Monetary policy perceptions and risk-adjusted returns: Have investors from G-7 countries benefitted?

Monetary policy perceptions and risk-adjusted returns: Have investors from G-7 countries benefitted? Abstract We examine the effect of the implied federal funds rate on several proxies for riskadjusted returns in stock exchanges from the G-7 countries. Using monthly data from Jan. 1993 to June 2016 we employ a GARCH model and find partial evidence that the expansionary monetary policy of the Federal Reserve improved the stock returns in some developed markets even after adjusting for risk. Robustness checks suggest that the implied fed funds rate also increased volatility during the same period in the U.K and the U.S. equity markets. The results are confirmed in tests on several risk adjusted return measures (Sharpe ratio, Treynor ratio, and Information ratio). Our results are consistent with previous research supporting the ideal that the (perceived) increase in returns has been due to a lower discount rate, consistent with the discounted cash flows valuation models. However, the result is conditional on what proxy is used in the risk adjusted returns. Lastly, our stock return models do not support the idea that G-7 markets generated abnormal returns as, adjusting for a number of controls, alpha is not statistically significant. Keywords: Implied federal funds rates, interest rates, monetary policy, risk-adjusted returns, G-7 countries. JEL Classification: G12, G15, F30. 1

I. Introduction Previous research has found that the expansionary monetary policy has contributed significantly to the increase in stock returns in developed markets (Assefa et al., 2017). Whereas the same relationship (interest rates stock returns) holds in emerging markets, the effect has been stronger in developed economies as interest rates have declined and stock returns have been substantially higher. Yet, as asset pricing models assume stock returns offer a compensation for risk, we must also adjust for the risk that investors have taken during the same period. We extend previous research in two ways explained below. We use the implied Federal funds rate (as a proxy for expectations on the future of monetary policy) rather than the realized fed funds rate. This has important implications has the stock market fluctuates based on expected movements in the discount rate, rather than on the actual announcement of the rate increase. For instance, Federal Reserve Chair Jeaneth Yellen multiple press conferences and interviews substantially influenced equity markets, without a realized change in the federal funds rate. Second, we use the risk-adjusted returns to measure whether the increase in returns has been beyond the inherent increased in equity risk. In finance terms, this will be equivalent to indicate that changes in the discount rate influences the price of risk, as expected by asset pricing models such as the CAPM. Also the discounted cash flows model suggests that the price of an asset increases as the discount rate (denominator) goes down, holding the cash flows (numerator) constant. We use a number of measures for risk-adjusted returns such as the Sharpe ratio, adjusted Sharpe ratio, Treynor ratio, among others; as proposed by Dowd (2000), Hubner (2005), Lou and Qi (2017). Using a GARCH model similar to Loudon (2017) and Zakamouline and Steen (2009), 2

we find robust evidence that the expansionary monetary policy of the Federal Reserve improved the stock returns in developed markets even after adjusting for risk. This result is puzzling since a lower discount rate implies a lower price of risk (i.e. in asset pricing models), suggesting a lower reward per unit of risk. This may be due to the difference between expected and realized returns as the market has exceeded expectations in the last few years. Our findings suggests that the lower implied interest rates in the U.S. have increased returns and risk-adjusted returns in G-7 countries. Further robustness tests indicate that changes in the IFFR have a positive effect on volatility; as the implied discount rate increases so does risk. This has occurred particularly in the latter part of the sample when markets became more concerned about the rate increase and (as suggested by the DCF) its impact on the discounted cash flows. II. Data description All data are collected monthly from January 1993 to June 2016 from Datastream for the G-7 countries, namely: Canada, France, Germany, Italy, Japan, UK and United States of America. The data collected are real effective exchange rates (REER), Industrial Production (IP), Counties Stock Index returns, Implied Federal Fund Rate (IFFR), World Stock Returns - MSCI, S&P 500 stock volatility (VIX), deposit interest rate. Three factor model variables form French s Dartmouth website: HML, SMB, and Mkt-R f. Dummy variable set for the 2008/9 recession is set 1 from Dec. 07 until June 09, 0 else. Table 1 presents the descriptive statistics. Table 2 present the correlation among the variables under considerations by country. 3

Table 1 presents the descriptive statistics of all series by country for the whole study period Jan. 1993 June 2016. Canada monthly average stock return is 0.725 (8.7 percent annually) with monthly standard deviation of 5.8. Industrial production growth for Canada is 0.132 monthly (1.584 percent annually). The average monthly stock returns of France is 0.525 (6.3 percent annually) with standard deviation of 5.83 percent and industrial production growth of.002 percent monthly (0.024 percent annually). The average monthly stock return of Germany is 0.63 (7.56 percent annually) with standard deviation of 6.516 percent and monthly industrial production growth rate of 0.146 (1.75 percent annually). The average monthly stock returns of Italy is 0.333 percent (3.996 percent annually) with standard deviation of 7.118 and the average monthly industrial production growth of -0.015 (-0.180 percent annually). The average monthly stock return of Japan is 0.207 percent (2.48 percent annually) with standard deviation of 5.434 and the monthly average industrial production growth in the study period is 0.012 percent (0.144 percent annually). The average monthly stock return of United Kingdom is 0.358 percent (4.296 percent annually) with standard deviation of 4.569 percent and the monthly average industrial production of 0.02 percent (0.24 percent annually). The average monthly stock return of United States is 0.656 (7.872 percent annually) with monthly standard deviation of 4.32 percent and the monthly average industrial production growth of 0.158 percent (1.896 percent annually). [Insert Table 1 about here] Table 2 presents the correlations among variables, including stock return, MSCI, industrial production, industrial production growth, REER, REER growth, Implied Federal Fund Ra, IFFR growth, Beta, Sigma, VIX, Information ratio (ratio of excess return divided by the modified value at risk), Sharpe ratio, Treynor Ratio, SMB, HML, Mkt-R f, Dummy variable for all countries. Generally, Table 2 result indicates that the highest and significant correlation is 4

