whether hedge funds added more sensitivity to sensex? (using granger causality test)

8/9/2019 Whether Hedge Funds added more Sensitivity to Sensex? (Using Granger Causality test)

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MANAGEMENT THESIS-II

WHETHER HEDGE FUNDS ADDED

MORE SENSITIVITY TO SENSEX

MANAGEMENT THESIS II


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Whether Hedge Funds added more sensitivity to BSE-Sensex?

SUBMITTED

BY


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A.SRIDHAR NAG

ENROLLMENT NO. 8NBHM039

SUBMITTED TO:

Prof.Dr.SHAIK MOULALI, FACULTY GUIDE (MT-II)

INC ADAM SMITH HYDERABAD

A REPORT SUBMITTED IN PARTIAL FULFILMENT

OF THE REQUIREMENT OF

MASTERS DEGREE IN BUSINESS ADMINISTRATION

HYDERABAD

ACKNOWLEDGEMENT

I am extremely grateful to my Management Thesis-II,

Dr.SHAIK MOULALI Faculty guide, whose experienced guidance has

supported my honest efforts at all stages of my report.

I would like to express my heart-full gratitude to all those people

who had enabled the successful completion of my Final thesis of my

Management Thesis-II whose constant guidance and encouragement

crowned all my efforts with success.


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CONTENTS

TITLE PAGE

.

ACKNOWLEDGEMENT

..

ABSTRACT

..

CHAPTER I

INTRODUCTION

CHAPTER II

REVIEW OF LITERATURE


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CHAPTER III

RESEARCH METHODOLOGY

CHAPTER IV

RESULTS AND ANALYSIS

CHAPTER V

DISCUSSION OF IMPLICATION

CHAPTER VI

CONCLUSIONS & RECOMMENDATION

REFERENCES

ABSTRACT

This paper examines the relationship between stock prices and

Hedge Funds i.e. Equity Hedge Funds for past ten years using

monthly time series data. The study uses Granger causality test


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procedure developed by Granger, C.W.J. Hedge Funds are one

of the aim instruments on which market can bet on, not only to

reduce volatility and risk but also to preserve capital anddeliver positive returns under all market conditions

The causal relationship tested between the BSE index and

Hedge Funds. Hedge Funds is included in the model as an

additional variable, to examine whether Hedge Funds

added more Sensitivity to Sensex..

With the ADF UNIT ROOT TEST and JOHANSENS

COINTEGRATION TEST it is found that the trend lines are

deterministic and on applying GRANGERS CAUSALITY

TEST We found that Hedge Funds have causal relation with the

Sensex returns and vice versa

INTRODUCTION


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A hedge fund is a fund that can take both long and short positions, use

arbitrage, buy and sell undervalued securities, trade options or bonds, and

invest in almost any opportunity in any market where it foresees

impressive gains at reduced risk. Hedge fund strategies vary enormously --

many hedge against downturns in the markets -- especially important today

with volatility and anticipation of corrections in overheated stock

markets. The primary aim of most hedge funds is to reduce volatility and

risk while attempting to preserve capital and deliver positive returns under

all market conditions.

There are approximately 14 distinct investment strategies used by

hedge funds, each offering different degrees of risk and return. A macrohedge fund, for example, invests in stock and bond markets and other

investment opportunities, such as currencies, in hopes of profiting on

significant shifts in such things as global interest rates and countries

economic policies. A macro hedge fund is more volatile but potentially

faster growing than a distressed-securities hedge fund that buys the equity

or debt of companies about to enter or exit financial distress. An equity

hedge fund may be global or country specific, hedging against downturns

in equity markets by shorting overvalued stocks or stock indexes. A

relative value hedge fund takes advantage of price or spread

inefficiencies. Knowing and understanding the characteristics of the many

different hedge fund strategies is essential to capitalizing on their variety

of investment opportunities.

It is important to understand the differences between the various hedge

fund strategies because all hedge funds are not the same -- investment

returns, volatility, and risk vary enormously among the different hedge

fund strategies. Some strategies which are not correlated to equity markets

are able to deliver consistent returns with extremely low risk of loss, while

others may be as or more volatile than mutual funds. A successful fund of

funds recognizes these differences and blends various strategies and asset


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classes together to create more stable long-term investment returns than

any of the individual funds.

Hedge fund strategies vary enormously many, but not all, hedge

against market downturns especially important today with

volatility and anticipation of corrections in overheated stock

markets.

The primary aim of most hedge funds is to reduce volatility and

risk while attempting to preserve capital and deliver positive

(absolute) returns under all market conditions.

The popular misconception is that all hedge funds are volatile --

that they all use global macro strategies and place large directionalbets on stocks, currencies, bonds, commodities or Hedge Funds,

while using lots of leverage. In reality, less than 5% of hedge funds

are global macro funds. Most hedge funds use derivatives only for

hedging or dont use derivatives at all, and many use no leverage.

BSE SENSEX

The BSE SENSEX, short form of Sensitive Index, first compiled in 1986is a market Capitalization-Weighted index of 30 component stocks

representing a sample of large, well-established and financially sound

companies. The index is widely reported in both, the domestic

international, print electronic media and is widely used to measure the used

to measure the performance of the Indian stock markets.

The BSE SENSEX is the benchmark index of the Indian capital market

and one, which has the longest social memory. In fact the SENSEX is

considered to be the pulse of the Indian stock markets. It is the oldest index

in India and has acquired a unique place in collective consciousness of the

investors. Further, as the oldest index of the Indian Stock Market, it

provides time series data over a fairly long period of time. Small wonder


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that the SENSEX has over the years has become one of the most

prominent brands of the Country.

OBJECTIVES OF THE STUDY

To study if there is any dynamic relationship between sensitivity of

Sensex and Hedge Funds

To analyze the Causal relation of the Hedge funds with Sensex

returns

Literature review


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REVIEW OF LITERATURE

A significant amount of literature now exists that examines the relationship

between

Stock market returns and a range of macro economic and financial

variables over a

Number of different stock markets and time periods. Now a days financial

economics

Provide a number of models that helps to examine the relationship. Thereturn on stocks

is highly sensitive to both fundamentals and expectations. The latter in turn

is influenced

by the fundamentals which may be based on either rational or adaptive

expectation

models, as well as by many subjective factors which are unpredictable and

also non

quantifiable.


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Exchange rate and stock market: evidence from India and Japan,

Journal of International Finance and Economics, published in

September 2007.

This paper empirically studies the issues of possible Granger causality and

interactive feedback relationships between exchange rate changes and

stock market returns of India and Japan. Daily data from January 1998

through December 2005 are employed. The time series data are found

stationary in levels by ADF (augmented Dickey-Fuller) test for unit root.

