Global Financial Cycles and Risk Premiums

Abstract

This paper studies the synchronization of financial cycles across 17 advanced economies over the past 150 years. The comovement in credit, house prices, and equity prices has reached historical highs in the past three decades. While comovement of credit and house prices increased in line with growing real sector integration, comovement of equity prices has increased above and beyond growing real sector integration. The sharp increase in the comovement of global equity markets is particularly notable. We demonstrate that fluctuations in risk premiums, and not risk-free rates and dividends, account for a large part of the observed equity price synchronization after 1990. We also show that US monetary policy has come to play an important role as a source of fluctuations in risk appetite across global equity markets. These fluctuations are transmitted across both fixed and floating exchange rate regimes, but the effects are more muted in floating rate regimes.

Appendices

Appendix 1: Global Averages

Fig. 14

Global average cycles. Notes: Global means. All series were detrended with a Baxter–King filter isolating cycles in the 2- to 32-year period range. The equity return premium series and interest rate series are depicted in levels. Outliers have been dropped from the graph in order to simplify the graphical exposition

Fig. 15

Global average cycles (2–8 year cycles). Notes: Global means. All series were detrended with a Baxter–King filter isolating cycles in the 2–8-year period range. Outliers have been dropped from the graph in order to simplify the graphical exposition

Fig. 16

Global average cycles (Hamilton filter). Notes: Global means. All series were detrended with the Hamilton filter, using lags one to four. Outliers have been dropped from the graph in order to simplify the graphical exposition

Appendix 2: Average Bilateral Correlations

Fig. 17

Average bilateral correlation (2–8-year cycles). Notes: Spearman rank correlation coefficients based on 15-year rolling windows. 2–8-year period Baxter–King detrended series. Bars—95% cross-sectionally block-bootstrapped confidence bands

Fig. 18

GDP-weighted average bilateral correlation (2–32-year cycles). Notes: Spearman rank correlation coefficients based on 15-year rolling windows. 2–32-year period Baxter–King detrended series. Bars—95% cross-sectionally block-bootstrapped confidence bands

Fig. 19

Average bilateral correlation (Hamilton filter). Notes: Spearman rank correlation coefficients based on 15-year rolling windows. Hamilton filter detrended series (using lags one to four). Bars—95% cross-sectionally block-bootstrapped confidence bands

Fig. 20

Average bilateral correlation (annual growth rates and first differences). Notes: Spearman rank correlation coefficients based on 15-year rolling windows. First differences (for the equity return premium and interest rates) and growth rates for all other variables. Bars—95% cross-sectionally block-bootstrapped confidence bands

Fig. 21

Average bilateral correlation (Pearson correlation coefficient). Notes: Pearson correlation coefficients based on 15-year rolling windows. 2–32-year period Baxter–King detrended series. Bars—95% cross-sectionally block-bootstrapped confidence bands

Fig. 22

Average bilateral correlation (USA). Notes: Spearman rank correlation coefficients based on 15-year rolling windows. 2–32-year period Baxter–King detrended series. Bars—95% cross-sectionally block-bootstrapped confidence bands. Average of all bilateral US country-pair correlations

Fig. 23

Average bilateral concordance. Notes: Concordance based on 15-year rolling windows. Peaks defined as highest values in +/-2 year window. Minimum phase length 2 years. Minimum cycle length 4 years. Bars—95% cross-sectionally block-bootstrapped confidence bands

Fig. 24

Regional correlations: Europe. Notes: Spearman rank correlation coefficients based on 15-year rolling windows. All series were detrended with a Baxter–King filter isolating cycles in the 2–32-year period range. Bars –95% cross-sectionally block-bootstrapped confidence bands

Fig. 25

Regional correlations: Euro area. Notes: Spearman rank correlation coefficients based on 15-year rolling windows. All series were detrended with a Baxter–King filter isolating cycles in the 2–32-year period range. Bars—95% cross-sectionally block-bootstrapped confidence bands