between the stock returns and MSCI world stock returns with the value about (0.808) highly statistically significant. Stock return is also statistically significant and positively correlated with industrial production growth with value 0.092. Stock return is also negatively correlated with industrial production in level with value -0.052. Implied federal fund rate in levels and growth are not significantly correlated with stock returns. Stock returns also strongly correlated with Mkt R f with the value of 0.802. Treynor Ratio is also strongly and positively correlated with stock returns with the value of 0.781. MSCI the world stock index is highly positively correlated with Mkt-R f with the coefficient value of.991. MSCI is also significantly correlated with VIX with correlation value of -0.413. Implied federal fund rate is negatively and significantly correlated with VIX and Sigma. Finally, Implied Federal Fund Rate is negatively correlated with all stock volatility measures i.e. (Beta, Sigma and VIX). For all variables bivariate correlations see Table 2. Furthermore, Figure 1 shows monthly the stock returns of the G-7 countries. [Insert Table 2 about here] III. Methodology The methodology used is GARCH(1,1) since all the series are in return, except interest rates and yield which are in first differences (Bollerslev (1986)), GARCH is appropriate method. In all the models robust standard errors (Bollerslev-wooldrige) are reported. The GARCH model used in the analysis the following: R t R t-1 MSCI t + IndPro t + Risk-adj.ret. t + IFF t REER t Dum t t (1) Risk adjusted returns t Risk-adj. ret t-1 MSCI t + IndPro t + R t + IFF t REER t Dum t t (2) 5

t N(0, h t ) q h 2 t = α + k=1 βk t-k + l=1 γ p t h 2 t-l Where: R t stock index return R t-1 lagged stock index return MSCI t MSCI world stock return MSCI is replaced in the models with Fama and French three factor variables (i.e. Mkt-RF, SMB, and HML) IndPro t The change in industrial production Risk adjusted returns are: Sharpe Ratio, Information Ratio, and Treynor Ratio Risk Measures - (Beta and Std. deviation of stock return) IFF t - the change in implied federal fund rate REER t the change in real effective exchange rate Dum is dummy 1 from Dec., 2008 to June 2009 else 0 t error term The unexplained returns ( t ) are assumed to be normally distributed with zero mean and conditional variance governed by a standard GARCH(1,1) process. The maximum likelihood (ML) method is used to estimate the models. Risk adjusted stock returns are also used as a dependent variables: Information ratio (ratio of excess return divided by the modified value at risk), Sharpe ratio, Treynor ratio are also used. Sharpe ratio, Information ratio and Treynor ratio are defined below, for more information on these ratio s refer to Sharpe (1966), Goodwin (1998), and Treynor and Black (1973) respectively for more explanations. 6

Sharpe Ratio = R p R f σ p Where: R p Portfolio returns, R f risk free rate and σ p standard deviation of portfolio returns. Information Ratio = ER σ ER Where: ER - average excess return, σ ER Standard deviation of excess returns Treynor ratio = r i r f β i Where: r i Portfolio i s returns, r f risk free rate, and β i portfolio i s beta. The expected sign for ( MSCI coefficient is positive. The expected sign for Industrial production coefficient ( is also positive, as stock returns tend to be directly related with stock returns. The expected sign volatility measure (Beta, Sigma) are expected to be positive since risk and reward are positively related. The expected sign of the implied federal fund rate is negative since stock return is inversely related discount rate. Equation (1) is fitted also for the volatility measures as a dependent variable and stock return as independent variable. Including the stock returns lagged value as a control variable. IV. Results Table 3 Panel A shows that stock returns have been mainly influenced by the global stock market index, suggesting a relatively high integration to global markets, as expected, particularly among developed economies. In addition, stock returns are significantly sensitive to changes in real exchange rates; a stronger currency is associated with higher stock returns. When we control for the three factors (market risk premium, SMB, and HML) in Panel B of Table 3, the exchange rate variable remains strongly significant. Whereas the market risk premium (Rm-Rf) is statistically significant in all countries, risk factors SMB and HML are statistically significant 7

in about two third of the cases. Our variable of interest, change in the implied fed funds rate (IFFR_Growth) is only statistically significant in Germany, in both panels. The negative sign indicates that stock returns have benefited with lower implied yields. In Panel B, the constant (Alpha) is only statistically significant in the U.S. albeit, at a 10% level, suggesting that the U.S. stock market produced abnormal returns during our sample period. [Insert Table 3 about here] In Table 4 Panel A, we employ the Sharpe ratio, a proxy for risk adjusted returns as our dependent variable. In all countries, MSCI is statistically significant, at a less than 1% level, similar to Table 3. Interestingly, the Crises dummy variable becomes negative and statistically significant (at a 1% level) in all cases, suggesting that the crises period is associated with lower risk-adjusted returns; specifically, lower Sharpe ratios. Whereas real exchange rate is not equally significant as in the unadjusted stock returns, the implied federal funds rate is strongly significant in all models, suggesting that the perception of lower interest rates have increased stock returns, even after adjusting for risk. However, when we employ additional risk factors (market risk premium, HML, SMB) In Panel B of Table 4, the implied federal funds rate remains statistically significant in only Japan and the U.K. [Insert Table 4 about here] In Table 5, we run similar models to Table 4 but using a different proxy for risk-adjusted returns, the Treynor ratio. The results are similar in both Panel A and Panel B, except that the implied federal funds rate is not significant in any of the countries, unlike our previous models from Table 4. This finding suggests that we must be cautious about potential conclusions drawn 8

