This paper investigates the impact of financial equity market integration to international nonsynchronous trading effects (INTE). It should be emphasized that this paper looks into the cross market nonsynchronous trading. It is different from the nonsynchronous trading within one market, which most existing studies investigate. The paper employs a stochastic process to provide a theoretical framework. The contributions are clear: First it provides a theoretical framework to investigate the nonsynchronous trading effect. Second, it theoretically and empirically investigates the effect of equity market integration to INTE. And third, the paper provides price level evidence instead of return level evidence.

The paper finds the theoretical and empirical evidences that more integrated equity markets increases the INTE. However the empirical findings show that the increase is asymmetric between developed and emerging markets. Further investigation reveals that the higher volatility and autocorrelation in emerging equity markets mitigate the increase in INTE incurred by the equity market integration. The paper also finds that the size of the effect of equity market integration to nonsynchronous effects decreases over time.

It is well known that nonsynchronous trading causes auto correlation in equity price and return. There are plenty of literature that addresses problems of nonsynchronicity which can be thought of as the random, or deterministic, arrival of data within the interval of measurement and its consequences on the measurement of beta (See Atchison, Butler and Simonds, [1] and Dimson [2] ). More recent works include Barndorff-Nielsen et al. [3] and Fung, Liu and Tse [4] . Recent works tend to focus on the econometrics method of nonsynchronous trading problem.

A careful investigation of existing literature in nonsynchronous trading effects reveals that there are several potential aspects that could be further investigated. (1) The cross autocorrelation is much less explored compare to the autocorrelation within the index due to its complex nature. The latter induces autocorrelation mainly from thinly traded securities that have less liquidity while the first induces autocorrelation due to equity market operation time difference. This paper is interested in the cross market nonsynchronous trading effect and refers it to INTE. There could be two consequences of nonsynchronous trading to international equity market data. (2) Most of the existing literature investigate return series instead of price series. Although positive price autocorrelation means positive return autocorrelation in AR process, the direct effect of nonsynchronous trading is price autocorrelation. Return autocorrelation is a product of the price autocorrelation. This paper tackles the price autocorrelation.

(3) With more integrated world’s financial markets, such nonsynchronicity problem could be investigated in a different angle. Schotman and Zalewska [5] address the issue of nonsynchronous trading associated with financial market integration. They argue that controlling for time differences in trading hours of stock markets is important and show that time-adjustment improves estimates of market integration. This study shows that nonsynchronous trading effects may be affected by the degree of financial market integration. The current paper intends to expand the scope of Schotman and Zalewska [5] and investigate the relationship between the equity market integration and INTE.

The rest of the paper is organized as follows. Section 2 introduces the theoretical model. Section 3 empirically tests the two hypotheses. Section 4 reinvestigates the theoretical model to explain the discrepancy between developed and emerging markets. Section 5 concludes the paper.

In modeling shock emissions among international equity markets, there are some domestic shocks that are irrelevant to international markets. These shocks should be excluded from the analysis; hence the term “shock” in this paper refers to the shocks that have international influence only. For modeling purpose, I take a common practice in literature investigating international equity market volatility spill over (See Baele [6] and Bekaert and Harvey [7] ) and assume that there exists a common factor that is affected by all shocks immediately—if a shock occurs in country, the common factor is affected simultaneously, while the shock is only updated to the equity market of country when its market opens.

This paper employs a modified version of the model developed by Lo and Wang [8] . The basis for the model analyzed in this paper forms the bivariate Ornstein Uhlenbeck with some modifications permitting residuals of asset and market return to be correlated. This correlation may correspond to common factors, due to the indices’

dependence on factors. Assume that the logarithm of the index levels and have linear

trends and respectively. We consider the de-trended log price process,

Assume that satisfies the following pair of stochastic differential equations,

where stands for price, subscript indicates that the parameter is for country, subscript indicates that the parameter is for the common factor and and are the parameters of the OU process with the obvious use of subscripts. Furthermore, we assume, and denotes a Wiener process. and

are correlated standardized Wiener processes with correlation coefficient, i.e..

Therefore can be seen as the degree of equity market’s integration with the common factor. It could be also seen as the underlying systemic risks of the market with respect to the common factor, over and above the “market model” term given by. For most international equity markets, is expected to be positive.

According to Hong and Satchell [9] , the solution can be written as

where and

All results are conditional on time zero information.

Remark 1: The conditional covariance of index price and factor price can be written as

See Appendix A of Lo and Wang [8] for the proof for Remark 1.

