PERIODO DE RECUPERACIÓN DE LA INVERSIÓN (PRI)

In addition to most research that defines contagion as co-movement of index returns, in order to properly implement multinomial logistic regression, we adopt another contagion definition that is return coexceedance. The exceedance is defined as the returns falling into the set of the lowest and highest 5% observations on the return distribution, and coexceedance therefore is defined as the number of the returns’ exceedances observed on the same trading day. The negative coexceedances represent the level of negative contagion for the region, the more coexceedances are found, more contagious the crisis will be in this region. According to the requirement of multinomial Logit model, we firstly summarized the number of the trading days for coexceedances. The results are reported in table 1.8. More specifically, we report coexceedances for the bottom tail (negative extreme value) on the left hand side of table, and top tail (positive extreme value) on the right hand side. For each of the sample countries, we compute the joint exceedances of one country on the particular trading day with the other eight markets. If on one trading day, a extreme return is observed in benchmark market and i21 _{in the other eight, it would be signed as}

i+1 coexceedances for this market. In the light of the number of coexceedances, we classify seven categories indicating counts of the number of joint exceedances. First, the coexceedances on the bottom tail are summarized. Out of 3493 observations, 2884 trading days fall into the category of that there is no extreme return in any market. The number of trading days with only one negative exceedance is 273 in total. From table 1.8, we derive almost symmetric statistics between top tail and bottom tail. For 2853 trading days out of 3493 observations, there is no positive coexceedance found in the top tail. 283 trading days with only one exceedance are found. There is a slight asymmetry found from the category of two coexceedances

in the top tail and bottom tail. For instance, 137 observations with 2 coexceedances are found in the top tail, but only 112 trading days with 2 coexceedances can be computed in the bottom tail. Besides, the number of trading days with more than 6 coexceedances in the bottom tail is greater than that in the top tail. We therefore conjecture that the impact of the negative events may be stronger than the impact of the positive events on the European bond markets. In table 1.8, we not only present total counts of the number of coexceedances, but we also show the markets’ frequency of extreme returns in sample period.

The markets with the most frequent negative coexceedances are Belgium and Netherland which have 73 trading days with more than six markets’ coexceedances, 22 and 27 out of all 31 days with five markets’ coexceedances in bottom tail. France also shows highly regular negative coexceedances, there are 72 out of all 73 days with more than six coexceedances, and 26 out of all 31 days with 5 coexceedances. France and Netherland are the countries with the most regular positive coexceedances. In France and Netherland, there are all of 59 trading days with more than 6 coex- ceedances and, 31 and 39 out of all 41 trading days with 5 coexceedances in top tail. Greece sees the largest number of trading days with only one exceedance, 72 for the bottom tail and 77 for the top tail. It means that Greece has the most volatile mar- ket conditions over the whole sample period. Actually, the Greek bond market does not always have a large number of negative coexceedances with the other neighbour- ing markets, it may make sense that the changes of Greek bond returns are prior to the changes of neighbouring bond returns, therefore the Greek coexceedances across neighbouring countries cannot be always found on the same trading days.

Table 1.9 and 1.10 provide the estimations of the multinomial Logit model for the European markets. The results will help answer the central research questions of what and how the covariates can explain the probability of contagion occur- rence. We separately estimate the coefficients of models for negative and positive extreme returns, and also calculate the marginal effect. The negative and positive

coexceedances are estimated in six models. Models (1) to (3) exogenously estimate the negative coexceedances, and the others estimate the positive coexceedances. In model (1), we estimate for the bottom tail with constants only, model (2) includes the estimations of constants and one covariate of conditional volatility, and model (3) endogenously estimate the constants, and three covariates of volatility, exchange rate and interest rate. For top tail, models (4) to (6) repeat. For the first model of the bottom tail, only estimations of intercept are reported, and the constants in model (1) imply the corresponding probability of events for each category. Model (1) suggests the probability of 85.7% for the case that there is no exceedance in any European market (not reported in tables). β1 of -2.357 denoting the coefficient for

the contagion across one market (event of Y=1) implies the occurrence probability of 7.98% 22. In the same way, for the other events of bottom tail, the probabilities of contagion occurrence across two to five countries (Y=2, 3, 4 and 5) are 3.28%, 2.21%, 1.46% and 0.91%, respectively. Based on the constants of model (4), we also calculate the probabilities of contagion occurrence for top tail. They from event 1 to event 5 are 8.1%, 3.9%, 2.0%, 1.4% and 2.9%, respectively. Without the influence of covariates, the probabilities of contagion occurrence across countries are much closer to the frequency summarized in table 1.8. In model (2), we add a covariate of conditional variance to the multinomial logistic regression, and the statistically significant results are found for all categories from event 1 to 5.