about the relationship between the perceived interest rates and risk-adjusted stock returns as the effect is dependent on the proxy and model used. The coefficients of the remaining control variables are overall similar to the Sharpe ratio results from Table 4. Similarly, in Table 6 we shift the dependent variable for an alternative proxy of risk-adjusted returns, the information ratio. In Panel A we observe that the MSCI index has substantially reduced its previous significance level. Yet, real effective exchange rates remain a statistically significant variable as stronger currencies are associated with higher risk-adjusted returns, similar to previous models. Our variable of interest, perceived federal funds rate is statistically significant only in the U.S. at a 1% significance level. These findings indicate that the implied changes in the federal funds rate benefit particularly the returns from U.S. stock exchanges, as lower discount rate has improved financial asset prices. Overall, the results remain in Panel B of Table 6, where we add the market risk premium, SMB and HML. The positive effect of real exchange rate and the inverse relationship between changes in the implied federal funds rate and U.S. risk-adjusted returns remain statistically significant. Lastly, in Table 7, we show that the implied federal fund rates have impacted the level of risk among G-7 countries. Specifically the U.K and the U.S. stock markets have experienced more volatility as a result of both lower interest rates and particularly during the financial crises as indicated by the implied federal fund rates coefficient and the crises dummy variable. The GARCH models did not converge for Canada and Japan. [Insert Table 5 7 about here] V. Conclusions The perceived changes in the federal funds rate have had a positive impact on the riskadjusted returns of the U.S. stock market, and, to a much lesser degree, on Japanese and British 9

stock markets. Yet, the effect is dependent on the model used and the proxy for risk-adjusted returns. Returns from the German stock exchanges appear to have positive stock returns when the federal funds rate decreased. Overall, our findings indicate that the stock returns of members of the G-7 are explained by the real effective exchange rate, the market risk premium or the MSCI index, depending on the model employed. To a lesser degree stock returns, depend on the implied changes in the federal discount rate and the proxy for risk-adjusted returns. Our results are consistent with previous research supporting the ideal that the (perceived) increase in returns has been due to a lower discount rate, consistent with the discounted cash flows valuation models. Our stock return models do not support the idea that G-7 markets generated abnormal returns as, adjusting for a number of controls, alpha is not statistically significant. Lastly, the effect of changes in the discount rate has increased the volatility of stock returns but only in British and American stock exchanges. 10

References Assefa, T. Esqueda, O, Mollick, A. (2017) Stock returns and interest rates around the World: A panel data approach Journal of Economics and Business 89 pp 20 35. Bollerslev, T. (1986) Generalized Autoregressive Conditional Heteroskedasticity Journal of Econometrics vol. 31, no. 3: 307 327. Dowd, K. (2000) Adjusting for risk: An improved Sharpe ratio International Review of Economics and Finance 9 pp. 209 222 Goodwin, T. (1998) The Information Ratio Financial Analysts Journal July/August 1998 pp 34 43. Hubner, G (2005) The Generalized Treynor Ratio Review of Finance 9 pp. 415 435 Lou, X. and Qi, X. (2017) The Dynamic Correlations among the G-7 and China: Evidence from both Realized and Implied Volatilities Working paper Loudon, G. (2017) The impact of global financial market uncertainty on the risk-return relation in the stock markets of G-7 countries Studies in Economics and Finance, Vol. 34 Iss 1 pp 2 23. Sharpe, W F. (1966) Mutual Fund Performance. Journal of Business, vol. 39 no. 1, Part II (January): 119 38. Treynor, J. L. and Black, F. (1973) How to use security analysis to improve portfolio selection. Journal of Business vol. 46, 66 86. Zakamouline, Valeri, and Steen Koekebakker (2009) "Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance." Journal of Banking & Finance 33, no. 7: 1242-1254. 11

Table 1 Summary Statistics monthly data from January 1993 until June 2016 Variables N Mean Std. Dev. Min Max. Canada Stock Return 281 0.725 5.766-27.155 21.009 MSCI 281 0.521 4.288-19.045 10.905 Industrial Production 280 102.637 9.849 76.994 114.921 Industrial Production Growth 279 0.132 0.957-3.226 3.516 REER 276 86.525 10.100 69.800 105.600 REER Growth 275-0.042 1.594-9.107 5.524 Implied Fed. Fund Rate (IFFR) 2.750 2.289 0.070 6.540 IFFR Growth. 281 0.099 12.722-59.794 100.000 Beta 156 1.105 0.219 0.666 1.683 Sigma 258 5.105 1.931 2.765 10.768 VIX 19.980 7.773 10.420 59.767 Information Ratio (IR) 234 0.909 2.711-6.478 6.525 Modified Sharp Ratio (MSR) Treynor Ratio (TR) SMB HML Mkt-Rf Dummy 258 156-0.195-0.789 0.041 0.352 0.508 0.067 7.826 4.691 2.069 2.352 4.321 0.251-118.283-18.402-9.810-9.540-19.540 0.000 24.306 10.436 10.400 11.650 11.450 France Stock Return 281 0.525 5.834-22.432 15.301 MSCI 281 0.521 4.288-19.045 10.905 Industrial Production 280 107.072 5.900 93.958 116.848 Industrial Production Growth 279 0.002 1.385-4.931 4.479 REER 276 100.230 4.299 91.400 109.400 REER Growth 275-0.050 0.723-2.435 2.816 Implied Fed. Fund Rate (IFFR) 2.750 2.289 0.070 6.540 IFFR Growth. 281 0.099 12.722-59.784 100.000 Beta 156 1.297 0.160 0.988 1.556 Sigma 258 5.622 1.829 2.823 9.967 VIX 19.980 7.773 10.420 59.890 Information Ratio (IR) 234 0.595 1.902-3.616 5.679 Modified Sharp Ratio (MSR) Treynor Ratio (TR) SMB HML Mkt-Rf Dummy 258 156-0.421-0.789 0.041 0.352 0.508 0.067 9.059 4.691 2.069 2.352 4.321 0.251-138.916-18.402-9.810-9.540-19.540 0.000 16.560 10.436 10.400 11.650 11.450 12