No discernible evidence of Granger causality is observed between the

above variables for Japan. However, such relationship is discovered in the

case of India, although not quite substantial. Evidence of very short-runinteractive feedback relationships exists in both countries. Japanese stock

and foreign exchange markets depict no intra-market risk-transmissions. In

the case of India, stock market seems to transmit relatively more risk to

foreign exchange market than the vice versa.
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Martin Weber, The comovement of credit default swap, bond and

stock markets: an empirical analysis, published in January,2004

This paper analyzes the empirical relationship between credit

default swap, bond and stock markets during the period 2000-

2002. Focusing on the intertemporal comovement, we examine

weekly and daily lead-lag relationships in a vector autoregressive

model and the adjustment between markets caused by

cointegration. First, we find that stock returns lead CDS and

bond spread changes. Second, CDS spread changes Granger

cause bond spread changes for a higher number of firms than

vice versa. Third, the CDS market is significantly more sensitive

to the stock market than the bond market and the magnitude of

this sensitivity increases when credit quality becomes worse.

Finally, the CDS market plays a more important role for price

discovery than the corporate bond market

Mishra, Alok Kumar, Stock Market and Foreign Exchange Market in

India: Are they Related? South Asian Journal of Management,

published in April,2004.

This paper attempts to examine whether stock market and foreign

exchange market are related to each other or not. The study uses Granger's

Causality test and Vector Auto Regression technique on monthly stock

return, exchange rate, interest rate and demand for money for the period

April 1992 to March 2003. The major findings of the study are (a) there

exists a unidirectional causality between Exchange rate and interest rate

and between exchange rate return and demand for money; (b) there is no

Granger's causality between exchange rate return and stock return.

Through Vector Auto Regression


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Abdulnasser Hatemi-J a; Eduardo Roca, Exchange rates and stockprices interaction during good and bad times: evidence from theASEAN4 countries, Applied Economics, published in 2005

Using bootstrap causality tests with leveraged adjustments, the link

between exchange rates and stock prices in Malaysia, Indonesia,

Philippines and Thailand is investigated for the periods immediately before

and during the 1997 Asian crisis. Two variables are found to be

significantly linked in the non-crisis period but not at all during the crisis

period. The implications of this result in terms of hedging, market

efficiency, market integration and policy intervention are explained in the

paper.

Martin Bruand and Rajna Gibson-Asner, The effects of newly listed

derivatives in a thin stock market, Review of Derivatives

Research, published in April, 2005

This study examines the informational feedback effects associated to the

listing and trading of derivatives in Switzerland. The observed changes in

the price and higher moments of stock returns are representative of a thin

stock market. The listing of stock options and index futures generated

positive abnormal returns for large stocks and for the index while small

stocks essentially benefited from the launching of index options. While

reducing the variance of blue chips and of the index, their variance's

stochasticity increased (decreased) at index options' (futures) listings.

Finally, we detect significant stock and index derivatives' price leads

which do not however generate arbitrage opportunities.

J. Aaltonen and R. stermar, rolling test of granger causalitybetween the Finnish and Japanese security markets,Published byElsevier Science Ltd. In June 1998

In the paper we test the impact of the Japanese stock market on two

financial asset groups, free and restricted shares, on the Finnish market in

the early 90s. The causality is tested in the Granger sense. The research
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issue is particularly interesting, since the restrictions on foreign ownership

were abolished by the end of 1992. The linkage between the Japanese and

Finnish financial economies is seen to be stronger for free shares than for

restricted. In particular, significant Granger causality between Japanese

and Finnish free shares is observed at relatively long consecutive time

intervals, whereas the Japanese impact on the restricted shares is only

occasional. Thus, the decision to abolish the restrictions not only leads to

increased international dependence in the future, but will also change the

risk profile of the restricted shares.

The relationship between exchange rate and stock prices during the

quantitative easing policy in Japan, published in 2001

Japan experienced unprecedented recession and deflation for more than

10 years. The Bank of Japan enforced quantitative monetary easing at a

level never seen before. One purpose is to influence stock prices for

economic recovery. Recently, the Japanese economy has been in

recovery, and stock prices have increased. However, there is much dispute

over whetherquantitative easing has been effective. This paper

investigates the relationship between macroeconomic variables and stock

prices. Exchange rate is the main target variable and finds that interest

rates have not impacted Japanese stock prices but exchange rates and U.S.

stock prices have. Furthermore, the Bank of Japan's policy for

overcoming recession and deflation has been effective.

R. Smyth a; M. Nandha, Bivariate causality between exchange rates

and stock prices in South Asia, Applied Economic Letters,

published in September,2003

This article examines the relationship between exchange rates and stock

prices in Bangladesh, India, Pakistan and Sri Lanka using daily data over a
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six-year period from 1995 to 2001. Both the Engle-Granger two-step and

Johansen cointegration methods suggest that there is no long-run

equilibrium relationship between these two financial variables in any of the

four countries. Granger causality tests find that there is uni-directional

causality running from exchange rates to stock prices in India and Sri

Lanka, but in Bangladesh and Pakistan exchange rates and stock prices are

independent.

Feride Ozturk, Sezgin Acikalin, Is Hedge Funds a Hedge Against

Turkish Lira?South East European Journal of Economics and

Business, published in April,2008

This paper investigates whether Hedge Funds is an internal hedge and/or

an external hedge against Turkish lira (TL) by using monthly data from

January 1995 to November 2006. Cointegration test results confirm the

long-term relationships between the Hedge Funds price and consumer

price index and between the Hedge Funds price and TL/US dollar

exchange rate. The Granger Tests, based on vector error correction model

(VECM), indicate that Hedge Funds price Granger causes the consumer

price index and TL/US dollar exchange rate in a unidirectional way. It is

concluded that Hedge Funds acts as an effective hedge against potential

future TL depreciation and rising domestic inflation. Furthermore, Hedge

Funds price may be considered as a good indicator of inflation and hence it

can be used as a guide to monetary policy

Azman-Saini, W.N.W, Hedge funds, exchange rates and causality:

Evidence from Thailand and Malaysia, Journal of Econometrics,

published in 1995

This article contributes to the debate on hedge funds and exchange rates in

Thailand and Malaysia. It examines causal relations using a new Granger

non-causality procedure proposed by Toda and Yamamoto (Journal of

Econometrics, 66, 225-50, 1995). Monthly observations are utilized over a
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sample period from January, 1994 to April, 2002. The results show that the

funds lead Thai baht for the crisis period. The results also reveal that the

funds lead Malaysian ringgit for the pre-crisis period

Kausik Chaudhuri, Cointegration, error correction and Granger

causality: an application with Latin American stock markets,

Applied Economics Letters, published in August, 1997.

