Identifying Shock Propagation Mechanisms in Global Equity Markets
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Vance L. Martin
Abstract
The intertemporal capital asset pricing model with time-varying price and quantity risk factors, is used to study the propagation mechanisms linking expected risk premia with shocks in global equity markets. The model allows for linear and nonlinear propagation channels with the relationship between expected risk premia and world and country shocks characterized by a bivariate cubic. Using daily data on developed and emerging country equity returns, the empirical results show that country risk prices are exposed to world risks, although the signs differ between developed and emerging countries. Country risk factors are especially important for risk prices in Asia-Pacific countries as well as selected emerging countries. Of the financial risk factors investigated, volatility risk is important for all developed countries, and currency basis risk is important for all emerging countries. The nonlinear propagation mechanisms linking shocks and expected risk premia are economically significant and show that the size and sign of shocks are important. Implications of the empirical results for international portfolio diversification are also investigated using a range of simulation experiments.
Appendix A: Summary Statistics and Preliminary Tests
Descriptive statistics of daily percentage excess equity returns are given in Table 5, with plots of the data in Figure 7. Average excess returns are all positive with the exception of Japan which has a daily average excess return of −0.001 %. Finland has the highest average daily excess return of 0.040 %, or 252 × 0.040 = 10.08 % per annum, with the US having the next highest given by 0.037 %, or 252 × 0.037 = 9.32 % per annum. For comparison, the average daily excess equity return on the global developed equity market index including the US is 0.025 %, which is marginally higher than the average daily return of 0.021 % on the same index but excluding the US. Average daily returns for the emerging markets range from 0.027 % for Brazil which is comparable to the average returns on the developed market indexes, to as low as 0.009 % for Turkey. Overall average returns on emerging markets are lower than developed markets with an average return on the emerging market index of 0.016 %, or 252 × 0.016 = 4.03 % per annum.
Summary statistics of daily percentage excess log-returns on equities, August 4, 1992 to June 29, 2018.
| Country | Mean | Median | SD | Beta | Min. | Max. | Skew. | EKurt. | AR1 |
|---|---|---|---|---|---|---|---|---|---|
| Developed | |||||||||
| Australia | 0.011 | 0.000 | 1.266 | 0.799 | −14.604 | 13.228 | −0.576 | 7.204 | 0.072 |
| Canada | 0.015 | 0.049 | 1.250 | 1.055 | −12.364 | 9.125 | −0.699 | 6.347 | 0.054 |
| Denmark | 0.025 | 0.008 | 1.328 | 0.935 | −13.763 | 10.913 | −0.300 | 3.698 | 0.016 |
| Finland | 0.040 | 0.006 | 1.788 | 1.298 | −18.642 | 15.046 | −0.280 | 3.674 | 0.017 |
| France | 0.005 | 0.000 | 1.476 | 1.288 | −11.543 | 12.217 | −0.066 | 3.186 | −0.017 |
| Germany | 0.019 | 0.012 | 1.517 | 1.321 | −9.498 | 12.563 | −0.113 | 2.366 | −0.021 |
| Hong Kong | 0.014 | 0.000 | 1.569 | 0.708 | −14.709 | 17.221 | 0.023 | 7.015 | 0.004 |
| Japan | −0.001 | −0.004 | 1.419 | 0.559 | −12.264 | 12.765 | 0.052 | 2.570 | −0.060 |
| New Zealand | 0.010 | 0.000 | 1.078 | 0.516 | −11.354 | 8.244 | −0.596 | 3.803 | 0.069 |
