# Futures Trading On Spot Market In India Finance Essay

This study is an attempt to investigate the effect of futures trading on the volatility and operating efficiency of the underlying Indian stock market by analysing Index futures. Specifically, the study examines whether the index futures trading in India has caused a significant change in spot price volatility of the underlying stocks and how the index futures trading has affected market/trading efficiency in the Indian futures and stock markets. The effect of the introduction of futures trading is examined using an extended period of June 1995 to April 2010. We employed an event study approach to test whether the introduction of index futures trading has resulted in significant change in volatility and efficiency of the stock returns. The study compares spot price volatility changes before and after futures trading is introduced in the stock indices. The result shows that the introduction of Nifty index futures trading in India is associated with both reduction in spot price volatility and reduced trading efficiency in the underlying stock market. The results of this study suggest that there is a trade-off between gains and costs associated with the introduction of derivatives trading at least on a short-term perspective. This paper offers a unique contribution in examining the impact of introduction of index futures trading in NSE Nifty index and the index futures covering a period since introduction of index futures in Indian Capital Market. The results suggest that the market would have to pay a certain price, such as a loss of market efficiency for the sake of market stabilization. Hence, a desirable market policy for derivatives trading would be one that would preserve market stabilization while still not damaging market efficiency in the underlying spot market.

Also, derivatives contribute towards stabilizing stock market by taking the speculators of the spot market, and offer enough liquidity to hedgers and also provide low cost arbitrage opportunities.

## 1. Introduction

The rapidity with which corporate finance, banking and investment finance have changed in recent years has given birth to a new discipline that has come to be known as Financial Engineering. Financial Engineering deals with the design, development and implementation of financial instruments and processes; this also entails creative solutions to problems in finance. The last decade has witnessed the introduction of ‘derivatives’ as an innovative financial instrument in the Indian markets.

Derivatives are financial instruments that derive their value from the underlying, which can be a stock index, a stock, and a commodity like pepper or even a complex parameter like the interest rate. Derivatives give you a choice to trade on the underlying at a fraction of a cost i.e. Derivatives are leveraged products. The term “Derivative” is coined to mean that its value is dependent i.e. its value is completely “Derived” from its underlying. Financial engineers have played a tremendous role in investment and money management, and are heavily involved in risk management. Derivatives are instruments of risk hedging. Used mainly for the purpose of risk hedging, these instruments do not influence the fluctuation in the underlying prices. However since these instruments lock in future prices, derivative products reduces the effect of fluctuations in asset prices on the profitability and cash situation. A derivative contract is significantly different from the underlying asset bought/sold. Common derivatives include options, forward contracts, futures contracts, and swaps. In this paper, we study the impact of introduction of futures contracts on stock indices and its effect on the underlying spot market in India.

Derivatives such as index futures, stock futures, index options and stock options are now treated as important instruments of price discovery, portfolio management and hedging strategies in stock market throughout the world. In the last few decades many emerging and transition economies has introduced derivatives. Introduction of such contracts are controversial since it acts like double edged swords, it can be used to protect yourself also it can kill in time.

The introduction of derivatives in any economy has never been seen from a positive angle. It is in fact has been conceived as a market for speculators and feared to have adverse impact on volatility of spot market. Even Govt has declared complete ban on futures trading in commodities. Now trading of futures has resumed on four banned commodities ever since the inflation rate has moderated. It is hoped that Govt will soon lift the ban on food grains. This offers opportunities for importers and exporters to take advantage of different hedging strategies. Earlier an committee led by Anhijit Sen has done an study on future trading on agriculture commodity prices on Wheat, urad, tur and rice.

This paper also tries to examine whether decline or rise in volatility can be attributed to introduction of derivatives alone or due to some other macroeconomic reasons.