Table 1 Cont d Variables N Mean Std. Dev. Min Max. Germany Stock Return 281 0.630 6.516-24.351 22.389 MSCI 281 0.521 4. -19.045 10.905 Industrial Production 281 94.072 12.244 73.349 113.965 Industrial Production Growth 280 0.146 1.507-7.946 4.631 REER 276 103.479 6.475 91.800 120.700 REER Growth 275-0.064 0.891-2.455 4.018 Implied Fed. Fund Rate (IFFR) 2.750 2.289 0.077 6.540 IFFR Growth. 281 0.099 12.722-59.794 100.000 Beta 156 1.462 0.199 1.124 2.002 Sigma 258 6.241 2.213 2.582 10.623 VIX 19.980 7.773 10.420 59.890 Information Ratio (IR) 234 0.509 1.626-3.188 5.929 Modified Sharp Ratio (MSR) Treynor Ratio (TR) SMB HML Mkt-Rf Dummy 258 156-0.022-0.789 0.041 0.352 0.509 0.067 10.158 4.691 2.069 2.352 4.321 0.251-150.777-18.402-9.810-9.540-19.540 0.000 55.290 10.436 10.400 11.650 11.450 Italy Stock Return 281 0.333 7.118-23.625 21.407 MSCI 281 0.521 4.288-19.045 10.905 Industrial Production 281 106.906 9.651 90.522 122.371 Industrial Production Growth 280-0.015 1.278-4.931 4.479 REER 276 97.511 4.218 79.900 104.900 REER Growth 275-0.008 1.109-8.021 5.695 Implied Fed. Fund Rate (IFFR) 2.750 2.289 0.070 6.540 IFFR Growth. 281 0.099 12.722-59.784 100.000 Beta 156 1.319 0.309 0.837 2.087 Sigma 258 6.719 2.044 2.758 11.135 VIX 19.980 7.773 10.420 59.890 Information Ratio (IR) 234-0.255 1.947-4.967 4.374 Modified Sharp Ratio (MSR) Treynor Ratio (TR) SMB HML Mkt-Rf Dummy 258 156 0.455-0.789 0.041 0.352 0.508 0.067 3.129 4.691 2.069 2.352 4.321 0.251-6.890-18.402-9.810-9.540-19.540 0.000 46.601 10.436 10.400 11.650 11.450 13

Table 1 Cont d Japan Variables N Mean Std. Dev. Min Max. Stock Return 281 0.207 5.434-16.648 17.710 MSCI 281 0.521 4.288-19.045 10.905 Industrial Production 281 100.224 6.371 90.522 116.390 Industrial Production Growth 280 0.012 1.965-15.805 6.598 REER 276 101.924 16.774 67.600 147.500 REER Growth 275-0.121 2.560-6.882 5.695 Implied Fed. Fund Rate (IFFR) 2.750 2.289 0.070 6.540 IFFR Growth. 281 0.099 12.722-59.784 100.000 Beta 156 0.725 0.176 0.413 1.171 Sigma 258 5.095 1.223 2.402 7.523 VIX 19.980 7.773 10.420 59.890 Information Ratio (IR) 234-0.823 1.626-5.223 2.66 Modified Sharp Ratio (MSR) Treynor Ratio (TR) SMB HML Mkt-Rf Dummy 258 156-0.265-0.789 0.041 0.352 0.508 0.067 5.277 4.691 2.069 2.352 4.321 0.251-59.447-18.402-9.810-9.540-19.540 0.000 28.361 10.436 10.400 11.650 11.450 United Kingdom Variables N Mean Std. Dev. Min Max. Stock Return 281 0.358 4.569-19.127 13.241 MSCI 281 0.521 4.288-19.045 10.905 Industrial Production 281 104.325 5.291 93.800 112.521 Industrial Production Growth 280 0.020 0.890-4.675 2.602 REER 276 109.344 10.648 89.100 127.900 REER Growth 275 0.106 1.507-8.625 4.249 Implied Fed. Fund Rate (IFFR) 2.750 2.289 0.070 6.540 IFFR Growth. 281 0.099 12.722-59.784 100.000 Beta 156 1.013 0.146 0.688 1.280 Sigma 258 4.303 1.419 2.168 8.430 VIX 19.980 7.773 10.420 59.890 Information Ratio (IR) 234-0.516 1.806-5.307 3.359 Modified Sharp Ratio (MSR) Treynor Ratio (TR) SMB HML Mkt-Rf Dummy 258 156 0.171-0.789 0.041 0.352 0.508 0.067 8.538 4.691 2.069 2.352 4.321 0.251-119.823-18.402-9.810-9.540-19.540 0.000 51.614 10.436 10.400 11.650 11.450 14

Table 1 Cont d United States Variables N Mean Std. Dev. Min Max. Stock Return 281 0.656 4.232-17.247 10.833 MSCI 281 0.521 4.288-19.045 10.905 Industrial Production 281 98.368 11.357 71.039 112.877 Industrial Production Growth 280 0.158 0.647-4.303 2.047 REER 276 107.513 8.528 92.500 127.600 REER Growth 275 0.052 1.269-3.867 6.288 Implied Fed. Fund Rate (IFFR) 2.750 2.289 0.070 6.540 IFFR Growth. 281 0.099 12.722-59.784 100.000 Beta 156 0.874 0.085 0.629 1.029 Sigma 258 4.004 1.433 1.849 7.165 VIX 19.980 7.773 10.420 59.890 Information Ratio (IR) 234 1.022 3.725-8.178 13.220 Modified Sharp Ratio (MSR) Treynor Ratio (TR) SMB HML Mkt-Rf Dummy 258 156 0.155-0.789 0.041 0.352 0.508 0.067 4.434 4.691 2.069 2.352 4.321 0.251-54.679-18.402-9.810-9.540-19.540 0.000 15.781 10.436 10.400 11.650 11.450 15