In model (3), we add three covariates, which are conditional volatility, the level of exchange rate and the level of interest rate. We calculate the weighted average of the exchange rates (Ex.) from euro, Danish Krone and British pound to US dollar, and interest rate (Int.) is calculated by the equally-weighted average of interest rates in local currency. There are three results summarized from model (3). First, the coefficients of conditional volatility are strongly significant for the

22_{The probability of contagion occurrence can be calculated by the function, exppβ} 1q{r1

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events from ”Y=1” to ”Y=5”. Second, the coefficients of exchange rate for all events are statistically significant, with one exception of the event ”Y=5”. Finally, the coefficients of interest rate are less significant than volatility and exchange rate. The significant coefficients of interest rate are only found for the events of ”Y=1” and ”Y=2”. Top tail in model (6) presents the analogous results. For example, the coefficients of conditional volatility are significant for the contagion across in at least five countries, and coefficients of exchange rate are significant for the contagion across at least four countries. The interest rate is also weakly significant for the contagion across the European bond markets.

In order to look into the specific influence of the covariates on the probability of contagion occurrence, the marginal effect based on the coefficients displayed in table 1.9 is computed by following the approach ofGreene(2012). The marginal results are presented in table 1.10. In model (2), we find a strongly significant marginal effect for conditional volatility for all five categories. The strong significance denotes that the conditional volatility is able to explain and predict the contagion across at least five countries or more than five countries. In addition, the positive marginal effect also indicates that as every unit of conditional volatility increases, it will increase the probability of contagion occurrence (from ”Y=1” to ”Y=5”) more or less, but the power of the marginal effect along the line of categories from ”Y=1” to ”Y=5” gradually subsides. For example, if conditional volatility increases by one unit, then the probability of event ”Y=1” will increase by 0.479 unit, and the event ”Y=5” will increase by 0.043 unit. Symmetric effects of conditional volatility for top tail coexceedance is found in model (5). The marginal effect derived from model (3) will help us to answer the question of whether conditional volatility, exchange rate and interest rate significantly impact on the probability of contagion occurrence for bottom tail. As a result, the significant marginal effect of conditional volatility for all five categories shows that as the conditional volatility stays at very high level, it will increase the probability of contagion occurrence across at least five countries.

In other words, conditional volatility is able to strongly explain the contagion across the European bond markets. The level of exchange rate is also able to explain the contagion across at least four countries. The level of interest rate weakly explains the contagion in the European region. Model (6) estimates three covariates for top tail. The significant results for both of conditional volatility and exchange rate are found for all five categories. However, the marginal effect result of exchange rate for the top tail is mixed. For instance, two negative marginal effects at 5% significance level and two positive marginal effects at 10% significance level are observed. This indicates when the level of exchange rate increases, it may decrease the probability of positive coexceedances (at 5% level), and it also may increase the probability (at 10% level). In other words, exchange rate changes have bi-lateral effect on the probability of positive coexceedances. Consistent with Bae, Karolyi, and Stulz (2003), we also obtain the result that interest rate has only very limited explanatory power for either bottom tail or top tail coexceedances. It is worth noting that adding covariates of exchange rate and interest rate raises the P seudoR2_{, and the models of bottom}

tail have a little higher P seudoR2 _{than the models of top tail. It means that}

the models with three covariates will explain the negative coexceedances better than the positive coexceedances. However, there is a weird result that the explanatory power of interest rate for top tail is strongly significant for the events of ”Y=3” and ”Y=5”, but is strongly insignificant for other events of ”Y=1”, ”Y=2” and ”Y=4”. In addition, two significant marginal coefficients of interest rate for bottom tail are of opposite signs.

We surprisingly find that our results derived from the European bond markets are closely related to the results estimated by Bae, Karolyi, and Stulz (2003) in the international stock markets. They claim that conditional volatility and exchange rate are statistically significant in predicting the contagion across the international stock markets, and interest rate shows the relatively weak explanatory power and similarly weird results. In our opinion, stock and sovereign bond markets may share

the common underlying information channel linking with three covariates. The covariates possibly transmit the information to the stock and bond markets by a joint unobservable channel.

Overall, three findings are concluded from table 1.9 and 1.10. First, there is no evidence that the events (Y=1, 2, 3, 4, 5) are less or more likely for the top tail than for the bottom tail. Second, with the statistically significant partial derivatives (marginal effect) in the bottom tail, it can be seen that the influence of the exchange rate on the probability of contagion occurrence is almost same as of conditional volatility. In other words, both conditional volatility and exchange rate can strongly explain the contagion in the bottom tail. Finally, interest rate can merely explain the contagion across the European bond markets in bottom tail, and even does not have any explanatory power for contagion across 3, 4, and 5 or more than 5 countries in bottom tail, and across 1, 2 and 4 countries in top tail. Because our initially research focus is on the predictability of contagion in the European area, we additionally estimate the models with lagged covariates in the same way. The general results are same as of tests with contemporary covariates. That is to say, for both the bottom tail and top tail, we find the statistically significant results for conditional volatility and exchange rate, and the weak predictive power of interest rate. They therefore are not reported in tables.