Diversification, Cost Structure, and the Risk Appendix

For Online Publication Appendix A Derivation of the Model We present here the derivation of the results of Section 2. In the continuation region, each one of the three value functions of a firm (Vh , Vj , and Vjo ) satisfies: π(a, Y, X)M∆t + E[M∆t · V (a, Y ′ , X|Y )] − V (a, Y, X) = 0. (B.1) For ∆t → 0: π(a, Y, X)Mdt + E[d(M · V (a, Y, X))] = 0. (B.2) The term in the expectation can be written as: E[d(M · V )] = E[dM · V + M · dV + dM · dV ]   dV dM dV dM + + · = M ·V ·E M V M V      dV dM dV = M · V −rdt + E +E · V M V      dM dV dV +E · = Mdt −rV + E dt M dt (B.3) where the dependence of V on (a, Y, X) has been suppressed to ease the notation. Plugging (B.3) into (B.2): π − rV + E  dV dt  +E  dM dV · M dt  = 0. (B.4) By applying Ito’s Lemma and using the expressions for the Brownian motions ruling the evolution of Y , we can derive expressions for some of the terms in (B.4): 1 1 = VY′ dY + σ 2 Y 2 VY′′ dt = VY′ [µY dt + σY dz] + σ 2 Y 2 VY′′ dt 2 2 1 E[dV ] = µY VY′ dt + σ 2 Y 2 VY′′ dt . 2 dV Using these results and the equation describing the evolution of M, we can 36 rewrite (B.4) for the three value functions as: 1 πh dt − rh Vh dt + µh Yh Vh ′Y dt + σh2 Yh2 Vh ′′Y dt + ... 2    1 2 2 ′′ ′ ′ ...E (−rh dt − γσh dzh ) · µh Yh Vh Y dt + σh Yh Vh Y dzh + σh Yh Vh Y dt = 0. 2 1 πj dt − rh Vj dt + µj Yj Vj ′Y dt + σj2 Yj2 Vj ′′Y dt + ...   2  1 2 2 ′′ ′ ′ ...E (−rh dt − γσh dzh ) · µj Yj Vj Y dt + σj Yj Vj Y dzj + σj Yj Vj Y dt = 0. 2 1 −rh Vjo dt + µj Yj Vjo ′Y dt + σj2 Yj2 Vjo ′′Y dt + ...   2 1 2 2 o ′′ o′ o′ = 0. ...E (−rh dt − γσh dzh ) · µj Yj Vj Y dt + σj Yj Vj Y dzj + σj Yj Vj Y dt 2 The terms in expectations can be reduced to:  E (−rh dt − γσh dzh ) ·  µh Yh Vh ′Y dt + σh Yh Vh ′Y dzh  1 2 2 ′′ = ... + σh Yh Vh Y dt 2 ... − γσh2 Y Vh ′Y dt    1 2 2 ′′ ′ ′ = ... E (−rh dt − γσh dzh ) · µj Yj Vj Y dt + σj Yj Vj Y dzj + σj Yj Vj Y dt 2 ... − γρj σh σj Y Vj ′Y dt    1 2 2 o ′′ o′ o′ E (−rh dt − γσh dzh ) · µj Yj Vj Y dt + σj Yj Vj Y dzj + σj Yj Vj Y dt = ... 2 ... − γρj σh σj Y Vjo ′Y dt. So we obtain: 1 πh − rh Vh + (µh − γσh2 )Yh Vh ′Y + σh2 Yh2 Vh ′′Y 2 1 ′ πj − rh Vj + (µj − γρj σh σj )Yj Vj Y + σj2 Yj2 Vj ′′Y 2 1 2 2 o ′′ o o′ −rh Vj + (µj − γρj σh σj )Yj Vj Y + σj Yj Vj Y 2 = 0 = 0 = 0. Combining the three equations above and adding and subtracting the term 37 µh Yh Vh ′Y + X µj Yj Vj ′Y + X µj Yj Vjo ′Y : j6∈A j∈A 1 πh − rh Vh − γσh2 Yh Vh ′Y + µh Yh Vh ′Y + σh2 Yh2 Vh ′′Y +... {z2 } | E(dVh ) 1 πj − rh Vj − γρj σh σj Yj Vj ′Y + µj Yj Vj ′Y + σj2 Yj2 Vj ′′Y +... | {z2 } j∈A X + E(dVj )   X 1 2 2 o ′′    o′ o o′ + + µ Y V −r V − γρ σ σ )Y V σj Yj Vj Y  = 0.  h j j j j Y j h j j j Y 2  {z } | j6∈A E(dVjo ) Since E(dVh ) + X E(dVj ) + X E(dVjo ) = E(dV): j6∈A j∈A πh + X πj + E(dV) = rh Vh + γσh2 Yh Vh ′Y + j∈A X j∈A