Table 2 Correlation Coefficient Variables Stock Return Stock Return MSCI 0.808 (0.000 ) Industrial Production(IP) -0.052 (0.020 ) MSCI -0.082 Ind. Prod. (IP) Ind. Prod. Growth REER REER Growt h IFFR IFFR Growth Beta Sigma VIX Info. Ratio MSR Treyno r Ratio (TR) SMB HML Mkt-R F Dumm y Industrial Production Growth 0.092 (0.000 ) 0.099 0.015 (0.499) REER -0.004 (0.859) REER Growth 0.133 Implied Fed. Fund Rate 0.032 (IFFR) (0.157) 0.016 (0.497) -0.010 (0.671) 0.017 (0.465) -0.122 0.034 (0.133) 0.032 (0.159) -0.023 (0.310) -0.003 (0.886) 0.067 (0.003) 0.094 0.106-0.003 (0.890) IFFR Growth -0.033 (0.150) Beta -0.002 (0.956) Sigma 0.032 (0.179) VIX -0.331 Information Ratio (IR) 0.021 (0.388) Modified Sharp Ratio 0.010 (MSR) (0.663) -0.020 (0.375) -0.003 (0.928) 0.052 (0.028) -0.413 0.006 (0.825) 0.039 (0.100) -0.026 (0.260) -0.216-0.186 0.035 (0.118) 0.147-0.001 (0.984) 0.123-0.026 (0.397) -0.007 (0.761) -0.180 0.041 (0.096) 0.022 (0.358) 0.002 (0.924) 0.034 0.271) -0.123-0.016 (0.483) 0.050 (0.045) -0.018 (0.450) 0.004 (0.874) -0.004 (0.889) -0.007 (0.786) 0.044 (0.054) 0.068 (0.007) 0.001 (0.982) -0.003 (0.886) -0.133-0.330-0.105 0.243-0.017 (0.460) -0.036 (0.232) -0.051 (0.031) -0.294-0.029 (0.241) -0.001 (0.953) 0.541 0.032 (0.290) 0.050 (0.098) 0.012 (0.691) 0.284-0.104 0.033 (0.160) 0.006 (0.825) -0.025 (0.922) -.004 (0.858) Treynor Ratio (TR) 0.781 SMB -0.013 (0.571) HML -0.063 (0.005) Mkt-Rf 0.802 Dummy -0.140 t- Values in parenthesis 0.914-0.085-0.121 0.991-0.182-0.290-0.035 (0.118) 0.028 (0.220) -0.078 (0.001) 0.056 (0.013) 0.105 (0.001) -0.013 (0.578) 0.060 (0.007) 0.095-0.224-0.049 (0.114) 0.002 (0.916) 0.013 (0.562) 0.011 (0.634) -0.014 (0.534) -0.027 (0.386) 0.005 (0.816) -0.001 (0.985) -0.007 (0.752) -0.007 (0.776) -0.395-0.129 0.105-0.041 (0.071) -0.147-0.021 (0.492) 0.035 (0.117) -0.014 (0.550) -0.022 (0.334) -0.233 0.053 (0.081) -0.022 (0.465) -0.024 (0.422) 0.002 (0.958) 0.000 (0.999) 0.285 0.105-0.007 (0.752) 0.075 (0.002) -0.007 (0.783) -0.287-0.043 (0.054) -0.050 (0.027) -0.406 0.454-0.116-0.024 (0.324) 0.020 (0.412) -0.007 (0.788) 0.033 (0.183) 0.071 (0.019) 0.004 (0.872) -0.009 (0.706) 0.038 (0.104) 0.003 (0.909) 0.088 (0.004) 0.175 0.923-0.209-0.185 0.015 (0.508) 0.027 (0.232) -0.144-0.061 (0.007) -0.166 16

Table 3-A. Arch /Garch Models: G-7 Countries Stock returns dependent variable Canada France Germany Italy Japan UK USA StockReturnlag1-0.041-0.088*** -0.034-0.043 0.092* -0.031 0.017 (0.037) (0.028) (0.030) (0.047) (0.056) (0.030) (0.021) MSCI 1.013*** 1.219*** 1.348*** 1.189*** 0.823*** 0.951*** 0.960*** (0.048) (0.035) (0.054) (0.068) (0.091) (0.035) (0.018) IPGrowth 0.234-0.103 0.114-0.004 0.231-0.346** -0.128 (0.181) (0.086) (0.102) (0.139) (0.159) (0.137) (0.135) iffrgrowth 0.020-0.004-0.034*** -0.017-0.001-0.007 0.002 (0.018) (0.011) (0.011) (0.016) (0.024) (0.009) (0.005) reergrowth 0.939*** 1.007*** 0.872*** 1.195*** 0.261* 0.226** 0.322*** (0.126) (0.221) (0.259) (0.285) (0.158) (0.099) (0.066) dummy 1.754-0.277-0.323-0.643 0.663-0.852-0.225 (1.107) (0.505) (0.485) (0.818) (0.775) (0.579) (0.376) Cons -0.013 0.057 0.135-0.167-0.182-0.070 0.129 (0.173) (0.152) (0.180) (0.219) (0.256) (0.133) (0.089) L.arch 0.107** 0.080*** 0.416** 0.106*** 0.010 0.076* 0.042* (0.052) (0.030) (0.178) (0.030) (0.048) (0.044) (0.023) L.garch 0.729*** 0.908*** 0.529*** 0.884*** 0.993*** -0.606*** 0.948*** (0.153) (0.028) (0.151) (0.022) (0.080) (0.215) (0.025) N 274 275 274 274 274 274 274 Standard errors in parentheses * p<.10, ** p<.05, *** p<.01 17

