Macro Economics

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Acknowledgement I take this opportunity to pay my gratitude to all those people who have helped me carry out this project. This project could not have been complete without the contribution and support of few individuals. They helped me a lot in giving us a foresight of how to start, carry on and complete this project. I am grateful to my project guide Prof. Tamal Dutta Chaudhary for the guidance, inspiration and constructive suggestions that helped me in the preparation of this project. I am thankful to all our teaching and non-teaching staff of IBS for their constructive suggestions. Last but not the least, I also thank all my friends and seniors who have helped me in all possible ways and made this work a heavenly toil.

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Executive Summery This project mainly aims at the analyzing the current stock market volatility. The Indian stock market benchmark index BSE Sensex has witnessed some of the landmark events in the recent past. Sensex reached its highest point ever around the same time last year and this year the picture is just reversed. The current economic recession has affected the Indian Stock Market or not has been analyzed in this report. The volatility for two time phases has been measured in the report and some conclusions have been drawn. On the basis of results obtained by the use of some statistical methods like calculation of variance and standard deviation, we came to know that the volatility has increased in the second time phase. Also in this report, it has been tried to obtain the relationship between the Sensex values and the prices of Crude Oil. Again with the use of regression analysis we came to know that there is not a very significant relationship between Sensex and Crude Oil prices. Thus this report gives a statistical outlook to both the macro-economic phenomenon.

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Table of Content

Topic

Page No.

Acknowledgement

2

Executive Summary

3

1.

Introduction

5

2.

Motivation

6

3.

Hypothesis

7

4.

Methodology

5.

Reasons For High Volatility in Phase II

6.

Conclusion

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7.

References

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8-12 13-16

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1.

Introduction

Volatility refers to the a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. Volatility is easily the most common risk measure, despite its imperfections, which include the fact that upside price movements are considered just as "risky" as downside movements. We often estimate future volatility by looking at historical volatility. Looking at the Indian stock market benchmark index BSE Sensex we in this report are looking forward to calculate the historical volatility in two time Phases and will try to establish a relationship between the volatility in these two time phases. Another thing we will be doing in this report is to establish a relationship between the value of Sensex and Crude Oil prices so also find out a reason for change in volatility.

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2.

Motivation:

The current Economic downturn has created a sense of panic in the minds of savers. The stock markets world over have taken a serious impact on themselves and almost all of them have seen a series of steep falls. India, being the second fastest growing economy after China has also faced the impact of this global meltdown. The Indian Stock Markets have also shown a steep decline in their values for last one year or so. This global meltdown and its impact on Indian Stock Market is the source of motivation for me in doing this project One of the key indicators of Indian Economy is the Bombay Stock Exchange Sensitivity Index (BSE Sensex). BSE Sensex as it is popularly known as is a value-weight index composed of 30 stocks with the base April 1984 = 100. It consist of 30 largest and most actively traded stocks, representative of various sectors, on the Bombay Stock exchange. As these companies are from different sectors they combined together can give a broad idea about the Indian Economy as a whole. Thus a study of volatility of Sensex can give us a idea about the volatility of Indian Economy.

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3.

Hypothesis:

While preparing this report on the Stock Market benchmark index Sensex and its volatility, I have taken two hypothesis about the volatility of Sensex. a.

Null Hypothesis: The Stock Market benchmark index Sensex is less Volatile during the period of recession.

b.

Alternate Hypothesis: The volatility of Sensex has increased in the period of recession.

These are the basic hypotheses which have been taken to carryon this report. This hypothesis will be tested with a number of statistical tools and conclusion will be drawn on the basis of the result obtained. c.

Assumptions: There are a few assumptions which have been taken for the purpose of preparing this report.

1.

While preparing this report it has been assumed that the period of recession has started from 1st of January 2007 and is still not over. The period of economic upswing is assumed to have started from 1stof January 2005 and has continued till December 2006.

2.

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3.

4.

It has been assumed that the volatility is market only market driven without the effect of any extraneous factor working behind it.