| Singapore | 0.009 | 0.000 | 1.284 | 0.609 | −16.410 | 17.753 | −0.145 | 15.185 | 0.059 |
| UK | 0.002 | 0.000 | 1.239 | 1.075 | −11.598 | 11.113 | −0.287 | 5.466 | −0.004 |
| US | 0.037 | 0.061 | 1.695 | 0.549 | −11.125 | 17.183 | 0.061 | 3.500 | −0.054 |
| Emerging | |||||||||
| Brazil | 0.027 | 0.000 | 2.703 | 1.203 | −19.218 | 23.324 | −0.015 | 3.047 | 0.016 |
| Colombia | 0.016 | −0.010 | 1.518 | 0.487 | −12.526 | 15.073 | −0.231 | 6.049 | 0.138 |
| India | 0.016 | 0.000 | 1.638 | 0.683 | −19.143 | 19.541 | −0.223 | 6.117 | 0.077 |
| Pakistan | 0.019 | 0.000 | 1.526 | 0.108 | −15.543 | 13.001 | −0.602 | 6.337 | 0.068 |
| South Africa | 0.010 | 0.000 | 1.602 | 0.826 | −23.456 | 11.002 | −0.857 | 9.007 | 0.046 |
| Turkey | 0.009 | 0.000 | 2.861 | 0.894 | −29.469 | 30.712 | −0.390 | 7.819 | 0.039 |
| World | |||||||||
| Developed with US | 0.025 | 0.050 | 0.882 | n.a. | −6.670 | 9.200 | −0.268 | 5.044 | 0.150 |
| Developed excl. US | 0.021 | 0.050 | 0.960 | n.a. | −8.100 | 7.430 | −0.245 | 3.137 | 0.120 |
| Emerging | 0.016 | 0.010 | 1.137 | n.a. | −9.512 | 10.600 | −0.390 | 4.908 | 0.235 |
Daily percentage excess log-returns of country stock markets, August 4, 1992 to June 29, 2018.
The emerging markets tend to experience higher daily volatility than the equity markets of developed countries, with Turkey exhibiting the highest absolute volatility ranging from a minimum of −29.47 % to a maximum of 30.71 %, with an annualized volatility of
The descriptive statistics reveal evidence of higher-order moment effects, with Skew measuring skewness and EKurt measuring excess kurtosis. Most country returns exhibit negative skewness with the exception of the US, Hong Kong and Japan which all exhibit positive skewness. All excess equity returns exhibit excess kurtosis with Singapore experiencing the highest with excess kurtosis of 15.18, with Germany experiencing the lowest
Table 6 gives the results of some preliminary nonlinearity tests applied to the excess log-returns of stocks in developed and emerging countries. Both bivariate and univariate tests are presented. The bivariate test is based on the MIS statistic of Kahra, Martin and Sarkar (2018) which is a joint test of nonlinearities in both country and world excess returns, conditional on a linear relationship between current and past equity returns. The MIS statistic involves three steps. In the first step a bivariate GARCH model is estimated which is used to generate estimates of the conditional variances for country and world excess returns. The second step involves regressing country returns on a constant and lagged country and world returns, and extracting the residuals from this regression. The third step is a weighted least squares regression where the dependent variable is the residual series from the second step weighted by the inverse of the conditional standard deviation on country returns obtained in the first step. The explanatory variables consist of a constant, a cubic in lagged country returns and a cubic in lagged world returns, with the same weights used to weight the dependent variable. Under the null hypothesis the MIS statistic is distributed asymptotically as chi-square with 6 degrees of freedom. The univariate nonlinear tests consist of the LST test of Luukkonen, Saikkonen and Teräsvirta (1988), and the artificial neural network (ANN) test proposed by Teräsvirta, Lin and Granger (1993).
Nonlinearity tests of the daily percentage excess log-returns on country and world stocks.
