## Daily Returns

Moving average can be used to analyze the trend of the index and can also be used to predict the future movements. Depending on the type of moving average like 30 day moving day average it takes into account the latest 30 values and calculates the simple average of the values. It can also be called as the moving average as it takes latest values. So as the new data point comes in, the oldest data point is removed and average is calculated using the latest 30 values. This process is repeated and thus the moving average always takes the latest values. Thus it is also called as the moving average.

This is an example of simple moving average where we are giving equal weights to all the values. There are variations in the moving average methodology like exponential moving average or giving relative weights where the latest values are given more weights than the old values. (Hand & Jacka, 1998)

Moving average of different length like 30 day moving average or 365 day moving average will show different characteristics. 30 day moving average will be more volatile and also incorporate the latest data so will tend to change the shape faster than the moving average with more data points like 365 day moving average.

Here we have used simple moving average to analyze the relation between the stock indices and also for the purpose of analyzing them individually. We have also analyzed the daily returns of the stock to measure the volatility of the indices. Some indices have high volatility and some have low volatility.

Looking at the returns chart of the stock one can see that they always return to mean then go up and return back. This is due the fact that the returns series is stationary and so when one plots the graphs of the returns it will always goes up and then return back and then goes down and then returns to mean. If one plot the graph of the price of the stock then it will either be going up or down but it will not be mean reverting which means it is not stationary.

Looking at the graph one can see that the standard deviation of the Swiss Index is very high as compared to other indices. ATX index also shows a high volatility. (World Indices, 2013)

## Moving Average Graph

Here four types of moving average graph have been analyzed, 30 day, 90 day, 180 day and lastly 365 day moving average. Looking at the four graphs one can see that as the number of days of the graph is increased the graph smoothens. It is less volatile. Looking at the 30 day graph it is more volatile than the 90 day graph which is more volatile than 180 day.

Analyzing the graph one can see that BSE 30 and HangSeng Index have performed better than their counterpart. Index like S&P has remained stable over the past years. The movement in the S&P index is very less as compared to other Indices. The indices which have shown the highest movement are the indices of the developing countries. These indices were also the most affected during the crisis.

Moving average of different length like 30 day moving average or 365 day moving average will show different characteristics. 30 day moving average will be more volatile and also incorporate the latest data so will tend to change the shape faster than the moving average with more data points like 365 day moving average.

In the 30 day moving average is more volatile because it takes into consideration the most recent data and the lag in the data to respond to the news is less. If market starts rising, 30 day moving average graph will respond faster to the news. The other graphs are still incorporating the old data so the rise in the graph will be slower. All these graphs show the almost all the indices are following are the same pattern suggesting the interlinking of the economies which can be seen by their national indices. Only the magnitude change is more in some cases and less in other indices but the rise and fall is almost similar. If one looks at the 30 day moving average graph then the small patterns will be different as compared to other indices as in the short run the economies are affected by different factors. As we look at higher moving average charts, the differences seem to lessen and they follow the similar pattern. (Ruppert, 2004)

### Correlation Analysis

Correlation gives the linear relationship between two variables. Initial measure to check for the relationship between the movements of the two variables is covariance. Covariance has some drawbacks like the value can range from minus infinity to plus infinity. The magnitude of the covariance doesn’t tell anything about the strength of the relationship. Hence to overcome the drawbacks correlation is used. Correlation is covariance is divided by the standard deviations of the two variables. Thus correlation is the standardized version of the covariance. Correlation between two variables is always between -1 to +1.

**Implication of correlation values**

Correlation gives the linear relationship between the variables. A zero correlation doesn’t mean there is no relationship between the variables but instead it means that the linear relationship between the variables is not there but they can be non-linearly related.

A value of +1 means that they are perfectly positively correlated, meaning that if one variable value increases then the other variable will also increase in value. A value of 1 means that they are perfectly negatively correlated, meaning that if one variable value increases then the other variable will also increase in value. Correlation doesn’t give the causality but only the directional view, meaning that falling of one variable doesn’t mean is affect by the other variable. (Sclove, 2012)

## Analysis

### Period 1999-2013

Correlation matrix has been created using Excel functions. Some stock exchanges are positively correlated and some are negatively related. BSE 30 is positively related to CAC40, DAX, ATX Index and negatively correlated to S&P, HangSeng Index and S&P TSX Index. Similarly for other exchanges like S&P its is negatively related to BSE 30, CAC 40, DAX, FTSE 100 and positively correlated with HangSeng Index.

This is a very long period to look for the correlation. Correlation tends to change over time and so for any analysis only the recent data should be used for the analysis. Correlation is very important factor for analysis of different applications and thus it should be used carefully. Calculating correlation for such a long time period can be misleading and may lead to false results. Thus for analysis one should the shorter time frame as compared to this time frame. Correlation analysis of smaller periods will show that some of correlation relationship might have changed over the period. Markets which were positively correlated may have become negatively correlated.

### Period 1999-2005 & 2005-2013

As mentioned above the period from 1999-2013 is relatively long period to analyze the correlation, so one should use shorter period to check for the correlation.

The value of correlations for some of the stock exchange has changed in these periods. Correlation between BSE 30 and DAX was positive in the period 1999-2005 but it became negative in period 2005-2013. Similarly the correlation between S&P, Swiss Index and BSE 30 was positive in the period 1999-2005 but it became negative for the 2005-2013.

For CAC 40 and DAX it correlation turned to positive from negative value from the period of 1999-2005 to 2005 -2013 respectively, while the reverse thing happened between CAC40 and (S&P Index, Swiss Index), correlation turned from positive to negative. (World Indices, 2013)

For DAX, correlation between DAX and ATX Index turned from positive to negative, correlation between (S&P, S&P TSX Index) and DAX turned from negative to positive.

Similar things can be observed between the other stock exchanges, some correlations have changed the sign i.e. from positive to negative or negative to positive, some correlation have changed in magnitude, i.e. became more strong or weak in correlated, while some correlation have not changed.

Thus one needs to cautious while using this analysis for some research or real life application. Correlation is being used in different ways in world of finance. One of the application is to use correlation to select an optimal diversified portfolio.

Here as the correlation keeps changing over a period of time, one needs to take the latest available values and always incorporate the latest values to calculate the correlation table. It has also been observed that when the markets are rising i.e. economy is booming stock markets and the asset prices tend to follow the historical correlation. But as the market falls or during crisis all the historical correlation changes and all markets becomes positively correlated with each and thus the concept of diversification doesn’t apply to these markets as all the markets will be falling.

The change in correlations can be attributed to many factors which affect the variables. There can be new factors coming into play. Here the way economies of different countries have undergone a change in these periods and the ways is business is conducted have changed leading to change in correlations.

### Analysis of correlation groups

Analyzing the correlation and arranging them in the descending order one can see the order of correlation between them. Correlation groups here can be divided into 3 groups mainly strong positively correlated, weak positive correlated and negative correlated.

The negative correlation group can have combinations which are already there in the above two groups as the stock exchanges in the above two groups will interact with each and may be negatively related.

By looking at the chart like bar chart and the area chart, one can see that some stocks are strongly positively correlated, some are weakly correlated and some are strongly negatively correlated.