rh Vj + γρj σh σj Yj Vj ′Y + ...  X o o′ rh Vj + γρj σh σj Yj Vj Y ... j6∈A πh + X j∈A B γσh πj + E(dV) V σh Yh Vh ′Y + X γρj σj Yj Vj ′Y + j6∈A j∈A = rh + X V γρj σj Yj Vjo ′Y ! Robustness: Reduced Form Estimates In this section we include a number of robustness tests to ensure that our empirical results are not sensitive to changes in variable definitions or controls. We begin by controlling for a variety of factors that may impact stock returns including total firm sales, market capitalization, leverage, and the book-to-market ratio of the firm. We then replace our measure of country-specific entry costs with two alternative measures from the World Bank’s Doing Business Database: the number of procedures required to start a business and the average number of days required to start a business. Finally, we measure the co-movement of GDP shocks in the US and the host country using the correlation, rather than the covariance, of these shocks. 38 . Table B.1: Summary Statistics of Robustness Controls. N. Obs Mean Std. Dev. Min Max 21809 21809 21809 21809 21809 21809 21809 0.921 5.439 0.047 0.906 15.181 5.319 0.63 1.128 20.508 1.701 7.456 12.235 2.578 0.209 -12.487 0.0006 -122.097 -906.639 0 0 -0.355 23.552 511.887 206.254 66.022 195 17 0.918 5688 5688 5688 5688 5688 5688 5688 0.928 2.754 0.074 0.762 12.054 4.314 0.652 1.256 10.486 2.743 6.786 12.257 3.073 0.268 -5.94 0.001 -5.937 -479.385 0 0 -0.22 23.552 267.336 206.254 30.3 149 17 0.918 ALL FIRMS Firm beta Market cap. ($b) Leverage Book-to-market Nr. of days Nr. of procedures Correlation (ρf t ) HORIZONTAL FIRMS Firm beta Market cap. ($b) Leverage Book-to-market Nr. of days Nr. of procedures Correlation (ρf t ) We run all of these robustness tests for both the reduced form and the two-step regressions. Table B.1 provides summary statistics for the variables we use in the robustness checks. Columns I-III of Table B.2 report the reduced form estimates inclusive of additional potential determinants of annual stock returns, like market capitalization, leverage, and book-to-market. Total firm sales and market capitalization are conceptually similar, as they each proxy for firm size, so we do not include both of these variables in the same specification. The same applies to leverage and book-tomarket. Our results are robust to the inclusion of these measures. The coefficients on GDP growth covariances and entry costs are all positive and significant regardless of which combination of the firm-level controls are included. Columns IV-VI of Table B.2 report the results using the correlation of GDP shocks in the US and the host country, rather than the covariance of these shocks.1 1 Country-level correlations are aggregated into firm-level measures using the same methodology we used to aggregate covariances. 