This paper offers an empirical investigation of the presence of a long run

relationship in stock prices in six Latin Emerging Markets. We find

evidence of a long run relationship among all of these countries in a

bivariate framework. Results indicate the presence of bidirectional rather

than unidirectional causality suggesting the absence of weak exogeneity

among their stock prices.

Ralf Ostermark, Multivariate Granger causality in international asset

pricing: evidence from the Finnish and Japanese financial economies,

Applied Financial Economics, published in 1998

The present study combines the test of causality in multiple time series

with a rolling framework. The algorithm generates the time pattern of

causality of the underlying vector process. The algorithm is applied totesting whether the Japanese stock market Granger causes the Finnish

derivatives market. The Japanese stock market is seen to Granger cause the

Finnish derivatives market at distinct time intervals within the sample

period, possibly during periods of regime switches, trend changes or major

global disturbances.

Adnan Kasman, and Saadet Kasman, the impact of futures trading on

volatility of the underlying asset in the Turkish stock market,

published in 2007

This paper examines the impact of the introduction of stock index futures

on the volatility of the Istanbul Stock Exchange (ISE), using asymmetric

GARCH model, for the period July 2002October 2007. The results from


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EGARCH model indicate that the introduction of futures trading reduced

the conditional volatility of ISE-30 index. Results further indicate that

there is a long-run relationship between spot and future prices. The results

also suggest that the direction of both long- and short-run causality is from

spot prices to future prices. These findings are consistent with those

theories stating that futures markets enhance the efficiency of the

corresponding spot markets.

Heather Tarbert,Is commercial property a hedge against inflation?: A

cointegration approach,Journal of Property Finance, Published in

1996

Historically, investment in commercial property has been perceived as

providing a hedge against inflation. A complete hedge against inflation is

formally defined as an asset where the nominal returns vary in a positive

one-for-one way with inflation. The belief that commercial property is an

inflation hedge has persisted, notwithstanding the fact that many empirical

tests have proven inconclusive. Use of the traditional methodology in this

paper also produces poor results, although the hypothesis that commercial

property is a hedge cannot be rejected. Explores the reasons for these poor

results, and introduces a method of testing for a long-run hedging

relationship, based on cointegration. Cointegration techniques reject the

hypothesis that commercial property is a consistent long-run hedge against

inflation.


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Haus am Park, Rathausplatz 8-10, 61348 Bad Homburg, Germany,

The tactical and strategic value of hedge fund strategies:

a cointegration approach,Financial Markets and Portfolio

Management, published in August, 2007 .This paper analyzes

long-term comovements between hedge fund strategies and

traditional asset classes using multivariate cointegration

methodology. Since cointegrated assets are tied together over the

long run, a portfolio consisting of these assets will have lower

long-term volatility. Thus, if the presence of cointegration lowers

uncertainty, risk-averse investors should prefer assets that are

cointegrated. Long-term (passive) investors can benefit from the

knowledge of cointegrating relationships, while the built-in error

correction mechanism allows active asset managers to anticipate

short-run price movements. The empirical results indicate there

is a long-run relationship between specific hedge fund strategies

and traditional financial assets. Thus, the benefits of different

hedge fund strategies are much less than suggested by

correlation analysis and portfolio optimization. However, certain

strategies combined with specific stock market segments offerportfolio managers adequate diversification potential, especially

in the framework of tactical asset allocation.

Jan G. De Gooijer, Selliah Sivarajasingham, Parametric and

nonparametric Granger causality testing: Linkages between

international stock markets,bDepartment of Economics, University of

Peradeniya, Peradeniya, Sri Lanka, published in November,2007. This

study investigates long-term linear and nonlinear causal linkages amongeleven stock markets, six industrialized markets and five emerging markets

of South-East Asia. We cover the period 19872006, taking into account

the on-set of the Asian financial crisis of 1997. We first apply a test for the

presence of general nonlinearity in vector time series. Substantial
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differences exist between the pre- and post-crisis period in terms of the

total number of significant nonlinear relationships. We then examine both

periods, using a new nonparametric test for Granger noncausality and the

conventional parametric Granger noncausality test. One major finding is

that the Asian stock markets have become more internationally integrated

after the Asian financial crisis. An exception is the Sri Lankan market with

almost no significant long-term linear and nonlinear causal linkages with

other markets. To ensure that any causality is strictly nonlinear in nature,

we also examine the nonlinear causal relationships of VAR filtered

residuals and VAR filtered squared residuals for the post-crisis sample. We

find quite a few remaining significant bi- and uni-directional causal

nonlinear relationships in these series. Finally, after filtering the VAR-

residuals with GARCH-BEKK models, we show that the nonparametric

test statistics are substantially smaller in both magnitude and statistical

significance than those before filtering. This indicates that nonlinear

causality can, to a large extent, be explained by simple volatility effects

David Stewart, Swapan Sen, John Malindretos, Krishna M.

Kasibhatla,, Are daily price indices in Major European markets

Cointegrated?Tests and Evidence. American Economist, 2006

This study investigates short-run and long-run linkages among major West

European equity markets in London (FTSE100), Frankfurt (DAX30), and

Paris (CAC40). Long-run market co-movements of the three price indices

are detected employing cointegration and vector error correction

methodology. Empirical results of this study support the presence of one

cointegrating vector and two common trends. CAC index is found to be

weakly exogenous. The short run dynamics indicate short-run causal links

running both ways between FTSE and DAX.ABSTRACT FROM

AUTHORCopyright of American Economist is the property of American

Economist and its content may not be copied or emailed to multiple sites

or posted to a listserv without the copyright holder's express written


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permission. However, users may print, download, or email articles for

individual use. This abstract may be abridged. No warranty is given about

the accuracy of the copy. Users should refer to the original published

version of the material for the full abstract.

Kapil gupta, Balwinder singh,An Examination of Price Discovery and

Hedging Efficiency of Indian Equity Futures Market,10th Indian

Institute of Capital Markets Conference Paper ,published in

February,2007

Present study investigates the price discovery and hedging efficiency of

NIFTY and all those stock futures whose trading started on 9th November

2001 and are continuously traded till 30th June 2006. The study observes

information asymmetry in both futures and cash market and significant

Jarque-Bera test rejects the hypothesis that returns in both markets follow

normal distribution. Both futures and cash market returns are found to be

integrated of order 1, which implies that strong long-run relationship exists

between two markets and these results are strongly supported by

predictable and stationary basis. Presence of information asymmetry and

cointegration implies that both markets are inefficient in weak form.

