Table 1
The dependent variables for the financial contagion distribution channels tests (VAR model)
The financial contagion distribution channel
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Dependent variables
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Correlated-information channel
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treasury bond index return;
corporate bond index return;
major (determined by the market) industries index return;
major (determined by the market) resources futures prices return
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Liquidity channel
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major (determined by the market) resources futures open interest;
major (determined by the market) resources futures volume of trade
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Risk-premium channel
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interbank loans interest rate for different periods of time
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Mainly the following variables were used in assessing the role of the correlated-information channel in financial contagion distribution (depend on the information available):
national government yield curve3 (Finland, Canada);
national stock exchange main indexes4 return (Finland, Brazil, Canada);
important commodities5 prices (Finland, Brazil, Canada);
government bond auction average price (Canada).
The next time series were used for the purpose of assessing the liquidity channel role:
government bond transactions (Finland);
main indexes turnover (Finland, Canada);
stock market total amount (Brazil);
derivatives positions: swap, futures market and options market (Brazil);
operations with federal securities and derivatives (Brazil);
demand deposits (Brazil);
money supply type M16 (Brazil);
government bond auction alotted sums (Canada);
futures on the important commodities volume of trade (Canada);
futures on the important commodities open interest (Canada).
The series for the risk-premium channel are following:
national central bank interbank offered rate (Finland, Brazil, Canada);
Euro interbank offered rate (Finland);
Euro Over Night Index Average rate (Finland);
national financial government systemic institutions interest rates (Brazil);
settlement balances of a national payment system (Brazil);
interest rate used for the securities operations: purchase, resale, lending, bankers’ acceptances (Brazil).
The detailed information concerning the dependent variables and their description is listed in the Appendix 1. In order to reveal market risk through stock prices fluctuations, the stock prices need to be adjusted to splits, consolidations, subscription privileges and dividends – so to say, everything, that can influence stock price and doesn’t refer to market factors. As the data source had had that adjusted stock prices already, any further data preparation weren’t need.
In order to make the list describe the selected markets the assets were selected from the major indexes on the markets. For the purpose of the study the companies were selected those are included in the main stock market lists for the particular market. The list of the main stock market indicators was obtained from World Federation of Exchanges web page7. In the case when the number of items (depending on the asset type in each dataset - stocks, bonds and others) were less than 250, the other indexes were considered (entirely, the sector indexes). The sector share in the country GDP for the countries considered is shown in the Appendix 2. The data was obtained from The World Bank World Development Indicators database8. Figures from Appendix 2 visual analysis made it possible to notice, that as the World economy moves to postindustrial phase, in the markets considered the major added value to the GDP comes from services sector. The latter means that these markets are in industrial economic development stage.
So to summarize figures discussion, the major sector in all markets considered is the service sector. It is followed by the industry sector on the second place (the exception in this case is Indian market, where in 1990-1998 the agriculture sector was on the second place). So, the sector indexes as the lists of the companies, that can represent the particular market, were selected on the base of relations discussed .
If the period required was not covered by the time series (e.g. the time series length was not enough and any data for the early 1990-s was absent), the available for the particular market and asset class prices were used. Missing values in the dataset were filled using the previous observations, however, sometimes the missing values were at the beginning of the dataset, so the parametric method that assumes an underlying normal model for the partially observed imputed variable was used, that is based on the asymptotic approximation of the posterior predictive distribution of the missing data. The method was used for the vector autoregressive model that is based on the hypothesis that the random variable has normal distribution.
In order to confirm that time series do fit the models, three time series problems were considered in the study during the ARIMA(p,d,q) model specification:
First-order serial correlation;
Non-stationarity;
Residuals heteroscedasticity.
The data analysis was held in three main steps:
Time series models building using the Box-Jenkins approach to time-series modelling (ARMA(p,q) models);
Market risk models building using the results of the time series analysis;
CAPM model assessment with different market risk proxy variables.