Fig. 26

Regional correlations: Scandinavia. Notes: Scandinavia: Denmark, Finland, Norway, and Sweden. Spearman rank correlation coefficients based on 15-year rolling windows. All series were detrended with a Baxter–King filter isolating cycles in the 2–32-year period range. Bars—95% cross-sectionally block-bootstrapped confidence bands

Fig. 27

Regional correlations: Pacific. Notes: Pacific region: Australia, Canada, Japan, and United States. Spearman rank correlation coefficients based on 15-year rolling windows. All series were detrended with a Baxter–King filter isolating cycles in the 2–32-year period range. Bars—95% cross-sectionally block-bootstrapped confidence bands

Appendix 3: Equity Return Premium Covariance Decomposition

This section decomposes equity return premiums through a vector autoregression (VAR) decomposition in the spirit of Campbell (1991). The advantage of such decompositions over the comovement analyses presented so far is that they explicitly model investor expectations and thus do not require the equalization of ex ante expected values with ex post realized ones. A recent example for such a decomposition based on the long-run data we use is Kuvshinov (2018). In particular, we build on the two-country decomposition suggested by Ammer and Mei (1996). This approach attributes unexpected fluctuations in the current equity return premium of country i (${\tilde{e}}_{t+1}^i$) to news about future discounted dividends, risk-free rates and equity return premiums.

1.1 The Return Premium Model

Starting from the log gross equity return definition

$$\begin{aligned} h_{t+1} = log(P_{t+1} + D_{t+1}) - log(P_{t}), \end{aligned}$$

(15)

where P denotes the equity price and D the dividend paid. A first-order Taylor approximation yields

$$\begin{aligned} h_{t+1} \approx \delta _t - \rho \delta _{t+1} + \Delta d_{t+1} + k, \end{aligned}$$

(16)

where $\Delta d$ denotes the first difference of the log of the dividend payment D, $\delta$ is the dividend-price ratio, $\rho$ is a (discount) factor smaller than 1 and k is a linearization constant (see Campbell and Shiller 1988). Solving (16) forward¹⁰, taking expectations and plugging the resulting expectation equations for $\delta _{t}$ and $\delta _{t+1}$ back into (16) results in the following expression for the unexpected change in the log real return on equity:

$$\begin{aligned} h_{t+1} - E_t h_{t+1} = (E_{t+1} - E_t) \left[ \sum _{k=0}^{\infty } \rho ^k \Delta d_{t+1+k} - \sum _{k=1}^{\infty } \rho ^k h_{t+1+k} \right] , \end{aligned}$$

(17)

where $E_t$ is an expectation operator denoting expectations formed on the basis of information available through t. Put in terms of equity return premiums $e_{t+1} := h_{t+1} - r_{t+1}$, where r denotes the log real interest rate, Eq. (17) can be rewritten as

$$\begin{aligned} e_{t+1} - E_t e_{t+1} = (E_{t+1} - E_t) \left[ \sum _{k=0}^{\infty } \rho ^k \Delta d_{t+1+k} - \sum _{k=0}^{\infty } \rho ^k r_{t+1+k} - \sum _{k=1}^{\infty } \rho ^k e_{t+1+k} \right] , \end{aligned}$$

(18)

or more compactly, for any country i

$$\begin{aligned} {\tilde{e}}_{t+1}^i = {\tilde{e}}_{d,t+1}^i - {\tilde{e}}_{r,t+1}^i - {\tilde{e}}_{e,t+1}^i. \end{aligned}$$

(19)

The general intuition behind Eq.  19 is that innovations in the equity return premium of country i can be decomposed into news about the discounted sum of future dividend streams, news about the discounted sum of future risk-free real interest rates, and news about the discounted sum of future equity return premiums. Thus, if the equity return premium increases, this is either due to news about higher future dividends, lower future risk-free rates or lower future return premiums.

