business statistics project 2010

Comparative Analysis of Variation in BSE Sensex

Comparative Analysis of Variation in BSE Sensex w.r.t. its Top 10 Listed Companies, NASDAQ &

Nikkei and Gold

Group:

1. Aayush Akhauri 10IB-0022. Abhishek Agarwal 10FN-1223. Ajay Kumar Jha 10FN-0064. Ankit Rungta 10FN-015

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1. Summary:

1.1. Topic: Comparative Analysis of Variation in BSE Sensex with respect to its Top 10 Listed Companies, NASDAQ & Nikkei and Gold.

1.2. Objective:Our objective is to find out how the BSE Sensex varies according to variation in its top 10 listed companies (according to market capitalization). We will also find out whether there is any similarity in the variation of SENSEX and the price of GOLD.Moreover we will also find out , how the percentage change in SENSEX is dependent on that of NASDAQ and Nikki.

1.3. Methodology:First we have collected data from BSE, NASDAQ, Nikkei, and Yahoo Finance. Then we have used Regression Analysis using Microsoft Excel2007.

1.4. Result:From the Regression Analysis we have got the result that variation in BSE Sensex doesn’t depend much on NASDAQ & Nikkei or Gold, but its variation is highly dependent upon the variation of its top 10 listed companies.

2. Introduction:Our objective is to find out the amount of dependence SENSEX has on its top 15 companies in terms of market capitalization. We will also find out whether there is any similarity in the variation of SENSEX and the price of GOLD. Moreover we will also find out , how the percentage change in SENSEX is dependent on that of Nasdaq and Nikki.

2.1. SENSEX:Bombay stock exchange or BSE is the largest stock exchange in India in terms of number of listed companies in the exchange and the market capitalization of the listed companies. The prime index of the Bombay Stock Exchange is the BSE 30 that is popularly known as the Sensex. The Sensex is made with highly liquid stocks of 30 largest companies in terms of market capitalization. The Sensex was first constructed in the 1986 on 1st of January with just 30 stocks. Over the years of course these stocks have changed time and again according to the condition of the market and economy of the country. The selection of the stocks is made on the basis of market capitalization and liquidity of stocks. The BSE index committee decides on which stock to include in the Sensex and which stock should be removed from the Sensex. This committee is made up of highly placed experts and professionals from the field finance and industry that are well aware of the Indian stock market scenario.

2.2. NASDAQ:

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The NASDAQ Stock Market, also known as the NASDAQ, is an American stock exchange. "NASDAQ" originally stood for "National Association of Securities Dealers Automated Quotations," but the exchange's official stance is that the acronym is obsolete. ] It is the largest electronic screen-based equity securities trading market in the United States and fourth largest by market capitalization in the world. With approximately 3,700 companies and corporations, it has more trading volume than any other stock exchange in the world.It was founded in 1971 by the National Association of Securities Dealers (NASD), who divested themselves of it in a series of sales in 2000 and 2001. It is owned and operated by the NASDAQ OMX Group, the stock of which was listed on its own stock exchange beginning July 2, 2002, under the ticker symbol NASDAQ: NDAQ. It is regulated by the Securities and Exchange Commission.

2.3. Nikkei 225 It is a stock market index for the Tokyo Stock Exchange (TSE). It has been calculated daily by the Nikkei newspaper since 1950. It is a price-weighted average, and the components are reviewed once a year. Currently, the Nikkei is the most widely quoted average of Japanese equities, similar to the Dow Jones Industrial Average. In fact, it was known as the "Nikkei Dow Jones Stock Average" from 1975 to 198.

The Nikkei 225 began to be calculated on September 7, 1950, retroactively calculated back to May 16, 1949.Currently, the index is updated every 15 seconds during trading sessions.The Nikkei 225 Futures, introduced at Singapore Exchange (SGX) in 1986, the Osaka Securities Exchange (OSE) in 1988, Chicago Mercantile Exchange (CME) in 1990, is now an internationally recognized futures index.

The Nikkei average hit its all-time high on December 29, 1989, during the peak of the Japanese asset price bubble, when it reached an intra-day high of 38,957.44 before closing at 38,915.87. Its high for the 21st century stands just above 18,300 points. In January 2010, it was 72.9% below its peak.