Table 3-B. Arch /Garch Models: G-7 Countries Stock returns dependent variable Canada France Germany Italy Japan UK USA StockReturnlag1-0.060-0.100*** -0.022-0.069 0.033-0.063** 0.028 (0.038) (0.029) (0.036) (0.044) (0.048) (0.027) (0.019) Mkt_RF 1.017*** 1.220*** 1.340*** 1.197*** 0.843*** 0.971*** 0.921*** (0.049) (0.036) (0.051) (0.062) (0.065) (0.036) (0.018) SMB 0.121-0.195* -0.168-0.050 0.378*** -0.210*** -0.412*** (0.098) (0.101) (0.111) (0.125) (0.144) (0.055) (0.036) HML 0.004 0.188** -0.146 0.359*** 0.170* 0.233*** -0.119*** (0.122) (0.087) (0.111) (0.116) (0.097) (0.049) (0.033) IPGrowth 0.232-0.127 0.150 0.006 0.208-0.249** -0.225 (0.197) (0.081) (0.110) (0.140) (0.158) (0.122) (0.139) iffrgrowth 0.021 0.001-0.028*** -0.014-0.001-0.004 0.002 (0.020) (0.011) (0.011) (0.015) (0.016) (0.010) (0.005) reergrowth 0.857*** 0.869*** 0.771*** 1.079*** 0.297*** 0.261** 0.233*** (0.134) (0.213) (0.217) (0.295) (0.112) (0.115) (0.069) dummy 1.393-0.346-0.629-0.884 0.335-0.786-0.473 (1.144) (0.457) (0.581) (0.692) (0.718) (0.608) (0.428) Cons 0.032-0.037 0.114-0.320-0.252-0.159 0.146* (0.184) (0.165) (0.181) (0.243) (0.241) (0.133) (0.082) L.arch 0.099* 0.108 0.513*** 0.102*** 0.016 0.064 0.076** (0.060) (0.100) (0.196) (0.029) (0.018) (0.043) (0.039) L.garch 0.780*** 0.873*** 0.478*** 0.887*** 0.980*** 0.876*** 0.910*** (0.138) (0.111) (0.117) (0.023) (0.025) (0.099) (0.036) N 274 275 274 274 274 274 274 Standard errors in parentheses * p<.10, ** p<.05, *** p<.01 18

Table 4-A. Arch /Garch Models: G-7 Countries Sharpe Ratio dependent variable Canada France Germany Italy Japan UK USA Lag1 0.058*** 0.050*** 0.046*** 0.039*** 0.026** 0.034 0.049*** (0.009) (0.011) (0.007) (0.009) (0.013) (0.028) (0.008) MSCI 0.202*** 0.201*** 0.202*** 0.201*** 0.200*** 0.200*** 0.201*** (0.002) (0.001) (0.001) (0.003) (0.004) (0.007) (0.004) IPGrowth 0.017** -0.011-0.011** -0.003-0.006-0.005 0.010 (0.009) (0.008) (0.005) (0.006) (0.004) (0.012) (0.026) iffrgrowth -0.002*** -0.001*** -0.002*** -0.001** -0.001*** -0.002** -0.001** (0.001) (0.001) (0.001) (0.001) reergrowth -0.024*** 0.003 0.006 0.006-0.006** 0.014 0.016 (0.009) (0.010) (0.007) (0.013) (0.003) (0.023) (0.014) dummy -0.271** -0.302*** -0.313*** -0.307*** -0.286*** -0.312*** -0.275*** (0.123) (0.080) (0.080) (0.090) (0.087) (0.109) (0.106) Cons -0.035*** -0.031*** -0.026*** -0.027*** -0.024*** -0.032** -0.033*** (0.010) (0.010) (0.007) (0.007) (0.007) (0.015) (0.010) L.arch 0.818*** 1.046 1.072** 0.852** 0.808** 0.770 0.706* (0.289) (0.743) (0.456) (0.422) (0.388) (0.520) (0.392) L.garch 0.471*** 0.396 0.386*** 0.467*** 0.489*** 0.509** 0.539*** (0.102) (0.248) (0.134) (0.159) (0.161) (0.239) (0.180) N 173 174 173 173 173 173 173 Standard errors in parentheses * p<.10, ** p<.05, *** p<.01 19

