The reaction of stock markets to crashes and events: A comparison study between emerging and mature markets using wavelet transforms

We study here the behaviour of the first three eigenvalues (λ1,λ2,λ3)(λ1,λ2,λ3) and their ratios [(λ1/λ2),(λ1/λ3),(λ2/λ3)][(λ1/λ2),(λ1/λ3),(λ2/λ3)] of the covariance matrices of the original return series and of those rebuilt from wavelet components for emerging and mature markets. It has been known for some time that the largest eigenvalue (λ1)(λ1) contains information on the risk associated with the particular assets of which the covariance matrix is comprised. Here, we wish to ascertain whether the subdominant eigenvalues (λ2,λ3)(λ2,λ3) hold information on the risk of the stock market and also to measure the recovery time for emerging and mature markets. To do this, we use the discrete wavelet transform which gives a clear picture of the movements in the return series by reconstructing them using each wavelet component. Our results appear to indicate that mature markets respond to crashes differently to emerging ones, in that emerging markets may take up to two months to recover while major markets take less than a month to do so. In addition, the results appears to show that the subdominant   eigenvalues (λ2,λ3)(λ2,λ3) give additional information on market movement, especially for emerging markets and that a study of the behaviour of the other eigenvalues may provide insight on crash dynamics.