𝑐,𝑡. (3.7)

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This procedure has been chosen on basis of the previous research on the Global Financial Cycle, which has often employed the Dynamic Factor Model in order to estimate one common factor among asset prices. The Common Factor Analysis is a strategical procedure to identify common movements among large number of variables, as it is the case for our research (Jolliffe, 2002). It explores a reduced correlation matrix. This means, communalities are inserted on the diagonal of the correlation matrix, and the extracted factors are based only on the common variance, with specific and error variances excluded (Jolliffe, 2002). In our case, the CFA is conducted as explanatory procedure, since a possible underlying structure in asset returns is examined. As established in previous research we expect to see co-movements in asset returns due to the interconnectedness of financial markets. Similar to the PCA, the Common Factor Analysis requires the presence of correlation: To put it simple, without correlations, there is no underlying structure of the variables.

The CFA can be summarized in five Steps: (1) correlation matrix, (2) partition of variance into common and unique components, (3) extraction of initial factor solution, (4) rotation and interpretation, and (5) factor scores construction to be used for country-specific exposures. Firstly, the correlation of asset price returns display significant correlations between the equity and bond returns (Appendix C), which again provides an adequate basis for the CFA. Secondly, the Factor Analysis yields a Scree-Plot (Appendix F, Figure 2) which illustrates that it is appropriate to continue using 2 factors, since one can observe a considerable break between Factor 2 and 3. Similar to the PCA, the factor loadings refer to the correlation between the original variables (country-specific asset returns) and the factors, which illustrate the underlying “latent” structure of the respective factor. These factor loadings are presented in figure 37_{. From this, we can imply that all the asset returns are positively correlated with Factor}

7_{The following outliers found in the PCA are also dropped for the Common Factor Analysis:}

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1. remarkably, the majority of equity returns tend to be considerably more correlated with factor 1 and negatively correlated with factor 2, while the majority of bond returns are also positively correlated with factor 2. In turn we can conclude that factor 1 provides an appropriate common factor to represent the underlying structure of the asset price returns of the sample at hand.

Figure 3 Factor Loadings of country-specific asset returns (equity and bond)

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which is considerably above the 50% minimum and thus justified the factor analysis. The standardized factor 1 over time is displayed in Figure 4.

Figure 4 Standardized values of factor 1 over the time 1999-2018

In consequence, the factor constructed in the CFA represents the underlying structure of the asset returns at hand. In other words, and according to the economic intuition, this factor functions as the global price of risk und thus the Global Financial Cycle. This global factor of risk is necessary to identify the country-specific asset return exposure to the Global Financial Cycle;

𝑒𝑥𝑝_𝑐,𝑡𝑒𝑞𝑢𝑖𝑡𝑦= 𝒇𝟏,𝒕∗ 𝑒𝑞𝑢𝑖𝑡𝑦𝑐,𝑡 (3.2)

𝑒𝑥𝑝_𝑐,𝑡𝑏𝑜𝑛𝑑 _{= 𝒇}

𝟏,𝒕∗ 𝑏𝑜𝑛𝑑𝑐,𝑡, (3.3)

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5. Results and Discussion

5.1 One Global Factor reflecting worldwide asset returns

This section specifies the Common Factor Model for the relatively large heterogeneous sample of country-specific countries. As mentioned above the dataset includes end-of-month equity market index returns of 14 major financially significant markets and their corresponding 10-year sovereign bond return. The respective econometric set-up, which is guided by the research of Rey and Miranda-Agrippino (2015) and Rey (2015). In short, this section estimates the underlying structure of country-specific asset return (equity and bond), which functions as construct of one common factor. In other words, and according to the economic intuition, this factor is being referred to as ‘global price of risk’ by Adrian et al (2019) and thus represent the GFC. This global factor of risk is necessary to identify the country-specific asset return exposure to the GFC.