2.4. GOLD:Gold has been widely used throughout the world as a vehicle for monetary exchange, either by issuance and recognition of gold coins or other bare metal quantities, or through gold-convertible paper instruments by establishing gold standards in which the total value of issued money is represented in a store of gold reserves.However, the amount of gold in the world is finite and production has not grown in relation to the world's economies. Today, gold mining output is declining.With the sharp growth of economies in the 20th century, and increasing foreign exchange, the world's gold reserves and their trading market have become a small fraction of all markets and fixed exchange rates of currencies to gold were no longer sustainedMany holders of gold store it in form of bullion coins or bars as a hedge against inflation or other economic disruptions. However, some economists do not believe gold serves as a hedge against inflation or currency depreciation.

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3. Literature Review:

Is Indian Stock Market Integrated with the US and Japanese Markets?An Empirical Analysis

Khan Masood Ahmad, Shahid Ashraf* and Shahid Ahmed*

ABSTRACTThe paper attempts to understand the inter-linkages and causal relationship between the Nasdaq composite index in US, the Nikkei in Japan with that of NSE Nifty and BSE Sensex in India during the period of January, 1999 to August, 2004, using daily closing data. The Johansen co-integration test is applied to measure the long-term relationship between two indices and Granger-causality test is used to check the short- term causal relationship.The analysis reveals that there is no long-term relationship of the Indian equity market with that of the US and Japanese equity markets. Further, Nasdaq and Nikkei have stronger causal relationship in the period 1999-2001 which becomes either very weak or disappears in the period 2002-2004. There seems to be disassociation in the movements of the Nasdaq and Nikkei with that of the Sensex and Nifty. When the stock markets have no tendency to move together in the long-term and causal effects become weak in the short-term then the markets are segmented and provide ample room for diversification of investments. The recent surge of FIIs investments to the Indian equity market is primarily a reflection of this trend.

Financial Integration for Indian Stock MarketSadhan Kumar Chattopadhyay

&Samir Ranjan Behera†

IntroductionThe main objective of this paper is to investigate the issue of stock market integration in India in the light of financial liberalization. Following the global trend financial liberalization has also started in India since 1992. Increasing globalisation of the world economy should obviously have an impact on the behaviour of domestic stock markets (Cerny 2004). Since the work of Grubel (1968) on expounding the benefits from international portfolio diversification, the relationship among national stock markets has been widely studied. Hence the relationship among different stock markets has great influence on investment because diversification theory assumes that prices of different stock markets do not move together so that investors could buy shares in foreign as well as domestic markets and seek to reduce risk through global diversification. Under this backdrop, it is worth examining whether Indian stock market has really integrated with the world markets. The study finds that in the short run, while US, UK and Hong Kong stock markets Granger cause the Indian stock markets, the Indian stock does not Granger cause the above markets which appears to be plausible. However, the study finds that the Indian stock market (BSE Sensex) is not co-integrated with the developed markets and hence not sensitive to the dynamics in these markets in the long run.

Conclusion

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India is one of the emerging economies, which have witnessed significant development in the stock markets during the recent periods due to the liberalization policy initiated by the government. It is generally believed that due to liberalization policy and the consequent development of Indian stock markets, the latter might have integrated with the developed markets. One may argue that due to this integration, which appears to have taken place after liberalization, Indian stock market will mainly be governed by a common factor as in the case of the developed markets. However, our study does not support this view. Rather, it finds that Indian stock market is not at all integrated with the world markets. Of course, the study finds that baring Japan there is a unidirectional causality from the developed market. Hence we may conclude that Indian stock market is not influenced by other markets. Of course, some short-term sentiment in the world market does have impact but this is short-lived. That means the pr-requisites, which are required for long-run relationship has not been achieved by India so far.

The phenomenon of global stock market contagionA Srikanth

Men, it has been well said think in herds; it will be seen that they go mad in herds, while they only recover their senses slowly, and one by one.

THE WORLD markets catch cold when the US market sneezes. The recent reaction of the world markets to the steep fall in Nasdaq is a case in point. The 357-point (9.70 per cent) drop in Nasdaq on April 14 resulted in the Bombay Stock Exchange Sensex losing 291 points on April 17.

The impact is not limited to the Indian market. Most South-East Asian markets too felt the shock-waves of the Nasdaq crash. On April 17, when the market reopened after the weekend, Japan's Nikkei lost 1,426 points (6.98 per cent), Hong Kong's Hang Seng index 1,380 points (8.54 per cent) and Singapore's STI index 190 points (8.68 per cent). The European markets too reacted adversely to the Nasdaq fall.