| Country | MIS
|
MIS
|
LST | ANN |
|---|---|---|---|---|
| Developed | ||||
| Australia | 0.000 | 0.004 | 0.000 | 0.000 |
| Canada | 0.000 | 0.001 | 0.000 | 0.000 |
| Denmark | 0.010 | 0.010 | 0.083 | 0.589 |
| Finland | 0.091 | 0.001 | 0.011 | 0.001 |
| France | 0.020 | 0.094 | 0.079 | 0.011 |
| Germany | 0.040 | 0.000 | 0.158 | 0.041 |
| Hong Kong | 0.000 | 0.000 | 0.000 | 0.563 |
| Japan | 0.000 | 0.000 | 0.000 | 0.070 |
| New Zealand | 0.000 | 0.028 | 0.000 | 0.000 |
| Singapore | 0.000 | 0.005 | 0.000 | 0.000 |
| UK | 0.659 | 0.033 | 0.017 | 0.817 |
| US | 0.000 | 0.002 | 0.000 | 0.018 |
| Emerging | ||||
| Brazil | 0.006 | 0.002 | 0.000 | 0.001 |
| Colombia | 0.000 | 0.006 | 0.000 | 0.000 |
| India | 0.000 | 0.009 | 0.000 | 0.000 |
| Pakistan | 0.000 | 0.016 | 0.000 | 0.000 |
| South Africa | 0.034 | 0.005 | 0.000 | 0.000 |
| Turkey | 0.148 | 0.006 | 0.000 | 0.000 |
| World | ||||
| Developed with US | n.a. | n.a. | 0.000 | 0.000 |
| Developed without US | n.a. | n.a. | 0.000 | 0.000 |
| Emerging | n.a. | n.a. | 0.000 | 0.000 |
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Nonlinearity tests of the daily percentage excess log-returns on country
The results reported in Table 6 show that at least one of the nonlinearity tests provides evidence of nonlinearities in excess equity returns. The bivariate MIS tests identify nonlinearities in most country and world equity returns, with the exception of the UK and Turkey and to a lesser extent Finland in the case of country excess returns, and France in the case of world excess returns, where there is evidence of nonlinearities at the 10 % level.
The univariate nonlinearity tests LST and ANN, also find strong evidence of nonlinearities in most equity returns with the exception of Germany in the case of the LST test, and Denmark, the UK and Hong Kong in the case of the ANN test. These tests also results also reveal significant nonlinearities amongst the excess returns of the world aggregate indices for developed and emerging countries.
Appendix B: Robustness Tests
Three robustness tests of the ICAPM with time-varying price and quantities are performed. The first consists of autocorrelation diagnostic tests of the country and world disturbance terms. This analysis also includes an investigation of the effects on the parameter estimates from potential structural breaks. The second diagnostic test extends the financial risk factors to include credit default swaps. The third test investigates the sensitivity of the risk exposure estimates from replacing the financial risk factors by Fama and French (2015) global risk factors.
B.1 Diagnostics
Table 7 provides autocorrelation diagnostic tests of the country ui,t+1 and world uw,t+1 disturbance terms in equation (5), with the results reported in terms of asymptotic p-values. The first is AUTO which is a test for first order autocorrelation by estimating an AR(1) regression of the residual from the estimated bivariate model, and testing the statistical significance of the parameter on the lagged residual. The second is a Lagrange Multiplier test for first order autocorrelation (LM) by augmenting the AR(1) regression with a set of control variables. The control variables consist of the risk quantity σiw,t from equation (6), the full set of financial risk factors x t in equations (1) and (2), and the interaction terms between the risk quantity and the components of the risk price γ t in (9), evaluated at the maximum likelihood parameter estimates. The choice of the interaction terms is based on the need to condition the test for the presence of nonlinearities. The tests have asymptotic chi-square distributions under the null hypothesis of no autocorrelation with one degree of freedom.
Diagnostic autocorrelation tests applied to the disturbance terms.