To start off, the common factor which represents the underlying structure of asset returns serves as an adequate proxy for the GFC. For instance, as established above the correlation matrices in Appendix C reveal considerably positive correlation between both equity and asset price returns. More importantly, the factor loadings in Figure 3 illustrate that the equity returns and bond returns (to a lesser extent) are positively correlated with the common factor. Thus, the majority of asset returns load significantly, which suggests gives reason to assume a strong common factor of global asset returns. However, nonlinearity matters, since the few sovereign bonds do not only load on the first common factor, but also on the second factor.8_{Still, one can} infer legitimate adequacy of the common factor when comparing it to the VIX. To that end, the estimated global factor of the Common Factor is plotted against the VIX in Figure 4, where both indices are standardized around zero. One can observe significant negatively related behaviour between the global factor and the volatility index of the S&P 500. In turn, the factor displays an inverse pattern of the VIX. For instance, that the index declines with all recession periods, while the VIX peaks similarly into the opposite direction. This way, Figure 4 pinpoints crucial periods such as the global financial crisis in 2008 through the collapse of the subprime market, the bursting of the dot-com bubble in 2004 as well as the European currency crisis in 2012. During those crises this signals the increased vulnerability of financial markets and thus the respective asset returns of this sample. This leads to an increase of the VIX during those

8_{This is why the robustness check of the regression analysis will built a different interaction term in order to}

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periods. This finding is coherent with the economic intuition; as the factor reflect the collective evolution of risk appetite of the market as well as realised market volatility, it is to expect that the factor is negatively correlated with the VIX (Rey, 2015). On a similar note, one can also observe a relatively long period high returns of the global factor associated with low values of the VIX. The inverse relation between the VIX and the global factor is well argued by asset pricing models; as uncertainty increases (read: increase in the VIX) global asset returns tend to decrease. This is why the VIX also often being referred to as the so called ‘fear gauge’. Therefore, this illustrates the development of risk appetite and released market volatile across the corresponding period. Given the value-at-risk (VaR)9_{constraint that investment decision} makers (e.g. financial intermediaries) are bound to, the negative correlation between the global factor and the VIX is justified. Also, this negative correlation is coherent with the findings of Rey (2015) as well as Miranda-Agrippino and Rey (2015). Similarly, Adrian et al (2019) provide evidence for the co-movements of the VIX with median VaR. Additionally, this is coherent with Brunnermeier et al (2009), which describes the feedback loop, where relatively low measured risk (i.e. volatility) leads to asset price inflation through the channel of greater credit supply and vice versa.

In short, the estimated common factor establishes a significant indication of a global financial cycle for the asset returns for the 14 countries at hand.. Note, that the analysis up until this point only indicate correlations and patterns, but does not provide evidence for causal argumentation.

9_{The value-at-risk constraint according to Brunnermeier et al (2009) affects the investor portfolio choices and}

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27 Figure 4: Global Factor and volatility index VIX

Note: The global factor is represented by the solid blue line , while the VIX denotes the red dashed line. The VIX refers to the

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5.2 Global price of risk and macroeconomic outcomes

In the previous section, the global factor of risk has been established and its relation to the VIX, which shows considerable proxy for the GFC. This section deals with the main three-folded research objectives; first we look at the country specific macroeconomic risk-return trade-off between GDP growth and GDP volatility. Secondly, we examine whether the country-specific exposure of asset returns to the global price of risk has an effect on GDP volatility and GDP growth. And finally, whether this country specific exposure alters the macroeconomic risk-return trade-off that output growth and volatility poses. Table 1 presents the country-specific results where column (1) present the classical risk-return trade-off, column (2) presents the result of the model that includes country-specific equity and bond returns, and column (3) comprises the complete regression including the interaction terms, which is constructed of GDP growth with equity and bond exposure to the global price of risk.

To begin with, this analysis finds confirmation for a positive relation between GDP growth and GDP volatility. For all of the countries, one can observe a significantly positive relationship between GDP growth and GDP volatility.10_{For instance, a 1 percent increase in} the GDP growth of Australia rate is associated with a .9% increase in GDP volatility. Nevertheless, the sample includes some ‘outliers’ in that matter. For example, in the case of Sweden and Hong Kong (China) we cannot provide significant evidence for a positive risk-return relationship. Still, these findings support the economic intuition that countries with higher growth rates, tend to have relatively higher fluctuations in GDP, as well. Therefore, one can conclude that this study delivers strong evidence for a positive relation between GDP growth and GDP volatility and thus can thus verify the macroeconomic risk-return trade-off for the majority of the 14 countries in the sample.