39 Table B.2: The relationship between annual returns, GDP growth covariances and correlations, and entry costs: robustness. covariances (Covf t ) I II III 1.7** (0.693) 1.705** (0.694) 1.714** (0.692) correlations (ρf t ) entry costs (Ff t ) nr. of countries beta GDP distance global sales 0.0005** (0.0002) 0.035 (0.102) 4.253** (1.793) -0.002 (0.001) -0.00003 (0.0002) 3.1e-08 (6.53e-08) 0.0005** (0.0002) 0.036 (0.102) 4.242** (1.785) -0.002 (0.001) -0.00003 (0.0002) 3.07e-08 (6.43e-08) market cap. 0.0005** (0.0002) -0.032 (0.1) 4.227** (1.785) -0.002 (0.001) 0.00001 (0.0002) IV V VI 6.115** (3.065) 0.0005** (0.0002) 0.032 (0.1) 4.288** (1.784) -0.002 (0.001) -0.00001 (0.0002) 3.03e-08 (6.49e-08) 6.152** (3.118) 0.0005** (0.0002) 0.034 (0.101) 4.278** (1.809) -0.002 (0.001) -0.00002 (0.0002) 2.99e-08 (6.5e-08) 6.124** (3.102) 0.0005** (0.0002) -0.034 (0.1) 4.263** (1.776) -0.002 (0.001) 0.00003 (0.0002) 0.0002*** (0.00009) leverage 0.0002*** (0.00009) -0.393 (2.714) -0.393 (2.783) book-to-market industry and year FE YES YES 0.07 (0.49) YES N R-sq 5658 0.075 5658 0.0755 5658 0.0772 YES YES 0.073 (0.491) YES 5658 0.0745 5658 0.0749 5658 0.0766 Notes: *,** and *** indicate significance at the 10, 5 and 1 percent levels, respectively. Bootstrapped standard errors are in parentheses. Correlations are convenient measures to interpret the coefficients of our regressions. We can compare risk exposures in the extreme cases of perfect diversification (ρf t = 0) and no diversification (ρf t =1): ceteris paribus, a firm that has affiliates only in a host country whose GDP growth is perfectly correlated with the US has a risk premium about 6% higher than a firm with affiliates only in a host country whose GDP growth is uncorrelated with the US. Table B.3 uses alternate measures of country-level entry costs from the World Bank’s Doing Business Database. Columns I-III report the results using the number 40 Table B.3: The relationship between annual returns, GDP growth covariances, and entry costs: robustness. Entry costs measured as the number of days or the number of procedures necessary to start a business. covariances (Covf t ) entry costs (days) I II III IV V VI 1.609** (3.354) 0.125** (0.063) 1.613** (3.351) 0.124* (0.064) 1.618** (3.354) 0.116* (0.063) 1.565** (3.351) 1.569** (3.356) 1.579** (3.353) 0.84** (0.373) 0.048 (0.1) 4.242** (1.766) -0.002* (0.001) -0.0002 (0.0003) 3.92e-08 (6.63e-08) 0.841** (0.376) 0.05 (0.101) 4.232** (1.786) -0.002* (0.001) -0.0002 (0.0003) 3.89e-08 (6.62e-08) 0.803** (0.371) -0.014 (0.096) 4.217** (1.805) -0.003* (0.001) -0.0002 (0.0003) entry costs (procedures) nr. of countries beta GDP distance global sales 0.058 (0.1) 4.25** (1.822) -0.002 (0.001) -4.15e-06 (0.0002) 3.97e-08 (6.61e-08) 0.06 (0.1) 4.24** (1.795) -0.002 (0.001) -5.65e-06 (0.0002) 3.94e-08 (6.6e-08) market cap. 0.0002*** (0.0001) leverage N R-sq 0.0002*** (0.0001) -0.379 (2.754) book-to-market industry and year FE -0.004 (0.097) 4.226** (1.823) -0.002 (0.001) 0.00004 (0.0002) -0.381 (2.723) YES YES 0.068 (0.482) YES 5658 0.0739 5658 0.0743 5658 0.076 YES YES 0.067 (0.479) YES 5658 0.0744 5658 0.0749 5658 0.0765 Notes: *,** and *** indicate significance at the 10, 5 and 1 percent levels, respectively. Bootstrapped standard errors are in parentheses. of days necessary to start a business. Columns IV-VI report the results using the number of required procedures. Consistently with the predictions of the model, both of these measures are positively and significantly related to annual returns. We run all the robustness test above also for the second step regressions of our two-step approach. We do not report here all the results, however the two-step results are also robust to the different definitions of entry costs, as well as to using 41 Table B.4: Summary statistics by affiliate presence: Robustness to different measures of entry costs. Entry cost (nr. of days) Entry cost (nr. of procedures) 15.181 22.287 5.319 7.478 12.054 21.567 4.314 7.318 ALL FIRMS Countries with affiliates Countries without affiliates HORIZONTAL FIRMS Countries with affiliates Countries without affiliates the GDP growth correlations instead of the covariances.2 Regarding our alternative specifications of entry costs, Table B.4 shows the weighted average number of days and procedures necessary for starting a business in countries in which the firms do and do not have affiliates. As with the paid in capital requirement used in our primary specification, these summary statistics show that the firms in our sample are much more likely to open affiliates in countries with lower entry costs. Our two-stage results are robust to using both of these measures. C Robustness: Model-Based Estimates Table C.1 shows the full set of country-level results described in Section 4.3.1. 2 The results are available upon request to the authors. 42 Table C.1: Country-specific estimates of risk premia, observations at the firm-year level. coefficients ψj Country US Domestic United Kingdom Canada Germany Singapore Switzerland Ireland Japan Netherlands France Mexico China Brazil Australia Belgium Italy Hong Kong Spain I 0.036*** (0.010) 0.011 (0.01) 0.034*** (0.012) -0.008 (0.006) 0.075*** (0.021) 0.031 (0.028) 0.001 (0.002) 0.011 (0.009) 0.032 (0.022) -0.01 (0.014) 0.037 (0.036) 0.951 (0.599) -0.018 (0.04) 0.125** (0.052) 0.017 (0.033) 0.032 (0.025) 0.026** (0.013) -0.004 (0.01) risk premia ψjo ψj II 0.058*** (0.019) 0.010 (0.01) 0.033*** (0.012) -0.007 (0.007) 0.064*** (0.022) 0.021 (0.028) 0.005 (0.004) 0.011 (0.01) 0.029 (0.02) -0.007 (0.015) 0.040 (0.037) 0.818 (0.622) -0.018 (0.04) 0.109** (0.052) 0.016 (0.034) 0.033 (0.026) 0.021 (0.013) -0.006 (0.01) ψσh σj ρj εfj ψσh σj ρj εfj I 1.242** (0.611) 0.622 (0.813) 1.338 (1.02) -3.228 (2.983) -0.258 (3.863) -1.273 (0.921) -0.270 (0.926) 1.088 (1.547) -1.366 (1.333) 1.718 (1.363) -5.105 (8.955) -8.398 (10.96) -0.033 (4.906) 4.449 (3.064) -0.426 (1.445) -4.02 (3.164) -1.189 (2.35) 43 ψjo σh σj ρj Zjf II 0.23 0.371 0.060 0.055 0.496 0.137 0.133 0.136 -0.014 -0.012 0.292 0.491 0.419 -0.206 0.048 0.033 -0.014 0.014 0.069 -0.396 0.011 0.011 -0.042 0.155 0.140 0.060 -0.022 -0.015 -0.301 0.131 0.142 0.223 0.409 0.351 -0.066 -0.009 -0.009 -0.12 0.202 0.176 -0.001 0.030 0.030 0.461 0.087 0.090 -0.079 0.170 0.137 -0.192 0.001 0.001 -0.151 coefficients ψj Country South Korea Norway Malaysia India Sweden Thailand Argentina Poland Luxembourg Russia Chile Indonesia Austria Venezuela South Africa Turkey Denmark Hungary Colombia Czech Rep. ψjo ψj I 0.148* (0.082) -0.069 (0.131) 0.243** (0.105) 0.324* (0.189) 0.015 (0.026) 0.032 (0.052) 0.02 (0.046) -0.066* (0.038) 0.004 (0.006) -0.018 (0.015) 0.069 (0.093) 0.081 (0.053) 0.004 (0.024) -1.063 (1.115) -0.060 (0.084) 0.057 (0.082) 0.158*** (0.046) 0.022 (0.027) -1.743 (1.561) -0.021 (0.036) risk premia II 0.115 (0.085) -0.037 (0.13) 0.221** (0.105) 0.259 (0.186) 0.008 (0.026) -0.019 (0.046) 0.021 (0.045) -0.061 (0.038) 0.004 (0.007) -0.020 (0.015) 0.087 (0.093) 0.079 (0.053) 0.006 (0.024) -1.146 (1.121) -0.045 (0.083) 0.061 (0.081) 0.15*** (0.047) 0.018 (0.028) -1.756 (1.581) -0.007 (0.037) ψσh σj ρj εfj ψσh σj ρj εfj I 9.746 (6.018) -9.849 (7.01) -0.685 (5.49) 10.480 (12.477) 0.889 (2.622) -18.164** (11.523) 96.846* (50.321) 11.643*** (3.182) -12.414* (6.542) 5.520 (10.425) -6.277 (13.312) -6.542 (6.547) 10.765 (149.025) 18.842 (15.046) 14.127** (7.214) 2.223 (3.624) -4.592** (1.889) 4.533 (852.773) -2.240 (2.539) 44 ψjo σh σj ρj Zjf II 0.249 0.194 0.374 -0.105 -0.056 -0.610 0.576 0.526 -0.027 0.535 0.428 0.127 0.071 0.038 0.063 -0.037 -0.434 -0.014 -0.014 -0.445 -0.358 -0.331 0.685 0.059 0.059 0.030 0.030 -0.627 0.075 0.095 0.143 -0.079 -0.077 0.136 0.006 0.008 -0.433 0.128 0.138 -0.022 -0.071 -0.053 0.284 0.052 0.056 1.100 0.388 0.368 0.217 0.189 0.155 -0.623 -0.023 -0.023 -0.002 -0.030 -0.010 -0.337 coefficients ψj Country Philippines Israel Peru Finland Portugal New Zealand Greece Panama Ecuador R-Sq ψjo ψj I -0.019 (0.086) -0.73*** (0.228) 0.0007 (0.0014) 0.013 (0.018) -0.005 (0.046) 0.074 (0.098) 0.379*** (0.138) 0.005 (0.006) 0.00005 (0.01) 0.177 risk premia II -0.012 (0.086) -0.662*** (0.227) 0.0003 (0.014) 0.018 (0.019) -0.004 (0.047) 0.062 (0.098) 0.344** (0.136) 0.005 (0.006) 9.34e-06 (0.01) ψσh σj ρj εfj ψσh σj ρj εfj I 37.058*** (11.796) -42.397*** (15.916) -17.99 (37.649) 1.119 (4.008) 7.142 (5.979) -15.592 (11.056) 0.599 (12.326) 0.553 (5.781) -10.589 (34.415) ψjo σh σj ρj Zjf II -0.013 -0.008 0.776 -0.882 -0.800 -0.540 -0.001 -0.001 0.186 0.028 0.038 0.154 0.001 0.001 0.470 0.123 0.103 -0.396 0.674 0.612 0.030 0.075 0.075 -0.028 0.00005 9.34e-06 0.121 0.182 Notes: Bootstrapped standard errors are in parentheses. *,** and *** indicate significance at the 10, 5 and 1 & levels. Both specifications include year fixed effects and have n=25569. 45