Consider the same decomposition for another country j. In order to render real equity returns in j comparable to those in i it is necessary to introduce a real exchange rate term ${\tilde{e}}_{q,t+1}$:

$$\begin{aligned} {\tilde{e}}_{t+1}^j = {\tilde{e}}_{d,t+1}^j - {\tilde{e}}_{r,t+1}^j - {\tilde{e}}_{e,t+1}^j - {\tilde{e}}_{q,t+1}^j, \end{aligned}$$

(20)

where ${\tilde{e}}_{q,t+1} = (E_{t+1} - E_t) \sum _{k=0}^{\infty } \rho ^k q_{t+1+k}$ denotes news about the sum of future discounted log real exchange rates.¹¹

We are interested in characterizing the comovement of return premiums in countries i and j, ${\tilde{e}}_{t+1}^i$ and ${\tilde{e}}_{t+1}^j$. From Eqs. (19) and (20), it follows that the covariance in equity return premiums $Cov({\tilde{e}}^i,{\tilde{e}}^j)$ can be decomposed as follows:

$$\begin{aligned} Cov({\tilde{e}}^i,{\tilde{e}}^j)&= Cov({\tilde{e}}^i_d,{\tilde{e}}^j_d) - Cov({\tilde{e}}^i_d,{\tilde{e}}^j_r) - Cov({\tilde{e}}^i_d,{\tilde{e}}^j_e) - Cov({\tilde{e}}^i_d,{\tilde{e}}^j_q) \\&\quad - Cov({\tilde{e}}^i_r,{\tilde{e}}^j_d) + Cov({\tilde{e}}^i_r,{\tilde{e}}^j_r) + Cov({\tilde{e}}^i_r,{\tilde{e}}^j_e) + Cov({\tilde{e}}^i_r,{\tilde{e}}^j_q) \\&\quad - Cov({\tilde{e}}^i_e,{\tilde{e}}^j_d) + Cov({\tilde{e}}^i_e,{\tilde{e}}^j_r) + Cov({\tilde{e}}^i_e,{\tilde{e}}^j_e) + Cov({\tilde{e}}^i_e,{\tilde{e}}^j_q). \end{aligned}$$

(21)

This decomposition allows us to analyze whether the rise in equity return premium comovement was due to a rise in the comovement of dividend news $Cov({\tilde{e}}^i_d,{\tilde{e}}^j_d)$, risk-free rate news $Cov({\tilde{e}}^i_r{\tilde{e}}^j_r)$, or return premium news $Cov({\tilde{e}}^i_e,{\tilde{e}}^j_e)$.

Note that in contrast to the comovement analyses presented in the main text, which have looked at equity prices, the covariance analysis presented here directly looks at the comovement in equity return premiums. The results of the two approaches are comparable in that they both indicate the extent to which international comovement in equities can be accounted for by fundamentals—dividends and risk-free rates—and how much must be attributed to other factors—risk appetite, or news about future return premiums.

1.2 The VAR Model

In order to compute the variance decomposition (21), we need estimates of the various news terms in Eqs. (19) and (20). A VAR model serves this purpose. The assumption is that changes in expectations due to new information arriving between t and $t+1$ can be isolated through the VAR model. We estimate bilateral VARs on the basis of the following variables: log equity return premiums $e_{i,t}, e_{j,t}$, log real interest rates $r_{i,t}, r_{j,t}$, dividend-price ratios $\delta _{i,t}, \delta _{j,t}$ and the first differences of the log bilateral real exchange rate $\Delta q_{t}$. Collecting these variables in the vector $\varvec{z}_t = \begin{pmatrix} e_{t}^i&r_{t}^i&\delta _{t}^i&e_{t}^j&r_{t}^j&\delta _{t}^j&q_{t}^j \end{pmatrix}^T$ the VAR model for $\varvec{z_{t+1}}$ in companion form is

$$\begin{aligned} \varvec{z}_{t+1} = \varvec{A} \varvec{z}_t + \varvec{\epsilon }_{t+1} \, , \end{aligned}$$

(22)

where $\varvec{A}$ is the VAR parameter matrix and $\varvec{\epsilon }$ contains the error terms. The inclusion of variables from countries i and j enables us to study the linkage between both countries.