Secondly, the effect of country-specific exposure to the global price of risk on GDP growth and volatility can be observed to differ among nations (Table 1, column 2). Regarding the effect of exposure the sample can be split into two groups. On the one hand, country-specific exposure to the Global Financial Cycle of some countries does not seem to play a role when it comes to the effect on GDP volatility and GDP growth. Specifically, for countries such as Austria, Belgium, Switzerland, Germany, France, Hong Kong (China), and Japan we find no significant evidence in this regard. On the other hand, country-specific exposure to the Global Financial Cycle of some countries does have an effect on GDP volatility and GDP growth. These

10_{Evidence for a positive macroeconomic risk-return trade-off: Australia, Austria, Belgium, Canada, Switzerland}

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countries include Australia, Canada, Ireland, Netherlands, Sweden and the United States. For all these countries the equity return exposure to the GFC presents significant positive effect on GDP volatility. For example, a one unit increase in the equity market exposure of Canada to the GFC, is associated with about 33% increase in GDP volatility. We can thus infer that an increase in the country-specific equity return exposure to the GFC comes at the cost of more volatile GDP growth. Notably, these countries comprise the relatively smaller countries with respect to GDP as well as the monetary hegemon – United States11_{. However, the} country-specific bond exposures do not present significant proof for having an effect on GDP volatility. This requires a robustness to be executed in section 5.3. In addition, one can observe a decrease in the coefficient of the GDP growth for the majority of these countries. This, in turn, might suggests that there is a correlation between GDP growth and equity exposure. Nevertheless, these changes are considerable insignificant, which does not provide much room for interpretation. Consequently, one can conclude that for some countries the equity return exposure to the global price of risk does have a positive effect on GDP volatility, but not a significant effect on GDP growth.

Thirdly, the results suggest that country-specific exposure to the global price of risk does not alter the macroeconomic risk-return trade-off. For none of the countries in the sample does the interaction terms of GDP growth with bond and equity exposure reveal significant results. Thus, we are unable to infer that the exposure to the global price of risk intensifies the macroeconomic risk-return trade-off.

To sum up, this analysis validates the macroeconomic risk-return trade-off suggested by Adrian et al (2019), nevertheless, it also suggests that equity return exposure to the GFC for plays a role within this risk-return trade-off for some countries in the sample

11_{Monetary hegemon according to Miranda-Agrippino and Rey (2015) refers to one or few countries, which}