The Box-Jenkins approach was performed through the following steps (Baum, 2005; Канторович, 2002):
Checking for variables stationarity and finding the integration degree of the time series;
ARIMA(p,d,q) model identification based on Sample Autocorrelation Function and Partial Autocorrelation Function behavior and information criteria (Akaike9 and Schwarz criteria) also using integration degree known from first step.
ARIMA(p,d,q) model assessment based on p, d, and q parameters.
Model diagnostics based on residuals analysis.
This algorithm was automated using Stata program (Appendix 3).
The null hypothesis of no first-order serial correlation was tested using Breush-Godfrey test for autocorrelation.
Models
In the research vector autoregressive model of the financial contagion is considered. In the research the conclusions are made concerning the type of model with higher quality value and with better adequacy to credit ratings market risk level. So, the aim was to determine the model that would be able to become an alternative to market risk indicators based on credit ratings. Such an assessment can be performed not only for country, but also for the particular industry (if companies belong to this industry are selected), for the asset portfolio and for the company, at last.
The awareness concerning market risk level permits investor to know, if this risk degree is affordable for him – this particularly is the practical sense of this study. On the other hand, market risk variable is used in theoretical constructions, for example, CAPM, that’s why is it critical to determine the market risk value correctly. The latter is the theoretical sense of the study. CAPM model has much critique concerning it’s pure ability to reflect market situation. The problem may lie in wrong market risk assessment. As far as CAPM is one of the key financial models and it is used in case of equity assessment, this topic is of great concern for a long time yet.
Traditionally major market index return variance is used as the market risk variable. In the study the financial contagion theory is proposed as the alternative method for market risk assessment. And one of the main questions here is if the financial contagion approach to the market risk assessment is affordable and whether it is better than traditional approach.
VAR models are used among others in the macroeconomic variables dynamics studies. For example, C.A. Sims, a Nobel prize winner, proposed using VAR models for the describing macroeconomic processes “without restrictions based on supposed a priori knowledge” (Sims, 1980). The predecessor of VAR is the structural equation model, that has an extensive application in macroeconomic empirical research (Hurwicz, 1966; McFadden, 1973). During the 1960-1970-s the VAR concept formation took place. The proper lag number selection and the most common regression problems (residuals heteroskedasticity, serial correlation and the non-stationarity) were the point of attention in the area of study (Author & Sargan, 1961). The idea of including simultaneously several lags in the equation belongs to M. Hatanaka (Hatanaka, 1975). Another question concerns variables, that are strictly exogenous and the ways of proving that (Sims, 1980).
Autoregressive models provide a flexible, estimable, and interpretable model. In econometrics the situation names “real life” is considered to be extremely complicated, and the “real model” is infinite-dimensional (Hurvich, 2002).
In resent research VAR is also popular as the instrument of macroeconomic hypothesis testing. Despite the fact that a regression model isn’t possible to disclosure the cause and the effect relation between the exogenous and the endogenous variables, the particular field of research is aimed at the revelation of the vector variables that influence macroeconomic dynamics. “A VAR can be considered to be the reduced form of a dynamic structural equation (DSE) model, and the ordering of the recursive structure is that imposed in the Cholesky decomposition, which is that in which the endogenous variables appear in the VAR estimation”, as Ch.F. Baum pointed (Baum, 2013). The VAR model used in the study had the following configuration (1).
where Mt - the major macroeconomic indicator index return;
At-p – assets return;
 – random error;
t – time moment.
The number of lags in the model for the dependent and the independent variables were defined using Box-Jenkins approach to time-series modeling. The lags order proposed by ARIMA(p,d,q) were used as the lags order for the dependent and independent variables accordingly. As C.A. Sims mentioned, “truncating lag distributions is part of the process of estimation – lag length is itself estimated one way or another – and that when our model is not identified without the pretense that we know lag length to begin with” (Sims, 1980). Introducing too many lags leads to the model loosing degrees of freedom, while too few lags too few lags can make the model misspecified, that in the same time leads to the residuals autocorrelation (Baum, 2013).
