Performances of Emerging Stock Exchanges During the Fed’s Tapering Announcements

Abstract

This paper investigates abnormal returns of 19 emerging market equity portfolios during the Fed’s tapering period. Event study methodology is used during the early Fed’s announcements at 2013. The aim of the study is to evaluate both the event study methodology and abnormal return performance of the emerging market stock exchanges during tapering period. The authors also check for abnormal volatility during tapering announcements, specifying it with GARCH (1,1) model. The results indicate that, together with China and Greece, the fragile five economies are differentiated from the rest of the emerging markets during tapering announcements. Moreover, the striking result that the authors see is Turkey is affected more negatively than any other fragile five members in this period. Yet, the authors did not find any significant abnormal volatility effect brought by tapering announces. In addition, the authors find emerging markets are not semi-strong form efficient during tapering period.

Appendix

Basically, the authors add lagged variable in linear regression to overcome autocorrelation between error terms which leads to statistical inference conducted fallaciously in least squares.

Now let us clarify the technicality of the autocorrelation problem with some matrix notation. As it’s well known, abnormal returns are by definition prediction errors:

$$ \mathrm{AR}=y-{y}^{\ast } $$

where AR is the vector of abnormal return, y = Xβ + u is the vector of actual return, y ^∗ = Xb is the normal return vector, and X is the market returns on event window.

Rearranging terms the authors have

$$ \mathrm{AR}=X\left(\beta -b\right)+u $$

where u is the vector of residuals with variance ${\sigma}_u^2\varOmega$.

The authors are now interested in variance, and since the authors are dealing with statistical inference, the authors need variance terms to be well specified.

Variance of abnormal returns is

$$ \operatorname{var}\left(\mathrm{AR}\right)=X\operatorname{var}(b){X}^{\prime }+{\sigma}_u^2\varOmega $$

First part of the rhs of above equation is additional variance due to prediction error. Asymptotically, that first part goes zero, and the authors are left with ${\sigma}_u^2\varOmega$ term, if the authors have uncorrelated error terms in event period. Yet it may not be the case or the authors may not have variance of error terms equal to a constant, the authors will come to latter one soon.

For the case: 

$$ {\sigma}_u^2\varOmega ={\sigma}_u^2I $$

where I is identity matrix, i.e., uncorrelated error terms, then statistical inference based on ${\sigma}_u^2I$will be correctly specified. But for the case below:

$$ {\sigma}_u^2\varOmega \ne {\sigma}_u^2I $$

i.e., correlated error terms, statistical inference that the authors made will be misleading since cross correlations in between error terms are underestimated with least squares, since least squares assumes Ω = I above equation.

Additionally, variance of the estimated parameters of OLS:

$$ \operatorname{var}(b)={\sigma}_u^2{\left({X}^{\prime }X\right)}^{-1} $$

Actually it’s simplified to above equation when

$$ E\left({e}^{\prime }e\right)={\sigma}_u^2I $$

But in case of autocorrelation, this assumption leads to problematic conclusion in hypothesis testing due to biased estimation of last equation above. That is, this conclusion is well specified when errors are white noise.

When

$$ E\left({e}^{\prime }e\right)={\sigma}_u^2\varOmega $$

the authors have

$$ \operatorname{var}(b)={\left({X}^{\prime }X\right)}^{-1}{X}^{\prime }{\sigma}_u^2\varOmega X{\left({X}^{\prime }X\right)}^{-1} $$

Then the hypothesis testing based on ${\sigma}_u^2\varOmega$ will fail obviously. If correlation between error terms is persistent, then bias will be severe. The authors know that ${\sigma}_u^2{\left({X}^{\prime }X\right)}^{-1}$ is biased estimation for ${\left({X}^{\prime }X\right)}^{-1}{X}^{\prime }{\sigma}_u^2\varOmega X{\left({X}^{\prime }X\right)}^{-1}$. T or F distributions that are calculated by this ${\sigma}_u^2{\left({X}^{\prime }X\right)}^{-1}$ will be misleading.

Other than that, there are no problem with unbiasedness; consistency, i.e., plimb=beta; or asymptotically normality of least square estimation. However, the authors cannot conclude it’s an efficient estimation, since heteroscedasticity leads us some fallacious conclusion in hypothesis testing due to biased estimation of variance of error terms.

Again, if the authors assume error terms as above,

$$ E\left({e}^{\prime }e\right)={\sigma}_u^2\varOmega $$

Again least square estimate will be misleading. Since variance is not equal to some constant ${\sigma}_u^2$, least squares estimation will fail, therefore MLE should be employed for parameter estimation. The authors replace the variance of error terms in the conditional density with conditional variance; it’s a generic way.

The statistical reasoning behind this specification above is the following:

The authors now, in addition to autocorrelation problem, constant variance assumption may lead some misleading inference.

Having nonconstant variance requires modeling the variance as a process:

$$ {u}_t={v}_t{h}_t $$

where

$$ {h}_t^2={\alpha}_0+\alpha {\prime}_1{u}_{t-1}^2+{\beta}^{\prime }{h}_{t-1}^2 $$

$$ E\left[{v}_t\right]=0\ \mathrm{and}\ E\left[{v}_t^2\right]=1 $$

$$ f\left({u}_t|\Omega \right)=\frac{1}{\sqrt{2{\uppi h}_t^2}}\exp \left[-\frac{u_t^2}{2{h}_t^2}\right] $$

The log likelihood becomes

$$ L\left({\alpha}_0,{\alpha}_1,\beta, \gamma \right)=-\frac{n}{2}\log \left(2\uppi \right)-\frac{1}{2}\sum \limits_{t=1}^n\left\{\log \left({h}_t^2\right)+{u}_t^2/{h}_t^2\right\} $$

And the authors know MLE is unbiased, consistent, asymptotically normal, and efficient in this specification. Therefore hypothesis testing will be correctly specified in this way.