Table 4-B. Arch /Garch Models: G-7 Countries Sharpe Ratio dependent variable Canada France Germany Italy Japan UK USA Sharpratiolag1 0.056*** 0.029 0.033 0.029-0.002 0.010 0.055*** (0.021) (0.028) (0.027) (0.030) (0.022) (0.023) (0.020) Mkt_RF 0.203*** 0.200*** 0.199*** 0.200*** 0.193*** 0.197*** 0.200*** (0.005) (0.007) (0.006) (0.007) (0.004) (0.005) (0.006) SMB -0.059*** -0.059*** -0.060*** -0.060*** -0.054*** -0.059*** -0.055*** (0.011) (0.011) (0.010) (0.011) (0.012) (0.012) (0.012) HML -0.021-0.026-0.032-0.028-0.024* -0.029* -0.028 (0.015) (0.016) (0.021) (0.017) (0.013) (0.018) (0.021) IPGrowth 0.043*** 0.005-0.016 0.004-0.005-0.002 0.024 (0.013) (0.019) (0.017) (0.010) (0.004) (0.021) (0.042) iffrgrowth -0.000-0.001-0.001-0.001-0.001* -0.002** -0.001 (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) reergrowth -0.031** -0.063** -0.050* -0.065** -0.012 0.027 0.044*** (0.013) (0.028) (0.026) (0.030) (0.008) (0.018) (0.015) dummy -0.150-0.186** -0.178* -0.187** -0.189** -0.224** -0.169** (0.094) (0.089) (0.091) (0.090) (0.077) (0.093) (0.082) Cons -0.120*** -0.150*** -0.144*** -0.145*** -0.114*** -0.142*** -0.127*** (0.031) (0.043) (0.037) (0.044) (0.027) (0.039) (0.036) L.arch 0.588*** 0.532*** 0.521*** 0.513*** 0.624*** 0.595*** 0.533*** (0.184) (0.146) (0.162) (0.143) (0.202) (0.180) (0.154) L.garch 0.564*** 0.579*** 0.584*** 0.588*** 0.555*** 0.558*** 0.593*** (0.081) (0.061) (0.063) (0.061) (0.073) (0.070) (0.060) N 173 174 173 173 173 173 173 Standard errors in parentheses * p<.10, ** p<.05, *** p<.01 20

Table 5-A. Arch /Garch Models: G-7 Countries Treynor ratio dependent variable Canada France Germany Italy Japan UK USA treynorlag1-0.000-0.001* -0.001-0.001** -0.001-0.001* -0.000 (0.001) MSCI 0.997*** 0.997*** 0.997*** 0.997*** 0.997*** 0.997*** 0.997*** (0.001) IPGrowth -0.001 0.001* -0.003 0.002* 0.000-0.002-0.007* (0.002) (0.001) (0.002) (0.001) (0.001) (0.002) (0.004) iffrgrowth -0.000-0.000-0.000-0.000-0.000-0.000-0.000 reergrowth -0.001-0.005*** -0.002-0.005*** -0.001 0.004** 0.002* (0.001) (0.002) (0.002) (0.002) (0.001) (0.002) (0.001) dummy -0.003-0.174*** -0.172*** -0.169*** 0.007-0.186*** -2.161*** (0.045) (0.043) (0.041) (0.042) (0.036) (0.049) (0.207) Cons -0.028*** -0.029*** -0.028*** -0.028*** -0.028*** -0.028*** -0.028*** (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) L.arch 1.106*** 1.123*** 1.139*** 1.116*** 1.126*** 1.006*** 1.279*** (0.221) (0.210) (0.216) (0.216) (0.205) (0.171) (0.218) L.garch 0.156** 0.172*** 0.146*** 0.164*** 0.133* 0.206*** 0.142*** (0.076) (0.063) (0.053) (0.062) (0.070) (0.067) (0.050) N 149 150 149 149 149 149 149 Standard errors in parentheses * p<.10, ** p<.05, *** p<.01 21

Table 5-B. Arch /Garch Models: G-7 Countries Treynor ratio dependent variable Canada France Germany Italy Japan UK USA Treynorlag1-0.007-0.005-0.003-0.004-0.007-0.007-0.001 (0.006) (0.005) (0.006) (0.006) (0.007) (0.007) (0.007) Mkt_RF 0.983*** 0.984*** 0.987*** 0.986*** 0.986*** 0.984*** 0.988*** (0.006) (0.007) (0.006) (0.006) (0.009) (0.005) (0.006) SMB -0.184*** -0.188*** -0.184*** -0.187*** -0.179*** -0.196*** -0.185*** (0.024) (0.013) (0.018) (0.018) (0.026) (0.021) (0.016) HML -0.031-0.029-0.028-0.031-0.027-0.029-0.029 (0.021) (0.018) (0.023) (0.020) (0.023) (0.019) (0.019) IPGrowth 0.041 0.033-0.017-0.012 0.006-0.031-0.031 (0.026) (0.029) (0.018) (0.017) (0.015) (0.036) (0.054) iffrgrowth 0.001 0.000 0.001 0.001 0.001 0.001 0.001 (0.001) (0.001) (0.001) (0.002) (0.002) (0.002) (0.002) reergrowth 0.004-0.031-0.036-0.016 0.009 0.015 0.026 (0.016) (0.035) (0.033) (0.034) (0.016) (0.015) (0.022) dummy -0.215* -0.289*** -0.254** -0.290*** -0.290*** -0.309*** -0.312** (0.120) (0.096) (0.103) (0.093) (0.095) (0.092) (0.133) Cons -0.252*** -0.236*** -0.247*** -0.236*** -0.240*** -0.222*** -0.242*** (0.058) (0.033) (0.045) (0.042) (0.057) (0.051) (0.044) L.arch 0.749*** 0.849*** 0.675*** 0.732*** 0.640*** 0.770*** 0.728*** (0.136) (0.240) (0.163) (0.188) (0.238) (0.249) (0.183) L.garch 0.195** 0.153 0.247** 0.202 0.270 0.195 0.211* (0.096) (0.112) (0.126) (0.124) (0.210) (0.145) (0.118) N 149 150 149 149 149 149 149 Standard errors in parentheses * p<.10, ** p<.05, *** p<.01 22