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AUT AUT BEL CAN

GDP Volatility (1) (2) (3) (1) (2) (3) (1) (2) (3) (1) (2) (3) GDP Growth 0.914*** 0.840*** 0.847*** 0.917*** 0.906*** 0.916*** 0.899*** 0.893*** 0.894*** 0.917*** 0.914*** 0.919*** (0.0555) (0.0662) (0.0770) (0.0563) (0.0632) (0.0746) (0.0597) (0.0659) (0.0746) (0.0589) (0.0603) (0.0817) Equity exposure 57.83** 49.67** -5.873 -6.879 -7.726 -7.162 32.71** 32.63** (23.54) (24.26) -9.713 (10.26) (11.20) (11.32) (14.80) (15.56) Bond exposure 17.89 20.42 26.68* 31.67* 0.0575 0.104 -5.283 -3.038 (16.88) (20.65) (15.86) (18.70) (0.719) (0.736) (14.01) (15.10) GDP Growth* Equity exposure 5.904 -0.931 0.944 0.429 (4.612) (3.498) -4.751 (2.321) GDP Growth* bond exposure -1.608 -0.141 (4.751) 0.761 (3.303) (3.161) (0.145) (3.798) Observations 224 178 147 192 158 151 188 151 143 216 166 155 R-squared 0.549 0.561 0.601 0.581 0.595 0.578 0.548 0.560 0.574 0.530 0.596 0.586 Standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1 CHE DEU GBR HKG GDP Volatility (1) (2) (3) (1) (2) (3) (1) (2) (3) (1) (2) (3) GDP Growth 0.941*** 0.925*** 0.907*** 0.846*** 0.821*** 0.783*** 0.909*** 0.902*** 0.912*** -3.203*** -2.731*** -2.860*** (0.0658) (0.0721) (0.0911) (0.0787) (0.0910) (0.112) (0.0468) (0.0532) (0.0680) (0.154) (0.175) (0.252) Equity exposure 22.47 16.93 10.15 9.940 0.583 -0.691 3.856 2.471 (22.24) (26.10) (11.57) (13.16) (14.52) (15.56) (3.288) (4.100) Bond exposure 1.645 10.42 -4.427 -3.031 8.078 11.03 -0.779 -0.292 (6.550) (11.60) (11.58) (16.28) (12.31) (14.26) (1.664) (1.909) GDP Growth* Equity exposure 0.150 2.533 -0.480 3.682 (6.345) (3.854) (1.542) (5.817) GDP Growth* bond exposure 0.298 -0.118 -0.553 0.959 (2.397) (3.968) (2.161) (2.844) Observations 204 158 147 180 141 131 204 169 159 80 41 30 R-squared 0.502 0.533 0.511 0.392 0.386 0.387 0.650 0.645 0.626 0.845 0.878 0.880 Standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1 FRA IRL JPN NLD GDP Volatility (1) (2) (3) (1) (2) (3) (1) (2) (3) (1) (2) (3) GDP Growth 0.956*** 1.021*** 1.041*** 0.941*** 0.840*** 0.850*** 0.911*** 0.883*** 0.871*** 0.893*** 0.850*** 0.837*** (0.0641) (0.0613) (0.0764) (0.0584) (0.0667) (0.0753) (0.0660) (0.0925) (0.105) (0.0659) (0.0692) (0.0800) Equity exposure -0.807 -1.071 36.15** 35.86* 6.542 9.984 22.87* 21.27* -8.156 -8.676 (17.56) (18.42) (11.64) (11.78) (12.44) (12.78) Bond exposure -9.911 -13.88* 77.74** 84.50** 2.728 -4.060 23.97 31.83* -6.609 -8.200 (35.22) (39.56) -8.689 -9.003 (16.92) (18.57) GDP Growth* Equity exposure -2.580 -1.010 0.907 0.562 (6.031) (1.892) (3.159) (1.661) GDP Growth* bond exposure 1.261 0.431 0.185 -0.407 (3.092) (1.413) (2.447) (1.760) Observations 196 161 151 168 138 135 164 142 135 184 160 155 R-squared 0.533 0.643 0.645 0.608 0.661 0.654 0.539 0.397 0.410 0.500 0.535 0.539 Standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1 SWE USA GDP Volatility (1) (2) (3) (1) (2) (3) GDP Growth 0.0382 0.0344 -0.0244 0.465*** 0.386*** 0.450*** (0.0648) (0.0748) (0.0828) (0.112) (0.115) (0.128) Equity exposure 36.79** 39.43** 50.69*** 48.28** (16.73) (18.17) (19.29) (19.80) Bond exposure 6.365 5.372 0 0 (20.77) (24.46) (0) (0) GDP Growth* Equity exposure 0.00334 -4.741 (4.324) (5.684) GDP Growth* bond exposure 2.957 -(2.163) Observations 188 155 150 196 158 150 R-squared 0.002 0.050 0.089 0.082 0.116 0.124 Standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

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6. Robustness

At this point, it is important to check the robustness of the findings at hand. The analysis above has confirmed the macroeconomic risk-return trade-off as well as a positive effect of equity return exposures on GDP volatility. This gives rise to the question why bond exposures to the GFC did not deliver any significant results. The answer might lay in the non-linearity of the common factor that forms the underlying structure of equity returns and bond returns. In section 4.1 we have established that the sovereign bond returns also tend to load on the a second factor. Similar to the findings of this paper, Adrian et al (2019) have failed to establish evidence that the common factor by itself can jointly explain global equity and bond returns in a linear function. This points at a nonlinear relation between risk aversion and asset returns and points toward the so-called principle of flight to safety (explained below).