| Country | u i,t+1 | u w,t+1 | ||
|---|---|---|---|---|
| AUTO | LM | AUTO | LM | |
| Developed | ||||
| Australia | 0.111 | 0.489 | 0.010 | 0.002 |
| Canada | 0.049 | 0.053 | 0.003 | 0.001 |
| Denmark | 0.257 | 0.926 | 0.167 | 0.051 |
| Finland | 0.058 | 0.226 | 0.080 | 0.016 |
| France | 0.045 | 0.441 | 0.008 | 0.005 |
| Germany | 0.410 | 0.469 | 0.065 | 0.008 |
| Hong Kong | 0.024 | 0.964 | 0.205 | 0.011 |
| Japan | 0.407 | 0.032 | 0.067 | 0.015 |
| New Zealand | 0.388 | 0.015 | 0.072 | 0.008 |
| Singapore | 0.116 | 0.256 | 0.032 | 0.252 |
| UK | 0.421 | 0.652 | 0.031 | 0.007 |
| US | 0.000 | 0.012 | 0.896 | 0.750 |
| Emerging | ||||
| Brazil | 0.001 | 0.335 | 0.063 | 0.044 |
| Colombia | 0.012 | 0.334 | 0.014 | 0.271 |
| India | 0.930 | 0.336 | 0.018 | 0.008 |
| Pakistan | 0.003 | 0.015 | 0.358 | 0.963 |
| South Africa | 0.591 | 0.028 | 0.274 | 0.183 |
| Turkey | 0.477 | 0.646 | 0.062 | 0.118 |
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Diagnostic autocorrelation tests applied to the disturbance terms ui,t+1 and uw,t+1, with the results reported in terms of asymptotic p-values. The tests consist of AUTO which is a test for first order autocorrelation by estimating an AR(1) regression of the residual from the estimated bivariate model, and testing the statistical significance of the parameter on the lagged residual. The LM test is a Lagrange Multiplier test for first order autocorrelation (LM) by augmenting the AR(1) regression with a set of control variables. The tests have asymptotic chi-square distributions under the null hypothesis of no autocorrelation with one degree of freedom.
In general the prototype model specification allowing for time-varying risk prices and quantities satisfies the autocorrelation tests. All developed countries satisfy at least one of the autocorrelation tests applied to ui,t+1 at the 1 % nominal significance level. Similar qualitative results are obtained for uw,t+1, with the exception of Canada and France. The autocorrelation tests applied to the emerging market countries show no evidence of autocorrelation in the disturbance terms for at least one of the tests at the 1 % level.
As a complement to the autocorrelation diagnostic tests the presence of outliers are investigated by including dummy variables to capture potential structural breaks. Examples include the impact of the Global Financial Crisis on US equity markets between June 2008 to the end of 2009, which capture the extreme movements in the US equities associated with specific bank failures including the Lehman Brothers in September 2008; the effect of the tsunami on the Fukushima Daiichi nuclear power plant on March 11, 2011 combined with increased volatility in the Japanese equities; and the change in monetary policy regimes in South Africa such as the move to inflation targeting in February 2000. In all cases investigated the parameter estimates of the model, including the exposure parameter estimates of the risk price for each country, remain robust to conditioning on structural break dummy variables.
B.2 Credit Default Swaps
A further robustness check of the model presented in Table 2 extends the set of financial risk factors to include credit default swaps (CDS). Estimation of the model is restricted to start on October 7, 2008, which is when data on CDS begin. Estimates of the model reveal no significant effect of CDS on risk prices in developed and emerging countries, thereby ruling out potential nonlinear risk channels operating. There is limited evidence that CDS operate through linear channels in some Asian Pacific countries such as Australia, Hong Kong, Japan and New Zealand, but not in any of the other developed countries or emerging countries.
B.3 Fama-French Risk Factors
As a robustness experiment to the risk price exposure estimates of world and country risk factors reported in Table 2, Table 8 gives the risk price parameter estimates of the model with the financial risk factors replaced by the Fama and French (2015) global risk factors consisting of size (r smb,t ), value (r hml,t ), profitability (r rmw,t ) and investment (r cma,t ) risks. Data on the risk factors are taken from Ken French’s database.
Time-varying risk price parameter estimates with Fama-French risk factors.