The equity return premium model summarized by Eqs. (19) and (20) imposes a tight set of cross-equation restrictions on the VAR. On the basis of these and the estimated VAR, we compute each of the news components in Eqs. (19) and (20) for each bilateral country-pair i, j. For this purpose, we define picking vectors $\varvec{g}_k$ (row k of the identity matrix) that select the relevant rows from the VAR system:

$$\begin{aligned} \varvec{{\tilde{e}}}_{t+1}^m= & {} \varvec{g}_1^m \varvec{\epsilon }_{t+1} \, , \quad m=i,j \end{aligned}$$

(23)

$$\begin{aligned} \varvec{{\tilde{e}}}_{e,t+1}^m= & {} \varvec{g}_1^m \rho _m \varvec{A} (\varvec{I}-\rho _m \varvec{A})^{-1} \varvec{\epsilon }_{t+1} \, , \quad m=i,j \end{aligned}$$

(24)

$$\begin{aligned} \varvec{{\tilde{e}}}_{r,t+1}^m= & {} \varvec{g}_2^m (\varvec{I}-\rho _m \varvec{A})^{-1} \varvec{\epsilon }_{t+1} \, , \quad m=i,j \end{aligned}$$

(25)

$$\begin{aligned} \varvec{{\tilde{e}}}_{q,t+1}^j= & {} \varvec{g}_3^j (\varvec{I}-\rho _j \varvec{A})^{-1} \varvec{\epsilon }_{t+1} \, , \end{aligned}$$

(26)

$$\begin{aligned} \varvec{{\tilde{e}}}_{d,t+1}^i= & {} \varvec{{\tilde{e}}}_{t+1}^i + \varvec{{\tilde{e}}}_{r,t+1}^i + \varvec{{\tilde{e}}}_{e,t+1}^i \, , \end{aligned}$$

(27)

$$\begin{aligned} \varvec{{\tilde{e}}}_{d,t+1}^j= & {} \varvec{{\tilde{e}}}_{t+1}^j + \varvec{{\tilde{e}}}_{r,t+1}^j + \varvec{{\tilde{e}}}_{e,t+1}^j + \varvec{{\tilde{e}}}_{q,t+1}^j \, , \end{aligned}$$

(28)

We set $\rho$ to 0.96.¹² We can use the thus calculated news components in order to determine whether correlated dividend news (${\tilde{e}}_d$), monetary policy news (${\tilde{e}}_r$) or news about future equity return premiums (${\tilde{e}}_e$) have historically been most important in driving the comovement in international equity return premiums.¹³

1.3 Covariance Decomposition

Table 6 shows the covariance decomposition for a pre-WW2 sample, a post-WW2 sample, as well as a post-1980 sample zooming in on the period of high equity price synchronization. The top row states the equity return premium covariance in our sample, and all following rows state the median bilateral component covariances.

Clearly equity return premium covariance has increased over time, from 1.61 in the pre-WW2 sample to 1.99 in the post-WW2 sample, and 3.48 in the post-1980 sample. Among its components, dividend news covariance is the largest. However, dividend covariance has neither increased, nor decreased substantially over time. One covariance component that clearly increases over time is the covariance in news about future return premiums, which roughly doubles in size in the post-1980 sample.

Covariance in risk-free rate news exhibits a downward trend over time. This is consistent with many countries moving toward a floating exchange rate regime after the end of the Bretton Woods system of fixed exchange rates. As a consequence, international risk-free rate covariance explains little of the covariance in return premiums after 1980. Finally, an absolute decrease in some cross-covariance terms, such as the covariance between dividends and risk-free rates, also contributed to the increase in equity return premium comovement.

Overall, the VAR decomposition confirms our earlier result, that neither dividends, nor risk-free rates can explain the late twentieth-century surge in equity comovement. Instead it is risk appetite or, put in terms of the terminology used here, revisions to expected future return premiums, that are the primary explanation for the increasing comovement of equities.