In the same way, the recovery on Nasdaq on April 17 and 18 reversed the trends in most South-East Asian and European markets (except India) the next day. In India, the impact of the Nasdaq crash seems far from over as the Sensex lost a further 135 points on Tuesday and 79.66 points on Wednesday. A similar contagion effect was observed when the Dow Jones index crashed in October 1997.

However, the contagion effect has become more pronounced in recent years because of the rapid global economic integration. It may also be observed that the phenomenon of global stock market contagion always comes for debate only when a major crisis hits the US market.

In this context, it is interesting to look at the nature of the long-term relationship between the US and markets around the world. Empirical analysis abroad has shown that the average correlation between the US and other foreign markets (the UK, France, Germany, Switzerland, Japan and East-Asian markets) between 1958 to 1995 was around 0.40. It is possible that the correlation would have gone up over the last five years. Yet, it is not high enough to say that the global markets are fully inter-connected.The relationship between the markets was studied since January 1999 till date. The period is relevant in the sense that both Infosys Technologies (March 1999) and Satyam Infoway (October 1999) got listed on Nasdaq. Though the extent of correlation between Nasdaq and the Sensex rose subsequent to the listing of these stocks, the movement between the

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indices have been quite close during March-April 1999. Again since August 1999, the correlation between the two indices has been quite high (see graph).

Apart from accounting for the listing of Infosys Technologies and Satyam Infoway, the period of high correlation also coincided with periods of high volatility both the in the US and the Indian markets (see Business Line, April 9, 2000 for a story about increase in volatility). A similar analysis of the Infosys Technologies stock both at Nasdaq and in the Indian market conforms the above trend.

The Infosys Technologies stock was not only as volatile as the Sensex, its correlation with the US stock was also found to be high during these periods of high volatility. However, the correlation between the US and the Indian stock of Infosys Technologies was not as strong as between the Nasdaq index and the Sensex. This means that in times of high volatility, the Sensex was reacting more to the Nasdaq movement as a whole than that of the Infosys Technologies stock alone.

One implication of this result is that it could undermine the logic behind international portfolio diversification. If the benefits of diversification are not available when it is needed most, there would seem to be little point in diversification, in the first place.

It is equally interesting to know the driving force behind the financial contagion. To some extent the integration of the global economies has a role to play. Arbitrage activity in commodity and security markets along with the dynamics of the currency market are important forces behind international propagation of crisis.

In panic situations, lack of information encourages herd behaviour among investors. Disposal of stock by one investor is assumed to be based on news that is not yet known, so that investors interpret this action as a signal to sell their holdings. Lack of information also encourages investors to take poor performance in one market as a signal that bad news is imminent in other markets too. The fact that the poor performance and the consequent fall of the net stocks in the US was interpreted as bad news for the entire Indian technology sector is a case in point.

THURSDAY, JUNE 04, 2009Sensex, rupee, gold link

When the Sensex shoots up, gold prices come down and the rupee appreciates against the US dollar. Can you please explain the correlation among these three?

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Well, the Indian stock market is dominated by foreign institutional investors (FIIs). When they pour in dollars into India, they get converted into rupees which find their way into the stock market. And the dollar finds its way into the currency market thus augmenting its supply.

When the supply of dollars increases, naturally its value vis-À-vis the rupee comes down. This is the immediate and direct explanation. A distant explanation could be that when the sentiments improve on the back of a Sensex upswing heralding a better state of the economy, the rupee appreciates.

As for gold prices, the simple logic is hardcore and big-ticket investors invest in many markets, including shares and gold. Obviously, when the share market sentiments improve, they shift some of their investments from gold to shares so as to be able to meet their payment commitments that would stare in their face two days later. Yes, there is a positive correlation between Sensex and the rupee and a negative correlation between the Sensex and gold.

Gold, oil and Sensex: Has the relationship gone awry?As oil corrected sharply, the relationship between oil, gold and equity began to

defy the usual pattern.S. Hamsini Amritha

After moving on predictable lines for several years, gold, oil and stocks have seen their three-way relationship go awry in the recent months.In the recently halted market rally, the Sensex shot up by 21 per cent (November 20, 2008 to January 6, 2009) even as global stock markets stabilised on the back of ‘stimulus’ packages and rate cuts. Normally, this would have been a cue for gold prices to cool off. Instead, gold prices actually rose by 13 per cent in this period.