METHODOLOGY:

Volatility refers to the deviation from a normal mean. Volatility is critical for risk measurement. Generally volatility refers to standard deviation. From the mean. If the volatility is high then there is a higher risk of value of a index moving up or down. We often predict future volatility calculating the historical volatility. This is very much important for future forecasting. For the purpose of calculating the volatility of an index we need to take two steps 1. Compute a series of periodic returns for eg. Daily returns. 2. Choose a weighting scheme. This includes the decision on the length or the size of the historical sample. In this report I have taken a period of four years, which is from 2005 to 2008. This time period has been divided into two phases a. Economic upswing (bull phase) from 1/1/2005 to 31/12/2006. b. Economic downswing (bear phase) from 1/1/2007 to 31 12/2008. 9

The periodic returns could be calculated by the formula given below Ui = ln (Vi / Vi-1 ) Where a. b. c.

Ui Vi Vi-1

= Return from sensex in period ‘I’ = Value of Sensex in period ‘I’ = Value of Sensex in period prior to ‘I’

The volatility can be calculated by calculating the variance of Ui by the formula given below.

Where σ2n = variance rate per period b. m = number of observations c. ū = the mean of periodic returns a.

After calculating the variance we calculate the standard deviation of that variance and we get the volatility of the Sensex. Volatility = (σ2)½

Now we calculate the descriptive statistics figures of the daily closing sensex values of both the time periods by using various statistical packages like MS Excel and SPSS 10

Descriptive Statistics N

Range

Minimum

Maximum

Mean Std. Deviation

PHASE_I

501

7869.29

6102.74

13972.03

9412.4296

2328.85961

PHASE_II

496

12422.32

8451.01

20873.33

15020.5225

2809.66986

Valid N (listwise)

496

Looking at the descriptive statistic of both the Phases first thing we can see that the range in Phase II has increased by 4553.03 points. Along with that the standard deviation has also increased in the second Phase. These are very clear indicators about the increased volatility of Sensex in the second Phase.

a.

Calculation of Volatility:

Using the above mentioned method for calculation the volatility and taking the two different time frames as mentioned above we can get the two different volatilities.

Phase I

Phase II

Variance

0.00019

0.000527

Standard Deviation Volatility

0.013779

0.022962

0.013779

0.022962

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b.

Analysis: Looking at the above mentioned volatility of both the Phases we can clearly see that the Volatility of Sensex has increased in Phase II. This concludes that the null hypothesis which we have taken is false and we have to reject the null hypothesis and accept the alternate hypothesis that is “The volatility of Sensex has increased in the period of recession.”

The above phenomenon could be clearly shown in the graphs shown in the next page.

A. Graph Showing the daily movement of Sensex in Phase I

B. Graph Showing the daily movement of Sensex in Phase II

Here from both the graphs we can see that the movement of the Sensex has increased a lot in the second phase. We can clearly see that in the first Phase the movement of Sensex has majorly been upward moving. On the other hand the movement of Sensex has been quite dynamic in the Phase II and it has moved both upward and downward. This shows the volatility of Sensex has increased in the Phase II. 12

5.

Reasons for high volatility in Phase II:

As we clearly saw that the volatility of Sensex has increased in the phase II, we should look about the possible reasons for increase in volatility of Sensex. For this purpose we again need to carry out some statistical tests depending upon the results of which we could give any conclusion about the increase in volatility of Sensex. 13

1.

2.

3.

4.

Hypothesis: For finding out the reasons for high volatility of Sensex, let us take Sensex values and crude oil prices as two variables. We assume the value of Sensex as the dependent variable and the crude oil prices as the independent variable. We now try to find out that is there a relationship between the two variables by taking two hypothesis. Null Hypothesis: There is no relationship between the value of Sensex and the crude oil prices and the increase in volatility of Sensex is caused by some extraneous variable. Alternate Hypothesis: There is some relationship between the value of Sensex and crude oil prices and the increase in volatility of Sensex is caused by the increase in volatility of crude oil prices.