Moreover, Granger causality and Vector Autoregression (VAR) results

provides significant evidence that futures market leads cash market, which

implies that futures market is an efficient price discovery vehicle. On the

basis of price discovery efficiency of the futures market, hedge ratio

through EGARCH (1,1) and VAR (based on Error correction

Methodology) have been estimated, which suggests that efficient price

discovery of futures market provides good opportunities for the traders to

hedge their market risk because hedging through futures (except for

RELIANCE) help the traders to reduce portfolio variance by

approximately 90% and even more in some cases.
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Paul Sarmas, CORRELATION AMONG STOCK MARKETSUNDER DIFFERENT EXCHANGE RATE SYSTEMS, Researchin Finance, published in 2004

This study investigates the linkage between the Hong Kong stock market

and Singapore stock market and the U.S. stock market during the pre- and

post-East Asia Financial Crisis in 1997 and 1998. It uses multivariate

regression models to study the impact of Hong Kongs fixed exchange rate

system and Singapores free-floating exchange rate system on their

respective stock markets. The results indicate that the exchange rate is not

a significant determinant of linkage between the U.S. and the two Asian

stock markets, but the evidence suggests that stronger post-crisis

relationships between the U.S. and the two Asian stock markets. The

evidence also supports a stronger short-run relationship between the U.S.

and Hong Kong stock markets relative to that between the U.S. and

Singapore stock markets.

Wing-Keung Wong,Aman Agarwal, Financial Integration for India

Stock Market, a Fractional Cointegration Approach, published in

2005

The Indian stock market is one of the earliest in Asia being in operation

since 1875, but remained largely outside the global integration process

until the late 1980s. A number of developing countries in concert with the

International Finance Corporation and the World Bank took steps in the

1980s to establish and revitalize their stock markets as an effective way of

mobilizing and allocation of finance. In line with the global trend, reform

of the Indian stock market began with the establishment of Securities and

Exchange Board of India in 1988. This paper empirically investigates the

long-run equilibrium relationship and short-run dynamic linkage between

the Indian stock market and the stock markets in major developed

countries (United States, United Kingdom and Japan) after 1990 by

examining the Granger causality relationship and the pairwise, multiple
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and fractional cointegrations between the Indian stock market and the

stock markets from these three developed markets. We conclude that

Indian stock market is integrated with mature markets and sensitive to the

dynamics in these markets in a long run. In a short run, both US and Japan

Granger causes the Indian stock market but not vice versa. In addition, we

find that the Indian stock index and the mature stock indices form

fractionally cointegrated relationship in the long run with a common

fractional, nonstationary component and find that the Johansen method is

the best reveal their cointegration relationship

Khan Masood Ahmad, Is the Indian Stock Market Integrated with the

US and Japanese Markets? South Asia Economic Journal, publishedin 2004

The paper attempts to understand the interlinkages and causal relationship

between the Nasdaq composite indexin the US, the Nikkei in Japan with

that of NSE Nifty and BSE Sensex in India during the period January 1999

to August 2004, using daily closing data.The Johansen co-integration test

is applied to measure the long-termrelationship between the two indices

and theGranger-causality test is used to check theshort-term causal

relationship.

The analysis reveals that there is no long-term relationshipof the Indian

equity market with that of theUS and Japanese equity markets. Further,

Nasdaq and Nikkei have stronger causal relationship in 19992001which

becomes either very weak or disappearsin 20022004. There seems to be a

disassociation in themovements of the Nasdaq and Nikkei with thatof the

Sensex and Nifty. When the stock marketshave no tendency to move

together in the long-term and causaleffects become weak in the short-term

then themarkets are segmented and provide ample room for diversification

of investments. The recent surge of FIIinvestments to the Indian equity

market is primarilya reflection of this trend.


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Foresti, Pasquale, Testing for Granger causality between stock prices

and economic growth, published in 2006

This paper has focused on the relationship between stock market prices

and growth. A Granger-causality analysis has been carried out in order to

assess whether there is any potential predictability power of one indicator

for the other. The conclusion that can be drawn is that stock market prices

can be used in order to predict growth, but the opposite it is not true.

C.Alexander,Optimal hedging using cointegration

Cointegration is a time-series modelling methodology that has many

applications to financial markets. When spreads are mean

reverting, prices are cointegrated. Then a multivariate model will

provide further insight into the price equilibria and returns

causalities within the system. Spotfutures arbitrage, yieldcurve

modelling, index tracking and spread trading are some of the

applications of cointegration that are reviewed in this paper. With

the demand for new quantitative approaches to active investment

management strategies there is considerable interest in

cointegration theory. This paper presents a model of cointegrated

international equity portfolios which is currently used for hedging

within the European, Asian and Far East countries.

Piccillo, Giulia, Foreign Exchange and Stock Market: Two Related

Markets? (September 00, 2008). Available at SSRN:

http://ssrn.com/abstract=1360621


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This paper studies the relationship between the stock market and the

exchange rate in several countries. The approach taken in the first part of

this study is a linear VAR, to be compared in the following part to a

MSVAR. The data is also analyzed by Granger causality tests in both

contexts and a thorough description of the empirical results obtained is

shown. The research uncovers a spread (but not constant over time)

causality from the exchange rate and American stock market to the local

markets of the different nations studied. The non-linear, time varying

approach allows several considerations on the dynamics of the

relationship. The markets analyzed are the Japanese, the British and the

German (pre-Euro) market against the US Dollar and the US stock market.

The frequency of the data used is daily

RESEARCH METHODOLOGY

Research Design

Research Design is the plan structure and strategy of investigation

conceived so as to obtain answers to research problems. It is the

specification of the methods and procedures for acquiring the information

needed.

The research will be based on secondary data analysis. The study will

be exploratory as it aims at examining the secondary data for analyzing the

previous researches that have been done in the area of technical analysis of

stocks. The knowledge thus gained from this preliminary study forms the

basis for the further detailed Descriptive research.

