3. Equity Stakes Acquisition of Foreign Financial Institutions
3.1 Proportional Hazard Survival Model and Principal Component Analysis…
國
立 政 治 大 學
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N a tio na
l C h engchi U ni ve rs it y
3. Equity Stakes Acquisition of Foreign Financial Institution
The merits of taking equity stakes in Chinese banks include the ability of foreign financial institutions to gain quick access into Chinese financial markets and facilitating expertise in business and product developments using Chinese bank’s channels, but it is also worth mentioning that the foreign financial institutions also face the problem of uneven quality of Chinese banks. Moreover, one single foreign institutional investor is confined by the limitations of 20 percent shareholding, and total foreign institutional investors can hold only up to 25 percent shareholdings in one Chinese bank. As foreign banks cannot obtain full ownership and control of Chinese banks, the majority of the foreign banks adopted a strategic minority equity stake investment to promote the acquired bank’s profitability and market value in order to create higher return on investment.
Some papers adopt Logit or Probit model to predict the probability of surviving in different times but only for one period, mentioned as the static model in Shumway (2001). In addition, Noh et al. (2005) pointed out that the survival model presents fewer type I and type II errors than other models. In addition to the biomedical field, the survival model has been applied to various areas in social science, such as econometrics, educational statistics, and finance, particularly in the measurement of default risk, financial institutions’ bankruptcy, and financial crisis prediction. Whalen (1991) adopts a proportional hazards model to estimate the probability that U.S. banks with a given set of characteristics (total loans/total assets, return of asset, and total domestic deposits/total assets) will survive longer than some specified length of time into the future. Wheelock and Wilson (2000) examine the hazard of banks disappearing due to either acquisition or to failure via survival model and find, not surprisingly, that the banks that are less well capitalized and have high ratios of loans to assets, poor-quality loan portfolios, low earnings, and high managerial inefficiency are at greater risk of either acquisition or failure. This paper adopts the survival model to analyze the strategy of foreign financial institutions in entering into the Chinese banking sector by taking equity stake acquisition. Here the hazard function is used to represent the probability of the intensity of equity stake acquisition.
3.1 Proportional Hazard Survival Model and Principal Component Analysis To further understand the intensity and timing of foreign financial institutions taking equity stake acquisitions in Chinese banks, we apply the survival model and
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principal component analysis and derive the intensity of investment and relative significant variables. The variables considered are macroeconomic variables, such as country origin of foreign financial institution and the interaction between foreign bank’s home country and China, and financial variables, such as financial ratios of foreign financial institutions and invested Chinese banks.
In this section, we illustrate the Cox’s proportional hazard survival model and then apply the principal component analysis to analyze and deal with data linearity and extraction in financial ratios of foreign financial institutions and Chinese banks.
3.1.1 Cox’s Proportional Hazard Survival Model and Parameters Estimation In the survival model, we treat the time of foreign financial institution taking equity stake acquisition as the survive-ending point, which also refers to the default time or bankruptcy time. The advantage of the proportional intensity model proposed by Cox is that it estimates parameters with unknown population distribution and needs no assumptions about baseline hazard function, which contains the characteristics of the semi-parameter model. In contrast, under the non-parameter survival model the potential effect of survival probability, hazard function and average survival time can not be easily measured from relevant variables.
To estimate the conditional probability of foreign financial institutions taking equity stake acquisition in Chinese banks according to Cox’s proportional hazard model, we assume T to be the time of investment, it also means the surviving-end point. Thus the probability of survival is represented as
)
where is the probability that the time of equity stake acquisition is more than , which is the same as the probability of survival time more than t . The hazard function (conditional probability) is defined by
)
According to the Cox proportional intensity model, the hazard function
h of foreign financial institution taking equity stake acquisition is defined as follows:
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where the baseline hazard function can be assumed to be model ( ) or the exponential model (
)
), which will not affect the estimation of parameters. Furthermore, le at time affecting
nction, and
) (t
x t
is the coefficient vector o s.
The maximum likelihood method is used to estimate f variable
in Cox s survival model. Assuming t be the equity stake acquisition tim
’
to of foreign financial
institu
i e
p
tion i, the proportion of information contained in this sam le to the whole risk set is
this ris oportion, obtain the log-like hood function :
Rj k
k information pr we li
This is viewed as complete data which could be observed when the sample firms default or bankrupt, meaning that taking equity stake acquisitions in the observable period. In contrast, it is from censored data, as the sample survival time is more than the observable period. Under this condition, we could obtain the partial likelihood function to estimate parameters (Cox, 1975):
)
To optimize the likelihood function, the maximum likelihood estimator contains the characteristics of asymptotical normal distribution (Casella and Ber 2002
ˆ ger, ), which causes it to be a consistent estimator of and asymptotically efficient.
In addition, the goodness-of-fit test of Cox’s proportional survival model follows the log-likelihood function as
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In addition, the significant variables in the model are tested by Wald test to reject the null hypothesis H0 :i 0 as ) ( )3.1.2 Principal Component Analysis
Considering the high correlated homogeneous variable and existence of linear dependent property that would cause inefficient analysis in the Cox survival model, this paper adopts the principal component analysis as a factor analysis for data subtraction and establishes a set of variables to serve as independent principal components. These principal components are the linear combination of original variables and explain most total variation without significant loss of information contained in the original data. In other words, the principal component analysis sets up L mutually independent components by linear combination of K original variables and still maintains its power of explanation, even with data subtraction. The principal components can be represented as the linear combination of original variables as principal components, and ji is the weighting of j ’s principal component on ’s original variable. The purpose of the principal component analysis is to assign higher weight to the significant variable and lower weight to non-significant variables to maintain sufficient power of explanation.
i
When the cumulative factor loading is 100%, the principal component number is the same as that of original variables, and communality is equal to one. For the linear combination P1X12X2 KXK as a'a1 , the eigenvector is corresponding to the eigenvalues of thus maximizing the variance of
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arger than 1 by Kaiser criterion (Kaiser, 1960). Under the low correlation coefficient, the principal component analysis model does not have completeness in general, such that it is unsuitable for data subtraction, and cumulative factor loading of principal components subtracted shall be reached above the specified level. In addition, the factor rotation approach sifts the original variables that are highly correlated with the principal component. The principal component score is determined by subtracting and translating by weighting for the application of statistics or survival analysis.eigenvalue is l
obability ard Threshold
intensity in equity stakes
e of equity stake acquisition of foreign financial
in equity stake acquisition and setting Haz
After deriving the probability of intensity
In this section, we estimate the probability of
sition in the observable time via maximum likelihood estimator in survival model and principle component analysis which are mentioned in previously, and figure out the optimal probability hazard threshold with minimizing type I and type II error.
For the tim
tionti;i1,2,,N , and correspondent variable xi(t) , where N is the number of in the observed period, we can e its relative hazard function h(t,x;ˆ) by maximum likelihood estimator ˆ in the specific baseline hazard function. Furthermore, the estimated probability of intensity in equity stake acquisition is F(t,x;ˆ)1S (t,x;ˆ).
amples deriv
i
bility hazard threshold B(0,1) , we consider that the foreign financial institution will take equity stakes acq e observed period if F(t,x;ˆ B. Therefore, the type I error, defined as the ratio to which samples are clas wrongly as not taking equity stake acquisition to those total samples taking equity stake acquisition in the observed period, is represented as
uisition in th