Alongside with lag selection by ARIMA(p,d,q) specification according to Box-Jenkins approach to time series modeling, Hatanaka’s criterion is used for VAR’s lag number selection. It is that the exogenous variable lag number shouldn’t be less than the endogenous variable lag number (Hatanaka, 1975; Sims, 1980).
At the same time, as ARIMA(p,d,q) proposes the order of time series smoothing to avoid the residuals heteroskedasticity and implies that the time series are stationary (that means, the original time series must be modifies so that the time series analyzed are stationary: the trend, if any, should be extracted from the time series, and, in case of random walk process, take the differences of the required order). The constant term of the VAR model, α, can be interpreted as the influence of other factors on the macroeconomic parameter M, that are not considered in the model. This model was assessed for each pair of the asset price and the macroeconomic indicator.
The vector autoregressive model shows the probability of the error and in this sense it is the risk measure. As far as the model itself assess the financial contagion, the probability of the error is low then the financial contagion is strong and there exists a significant interconnection between the variables. And them the model error probability is high, the financial contagion is low.
As the periods of economic crises differs from market to market, the period of assessment was 1 year in order to make historical risk dynamic comparable for different markets. According to the scheme, presented in the Appendix 1, the financial contagion indicator, based on the VAR model, was derived from the p-value of the model of financial contagion. As the p-value itself shows the probability of the situation then the VAR model is not significant, the 1 – p-value can be interpreted as the probability, that the model is significant, so the financial contagion does exist. But, as the results show, the most trivial situation is then the financial contagion indicator (1 - p-value) is lower than 90% (traditionally, three confidence levels are used during the hypothesis of non-significance of the model testing: 0,1; 0,5 and 0,01 error probability).
The next step after obtaining the financial contagion indicator value for each pair of the dependent variable and the independent variable was to calculate the aggregated p-value for each dependent variable. The weight of each dependent variable p-value was obtained on the base of the following equation (2)
where T - the period (one year);
t - the defined time moment (one day) inside this period;
Vi,t – the turnover of the ith asset in the day t;
n – the number of assets.
Results
The research results are presented for the three channels of the financial contagion and in the Appendix 4 with the network analysis using ORA-NetScenes software.
Finnish market, 1997-2014
Table 2
Results for Finnish market: the financial contagion indicator for the different dependent variables (market risk factors), 1997-2014
The situation on Finnish market is depicted precisely for the three channels on the Figure 1.
Fig. 1. The financial contagion distribution channels’ factors for Finnish market, 1997-2014
As the Figure 1 shows, the financial contagion on Finnish market was absent during the period considered, but there can be pointed the years of comparatively higher (1999-2003; 2006-2010) and lower (2012-2014) financial contagion levels. The interconnections revealed are presented in the net maps (Appendix 5). During the period 1999-2002 the main part of the financial contagion level existed was brought by the following factors: crude oil Brent price in Europe, London fixed silver prices, Finnish government 16-bond transactions and Bank of Finland interbank offered rate (helibor) for 1 year period.
Brazilian market, 1991-2015
Table 3
Results for Brazilian market: the financial contagion indicator for the different dependent variables (market risk factors), 1991-2015
Fig. 2. The financial contagion distribution channels’ factors for Brazilian market, 1991-2015
During the period 1991-2015 crisis 1992-1993 on Brazilian market isn’t reflected by the financial contagion indicator. In 1997 the liquidity channel was a little more active. This fact can be connected with the Asian financial crisis 1997-1998. The risk-premium channel shows some fluctuations in 1998, when, as (Kaminsky et al., 2003) pointed, Brazilian economy was affected by Russian debt crisis. Serious financial contagion indicator value growth can be registered during 2007-2009 global financial crisis. And, at last, the trend of Banco Central do Brasil base financial interest rate contribution to financial contagion is clearly seen from 2010. It is also can be pointed, that from the second half of the 2014 the correlated-information channel become expansion again, as during the previous periods. The net maps of the Brazilian market macroeconomic variables and Brazilian companies stock prices interconnections are presented in Appendix 6.
Canadian market, 1990-1992, 1995-1998 |