## 2. Theoretical Background

The Indian capital market has witnessed a major transformation and structural change from the past one decade as a result of ongoing financial sector reforms initiated by the Government of India. One of the major objectives of these reforms was to bring the Indian capital market up to a certain international standard. Due to such reforming process, one of the significant step taken in the secondary market is the introduction of derivative products in two major Indian stock exchanges viz. National Stock Exchange (NSE) and Bombay Stock Exchange (BSE) , with a view to provide tools for risk management to investors and to improve the informational efficiency of the cash market. Though the onset of derivative trading has significantly altered the movement of stock prices in Indian spot market, it is yet to be proved whether the derivative products have served the purpose as claimed by the Indian regulators.

Derivatives are specific type of financial instruments which are linked to a specific financial instrument or indicator or commodity and this facilitates trading of financial risk that the underlying holds. The value of a financial derivative is derived from the price of an underlying item, such as an asset or an index. Derivative products includes futures, forwards, options and swaps, and these can be combined with each other or traditional securities and loans to create hybrid instruments. These instruments are used for risk management by hedging i.e. taking opposite position in the futures market. A futures contract is a type of derivative instrument or financial contract in which two parties agree to transact a set of financial instruments or physical commodities for future delivery at a particular price. In other words, a future contract is a standardized agreement between the seller (short position holder) of the contract and the buyer (Long position holder), traded on a futures exchange, to buy or sell a certain underlying instrument at a certain date in the future, at a pre-set price. The future date is called the delivery date or final settlement date. The pre-set price is called the futures price. The price of the underlying asset on the delivery date is called the settlement price.

Trading on equity derivative started on June 9, 2000 with introduction of stock index futures by Bombay Stock Exchange (BSE). National Stock Exchange (NSE) also introduced its trading on 12 June, 2000 based on S&P Nifty. NIFTY futures’ trading was introduced on the 12th of July 2000. Trading on stock futures was introduced in the NSE in the 9th November, 2001. Subsequently, other derivatives such as stock futures on individual securities, index options and options on individual securities were introduced.

## 3. Derivatives trading in India

In the context the Securities Contracts (Regulation) Act, 1956 (SCRA) defines “derivative” as a security that is derived out of a debt instrument, share, loan whether secured or unsecured, risk instrument or contract of differences or any other form of security, same as a contract which derives its value out of the prices, or index of prices, of underlying securities. Derivatives are securities under the SCRA and hence the regulatory framework under the SCRA governs the trading of derivatives.

The National Stock Exchange (NSE) introduced stock index futures and options on the NSE’s index of 50 stocks (S&P CNX NIFTY) in June 12, 2000 and June 4, 2001 respectively. Subsequently on November 9, 2001 single stock futures were launched. An important step for the preparation of the futures and options trading is the construction of an underlying index. The NSE had constructed the S&P CNX NIFTY (containing 50 stocks) keeping in mind the need to design a market index which will be diversified and well liquid. Since its construction it has been professionally managed to keep pace with the changes in the economy. The composition of Nifty has been subject to continuous change since its construction due to addition and deletions from the list over the years. While India’s derivatives markets have grown dramatically since their introduction, they are still in an early development stage. In this regard implications from a carefully designed and executed study will not only help assess the economic usefulness of derivatives markets but they will also help build a more effective market operation system in India. SEBI granted the approval of derivative trading in may 2000 on two of its Stock exchanges, i.e. NSE and BSE and their clearing house/corporation. Initially SEBI has approved trading on those two indices and individual securities.

## 4. Motivation for the study

Policy makers and regulators are concerned about the impact of futures on underlying since it was believed that it creates a market for only speculators and that leads to price fluctuation. Debates on impact were intensified as futures trading moves from commodity to financial futures. If we want to further put regulation in place we need to determine if there is even a causal link exist there between the introduction of futures and spot market volatility. So we started out with following questions in mind:

What is the effect of derivative on market efficiency and liquidity of the underlying?

To what extent derivatives destabilizes the financial system and what are the possible remedies?

Can the conclusions and remedies from developed markets also be extended to emerging economies?