| Country | Risk price factors | ||||||
|---|---|---|---|---|---|---|---|
| Const. | Ctry | World | Size | Value | Profit | Invest. | |
| Developed | |||||||
| Australia | −0.004 | −0.032 | 0.153 | 0.197 | 0.024 | 0.229 | 0.120 |
| (0.809) | (0.001) | (0.000) | (0.000) | (0.625) | (0.000) | (0.049) | |
| Canada | −0.000 | 0.005 | 0.045 | 0.066 | −0.005 | 0.131 | 0.140 |
| (0.960) | (0.539) | (0.012) | (0.045) | (0.905) | (0.010) | (0.004) | |
| Denmark | 0.005 | −0.030 | 0.084 | 0.076 | 0.000 | 0.115 | 0.058 |
| (0.775) | (0.001) | (0.000) | (0.042) | (0.987) | (0.076) | (0.331) | |
| Finland | −0.007 | −0.024 | 0.106 | 0.115 | −0.019 | 0.149 | 0.124 |
| (0.709) | (0.003) | (0.000) | (0.004) | (0.675) | (0.021) | (0.030) | |
| France | −0.000 | −0.015 | 0.118 | 0.130 | −0.000 | 0.154 | 0.168 |
| (0.981) | (0.108) | (0.000) | (0.001) | (0.990) | (0.025) | (0.004) | |
| Germany | 0.000 | −0.023 | 0.136 | 0.144 | −0.001 | 0.174 | 0.174 |
| (0.970) | (0.025) | (0.000) | (0.000) | (0.970) | (0.004) | (0.001) | |
| Hong Kong | −0.006 | −0.025 | 0.120 | 0.152 | 0.020 | 0.209 | 0.119 |
| (0.733) | (0.000) | (0.000) | (0.000) | (0.603) | (0.000) | (0.033) | |
| Japan | 0.003 | −0.034 | 0.100 | 0.181 | −0.008 | 0.183 | 0.139 |
| (0.826) | (0.000) | (0.000) | (0.000) | (0.815) | (0.000) | (0.002) | |
| New Zealand | −0.002 | −0.020 | 0.083 | 0.114 | 0.017 | 0.150 | 0.114 |
| (0.883) | (0.089) | (0.001) | (0.007) | (0.685) | (0.018) | (0.048) | |
| Singapore | 0.006 | −0.015 | 0.091 | 0.120 | 0.001 | 0.152 | 0.115 |
| (0.749) | (0.107) | (0.000) | (0.001) | (0.971) | (0.010) | (0.041) | |
| UK | 0.002 | −0.012 | 0.115 | 0.128 | −0.002 | 0.145 | 0.165 |
| (0.896) | (0.293) | (0.000) | (0.002) | (0.964) | (0.029) | (0.004) | |
| US | 0.008 | 0.062 | −0.070 | 0.180 | 0.069 | −0.026 | −0.037 |
| (0.618) | (0.000) | (0.000) | (0.001) | (0.406) | (0.793) | (0.691) | |
| Emerging | |||||||
| Brazil | 0.000 | 0.030 | −0.023 | 0.017 | 0.005 | −0.131 | 0.077 |
| (0.997) | (0.000) | (0.000) | (0.373) | (0.898) | (0.011) | (0.065) | |
| Colombia | −0.010 | 0.021 | −0.028 | −0.050 | −0.008 | −0.092 | −0.026 |
| (0.483) | (0.000) | (0.000) | (0.002) | (0.810) | (0.044) | (0.530) | |
| India | −0.014 | 0.001 | −0.005 | −0.078 | −0.029 | −0.145 | 0.059 |
| (0.394) | (0.827) | (0.495) | (0.000) | (0.469) | (0.017) | (0.226) | |
| Pakistan | −0.028 | −0.001 | −0.018 | −0.079 | −0.002 | −0.125 | −0.006 |
| (0.080) | (0.749) | (0.010) | (0.000) | (0.947) | (0.030) | (0.891) | |
| South Africa | −0.005 | 0.023 | −0.014 | −0.029 | −0.016 | −0.105 | 0.068 |
| (0.732) | (0.000) | (0.039) | (0.125) | (0.615) | (0.022) | (0.114) | |
| Turkey | −0.019 | 0.005 | −0.016 | −0.076 | −0.020 | −0.124 | 0.026 |
| (0.240) | (0.096) | (0.022) | (0.000) | (0.601) | (0.030) | (0.569) | |
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Time-varying risk price parameter estimates of equation (9) allowing for Fama-French risk factors, with asymptotic p-values in parentheses.