Table 6A. Arch /Garch Models: G-7 Countries Information Ratio dependent variable Canada France Germany Italy Japan UK USA InfoRatiolag1 0.963*** 0.929*** 0.905*** 0.936*** 0.943*** 0.953*** 0.977*** (0.018) (0.026) (0.029) (0.029) (0.027) (0.023) (0.025) MSCI -0.015* 0.005-0.001 0.001 0.003 0.004 0.005 (0.009) (0.010) (0.007) (0.009) (0.006) (0.006) (0.009) IPGrowth -0.039-0.001 0.021 0.060* -0.008 0.040 0.078 (0.031) (0.035) (0.025) (0.031) (0.017) (0.031) (0.068) iffrgrowth 0.003 0.001 0.004 0.002 0.002 0.001-0.006*** (0.003) (0.003) (0.003) (0.003) (0.002) (0.003) (0.002) reergrowth 0.119*** 0.218*** 0.091** 0.145*** 0.032** 0.044* 0.099*** (0.024) (0.066) (0.040) (0.054) (0.014) (0.024) (0.035) dummy 0.372* -0.185 0.084-0.110 0.135** -0.047 0.168 (0.196) (0.174) (0.150) (0.164) (0.068) (0.145) (0.144) Cons 0.032 0.064 0.048 0.017-0.037-0.036-0.011 (0.036) (0.050) (0.044) (0.047) (0.043) (0.039) (0.047) L.arch 0.315*** 0.099 0.359** 0.218 0.201*** 0.216** 0.236*** (0.107) (0.070) (0.148) (0.146) (0.070) (0.095) (0.087) L.garch 0.669*** 0.358 0.378** 0.415 0.622*** 0.736*** 0.660*** (0.091) (0.313) (0.148) (0.417) (0.153) (0.097) (0.090) N 227 228 227 227 227 227 227 Standard errors in parentheses * p<.10, ** p<.05, *** p<.01 23

Table 6B. Arch /Garch Models: G-7 Countries Information ratio dependent variable Canada France Germany Italy Japan UK USA InfoRatiolag1 0.964*** 0.929*** 0.911*** 0.937*** 0.943*** 0.955*** 0.977*** (0.018) (0.026) (0.032) (0.030) (0.028) (0.025) (0.024) Mkt_RF -0.018* 0.002 0.001 0.001 0.002 0.005 0.006 (0.009) (0.010) (0.007) (0.010) (0.006) (0.007) (0.010) SMB 0.002-0.008 0.007-0.011-0.000-0.003-0.003 (0.014) (0.025) (0.019) (0.022) (0.014) (0.012) (0.020) HML -0.012-0.008 0.020* 0.009-0.003 0.009-0.004 (0.011) (0.019) (0.012) (0.013) (0.010) (0.010) (0.015) IPGrowth -0.042 0.002 0.015 0.059* -0.007 0.042 0.076 (0.031) (0.035) (0.024) (0.033) (0.018) (0.032) (0.069) iffrgrowth 0.003 0.001 0.004 0.002 0.002 0.001-0.006** (0.003) (0.003) (0.003) (0.003) (0.002) (0.003) (0.003) reergrowth 0.122*** 0.226*** 0.081** 0.145*** 0.032** 0.045* 0.098** (0.024) (0.067) (0.040) (0.055) (0.014) (0.026) (0.040) dummy 0.356* -0.192 0.081-0.104 0.131* -0.030 0.161 (0.197) (0.175) (0.157) (0.171) (0.070) (0.151) (0.151) Cons 0.044 0.069 0.036 0.013-0.035-0.044-0.007 (0.040) (0.051) (0.044) (0.048) (0.044) (0.040) (0.054) L.arch 0.340*** 0.097 0.394** 0.227 0.200*** 0.216** 0.236*** (0.127) (0.070) (0.171) (0.173) (0.069) (0.098) (0.086) L.garch 0.647*** 0.351 0.351** 0.371 0.620*** 0.735*** 0.659*** (0.106) (0.302) (0.165) (0.528) (0.156) (0.099) (0.091) N 227 228 227 227 227 227 227 Standard errors in parentheses * p<.10, ** p<.05, *** p<.01 24

Table 7. Arch /Garch Models: G-7 Countries Sigma of the stock returns dependent variable Canada France Germany Italy Japan UK USA Sigmalag1-0.984*** 0.986*** 0.999*** - 0.996*** 0.986*** (0.010) (0.009) (0.009) (0.011) (0.008) StockReturn - -0.001-0.001-0.005* - -0.003-0.001 (0.005) (0.003) (0.003) (0.004) (0.003) Skewness - -0.056-0.036-0.020-0.048-0.024 (0.045) (0.046) (0.050) (0.059) (0.038) IPGrowth - -0.011-0.037** -0.017 - -0.012 0.020 (0.018) (0.015) (0.017) (0.013) (0.025) iffrgrowth - -0.002-0.003-0.001 - -0.002* -0.002* (0.002) (0.002) (0.002) (0.001) (0.001) dummy - 0.229** 0.216* 0.305*** - 0.260*** 0.220*** (0.114) (0.111) (0.098) (0.076) (0.058) Cons - 0.067 0.071-0.030 - -0.003 0.032 (0.059) (0.056) (0.060) (0.045) (0.034) L.arch - 0.117-0.035** -0.033* - 0.419** -0.027** (0.214) (0.015) (0.020) (0.168) (0.011) L.garch - 0.005 0.830*** 0.785** - 0.028-0.777*** (0.345) (0.250) (0.378) (0.159) (0.076) N 256 256 256 256 257 Standard errors in parentheses * p<.10, ** p<.05, *** p<.01 Canada and Japan did not converge. 25

-20 0 20 StockReturn -20 0 20-20 0 20 Figure 1. Monthly stock returns G-7 countries (Jan. 1993 June 2016 ) Canada France Germany Italy Japan UK Jan-95Jan-00Jan-05Jan-10Jan-15 Jan-95Jan-00Jan-05Jan-10Jan-15 USA Jan-95Jan-00Jan-05Jan-10Jan-15 Graphs by country time 26