## 5. Need for the study

It had long been argued that a very undesirable feature of the Indian stock market was the mixing of cash and futures trading. Such mixing was caused by the existence of the ‘badla system’, combined with long settlement cycles. All this has been ended by the package of reforms implemented after the stock market crisis of March 2001. These reforms comprise the abolition of badla, the adoption of rolling settlement and finally the introduction of individual stock futures. There is need for assessing the resulting new situation which is still in transition but some useful experience has been gathered over the last few months. Such assessment has to be based on an examination of the nature of inter-relationships, both direct and indirect, between the operation of the futures market and the cash markets. An important aspect to study is the migration of most of the speculative activity from the cash market to the futures market which provides easier facilities for speculation. Also, in the presence of individual stock futures trading, the relevance of regulation of short selling and margin trading in shares is likely to be lost. Much rethinking on regulatory policies would be needed as a result of individual stock futures in order to steer the market’s over-all development on the right lines. The impact of individual stock futures on a country’s stock market is a pertinent issue of great concern and observation. The reason is that while many countries have flourishing markets in commodity futures, stock index futures, bond futures and currency futures, individual stock futures have not developed in significant way. The situation in India is different in as much as the volume of individual stock futures trading promises to be substantial in relation to the cash market. There is a distinct possibility that it may exceed the cash market trading within next few years.

For this reason, India could be a good case study of trading in individual stock futures. Yet, such trading in India is still in its infancy and transition, even though it is growing faster. The advent of stock index futures has profoundly changed the nature of trading on stock exchanges. The concern over how trading in futures contracts affects the spot market for underlying assets has been an interesting subject for investors, market makers, academicians, exchanges and regulators alike. These markets offer investors flexibility in altering the composition of their portfolios and in timing their transactions. Futures markets also provide opportunities to hedge the risks involved with holding diversified equity portfolios. As a consequence, significant portion of cash market equity transactions are tied to futures and options market activity. However, it is yet to be known if the introduction of stock index futures has served the purpose claimed by the regulators.

The ultimate objective of this study is to create a deeper understanding of this new phenomenon especially in Indian scenario the specific Indian setting. It aims to find out whether the introduction and trading of individual stock futures has contributed towards the improvement of the cash market’s functioning in terms of pricing efficiency, liquidity and stability through the informational role of futures trading.

## 6. Objectives of the study

In this paper, we investigate the effect of futures trading on the volatility and operating efficiency of the underlying Indian stock market by taking a sample of individual stocks. Specifically, we examine two issues of interest:

Whether the index futures trading in India has caused a significant change in spot market volatility of the selected underlying individual stocks?

How the index futures’ trading has affected trading efficiency of the stocks?

Whether futures trading acts as a ‘Destabilising Force’ or a ‘Stabilising Force’ in the markets?

## 7. Literature review

Since the introduction of financial futures and options during the 1970s, the effect of financial derivatives trading on the underlying spot markets has been of great interest to both academics and practitioners. One of the primary issues widely investigated by finance researchers is whether futures and/or options trading increases the price volatility of underlying stock markets and thus leads to a destabilization of the markets. Previous studies document mixed evidence on the effect of futures trading in various market environments including the U.S. A number of previous studies have examined the effect of futures trading on the operation of U.S. stock markets. Harris (1989), Damodaran (1990), Lockwood and Linn (1990), and Schwert (1990), among others, report a positive relation between futures market trading and variances of the S&P 500 index stock returns, implying that volatility of the S&P 500 stock index increased after the S&P 500 index futures trading began. On the contrary, Santoni (1987) and Brown-Hruska and Kuserk (1995) find a negative correlation between S&P 500 futures trading volume and volatility of the S&P 500 index, indicating that an increase in futures volume leads to a decrease in spot market volatility. Still, studies by Edwards (1988a, 1988b), Grossman(1988), Conrad(1989), Smith (1989), Bechetti and Roberts (1990), Darrat and Rahman (1995),and Board, Sandman, and Sutcliffe (2001) show that futures trading has no significant, little if any, impact on spot market volatility. Bessembinder and Seguin (1992) provide some reconciling evidence that stock market volatility is positively related to unexpected trading activity, but negatively to expected trading activity of the S&P 500 index futures.