Remark 2: The conditional -period autocovariance of index return and factor return can be written as

A proof of Remark 2 is in the Appendix. Equation (6) is the amount of autocovariance induced from nonsynchronous trading.

The system of Equations (2) and (3) represents the one factor model that the demeaned log price of index is influence by the demeaned log price of the factor. Beta of this one factor model measures the responsiveness of the index price to the factor price. Since we are interested in lagged relationship, the beta is computed with lagged time series, and, and will be denoted as. I refer as auto-beta because it captures the beta-type relationship of a one factor model between lagged terms, like autocorrelation. The difference between and autocorrelation is that the former captures the lagged relationship of two different prices while the latter captures the lagged relationship within one price. Although the notation beta is used to indicate this is a measure of responsiveness, current model is very different from the CAPM in many aspects. Current model should be considered as price one factor model.

Proposition 1: The nonsynchronous trading effect, , can be written as

Proposition 1 is an immediate result of Remark 2, dividing the both sides by the variance.

Proposition 2: The impact of equity market integration to nonsynchronous trading effects can be expressed as

Proposition 2 is a partial derivative of Proposition 1 with respect to kappa. This measure becomes positive as long and have the same sign. This condition indicates that both index and factor prices revert back to mean or both do not revert back to mean. It would be reasonable to assume that this is true since de-trended equity indices are known to be mean-reverting. When both the index and the factor prices exhibit mean-reverting feature, Equation (8) is positive.

Proposition 2 implies that more integrated international financial equity markets increases the level of INTE. Intuitively, this is because more integrated financial markets allow shocks from one market to be transferred more widely to other markets.

Proposition 3: The sensitivity of with respect to financial integration and lag time period can be written as

Proposition 3 is a partial derivative of Proposition 2 with respect to s. Given and have the same sign, Equation (9) becomes negative if is positive and becomes positive if is negative. Since it is more likely that the de-trended index equity price series to be mean-reverting, hence, Equation (9) is likely to be negative. This indicates that the size of the INTE monotonically decreases over time. This should intuitively make sense.

From the theoretical finding of Proposition 2 and 3, two hypotheses could be drawn.

H1: The more integrated financial market equity market increases the INTE.

H2: INTE monotonically decreases with respect to time.

In next section, the two hypotheses are empirically tested.

Sections 2 and 3 of this paper investigate the sensitivity of the most recent five day factor price with respect to the current index and factor price correlation. The theoretical findings using a bivariate OU process model predict a positive significant relationship between the degree of equity market integration and INTE in international equity markets. However the empirical evidences show that the more integrated equity market increases INTE in developed economies but it does not have significant effect to emerging economies. In order to resolve the discrepancy, we need to take advantage of using a theoretical model and analyze exactly what induces the sensitivity of INTE with respect to the equity market integrity.

Although they are not statistically significant, we still observe positive estimated parameters. This indicates that noise in the data could hide the relationship to be empirically observed. This could be the reason why the empirical result for developing countries is not consistent with the theoretical outcome. One potential explanation could be that developed markets have parameters that make empirical positive and significant while emerging markets do not. Hence we are interested in which values of country specific parameters, and, make Equation (10) large and positive.

Proposition 4: The sensitivity of with respect to country specific parameters, and, can be written as

We can see that the larger and smaller increases. An equity market with lager indicates that the equity market has higher volatility. The smaller indicates the larger price autocorrelation, hence less information efficient market. This is consistent with the empirical findings. Emerging markets tend to have higher volatility and larger price autocorrelation in their domestic equity markets.

While financial market integration worsens the problem of nonsynchronous trading among the international equity markets in general, emerging markets suffer less from it compared to developed markets. The paper finds that this is due to emerging markets’ higher level of volatility and higher price autocorrelation compared to those of developed markets. These could be indicators of less information efficient market. Ironically speaking, less efficient equity markets of emerging countries mitigate the increase in INTE from more integrated financial equity markets.

This paper builds a theoretical model, using a bivariate Ornstein Uhlenbeck process, to investigate the impact of the international equity market integration to INTE. The paper finds that the financial market integration would increase the effect, in general, and the impact monotonically decreases over the lag length. However the paper empirically finds that the increase is asymmetric between developed and emerging markets. Further theoretical investigation reveals that the level of volatility and autocorrelation in equity market are positively related to the increase in INTE due to financial market integration. The paper finds that relatively higher level of equity index volatility and autocorrelation in emerging markets could mitigate the increase in INTE from financial market integration.