This why, this part checks a robustness check is needed in order see whether the nonlinearity also matters when it comes to the effect of bond exposure to the GFC on output volatility. This means, since bond returns also significantly load on the a second factor, another exposure term is created as part of the macroeconomic risk-return regression. This exposure term is constructed in the following way:

𝑒𝑥𝑝_𝑐,𝑡𝑏𝑜𝑛𝑑 _{= 𝑓}

2,𝑡∗ 𝑏𝑜𝑛𝑑𝑐,𝑡,

Sovereign bond exposure to the GFC is thus constructed as a product of country-specific bond returns and the second factor that is estimated by the Common Factor Model. This second factor is plotted against the first in Figure 5. Even though these to display similar movements, one can observe some distinctions during major events such as the after the collapse of the subprime market. These distinctions confirm the economic intuition of flight to safety (or quality): during times of financial turmoil investors tend to sell relatively risky assets (equity)

in exchange for safer investments such as 10-year sovereign bonds. This indicates that it might

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32 Figure 5 Global Factor 1 vs Global Factor 2

Based on the analysis enclosed in table 2 one can infer that nonlinearity of asset price movements matter for the relationship of GDP growth and GDP volatility. Specifically, table 2 documents significant effect of the newly constructed bond exposure on GDP volatility for five countries12_{. Note that the effect of equity exposures remain significant, which confirms the} robustness of the results of the original model in this regard. An increase of bond exposure to the GFC of say United Stated is accompanied by a 57% increase in GDP volatility. In consequence, this does not provide unanimous evidence for one global factor that explains all asset price movements. We need to distinguish between asset price classes and their relative quality. Additionally, when one accounts for this nonlinearity then the bond exposure to the GFC has positive effect on macroeconomic risk.

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33 Table 2 Macroeconmic risk-return tarde-off and Country-specific exposures to the GFC including bond specific factor

AUS AUT BEL CAN

GDP Volatility (1) (2) (1) (2) (1) (2) (1) (2) GDP Growth 0.840*** 0.830*** 0.906*** 0.905*** 0.893*** 0.871*** 0.914*** 0.900*** (0.0662) (0.0666) (0.0632) (0.0629) (0.0659) (0.0655) (0.0603) (0.0606) Equity Exposure 57.83** 64.66*** -5.873 1.965 -7.726 -6.950 32.71** 29.70** (23.54) (23.11) (9.713) (8.466) (11.20) (10.32) (14.80) (14.06) Bond Exposure 17.89 26.68* 0.0575 -5.283 (16.88) (15.86) (0.719) (14.01) Bond Exposure 2 50.13** 25.91* 28.72* 23.76 (20.65) (13.64) (14.85) (18.09) Observations 178 167 158 158 151 151 166 166 R-squared 0.561 0.570 0.595 0.597 0.560 0.570 0.596 0.600

Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

CHE DEU FRA GBR

GDP Volatility (1) (2) (1) (2) (1) (2) (1) (2) GDP Growth 0.925*** 0.918*** 0.821*** 0.822*** 1.021*** 1.026*** 0.902*** 0.894*** (0.0721) (0.0783) (0.0910) (0.0909) (0.0613) (0.0615) (0.0532) (0.0587) Equity Exposure 22.47 17.41 10.15 7.934 -0.807 0.0567 0.583 -0.206 (22.24) (24.89) (11.57) -9.878 -8.156 -8.155 (14.52) (15.46) Bond Exposure 1.645 7.568 -4.427 -9.911 8.078 10.49 -6.550 (11.66) (11.58) -6.609 (12.31) (14.28) Bond Exposure 2 17.10 3.886 -7.847 3.979 (14.58) (10.06) -7.380 (16.22) Observations 158 147 141 141 161 161 169 159 R-squared 0.533 0.516 0.386 0.386 0.643 0.640 0.645 0.625

Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 USA JPN HKG IRL GDP Volatility (1) (2) (1) (2) (1) (2) (1) (1) GDP Growth 0.386*** 0.347*** -2.731*** -2.706*** -2.731*** -2.706*** 0.840*** 0.883*** (0.115) (0.115) (0.175) (0.175) (0.175) (0.175) (0.0667) (0.0925) Equity Exposure 50.69*** 20.62 3.856 2.618 3.856 2.618 36.15** 6.542 (19.29) (22.86) (3.288) (2.281) -3.288 -2.281 (17.56) (11.64) Bond Exposure 0 -0.779 -0.779 77.74** 2.728 0 (1.664) -1.664 (35.22) -8.689 Bond Exposure 2 57.79** -1.192 -1.192 (24.38) (1.242) -1.242 Observations 158 158 41 41 41 41 138 142 R-squared 0.116 0.147 0.878 0.880 0.878 0.880 0.661 0.397

Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 JPN NLD SWE GDP Volatility (2) (2) (1) (2) (1) (2) GDP Growth 0.848*** 0.878*** 0.850*** 0.832*** 0.0344 0.00895 (0.0675) (0.0920) (0.0692) (0.0692) (0.0748) (0.0770) Equity Exposure 48.30*** 6.797 22.87* 33.55*** 36.79** 45.25*** (17.78) (11.23) (12.44) (10.33) (16.73) (15.87) Bond Exposure 23.97 6.365 (16.92) (20.77) Bond Exposure 2 46.11* 16.33 48.98** 23.17 (26.85) (12.41) (20.95) (20.14) Observations 138 142 160 160 155 155 R-squared 0.656 0.404 0.535 0.545 0.050 0.058

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7. Conclusion

This research aims to validate the macroeconomic risk-return trade-off between output growth and output volatility, whether country-specific exposure to the Global Financial Cycle has an effect on GDP volatility and GDP growth, and finally, whether these exposures actually alter the macroeconomic risk-return trade-off.

With regard to the first objective, this paper delivers significant evidence for a positive relation between GDP growth and GDP volatility during the last two decades for the majority of the countries in the sample. This in turn, verifies the macro-economic risk-return trade-off per country that was established by Adrian et al (2019) for part of the authors’ sample.

Secondly, this study also suggests that country-specific equity return and bond return Exposure to the GFC has a positive effect on GDP volatility, when accounting for nonlinearity of common factors. When only accounting for one underlying structure of asset returns (one factor), then bond exposure to not show significant effects on output volatility. In other words, this does not deliver an unanimous evidence for one global factor that explains all asset price movements. When, however, one accounts for this nonlinearity then the bond exposures to the GFC has positive effect on macroeconomic risk. So, there is not one factor that describes the GFC, instead one needs to distinguish between asset price classes and quality to arrive at an adequate measure of exposure to the GFC. Consequently, this study provides a specification of the cross section regression of Adrian et al (2019), since it establishes for which of the countries in their sample the individual exposure to the Global Financial Cycle plays into the macroeconomic risk-return trade-off.

Thirdly, based on the regression analysis one is unable to infer that exposure to the global price of risk intensifies the macro-economic risk-return trade-off that growth and GDP volatility form.

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included in monetary policy measures of the ECB (Basel III), as well. As market conditions dictate funding condition, financial institutions mark their balance sheet to the market and use market sensitive risk measures such as value-at-risk (Brunnermeier et al, 2009). Thus, macro-prudential measures could dampen the asset price boom that arises from favourable financing conditions. Finally, limiting leverage for financial intermediaries, according to Rey (2015), targets the heart of the transmission channel. This measure is closely related to the economic intuition behind the third measure. In this regard, Adrian et al (2019) finds evidence that monetary, fiscal and particularly macro-prudential policies can tilt the risk-return trade-off favourably by insulating the impact of exposure to the Global Financial Cycle. This means, counter-cyclical monetary policy alleviates the risk-return trade-off due to its interaction with the exposure to the global price of risk. As a result, the authors conclude macroeconomic policies should not be separated from policies that affect the stability of financial market. In consequence, these arguments strengthen the need macro-prudential policy measures in order to limit negative externalities to the real economy

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38 Appendix A: Dynamic Factor Model for country-specific market returns

This dynamical Factor model is extracted from Miranda-Agrippino and Rey (2015) in order to be applied on this study’s 28 country-specific asset returns. The authors set the model up in the following way: Let 𝑝_𝑡 be an n-dimensional vector collecting monthly (log) asset price series 𝑝_{𝑖,𝑐,𝑡}, which denotes asset return i of country c at date t. the model assumes

𝑝_𝑡 = 𝛬𝐹_𝑡+ 𝜉_𝑡 . (B.1)