Data collection process

Data needed for this study has been collected from various sources which

can be classified as Primary and Secondary data


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Primary data

Primary data is the data collected by the researcher at first hand for a

specific study. For the purpose of this study the primary data has been

collected through interaction with the staff of Tradewell Securities Ltd andalso from interactive management forums (like Management paradise,

Cool Avenue, Traderji etc)

Secondary Data

Published data and the data collected in the past or otherparties is

called secondary data. For the purpose of this study, the secondary data has

been collected from various sources such as Internet, magazines, Journals

etc. which are disclosed in the later part i.e. in references

Scope of the Study

The Scope of this study is limited to BSE Sensex, thus the conclusions

derived from this study may not be applicable to other exchanges in India

or other Global exchanges

Limitations of the Study

Scope of the Study is limited to Equity Hedge Funds of India thus

the conclusions derived from this study may not be applicable to

other exchanges in India or other Global exchanges

This study considers only Equity Hedge Funds (Other Hedge Funds

like Commodity, Real estate etc)

Sample Size

Past ten years monthly time series data of Hedge funds and Sensex

Analytical Procedures

For the purpose of the study, various tools will be considered. Some of

them are as follows
http://www.businessdictionary.com/definition/party.htmlhttp://www.businessdictionary.com/definition/party.html


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Unit Root Test and Co integration:

Empirical studies (for example, Engle and Granger, 1987) have shown that

many time

series variables are non-stationary or not integrated of order zero. The time

series

variables considered in this paper are the stock prices and fii flows. In

order to avoid a

spurious regression situation the variables in a regression model must be

stationary or

cointegrated. Therefore, in the first step, we perform unit root tests to

investigate whether

they are stationary or not. The Augmented Dickey-Fuller (ADF) unit root

test is used for

for this purpose

ADF UNIT ROOTS TEST

The tests are based on the

null hypothesis (H0): Yt is not I (0). If the calculated ADF statistics are

less than their

critical values from Fuller.s table then the null hypothesis (H0) is rejectedand the

series are stationary or not integrated of order zero

Co integration

In the second step we estimate cointegration regression using variables

having the same order of integration

Granger Causality Test

Granger causality is a technique for determining whether one time series

is useful in

forecasting another. Ordinarily, regressions reflect "mere" correlations.

A time seriesXis said to Granger-cause Yif it can be shown, usually

through a series of


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F-tests on lagged values ofX(and with lagged values ofYalso known),

that thoseX

values provide statistically significant information on future values ofY.

The test works by first doing a regression of Y on lagged values of Y.

Once the

appropriate lag interval for Y is proved significant (t-stat or p-value),

subsequent

regressions for lagged levels of X are performed and added to the

regression provided

that they 1) are significant in of themselves and 2) add explanatory power

to the model.

This can be repeated for multiple Xs (with each X being tested

independently of other Xs, but in conjunction with the proven lag level

of Y). More than 1 lag level of a variable can be included in the final

regression model, provided it is statistically significant and provides

explanatory power


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RESULTS AND ANALYSIS

EMPIRICAL RESULTS:

AUGMENTED DICKEY FULLER TEST:

THE FOLLOWING TESTS ARE CONDUCTED TO TEST THE

STATIONARITY OF THE RETURNS OF THE SENSEX.

The augmented dickey fuller test for the time series values of Sensex

returns. To check that values are stationary we conduct the unit root test

and thus the result indicates the following information

ADF Test Statistic -9.899615

Null Hypothesis: tseries has a unit rootExogenous: Constant

Lag Length: 0 (Automatic Based on AIC, MAXLAG=10)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -9.899615 0.000000Test criticalvalues: 1% level -3.486121

5% level -2.885858

10% level -2.579823

*MacKinnon (1996) one-sided p-values.

Augmented Dickey-Fuller Test Equation


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Dependent Variable: D(tseries)

Method: Least Squares

Date: 2/27/2010 Time: 9:26:33 AM

Included observations: 119 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob

tseries(-1) -0.912694 0.092195 -9.899615 0.000000

C 94.27563278.88344

9 1.195126 0.234455

R-squared 0.455820Mean dependentvar 2.849748

Adjusted R-squared 0.183730 S.D. dependent var 1153.567623

S.E. of regression 854.599100

Akaike info

criterion 16.355806

Sum squared resid85449735.78455

0 Schwarz criterion 16.402514

Log likelihood -971.170451 F-statistic 98.002377Durbin-Watsonstat 2.019055 Prob(F-statistic) 0.000000

Here the null hypothesis is rejected since the t-statistics value is -9.899615,

which is less than the critical values at 5% and 1% significance level.

Thus we can conclude that, the values are stationary and the trend is

deterministic

TEST FOR THE STATIONARITY OF THE HEDGE FUNDS

THE FOLLOWING TESTS ARE CONDUCTED TO TEST

THE

STATIONARITY OF THE HEDGE FUND RETURNS

The augmented dickey fuller test for the time series values of Hedge Fund

returns. To check the values are stationary we conduct the unit root test

and thus the result indicates the following information

ADF Test Statistic -3.831425


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Null Hypothesis: tseries has a unit root

Exogenous: Constant

Lag Length: 3 (Automatic Based on AIC, MAXLAG=10)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -3.831425 0.003476Test criticalvalues: 1% level -3.487607

5% level -2.886503

10% level -2.580168

*MacKinnon (1996) one-sided p-values.

Augmented Dickey-Fuller Test Equation

Dependent Variable: D(tseries)

Method: Least Squares

Date: 2/27/2010 Time: 9:19:51 AM

Included observations: 116 after adjusting endpoints

Variable CoefficientStd.

Error t-Statistic Prob

tseries(-1) -0.5496590.14346

1 -3.831425 0.000212

D(tseries(-1)) -0.2571250.13259

6 -1.939160 0.055020

D(tseries(-2)) -0.1271430.11848

0 -1.073113 0.285548

D(tseries(-3)) -0.1799650.09254

7 -1.944576 0.054356

C 0.7553490.87412

1 0.864124 0.389383

R-squared 0.424102Mean dependentvar 0.095259

Adjusted R-squared -0.036617 S.D. dependent var 12.029031

S.E. of regression 9.291608Akaike infocriterion 7.338247

Sum squared resid9583.07171

9 Schwarz criterion 7.456936


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Log likelihood -420.618339 F-statistic 20.435610Durbin-Watsonstat 2.019349 Prob(F-statistic) 0.000000

Here the null hypothesis is rejected since the t-statistics value is --3.831425,

which is less

than the critical values at 5% and 1% significance level.

Thus we can conclude that, the values are stationary and the trend is

deterministic

JOHANSEN COINTEGRATION TEST

The cointegration test, suggests the likelihood of the existence of the other

model due to the initial model.Thus calculating the likelihood ratio will

show the probability of the regression of otherequation with initial

equation.

