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2.4 Causality in volatilities

In the preceding section a recognizable spillover effect between the Asian markets index and Ibovespa was supported by the Granger test. In this section the test is repeated, now using the series of squared returns instead of the series of returns. Thus, the equations in Section 2.2 are replaced by:

where R_1,t is the series RIBOV-ON;
R_2,t is the series of returns from MSEMF-ASIA;
a_i, b_i, l_i and d_i are constant coefficients;
n is the number of lagged terms used; and
e_1,t and e_1,t are uncorrelated innovations, i.e. S(e_1,t e_1,t)=0.

The object of investigation is a spillover effect between volatilities, whose proxies are in this case the squared returns. The results of the Granger test are shown next in a similar format to that of the preceding section. Comments follow.

Now H₀⁽¹⁾ stands for the null hypothesis "Ibovespa overnight returns do not cause MSEMF-ASIA daily returns" and H₀⁽²⁾ stands for the null "MSEMF-ASIA daily returns do not cause Ibovespa overnight returns". A small p-value for H₀⁽¹⁾ means high credibility to the claim "Ibovespa overnight returns cause MSEMF-ASIA daily returns"; and a small one for H₀⁽²⁾ strengthens the claim "MSEMF-ASIA daily returns do not cause Ibovespa overnight returns".

For sample A, the full year of 1997 (Figure 13), the graph of p-values contains an abrupt discontinuity at lag 6. With less than 6 lags included in the regression, p-values for both hypotheses are low (most under 20%); when 6 or more lags are included, both p-values fall under the 1% confidence level. At first sight this could be interpreted as volatility feedback, a regime under which the market turbulence would be transmitted reciprocally between both regions, with delays of a week or more. The full sample, however, contains two periods which the previous tests have clearly identified as different regimes. The test must be performed with the other samples before final conclusions can be drawn in favor of feedback mechanisms.

The use of sample B, the first half of the year before the Thailand event (Figure 14), results in higher p-values for H₀⁽²⁾ compared to sample A, but they are still consistently low (under 15% for all lag structures except 1, 3 and 15) — an indication of causality from Asia to Brazil even before the Thailand event. From Brazil to Asia no causality can be seen, as p-values for H₀⁽²⁾ are unstable and high for most lag structures.

The period after the Thailand event represented by sample C (Figure 15) brings back the curious pattern from sample A. Up to 5 lags, no visible causality; 6 lags or more, extremely low p-values for both hypotheses. Again, an indication of volatility feedback with a delay of a week or more.

If EVENT 2 is taken out of the post-Thailand period, sample D (Figure 16), the picture is substantially altered. P-values for H₀⁽²⁾ are now generally lower than 10% (except for 3, 10 and 11 lags), which indicates causality from Asia to Brazil. P-values for H₀⁽¹⁾ on the other hand are now unstable and mostly high. It could be that EVENT 2 is in fact responsible for the pattern in the p-values from samples A and C (Figures 13 and 15, above). The feedback detected would be in this case a spurious effect due to taking the square from the large ups and downs observed at the end of October, the worst days of the crisis.

The first half of the year, when we split it at the Hong Kong crash (sample E, Figure 17), shows low p-values for H₀⁽²⁾ from lag 3 on, all lower than 15% and most lower than 10%. P-values for H₀⁽¹⁾ are also lower than 10% in the lag 3 to lag 11 range, which could again indicate feedback. However, their increase after lag 12 reveals instability.

Finally, sample F, which represents the period after the Hong Kong crash (Figure 18), shows high and unstable p-values for both hypotheses. Causality can be distinguished neither from Asia to Brazil nor from Brazil to Asia — a result which shows some resemblance to that from the series of returns (Figure 12). Once again, it should be noted that the small sample size severely undermines any inferences from this last sample.

Although results are less clear with the series of squared returns than with those of the returns, we can hardly dismiss the hypothesis of a spillover effect in the volatilities. Samples B and D in particular (Figures 14 and 16) point to a causality from Asian volatility even before the Thailand event, which seems to last until the Hong Kong crash, at least. After the crash, as Figure 18 suggests, the effect is blurred and probably non-existent. There are some indefinite signs of feedback between the two series of squared returns, but they can be a spurious effect caused by the extreme swings during EVENT 2.

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CONCLUSION

In this paper the spillover effect was studied in a quantitative framework. Statistical tests were performed using regional indices and the Brazilian main market index in different sample periods during 1997. Their results support at reasonable levels of confidence (1) the perceived shift in volatility both at the Thailand currency crisis and the Hong Kong crash; and (2) the lagged spillover effect between the aggregate Asian index and a representative Latin American market, namely Brazil.

The Granger causality test was at first performed with the series of Ibovespa overnight returns and Asian daily returns. The results were indicative of a lagged spillover effect from the Asian markets to the Brazilian one, beginning at the Thailand currency crisis, on July 15^th, and lasting until the Hong Kong crash, on October 23^rd. After that date the spillover could not be clearly observed, although sample size limits the power of the test.

Afterwards, the tests were repeated with the series of Ibovespa squared overnight returns and Asian squared daily returns. Our objective was to test for the presence of a lagged spillover effect in the volatilities of both markets, as well as in their returns. The results again supported such an effect from the Asian to the Brazilian markets. In this case, however, we were also able to observe some evidence of volatility feedback, specially in those samples including the Hong Kong event. In other words, the Ibovespa overnight squared returns also appear to contain relevant information in explaining the Asian squared returns. Also, the p-values displayed a curious pattern in some samples, in which there was a cutoff around lag six. We conjecture that this can be a spurious effect caused by the large swings during the last week of October, but it remains an open question.

We conclude with some suggestions for further research. The first is to enlarge the scope of the Granger tests by collecting intraday data from other Latin American markets (preferably those included in the MS EMF Latin America Index) and to build a regional series of overnight returns. In this way, lagged spillovers across both regions could be tested. An important issue which was left out of the analysis is whether the North American markets were also determinative over the markets in Latin America and even in East Asia. A test similar to the preceding ones could be designed using the regional indices. Finally, an advance in this analysis should have as a first aim to explain or dismiss as a spurious effect those suspicious patterns encountered in the Granger tests with the squared returns.

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