Variant behavior:Crude oil, from November 20 actually plunged 11 per cent, taking the opposite direction to gold prices. These trends are at variance with the historic movements in gold prices. Traditionally, prices of gold have moved hand in hand with crude oil, as gold is considered an inflation hedge. Similarly, gold has usually risen when stocks have performed badly; as gold is viewed as a substitute for risky assets like stocks.

Gold prices have usually firmed up in the midst of severe stock market corrections. Take for example September 2001 (9/11), when markets worldwide experienced turmoil. While the Sensex tumbled by over 12 per cent for the month, gold posted a gain of over 6 per cent. Or take the case of May 17, 2004 when the Sensex registered its biggest ever single day fall of 11.4 per cent; prices of gold went up by 1.7 per cent from $373 to $380 an ounce that day.

Gold and Oil:Similarly, history suggests that gold enjoys a direct relationship with crude oil prices. Between January and July 2008, steadily climbing oil prices propelled gold higher. If a barrel of crude oil rose from $94 to a record $148 a barrel by July, gold too hit a new record.One explanation for they move in tandem during this period could be that price rises were fuelled by the same speculative forces. On March 17, 2008 when the Sensex fell by 6 per cent after shedding close to 950 points, gold touched its all-time high price of $1,024 an ounce, gaining close to 3 per cent.

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All this suggests that investors looking to switch between stocks and gold to capitalise on their relative returns may have to rework their equations quite a bit.

Sensex, Nifty dance to the tune of global forces — Correlation with emerging markets

Suresh Krishnamurthy

FOR those of you who lost money last week, it may be of some consolation to know that your experience was not unique. You could almost say that stock meltdowns, like inflation and corruption, are global in sweep.

Fund flows from institutional investors have ensured that markets move in a synchronised fashion. They make sure your woes are shared by that elsewhere. By the same token, you too are hostage to what happens outside.

For instance, in the period since April 30, markets in Taiwan and Korea have lost as much as the Indian markets. Political uncertainty has sparked a meltdown in prices even in these countries. The Sensex and the Nifty have been swaying not only to the proximate domestic causes but also to the pull of global forces, for some years now. The correlation has existed since 1996 and has increased in the period since 2001.

The relationship between Sensex and such indices can be measured by calculating the correlation between Morgan Stanley Capital International (MSCI) and Sensex. MSCI's index is the benchmark for emerging global market funds. In the period since end-1996, just more than 50 per cent of the monthly return generated by Sensex is explained by the changes in Morgan Stanley Capital International's Emerging Market Index. In the period since April 2001, the explanatory power of the emerging market index has risen to 66 per cent. The correlation of MSCI with BSE 200 is also high, as it is with the monthly returns of the net asset values of schemes such as Franklin India Bluechip, Templeton India Growth and HDFC Equity.

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On whether the correlation would rise in future, their opinions were, however, divided. Mr Bagga said the correlation would keep increasing since rising trade would integrate the Indian economy with the rest of the world. Mr Prasad, however, contented that if large domestic funds emerged to counterbalance the effect of FIIs, then correlation would decline.

ITC, RIL to decide fate of market rallyDeepak Singh Tanwar

August 21: The 100-points plus rally witnessed on Thursday failed to sustain. On Friday, except the pharmaceutical and software stocks, most of the specified stocks have lost a major part of gain recorded on Thursday. On Friday, the sensex lost 67 points and closed at 2922 points.

The termination of Thursday's rally has put the market in a fix. With Thursday's rally, the sensex had broken the short-term falling trendline. It was certainly a good sign. But Friday's move has somehow reduced this optimism. In fact, in monthly chart, the sensex has broken the 9-year upward trendline. This breach, without any doubt is negative for the health of the sensex.

From the present level, the sensex is certainly targeting the December 1996 level of 2713 points which is around 200 points away from the current level.

Although the chances of touching 2713 level are high, the movement in ITC stock would be crucial for the market. In fact, ITC is the only stock which can trigger a rally in the near future. Reliance also August 21: The 100-points plus rally witnessed on Thursday failed to sustain. On Friday, except the pharmaceutical and software stocks, most of the specified stocks have lost a major part of gain recorded on Thursday. On Friday, the sensex lost 67 points and closed at 2922 points.

The termination of Thursday's rally has put the market in a fix. With Thursday's rally, the sensex had broken the short-term falling trendline. It was certainly a good sign. But Friday's move has somehow reduced this optimism. In fact, in monthly chart, the sensex has broken the 9-year upward trendline. This breach, without any doubt is negative for the health of the sensex.