Date: 27/02/10 Time: 13:54

Included observations: 116

Test assumption:

Linear deterministic trend in the data

Series: HEDGE SENSEX

Lags interval: No lags

EigenvalueLkelyhoodRatio (LR)

5 PercentCriticalValue

1 PercentCriticalValue

HypothesizedNo. of CE(s)

0

.53 87.54 15.41 20.04 None **0

.412 30.89 3.766.65

At most 1 **

*(**) denotes rejection of the hypothesis at 5%(1%) significanceLevel L.R. test

indicates 2cointegratingequation(s) at 5%significance level


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Here, the likelihood ratio is 87.54 which is greater than critical values at 5

%

significance value. Hence by looking at the table we can say that

rejection of the

hypothesis at 5%(1%) significance level

GRANGER CAUSALITY TEST

Pairwise Granger Causality Tests

Date: 27/02/10 Time: 17:57Sample:116

Lags: 1

Null Hypothesis: Obs F-Statistic Probability

SENSEX does not Granger Cause Hhedge Funds 116 2.10852 0.35191

Hedge Funds does not Granger Cause SENSEX 1.96900 0.21037

HYPOTHESIS:

We took the null hypothesis, that Sensex Granger cause Hedge Funds and

vice versa,

In case 1:

Sensex on Granger cause to Hedge Funds

Here, f-statistic value is 2.10852 which is more than the critical value of

1.7 and 1.58 at 5 % and 1 % significance level respectively.

Thus we accept the null hypothesis and can say Sensex causes the Hedge

Funds

On the other hand analyzing the impact of Hedge Funds on Sensex for

daily returns we see that


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F-statistic value is 1.96900 which is more than the critical value of 1.7 and

1.58 at 5 %

and 1 % significance level respectively.

Thus we again accept the null hypothesis and can say Hedge Funds has

cause on Sensex returns.

Now following is the finding for grangers causality test.:

There is causal relation between Hedge Funds and Sensex returns.

DISCUSSION & IMPLICATION

It is found that the times series values of Hedge Funds

and Sensex returns are Stationary and Deterministic

It is found that the Sensex returns and Hedge Fund

returns are cointigrated from the past one year Timeseries data

There exists a Causal relation between Sensex and Hedge

Funds


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CONCLUSION & RECOMMENDATION

The causal relationship was tested between the BSE index and

Hedge Funds . Hedge Funds is included in the model as an additional

variable, to examine whether Hedge Funds Added more Sensitivity toSensex In this highly volatile market conditions. Hedge Funds are one of

the aim instruments on which market can bet on, not only to reduce

volatility and risk but also to preserve capital and deliver positive returns

under all market conditions.


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After looking at the following testing , we found the times series

for the year 2009 for Hedge Fund Returns and Sensex returns, which

shows both the trends are deterministic, and the values are stationary,

these trends were tested for cointigration, and were found that the

multicollinearity exits as the likelihood ratio was high . The causality test

proved that null hypothesis doesnt exits and thus proved there is a

causal relation between the Hedge Fund returns and Sensex returns.

Hence it is concluded that Hedge Funds added more Sensitivity to

Sensex

RECOMMENDATION

While making an investment decision, it is recommended that both Hedge

Funds and Sensex are to be considered to take both long and short

positions, use arbitrage, buy and sell undervalued securities, trade options

or bonds, and invest in almost any opportunity in any market where it

foresees impressive gains at reduced risk

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Stock market and macroeconomic aggregates in India: An

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http://www.springerlink.com/content/kh13184443310607/http://ideas.repec.org/p/cfs/cfswop/wp200420.htmlhttp://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVG-4RP0MKN-4&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=a0d3124a13c5e6b5f60269de95fdf6e5http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVG-4RP0MKN-4&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=a0d3124a13c5e6b5f60269de95fdf6e5http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVG-4RP0MKN-4&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=a0d3124a13c5e6b5f60269de95fdf6e5http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVG-4RP0MKN-4&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=a0d3124a13c5e6b5f60269de95fdf6e5http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVG-4RP0MKN-4&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=a0d3124a13c5e6b5f60269de95fdf6e5http://versita.metapress.com/content/0x58315566577527/http://www.thefreelibrary.com/The+relationship+between+exchange+rate+and+stock+prices+during+the...-a0168399550http://www.thefreelibrary.com/The+relationship+between+exchange+rate+and+stock+prices+during+the...-a0168399550http://sourceforge.net/projects/jmulti/files/http://www.springerlink.com/content/kh13184443310607/http://ideas.repec.org/p/cfs/cfswop/wp200420.htmlhttp://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVG-4RP0MKN-4&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=a0d3124a13c5e6b5f60269de95fdf6e5http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVG-4RP0MKN-4&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=a0d3124a13c5e6b5f60269de95fdf6e5http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVG-4RP0MKN-4&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=a0d3124a13c5e6b5f60269de95fdf6e5http://versita.metapress.com/content/0x58315566577527/http://www.thefreelibrary.com/The+relationship+between+exchange+rate+and+stock+prices+during+the...-a0168399550http://www.thefreelibrary.com/The+relationship+between+exchange+rate+and+stock+prices+during+the...-a0168399550http://sourceforge.net/projects/jmulti/files/


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GLOSSARY

Acceptance region: The set of values of a test statistic for which the null

hypothesis is accepted (is not rejected).

Adjusted R2( ): A modified version of R2 that does not necessarily

increase when a new regressor is added to the regression.

Akaike information criterion: See information criterion.

Alternative hypothesis: The hypothesis that is assumed to be true if the

null hypothesis is false. The alternative hypothesis is often denoted H1.

Asymptotic distribution: The approximate sampling distribution of a

random variable computed using a large sample. For example, the

asymptotic distribution of the sample average is normal.

Asymptotic normal distribution: A normal distribution that

approximates the sampling distribution of a statistic computed using a

large sample.

Attrition: The loss of subjects from a study after assignment to the

treatment or control group.

Augmented Dickey-Fuller (ADF) test: A regressionbased test for a unit

root in an AR(p) model.

Autocorrelation: The correlation between a time series variable and its

lagged value.The jth autocorrelation of Y is the correlation between Yt and


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Yt2j.

Autocovariance: The covariance between a time series variable and its

lagged value.The jth autocovariance of Y is the covariance between Yt and

Yt2j.

Autoregression: A linear regression model that relates a time series

variable to its past (that is, lagged) values. An autoregression with p lagged

values as regressors is denoted AR(p). Autoregressive conditional

heteroskedasticity

(ARCH): A time series model of conditional heteroskedasticity. R2

Autoregressive distributed lag model: A linear regression model in

which the time series variable Yt is expressed as a function of lags of Yt

and of another variable, Xt.The model is denoted ADL(p,q), where p

denotes the number of lags of Yt and q denotes the number of lags of Xt.

Average causal effect: The population average of the individual causal

effects in a heterogeneous population. Also called the average treatment

effect..