Here, 𝐹_𝑡 denotes a (r x 1) vector of common factor (𝐹_𝑡 = [𝑓_1,𝑡, … , 𝑓_1,𝑡]′) which capture systematic sources of variation among returns and are loaded via the coefficients in 𝛬 determining how each return reacts to common shocks. 𝜉_𝑡 us a (n x 1) vector idiosyncratic shocks 𝜉𝑖,𝑡 which capture series-specific variability or measurement errors. As Miranda-Agrippino and Rey (2015), some degrees of autocorrelation of elements in 𝜉𝑡, but pairwise correlation between returns are ruled out assuming that all the co-variation is accounted for the common component. Also, common factors as well as idiosyncratic terms are assumed to be zero mean processes.

The factors are assumed to follow a vector autoregressive (VAR) process of order p

𝐹_𝑡 = 𝛷₁𝐹_𝑡−1+ ⋯ + 𝛷_𝑝𝐹_𝑡−𝑝 + 𝜀_𝑡, (B.2)

where the autoregressive coefficients are collected in the p matrices 𝛷1, … , 𝛷𝑝 each of which is (r x r); the error term 𝜀𝑡 is a normally distributed zero mean process with covariance matrix Q. Any residual autocorrelation is captures by the idiosyncratic component which is assumed being a collection of independent univariate autoregressive processes.

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one can distinguish between co-movements at different levels of aggregation. Thus, the vector of common shocks is allowed to include both aggregate shocks that affect all series in 𝑦𝑡, and shocks that affect many but not all of them

𝑝_{𝑖,𝑐,𝑡} = 𝜆_𝑖,𝑔𝑓_𝑡𝑔+ 𝜆_𝑖,𝑚𝑓_𝑡𝑚_{+ 𝜀}

𝑖,𝑐,𝑡. (B.3)

In equation (B.3) the common component 𝛬𝐹 from (B.1) is split up into a global factor (𝑓_𝑡𝑔) and a regional or market specific factor ( 𝑓_𝑡𝑚_{), which is captures commonalities among} many but not all asset return series. Therefore, each 𝑝_{𝑖,𝑐,𝑡} is thus a function of a global factor loaded by all the variables in 𝑝𝑡, regional or market-specific factor only loaded by those series in the 𝑝𝑡 which belong to the (geographical) market m, and of a series-specific factor.

This hierarchical structure is imposed via zero restrictions on some of the elements in 𝛬. Specifically, the common component is assumed to be partitioned into a global and several regional factors. To this aim, let the variables in 𝑦𝑡 be such that it is possible to univocally allocate them in B different blocks or regions and, without loss of generality, assume that they are ordered according to the specific block they refer to such that 𝑦_𝑡 = 𝑦_𝑡1_{, 𝑦}

𝑡2, … , 𝑦𝑡𝐵 can be rewritten as 𝑝_𝑡 = ( 𝛬1,𝑔 𝛬1,1 0 𝛬_2,𝑔 0 𝛬_2,2 𝛬_𝐵,𝑔 0 0 0 : 𝛬_𝐵,𝐵) ( 𝑓_𝑡𝑔 𝑓_𝑡1 𝑓_𝑡𝐵_𝑔 ) + 𝜉_𝑡 . (B.4)

Furthermore, other restriction are imposed on the coefficients matrices in equation (B.2) such that 𝛷_𝑖(𝑖, … , 𝑝) and Q are diagonal.

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Reis and Watson, 2010; Banbura et al, 2011). In order to initialize the algorithm the principal component estimates of the factors that are proven to provide a good approximation of the common factors when the cross sectional dimension is large.13_{The model is estimated on the} asset returns in (log) first difference and obtains the factors through cumulation. 14

13_{According to Forni et al (2000), Bai among Ng (2002) and Stock and Watson (2002b)} 14_{The fist difference for any variable 𝑥}

𝑡 denotes 𝑥̃𝑡≡ 𝛥𝑥𝑡. Then the consistent estimates of the common factors

𝐹𝑡 can be obtained by cumulating the factors estimated from the stationary, yielding the first difference model:

Country-Specific Global Financial Cycle exposures and macroeconomic risk-return trade-off