From the present level, the sensex is certainly targeting the December 1996 level of 2713 points which is around 200 points away from the current level.Although the chances of touching 2713 level are high, the movement in ITC stock would be crucial for the market. In fact, ITC is the only stock which can trigger a rally in the near future. Reliance alsoenjoys a strong support of a 9-year old upward trendline at the level of around Rs 102. Other heavy weightage stocks like Bajaj Auto and Bhel are also better placed.

While the position of the heaviest stock (contributing 20 per cent to the sensex), HLL appears extremely weak in weekly chart, the position of daily chart is marginally better. Overall, the short-term outlook of HLL is grim. The position of State Bank is equally weak and hints at further decline. As such, the move in ITC and Reliance would decide the fate of a rally in the coming week.

While the market is around 200-points away from a major support level, some specified stocks offer an excellent opportunity for the long term investors. Traders however can stick to wait and watch policy for the time being. For investors, Bhel, Godrej Soaps, Indo Gulf

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Fertilisers, Reliance, Siemens, Thermax, Exide Industries, Carrier Aircon and ABB offer a good investment opportunity. However, there are stocks which are expected to remain weak in the comingdays. Cadbury, which recorded smart gains in the past few weeks is due for a correction. Profit booking should be considered on this counter.

Similarly, Cochin Refineries has also turned weak. Unlike other refinery stocks, Cochin Refineries had outperformed the market in the past few weeks. However, with a sharp dip on Friday, the stock has given a fresh exit signal. An exit should be made at the current level as the stock is expected to fall further. The position of other stocks like Hindalco, Colgate, Grasim and ACC is equally weak.

Making sense of Sensex movesEven if the Sensex is down, your investments in a particular company’s shares

can actually be unaffected.Kumar Shankar Roy

Sensational headlines such as “Sensex in free fall”, “Bloodbath on D-Street” and “Market faces mayhem” would have surely stirred up a storm in your teacup as you read the morning newspaper in recent weeks. But should you worry that with the Sensex down in the dumps, your equity investments too will take a similar hit? Not always.

Sensex: Just an indicatorThe Sensex is an index that is composed of only 30 stocks. This means that the level of index at any point of time (say 14,152 points as on August 17) reflects the market value of its component stocks relative to a base period.

While there is no doubt that the Sensex stocks are the most liquid (most traded) and well-known ones, one should not forget that it is, at the end of the day, just a basket of 30 stocks. This means the so-called market barometer gives you a picture of only large stocks from about 12 sectors.

The market value of a company is determined by multiplying the number of equity shares that it has issued by their market price. This market value is further multiplied by the free-float factor to determine the free-float market value.

To use a live example, the market value of Tata Consultancy Services (TCS) is Rs 103,351 crore since it has 97.86 crore shares having a value of Rs 1,056 (on August 17). Taking into consideration only those shares that are available for trading in the market. In our example, TCS might have a total of 97.86 crore shares but in reality only 19.57 crore shares are available as the rest are treated as ‘controlling/strategic holdings’. This pegs the free-float factor of TCS at 0.20 (19.57/97.86) and free-float market value at Rs 20,670.20 crore.

So, if you add up the current free-float market values of all the 30 companies, you will get the numerator for the Sensex formula. The Sensex is calculated using a methodology that focuses upon the base period. Since this base period of Sensex is taken as 1978-79 and the base value as 100 index points — what the index divisor does is to adjust the original base period of the Sensex to its present level. This keeps the Sensex comparable over time.

Calculate Sensex on your own: Find out the free-float market capitalisation of all the 30 companies that make up the Sensex.

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Then, add all them. Make all this relative to the Sensex base. For example, for a free-float market capitalisation of Rs 9,00,000 crore, if the Sensex value is 14,500 — then, for a free-float market capitalisation of Rs 9,50,000 crore, the Sensex value will be 15,306. Just use ratios and proportions learnt in junior school!

What moves the Sensex?Imagine a large joint family living in a big house. This would consist of individuals who represent different generations. Now visualise what would have happened if all of them were to decide on the family budget. The calculation of the actions that make up the Sensex is no less tricky!