Binary variable: A variable that is either 0 or 1.A binary variable is used

to indicate a binary outcome. For example,X is a binary (or indicator, or

dummy) variable for a persons gender if X 5 1 if the person is female andX 5 0 if the person is male. mY mY mY

Bivariate normal distribution: A generalization of the normal

distribution to describe the joint distribution of two random variables.

Break date: The date of a discrete change in population time series

regression coefficient(s).

Causal effect: The expected effect of a given intervention or treatment as

measured in an ideal randomized controlled experiment.

Chi-squared distribution: The distribution of the sum of m squared

independent standard normal random variables.The parameter m is called

the degrees of the freedom of the chi-squared distribution.

Chow test: A test for a break in a time series regression at a known break

date.


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Coefficient of determination: See R2.

Cointegration: When two or more time series variables share a common

stochastic trend.

Common trend: A trend shared by two or more time series.

Conditional distribution: The probability distribution of one random

variable given that another random variable takes on a particular value.

Conditional expectation: The expected value of one random value given

that another random variable takes on a particular value.

Conditional heteroskedasticity: The variance, usually of an error term,

depends on other variables.

Conditional mean: The mean of a conditional distribution; see conditional

expectation.

Conditional mean independence: The conditional expectation of the

regression error ui, given the regressors, depends on some but not all of the

regressors.

Conditional variance: The variance of a conditional distribution.

Confidence interval (or confidence set): An interval (or set) that contains

the true value of a population parameter with a prespecified probability

when computed over repeated samples.Confidence level: The prespecified probability that a confidence interval

(or set) contains the true value of the parameter.

Consistency: Means that an estimator is consistent. See consistent

estimator.

Consistent estimator: An estimator that converges in probability to the

parameter that it is estimating.

Constant regressor: The regressor associated with the regression

intercept; this regressor is always equal to 1.

Constant term: The regression intercept.

Continuous random variable: A random variable that can take on a

continuum of values.

Control group: The group that does not receive the treatment or


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intervention in an experiment.

Control variable: Another term for a regressor; more specifically, a

regressor that controls for one of the factors that determine the dependent

variable.

Convergence in distribution: When a sequence of distributions

converges to a limit; a precise definition is given in Section 17.2.

Convergence in probability: When a sequence of random variables

converges to a specific value; for example, when the sample average

becomes close to the population mean as the sample size increases; see

Key Concept 2.6 and Section 17.2.

Correlation: A unit-free measure of the extent to which two random

variables move, or vary, together.The correlation (or correlation

coefficient) between X and Y is sXY/sXsY and is denoted corr(X,Y).

Correlation coefficient: See correlation.

Covariance: A measure of the extent to which two random variables move

together.The covariance between X and Y is the expected value E[(X 2

mX)(Y 2 mY)], and is denoted by cov(X,Y) or by sXY.

Covariance matrix: A matrix composed of the variances and covariances

of a vector of random variables.Critical value: The value of a test statistic for which the test just rejects

the null hypothesis at the given significance level.

Dependent variable: The variable to be explained in a regression or other

statistical model; the variable appearing on the left-hand side in a

regression.

Deterministic trend: A persistent long-term movement of a variable over

time that can be represented as a nonrandom function of time.

Dickey-Fuller test: A method for testing for a unit root in a first order

autoregression [AR(1)].

Differences estimator: An estimator of the causal effect constructed as the

difference in the sample average outcomes between the treatment and

control groups.


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Differences-in-differences estimator: The average change in Y for those

in the treatment group, minus the average change in Y for those in the

control group.

Discrete random variable: A random variable that takes on discrete

values.

Distributed lag model: A regression model in which the regressors are

current and lagged values of X.

Dummy variable: See binary variable.

Dummy variable trap: A problem caused by including a full set of binary

variables in a regression together with a constant regressor (intercept),

leading to perfect multicollinearity.

Dynamic causal effect: The causal effect of one variable on current and

future values of another variable.

Dynamic multiplier: The h-period dynamic multiplier is the effect of a

unit change in the time series variable Xt on Yt+h.

Endogenous variable: A variable that is correlated with the error term.

Error term: The difference between Y and the population regression

function, denoted by u in this textbook.

Errors-in-variables bias: The bias in an estimator of a regression

coefficient that arises from measurement errors in the regressors.

Estimate: The numerical value of an estimator computed from data in a

specific sample.

Estimator: A function of a sample of data to be drawn randomly from a

population. An estimator is a procedure for using sample data to compute

an educated guess of the value of a population parameter, such as the

population mean.

Exact distribution: The exact probability distribution of a random

variable.

Exact identification: When the number of instrumental variables equals

the number of endogenous regressors.


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Exogenous variable: A variable that is uncorrelated with the regression

error term.

Expected value: The long-run average value of a random variable over

many repeated trials or occurrences. It is the probability-weighted average

of all possible values that the random variable can take on.The expected

value of Y is denoted E(Y) and is also called the expectation of Y.

Experimental data: Data obtained from an experiment designed to

evaluate a treatment or policy or to investigate a causal effect.

Experimental effect: When experimental subjects change their behavior

because they are part of an experiment.

Explained sum of squares (ESS): The sum of squared deviations of the

predicted values of Yi, ,from their average; see Equation (4.14).

Explanatory variable: See regressor.

External validity: Inferences and conclusions from a statistical study are

externally valid if they can be generalized from the population and the

setting studied to other populations and settings.

F-statistic: A statistic used to a test joint hypothesis concerning more than

one of the regression coefficients.

Fm,n distribution: The distribution of a ratio of independent randomvariables, where the numerator is a chi-squared random variable with m

degrees of freedom, divided by m, and the denominator is a chi-squared

random variable with n degrees of freedom divided by n.

Fm,` distribution: The distribution of a random variable with a chi-

squared distribution with m degrees of freedom, divided by m.

Feasible GLS: A version of the generalized least squares (GLS) estimator

that uses an estimator of the conditional variance of the regression errors

and covariance between the regression errors at different observations.

Feasible WLS: A version of the weighted least squares (WLS) estimator

that uses an estimator of the conditional variance of the regression errors.

First difference: The first difference of a time series variable Yt is Yt 2

Yt21, denoted DYt.


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First-stage regression: The regression of an included endogenous variable

on the included exogenous variables, if any, and the instrumental

variable(s) in two stage least squares.

Fitted values: See predicted values.

Fixed effects: Binary variables indicating the entity or time period in a

panel data regression.

Fixed effects regression model: A panel data regression that includes

entity fixed effects. Yi

Forecast error: The difference between the value of the variable that

actually occurs and its forecasted value.