Methodology: For the testing of above formulated hypothesis I will be using the regression analysis. For the regression analysis I have assumed that the sensex values are dependent on the crude oil prices values. For this purpose I have taken the monthly closing values of both BSE Sensex and crude oil prices. the movement of both the variables in last 24 months have been shown in the graph below. After taking the monthly values of both the variables and operating them on SPSS for the calculation of correlation and regression I got the following results.

A. Graph showing movement of Sensex and Crude Oil for last 24 month

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Descriptive Statistics Mean

Std. Deviation SENSEX 14965.1025 2992.70006 CRUDEOIL

81.7100

N 24

25.22409

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From the above given figures we can see the mean and standard deviation of both the variables.

Correlations SENSEX CRUDEOIL Pearson Correlation

Sig. (1-tailed)

N

SENSEX

1.000

.456

CRUDEOIL

.456

1.000

SENSEX

.

.013

CRUDEOIL

.013

.

SENSEX CRUDEOIL

24 24

24 24

From the fig. given above we can see that the correlation between the sensex values and the crude oil prices is o.456 This is though correlated is not significant enough for concluding anything about the relationship between the sensex volatility and crude oil prices.

Model Summary Model R

1

.456

R Square Adjusted R Std. Error of Square the Estimate .208

.172 2723.04569

a Predictors: (Constant), CRUDEOIL b Dependent Variable: SENSEX

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From the values given above we get the value of adjusted R Square. R Square value identifies the proportion of variance in Sensex values which is accounted by variance in Crude oil prices. We can clearly see that the Adjusted R Square value is 0.172. This indicates that the variance of sensex values is very less to do with the variance in the Crude oil price. Thus we can say that only 17.2% of the variance in the value of sensex is explained by the values of Crude Oil Prices.

ANOVA Model

Sum of Squares

1 Regression 42864321.9 35 Residual 163129511. 916 Total 205993833. 851 a Predictors: (Constant), CRUDEOIL b Dependent Variable: SENSEX

df

Mean Square

F

Sig.

1 42864321.9 35 22 7414977.81 4

5.781

.025

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From the figures above we can see that though the F statistic is 5.781 but still the Sig F is also high (2.5 %) thus the value of F statistic is possible by chance. Thus we can conclude that the value of volatility of Sensex could be related to the Crude oil price movement by chance. Thus we can say that the Volatility of Sensex has increased in the period of recession but the reason for the increase in volatility could not be attributed to the Crude Oil price movement only. There could be some extraneous variables which are working behind this phenomenon. 5.

Result:

Thus from the help of above statistical calculation we can see that the there is a significant difference between the correlation of Sensex values and the Crude Oil Prices. Thus we accept the null hypothesis that is “There is no relationship between the value of Sensex and the 16

crude oil prices and the increase in volatility of Sensex is caused by some extraneous variable”

6.

Conclusion:

From the above shown analysis of the results obtained from statistical tools we can conclude that the Volatility of Sensex has increased in the period of recession. Indian Stock Markets have also suffered the impact of the global meltdown and the risk has increased for the savers who allocate their savings in the Stock Markets. The other conclusion we can draw from this project report is that the reason for the increased volatility could not be solely attributed to the Volatility in the prices of Crude Oil. There are some extraneous variables operating in the market which might have higher impact on the stock 17

markets. These could be attributed to various macroeconomic indicators like expected growth rate (GDP growth), unstable inflation rates, and lastly one of the most important reasons for Volatility of Sensex could be the fluctuating movement of Foreign Institutional Investors (FII’s)

7.

References:

a.

Stock market index, from Wikipedia Article by David Harper, CFA, titled “Using Historical Volatility To Gauge Future Risk” BSE Sensex, from Wikipedia “SPSS for windows step by step” by Darren George and Paul Mallery

b.

c. d.

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e. f. g. h. i. j. k.

Marketing Research by Naresh K. Malhotra www.mopsi.nic.in www.energy.gov www.opec.org www.rbi.org www.Investopedia.com www.bseindia.org

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