As the Sensex consists of 30 different companies, all of them have different share prices, free-float adjustment factors, free-float market value and weightage in the index. Just like the grandfather in a joint family, the company that enjoys most weightage in the Sensex is Reliance Industries (RIL). Out of the 100 per cent weight of the Sensex, RIL currently has a 13.18 per cent weight.

With the top five companies, in terms of weightage, occupying nearly 50 per cent index — any movements in these five in the same direction could move nearly half of the Sensex!The accompanying table shows how the index value at any point reflects the ups and downs of the 30 constituents. On August 20, the index gained 286.03 points as five stocks pulled it down while the rest pushed it up.

Importance of weightage: In the chart, HDFC Bank has an index weight of 3.17 per cent — which is less than half of L&T (6.36 per cent). This is why a comparatively higher Rs 56 increase in share price has effectively contributed to 22.7 index points for HDFC Bank. On the other hand, L&T, which is two times heavier, has pitched in with 19.1 points with just a relatively lower gain of Rs 49.

Why is Sensex unimportant?As an investor, you should be aware that though the Sensex is a widely tracked barometer of the markets, your portfolio might not behave like the Sensex at all. Important sectors such as textiles, BPO services, niche service-oriented companies and segments such as auto ancillaries and consumer durables are not at all represented in the Sensex.

So if you happen to have investments in the other sectors, broader indices such as BSE 200 or even BSE 500 could be better benchmarks, as can the BSE sectoral indices. Even the most skilled investors assume that when the Sensex tanks by 400 points in a day, the whole stock market reacts…and that all stocks are affected in the same way. Truth be told, the Sensex captures the movement of 30 stocks, against the 7,000 or so listed companies in India. If the Sensex is down, your investments in a particular company’s shares can actually be unaffected.

4. Research Gap:4.1. PositivesThe current market is an indication of a vast collection of uncountable global and domestic cues. The analyses explained above in the literature review contain a fairly thorough study of wide varieties of such factors.

4.2. Negatives

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Though the analyses extensively cover a wide variety of factors in order to explain the movement of Sensex, it lacks objectivity. The conclusions/inferences are subjective and have less use of analytical tools which does not give a clear picture about the dependency of the factors on movement of Sensex Indices.

4.3. Filling up the GAPSWe have made use of regression analysis in order to find out the dependency of three factors which are generally believed to be impacting the Sensex Indices. With this we have ensured that the objectivity of analysis is maintained. We have been able to explain the dependencies in terms of numeric figures which is shown in the later part of the report.

5. Objectives: Our objective is to find out how the BSE Sensex varies according to variation in its top

10 listed companies (according to market capitalization). To find out whether there is any similarity in the variation of SENSEX and the price of

GOLD. To find out, how the percentage change in SENSEX is dependent on that of NASDAQ

and Nikkei.

6. Hypothesis:We have made three assumptions here:

1. BSE Sensex varies according to NASDAQ & Nikkei.2. BSE Sensex varies according to top 10 listed companies.3. BSE Sensex varies inversely to the price of Gold.

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7. Methodology:

7.1. Regression analysis:In statistics, regression analysis includes any techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps us understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables — that is, the average value of the dependent variable when the independent variables are held fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function, which can be described by a probability distribution.

Regression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Regression analysis is also used to understand which among the independent variables are related to the dependent variable, and to explore the forms of these relationships. In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables.

Tools Used Microsoft Excel 2007

Assumption1. The populations follow normal distribution.2. The populations are independent.

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8. Data Analysis:

8.1. Regression Analysis of BSE and top 10 Companies:

The regression output has three components: 1. Regression statistics table2. ANOVA table3. Regression coefficients table.

Overall equation would be:

BSE = 0.117662433*RIL + 0.069490297*ONGC + 0.149307239*SBI + 0.05761936*TCS + 0.065782683*NTPC + 0.166616347*Infosys + 0.166305861*BHEL + 0.049933532*Bharti Airtel + 0.107791553*ITC + 0.102230324*L&T - 0.000135078

The above result shows that variation in BSE index is highly dependent upon variations of its 10 major shares.

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Interpret Regression Statistics Table

This is the following output. Of greatest interest is Adjusted R Square.

Explanation

Multiple R 0.938169167 square root of R2

R Square 0.880161386 R2

Adjusted RSquare 0.871082703 Adjusted R2 used if more than one x variable

Standard Error 0.003725963This is the sample estimate of the standard deviation of the error u

Observations 143 Number of observations used in the regression (n)

R Square: This is the most important number of the output. R Square tells how well the regression line approximates the real data. This number tells you how much of the output variable’s variance is explained by the input variables’ variance. Here R2 = 0.88.