Forecast interval: An interval that contains the future value of a time

series variable with a prespecified probability.

Functional form misspecification: When the form of the estimated

regression function does not match the form of the population regression

function; for example, when a linear specification is used but the true

population regression function is quadratic.

GARCH: See generalized autoregressive conditional heteroskedasticity.

Gauss-Markov theorem: Mathematical result stating that, under certain

conditions, the OLS estimator is the best linear unbiased estimator of theregression coefficients conditional on the values of the regressors.

Generalized autoregressive conditional heteroskedasticity: A time

series model for conditional heteroskedasticity.

Generalized least squares (GLS): A generalization of OLS that is

appropriate when the regression errors have a known form of

heteroskedasticity (in which case GLS is also referred to as weighted least

squares, WLS) or a known form of serial correlation.

Generalized method of moments: A method for estimating parameters by

fitting sample moments to population moments that are functions of the

unknown parameters. Instrumental variables estimators are an important

special case.

GMM: See generalized method of moments.


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Granger causality test: A procedure for testing whether current and

lagged values of one time series help predict future values of another time

series.

HAC standard errors: See heteroskedasticity- and autocorrelation-

consistent (HAC) standard errors.

(HAC) standard errors: Standard errors for OLS estimators that are

consistent whether or not the regression errors are heteroskedastic and

autocorrelated.

Hypothesis test: A procedure for using sample evidence to help determine

if a specific hypothesis about a population is true or false.

i.i.d.: Independently and indentically distributed. I(0), I(1), and I(2): See

order of integration.

Identically distributed: When two or more random variables have the

same distribution.

Impact effect: The contemporaneous, or immediate, effect of a unit

change in the time series variable Xt on Yt.

Included endogenous variables: Regressors that are correlated with the

error term (usually in the context of instrumental variable regression).

Included exogenous variables: Regressors that are uncorrelated with theerror term (usually in the context of instrumental variable regression).

Independence: When knowing the value of one random variable provides

no information about the value of another random variable.Two random

variables are independent if their joint distribution is the product of their

marginal distributions.

Indicator variable: See binary variable.

Information criterion: A statistic used to estimate the number of lagged

variables to include in an autoregression or a distributed lag model.

Leading examples are the Akaike information criterion (AIC) and the

Bayes information criterion (BIC).

Instrument: See instrumental variable.

Instrumental variable: A variable that is correlated with an endogenous


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regressor (instrument relevance) and is uncorrelated with the regression

error (instrument exogeneity).

Lags: The value of a time series variable in a previous time period.The jth

lag of Yt is Yt2j.

Linear probability model: A regression model in which Y is a binary

variable.

Linear regression function: A regression function with a constant slope.

Local average treatment effect: A weighted average treatment effect

estimated, for example, by TSLS.

Log-linear model: A nonlinear regression function in which the

dependent variable is ln(Y) and the independent variable is X.

Logarithm: A mathematical function defined for a positive argument; its

slope is always positive but tends to zero.The natural logarithm is the

inverse of the exponential function, that is, X 5 ln(eX).

Logit regression: A nonlinear regression model for a binary dependent

variable in which the population regression function is modeled using the

cumulative logistic distribution function.

Maximum likelihood estimator (MLE): An estimator of unknown

parameters that is obtained by maximizing the likelihood function; seeAppendix 11.2.

Mean: The expected value of a random variable.The mean of Y is denoted

mY.

95% confidence set: A confidence set with a 95% confidence level; see

confidence interval.

Nonlinear least squares: The analog of OLS that applies when the

regression function is a nonlinear function of the unknown parameters.

Nonlinear least squares estimator: The estimator obtained by

minimizing the sum of squared residuals when the regression function is

nonlinear in the parameters.

Nonstationary: When the joint distribution of a time series variable and

its lags changes over time.


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Normal distribution: A commonly used bell-shaped distribution of a

continuous random variable.

Null hypothesis: The hypothesis being tested in a hypothesis test, often

denoted by H0.

Observation number: The unique identifier assigned to each entity in a

data set.

Observational data: Data based on observing, or measuring, actual

behavior outside an experimental setting. OLS estimator. See ordinary

least squares estimator.

OLS regression line: The regression line with population coefficients

replaced by the OLS estimators.

OLS residual: The difference between Yi and the OLS regression line,

denoted by in this textbook.

Omitted variables bias: The bias in an estimator that arises because a

variable that is a determinant of Y and is correlated with a regressor has

been omitted from the regression.

p-value: The probability of drawing a statistic at least as adverse to the

null hypothesis as the one actually computed, assuming the null hypothesis

is correct. Also called the marginal significance probability, the p-value isthe smallest significance level at which the null hypothesis can be

rejected.

Polynomial regression model: A nonlinear regression function that

includes X, X2, . . . and Xr as regressors, where r is an integer. ui

Population: The group of entitiessuch as people, companies, or school

districtsbeing studied.

Predicted value: The value of Yi that is predicted by the OLS regression

line, denoted by in this textbook.

Probability: The proportion of the time that an outcome (or event) will

occur in the long run.

Probit regression: A nonlinear regression model for a binary dependent

variable in which the population regression function is modeled using the


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cumulative standard normal distribution function.

Regression specification: A description of a regression that includes the

set of regressors and any nonlinear transformation that has been applied.

Rejection region: The set of values of a test statistic for which the test

rejects the null hypothesis.

Restricted regression: Aregression in which the coefficients are restricted

to satisfy some condition. For example, when computing the

homoskedasticityonly F-statistic, this is the regression with coefficients

restricted to satisfy the null hypothesis.

Root mean squared forecast error: The square root of the mean of the

squared forecast error.

Sample correlation: An estimator of the correlation between two random

variables.

Sample covariance: An estimator of the covariance between two random

variables.

Sample selection bias: The bias in an estimator of a regression coefficient

that arises when a selection process influences the availability of data and

that process is related to the dependent variable.This induces correlation

between one or more regressors and the regression error.Sample standard deviation: An estimator of the standard deviation of a

random variable.

Sample variance: An estimator of the variance of a random variable.

Sampling distribution: The distribution of a statistic over all possible

samples; the distribution arising from repeatedly evaluating the statistic

using a R2 series of randomly drawn samples from the same population.

Scatterplot: A plot of n observations on Xi and Yi, in which each

observation is represented by the point (Xi,Yi).

Serial correlation: See autocorrelation.

Serially uncorrelated: A time series variable with all autocorrelations

equal to zero.

Significance level: The prespecified rejection probability of a statistical


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whether hedge funds added more sensitivity to sensex? (using granger causality test)

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