Table 6 Decomposition of the covariance in equity return premiums

1.4 International Response to US Risk-Free Rate Changes

Fig. 28

Response to $+1ppt$ US policy rate increase. Notes: Median bilateral impulse response functions to +1ppt increase in US interest rates. Dashed gray — US short-term real risk-free rate own response. $95\%$ interval based on cross-sectional block-bootstrap procedure over bilateral country pairs

By extending the VAR framework introduced above, it becomes possible to trace the effects of US monetary policy on return premiums, dividend-price ratios and risk-free rates, within a framework that acknowledges that ex post realized variables can deviate from their ex ante expected counterparts. This is achieved by incorporating US interest rate policy innovations $\Delta R^{US}_t$ into the VAR system (see Bernanke and Kuttner 2005):

$$\begin{aligned} \varvec{z}_{t+1} = \varvec{A} \varvec{z}_t + \varvec{\phi } \Delta {R}^{US}_t + \varvec{\epsilon }_{t+1}. \end{aligned}$$

(29)

As our indicator for US short-term rate innovations, we use the residuals from a Taylor rule regression of US real short-term rate changes on changes in US real per capita GDP, US CPI inflation, and US real stock prices, as well as one lag of each regressor. The responses of international equity return premiums, dividend-price ratios, and real short-term rates can then be calculated as $\varvec{A}^k \varvec{\phi }$.

Figure 28 displays the resulting impulse response functions for the full sample, as well as the post-1980 sample of high equity return premium comovement. For the full sample dividends and risk-free rates react to US monetary policy innovations, but not equity return premiums. In contrast, after 1980, equity return premiums exhibit a marked response. International risk-free rates respond less after 1980, than before, while the dividend-price ratio responds similarly in the full- and the post-1980 samples.

In sum, these findings support the evidence presented earlier, which suggests that the effect of US monetary policy on international equity return premiums has gained strength in the past few decades.

1.5 Explaining the Reaction to US Risk-Free Rate Changes

We can also decompose the effect of US rate innovations on equity return premiums in order to determine whether US monetary policy affects international return premiums through revisions in expectations about future return premiums, dividends or risk-free rates. This can be achieved by multiplying equations (23) to (25) with $\varvec{\phi }$, the vector describing the contemporaneous response of all variables in $\varvec{z}$ to US risk-free rate innovations. Accordingly, the response of the return premium news of country i is

$$\begin{aligned} \varvec{g}_1^i \rho _i \varvec{A} (\varvec{I}-\rho _i \varvec{A})^{-1} \varvec{\phi }, \end{aligned}$$

(30)

and the response of real risk-free interest rate news is

$$\begin{aligned} \varvec{g}_2^i (\varvec{I}-\rho _i \varvec{A})^{-1} \varvec{\phi }. \end{aligned}$$

(31)

In accordance with Eq. (27), the response of the present value of expected future dividends is

$$\begin{aligned} \varvec{g}_1^i \varvec{\phi } + \varvec{g}_1^i \rho _i \varvec{A} (\varvec{I} -\rho _i \varvec{A})^{-1} \varvec{\phi } + \varvec{g}_2^i (\varvec{I}-\rho _i \varvec{A})^{-1} \varvec{\phi } . \end{aligned}$$

(32)

Table 7 displays the median response over all 16 country pairs for the full sample, and the post-1980 sample. The post-1980 results indicate that revisions in the expectation about future return premiums explain most of the current return premium response. News about dividends and risk-free rates plays smaller roles. In contrast, over the full sample revisions in the expectation about future dividends explains most of the current return premium response, while news about future returns and risk-free rates play a smaller role.

This confirms our earlier finding based on another methodology. The post-1980 increase in international equity comovement was driven by factors other than dividends and risk-free rates.

Table 7 The impact of US monetary policy on dividends, interest rates and future premiums