Adjusted R Square: This is quoted most often when explaining the accuracy of the regression equation. Adjusted R Square is more conservative the R Square because it is always less than R Square. Another reason that Adjusted R Square is quoted more often is that when new input variables are added to the Regression analysis, Adjusted R Square increases only when the new input variable makes the Regression equation more accurate (improves the Regression equations’ ability to predict the output). R Square always goes up when a new variable is added, whether or not the new input variable improves the Regression equation’s accuracy. Adjusted R2 = 0.871 means that 87.1% of the variation of BSE around its mean is explained by the regressors (top 10 companies).

Standard Error: The standard error here refers to the estimated standard deviation of the error term u. It is sometimes called the standard error of the regression. It is not to be confused with the standard error of y itself or with the standard errors of the regression coefficients given below.

Interpret ANOVA Table ANOVA table for our case is given:

df SS MS F Significance F

Regression 10 0.013459114 0.001345911 96.94813643 8.5407E-56

Residual 132 0.001832529 1.38828E-05

Total 142 0.015291644

Significance of F: This indicates the probability that the Regression output could have been obtained by chance. A small Significance of F confirms the validity of the Regression output. For example, if Significance of F = 8.5407E-56, there is only 8.5407E-54 % chance that the Regression output was merely a chance occurrence. In this case it is almost zero.

Interpret Regression Coefficients Table

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The regression output of most interest is the following table of coefficients and associated output:

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 90.0% Upper 90.0%

Intercept -0.000135078 0.000317461 -0.425494878 0.671168857 -0.000763047 0.000492891 -0.000660945 0.000390789

RIL 0.117662433 0.020994147 5.604534972 1.16836E-07 0.076133935 0.159190931 0.082886063 0.152438803

ONGC 0.069490297 0.021038086 3.303071308 0.001230869 0.027874885 0.111105709 0.034641144 0.104339449

SBI 0.149307239 0.026566969 5.620032777 1.08687E-07 0.096755148 0.20185933 0.105299605 0.193314873

TCS 0.05761936 0.028625688 2.012855034 0.046163983 0.000994921 0.114243799 0.010201501 0.105037219

NTPC 0.065782683 0.034615542 1.90038001 0.059563972 -0.002690278 0.134255645 0.008442756 0.12312261

Infosys 0.166616347 0.034629308 4.811425852 4.03061E-06 0.098116154 0.23511654 0.109253616 0.223979078

BHEL 0.166305861 0.03038016 5.474160087 2.13689E-07 0.106210902 0.22640082 0.115981755 0.216629967

Bharti Airtel 0.049933532 0.014443289 3.457213396 0.000734897 0.021363279 0.078503785 0.026008523 0.073858541

ITC 0.107791553 0.024548975 4.390877963 2.29397E-05 0.059231255 0.156351851 0.067126685 0.148456421

L&T 0.102230324 0.025236674 4.050863604 8.65757E-05 0.052309689 0.152150959 0.060426297 0.144034351

Coefficients: In simple or multiple linear regression, the size of the coefficient for each independent variable gives you the size of the effect that variable is having on your dependent variable, and the sign on the coefficient (positive or negative) gives you the direction of the effect. In regression with a single independent variable, the coefficient tells you how much the dependent variable is expected to increase (if the coefficient is positive) or decrease (if the coefficient is negative) when that independent variable increases by one. In regression with multiple independent variables, the coefficient tells you how much the dependent variable is expected to increase when that independent variable increases by one, holding all the other independent variables constant. Remember to keep in mind the units which your variables are measured in.

Standard Error: The standard error is an estimate of the standard deviation of the coefficient, the amount it varies across cases. It can be thought of as a measure of the precision with which the regression coefficient is measured. If a coefficient is large compared to its standard error, then it is probably different from 0.

t Stat: The t statistic is the coefficient divided by its standard error.

P-value: The P-Values of each of these provide the likelihood that they are real results and did not occur by chance. The lower the P-Value, the higher the likelihood that that coefficient or Y-Intercept is valid. For example, a P-Value of 1.16836E-07 (in the case of RIL) for a regression coefficient indicates that there is only 0.00001168% chance that the result occurred only as a result of chance.

