Excerpt
Exploring the characteristics of risk at the Istanbul Stock Exchange
Motivation
Financial markets became indivisible part of global economy in 20th century. Their importance is still a growing process. The great depression was triggered by stock market crash in US and similarly current crises took its origin from financial markets. So, stock markets and the risk in these markets are economic phenomena which need to be studied a lot.
This paper focuses on the characteristics of the risk at the Istanbul Stock Exchange(IMKB) and uses GARCH/ARCH framework for economic analysis. There are a lot of papers on this kind of markets, but they mainly investigate the risk in mature economies. The similar researches should be done for emerging markets as in nowadays their importance and influence is increasing. Hopefully this paper will be pharos for similar investigations.
Data
The estimations in this paper are done on the base of following variables: imkb, dax, dji, ftse, nasdaq which represents Istanbul Stock Market (IMKB) and major world markets. Variables are original daily closing indices. But in order to match them (missing values due to holidays and etc.) we introduce corrected indices: cimkb,cdax,cdji,cftse and cnasdaq. Returns on indices are calculated according to this formula: rcimkb=log(cimkb)-log(cimkb(-1)).
Estimation
So, first we run basic regression, id est try to identify the relationship between Turkey’s stock exchange market and main stock exchange markets of the world. Regression of rimkb on its lag and other indices’ lags reveals out that there is not significant relationship among them. Actually it is very unusual and surprising result. But we should consider that we are analyzing almost last two decades data, which were very problematic for Turkey. During the observed period there were one military revolution and two economic crises which were specific to Turkey. In 1994 and 2000-2001 crises Turkey’s economy demonstrated very different behavior in comparison with the world economy. So, insignificant relationship might stem from above mentioned reasons. Perhaps in smaller samples we would see significant relationship.
We shall continue our analysis only with own lag and constant:
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So now we have meaningful regression and we can move on. We shall first look at standardized Residuals graph. Standardized residuals are basically residuals divided by standard errors of regression, so in other words they are t values of the regression. It is obvious that residuals have very volatile structure. There are a lot of outliers in the residuals which go beyond 3 and -3 interval. Especially we have volatility clustering around 200th , 800th , 1200th , 1700th , 2000- 3000th and 4500th observations.
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By analyzing correlogram of squared residuals we can identify that there is correlation up to some order. It shows time dependence of residuals. Auto correlation fades out in 4th observation, but partial autocorrelation visible until 2nd observations. So it is obvious that we have correlation up to some order. So GARCH (1, 1) model may not be sufficient. And can do normality test and take into the account the histogram of residuals. The histogram graph shows that the distribution is quite abnormal. It has high kurtosis, 5, which is more than 3 and asymmetric structure with skewness. And there are a lot of extreme values which are far away from the tales. Median is negative and it means we had more negative days than positive days. Range is very high with 15% increase and 16%decrease. We have fat tales and overall very abnormal distribution.
After analyzing the residuals we should find ways for getting rid of volatility. If we do arch test we’ll see that it is significant up to 6 orders.
So, usually if we have GARCH (1, 1) then ARCH LM is significant up to 2nd order. Here the significance up to 6 orders may suggest that GARCH (1, 1) may be not sufficient model, which is unusual.
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