A comparison of Tables 2 and 8 show that the empirical results regarding world and country risk factors are largely robust to the two sets of risk factors. World and country risks are important determinants of country risk prices which in turn, generate significant nonlinear relationships between expected risk premia and the shocks in global equity markets. Two important difference in the two sets of results is that by conditioning on Fama-French risk factors Canada is at least exposed to world risks, while Finland is now exposed to both world and country risks.
The Fama-French size and profitability risk factors are significant for almost all countries, including developed and emerging countries. The investment risk factor is important for many of the developed countries, but only for Brazil (at the 10 %) amongst emerging countries. By comparison, none of the developed and emerging country risk prices exhibit any significant exposure to the value risk factor.
Appendix C: Regional Model
A property of the country risk price empirical results in Tables 2 and 8 is that the risk exposure of sub-groups of countries are qualitatively similar suggesting the presence of regional effects. Practically all countries have exposure to world risk factors which are positive for developed countries and negative for emerging countries. Asia-Pacific countries have negative exposure to country risk factors regardless of the choice of risk factors, and to a lesser extent so do European countries provided that conditioning is based on Fama-French risk factors. Of the financial risk factors, volatility risk is important for developed countries, whereas it is currency basis risk that is important for emerging countries. Of the Fama-French risk factors, most countries have exposure to size and profitability risk factors which is positive for developed countries and negative for emerging countries apart from Brazil in the case of the size risk factor which is positive but statistically insignificant.
To capture regional effects, an aggregated version of the model is estimated for four regions: Asia-Pacific, Europe, North America and Emerging. The market factor for each regional model is taken as the world developed market factor that excludes the US in the case of the North American model, while including the US in the case of the other three regions. The parameter estimates of the regional risk prices are given in Table 9 based on the same set of risk factors used for the country base model in Table 2, except that now the country risk factor represents the pertinent regional risk factor. The Asia-Pacific risk exposures mimic the country risk exposures of Table 2, with positive world risks and negative regional risks with the former risks dominating the latter in absolute terms. Similar results occur for the European regional model with significant positive exposure to the world factor and negative exposure to the regional factor. The North American regional results mimic the dominance of the US in the global economy as highlighted by the US results in Table 2, with the region having negative exposure to the world factor and positive exposure to the regional factor.
Time-varying regional risk price parameter estimates for regions.
| Region | Risk price factors | |||||||
|---|---|---|---|---|---|---|---|---|
| Const. | Region | World | Credit | Liquid. | Curr. | Basis | Vol. | |
| Asia Pacific | 0.002 | −0.031 | 0.104 | −0.028 | 0.011 | −0.024 | 0.019 | 0.039 |
| (0.889) | (0.001) | (0.000) | (0.868) | (0.955) | (0.404) | (0.034) | (0.000) | |
| Europe | 0.025 | −0.051 | 0.127 | −0.073 | 0.039 | −0.004 | 0.021 | 0.042 |
| (0.155) | (0.001) | (0.000) | (0.652) | (0.823) | (0.882) | (0.039) | (0.000) | |
| North Am. | −0.032 | 0.219 | −0.050 | −0.071 | −0.489 | 0.044 | 0.010 | 0.115 |
| (0.137) | (0.000) | (0.000) | (0.644) | (0.061) | (0.126) | (0.216) | (0.000) | |
| Emerging | 0.005 | −0.016 | 0.058 | −0.037 | 0.139 | −0.017 | 0.020 | 0.024 |
| (0.777) | (0.055) | (0.004) | (0.850) | (0.472) | (0.583) | (0.025) | (0.000) | |
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Time-varying regional risk price parameter estimates of equation (9) allowing for macroeconomic risk factors, with asymptotic p-values in parentheses.
The Emerging market regional results where the region has negative exposure to regional shocks, is consistent with the individual emerging market results presented in Table 2 as it is a reflection that the world emerging market index was used as the pertinent global market index in the latter models. The positive exposure of the emerging market region to world risks provides further support for the conclusion that developed and emerging aggregate risk factors capture different types of risks which move counter-cyclically to each other.
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