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8.2. Regression Analysis of BSE and NASDAQ & Nikkei:


BSE = 0.009958446*NASDAQ + 0.315843341*Nikkei + 0.000499004

The above result shows that variation in BSE index is not dependent upon the variation in NASDAQ & Nikkei indexes. Though, it’s the common perception that the BSE index varies according to the variation in the NASDAQ & Nikkei indexes, but our results shows that the perception is not true.

Interpret Regression Statistics Table This is the following output:

Explanation


R Square 0.204278065 R2

Adjusted RSquare 0.19184491 Adjusted R2 used if more than one x variable

Standard Error 0.009234468This is the sample estimate of the standard deviation of the error u


Adjusted R2 = 0.1918 means that 19.18% of the variation of BSE around its mean is explained by the regressors (NASDAQ & Nikkei). Which is very low.

Interpret ANOVA Table

ANOVA table for our case is given:

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Regression 2 0.002802168 0.001401084 16.43010658 4.45374E-07

Residual 128 0.010915252 8.52754E-05

Total 130 0.01371742

F = 4.45374E-07 means there is only 0.000045% chance that the Regression output was merely a chance occurrence. In this case it is almost zero.




Intercept 0.000499004 0.000810559 0.615629288 0.539232325 -0.001104825 0.002102832 -0.000843966 0.001841974

NASDAQ 0.009958446 0.071257129 0.139753674 0.889074281 -0.131035956 0.150952847 -0.108103588 0.128020479

Nikkei 0.315843341 0.068940107 4.581416432 1.08176E-05 0.179433562 0.45225312 0.201620253 0.430066429

P-Value of 0.889074281 (in the case of NASDAQ) for a regression coefficient indicates that there is only 88.9% chance that the result occurred only as a result of chance. However in the case of Nikkei it’s 0.0000108%.

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8.3. Regression Analysis of BSE and Gold:


BSE = -0.202475256*NASDAQ + 0.000229806

The above result shows that variation in BSE index is not dependent upon the variation in Gold. But the result is showing that there is some inverse relationship between the variation in BSE index and that in Gold price. It’s the common perception that the price of gold increases when the market is going down and our result confirms that, but our result explains only 2.06% of the variation.

Interpret Regression Statistics Table This is the following output:

Explanation


R Square 0.027507755 R2

Adjusted RSquare

0.020610647 Adjusted R2 used if more than one x variable

Standard Error 0.010269767 This is the sample estimate of the standard deviation of the error u


Adjusted R2 = 0.0206 means that 2.06% of the variation of BSE around its mean is explained by the regressors (Gold). Which is very low.

Interpret ANOVA Table

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ANOVA table for our case is given:


Regression 1 0.000420639 0.000420639 3.98830269 0.047741886

Residual 141 0.014871005 0.000105468

Total 142 0.015291644

F = 0.047741886 means there is only 4.77% chance that the Regression output was merely a chance occurrence.




Intercept 0.000229806 0.000859227 0.267457273 0.789507929 -0.001468826 0.001928439 -0.001192843 0.001652456

Gold -0.202475256 0.10138598 -1.997073531 0.047741886 -0.402908389 -0.002042124 -0.370343296 -0.034607216

P-Value of 0.047741886 (in the case of Gold) for a regression coefficient indicates that there is only 4.77% chance that the result occurred only as a result of chance.

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9. Policy Implications: N/A

10. Conclusion:From the Regression Analysis we have got the result that variation in BSE Sensex doesn’t depend much on NASDAQ & Nikkei or Gold, but its variation is highly dependent upon the variation of its top 10 listed companies.

11. Recommendation:As we have seen from the result that the variation in BSE Sensex is more dependent on the top 10 companies. However the common perception is that it varies according to the variation in NASDAQ and Nikkei. So based on our project report we would suggest the common trader to trade into the share market by seeing the result of top 10 companies like RIL, ONGC, TCS, Infosys rather than watching the Index of NASDAQ and Nikkei.

12. Bibliography:References

http://www.bseindia.com/http://www.nasdaq.com/http://e.nikkei.com/e/fr/marketlive.aspxhttp://in.finance.yahoo.comhttp://www.mcxindia.comhttp://www.wikipedia.org/

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http://www.wikipedia.org/

http://www.mcxindia.com/

http://in.finance.yahoo.com/

http://e.nikkei.com/e/fr/marketlive.aspx

http://www.nasdaq.com/

http://www.bseindia.com/

business statistics project 2010

Documents

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nasdaq stock market

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