Several other studies examine non-U.S. markets, with mixed evidence. A study by Kyriacou and Sarno (1999) shows a significant positive effect of both contemporaneous and lagged futures volume for the U.K. FTSE 100 index on spot market volatility, while Jochum and Kodres (1998) and Dennis and Sim (1999) document little or no significant impact of futures trading on spot market volatility for the Australian market and for the three nations of Mexico, Brazil, and Hungary, respectively. Lee and Ohk (1992) find increased spot market volatility after the Nikkei 225 futures trading was introduced on the Singapore International Monetary Exchange (SIMEX). Employing different tests, Chang, Cheng, and Pinegar (1999) report that spot stock portfolio volatility increases, although by a relatively small degree, with the introduction of Nikkei futures on the Osaka Securities Exchange, but not with their introduction on the SIMEX. In a study of 25 countries, Gulen and Mayhew (2000) provide diverse evidence depending on the country studied that expected futures volume has a positive effect on spot market volatility in Denmark, Germany, and Hong Kong, but a negative effect in Austria and the U.K., and no effect in the remaining 18 countries.

Also, There is a common belief that stock index futures are more volatile than underlying spot market because of their operational and institutional properties. The close relationship between the two markets makes the transfer of volatility possible from futures market to the underlying spot market. It is therefore, not surprising that the inception of futures contract relating to stock market has attracted the attention of researchers all over the world, and also led some observers to attribute stock market volatility to futures trading. Various studies have been conducted to assess the impact of derivatives trading on the underlying market mostly related to US and other developed country markets. Very few studies were aimed towards knowing the impact derivatives trading in emerging economies like India.

Both theoretical and empirical studies were carried out to assess the impact of listing of futures and options on the cash market. Two main bodies of theory about the aftermath of derivatives trading on the spot market are prevailing in the literature and both are contradicting each other. One school of thought argues that the introduction of futures trading increases the spot market volatility and thereby, destabilizes the market. They are the proponents of ‘Destabilizing forces’ hypothesis. (Lockwood and Linn, 1990)) They explain that derivatives market provides an additional channel by which information can be channelled to the cash markets. Frequent arrival and rapid processing of information might lead to increased volatility in the underlying spot market. They also attribute increased volatility to highly speculative and levered participants.

Others argue that the introduction of futures actually reduces the spot market volatility and thereby, stabilises the market. They are the proponents of ‘Market completion’ hypothesis. (Satya Swaroop Debasish, 2007). Kumar (1995) argued that derivatives trading helps in price discovery, improve the overall market depth, enhance market efficiency, augment market liquidity, reduce asymmetric information and thereby reduce volatility of the cash market. The impact that the derivatives market has on the underlying spot market remains an issue debated again and again with arguments both in favour and against them.

Overall, the above studies show that the effect of futures trading on the volatility of spot markets varies depending on time period, model specification, and/or country examined. Considering the short history of futures and options trading and the presence of several market frictions and restrictions that might have hindered the efficient operation of Indian securities markets, a study of the effect of futures and options trading on spot market volatility and market efficiency is warranted for the Indian futures and stock markets.

This study seeks to examine the volatility of the spot market due to the derivatives market. Whether the volatility of the spot market has increased, decreased or remained the same. If increased then, what extent it is due to futures market. We use Autoregressive framework to model returns volatility. To measure volatility in the markets, the VIX (Volatility Index) computed by the National Stock Exchange is used. To eliminate the effect of factors other than stock index futures (i.e., the macroeconomic factors) determining the changes in volatility in the post derivative period, the model is used for estimation after adjusting the stock return equation for market factors.

The studies is in the Indian context have evaluated the trends in NSE and not on the Stock Exchange, Mumbai (BSE) for the reason that the turnover in NSE captures an overwhelmingly large part of the derivatives market.

We use NSE Midcap 500 as surrogate indices to capture and study the market wide factors those contribute to the changes in spot market volatility. This gives a better idea as to whether the introduction of index futures in itself caused a decline in the volatility of spot market or the overall market wide volatility has decreased, and thus, causing a decrease in volatility of indices on which derivative products have been introduced. The volumes on NIFTY also has a large impact on the volatility, thus in the model to measure volatility volumes are also considered as a factor. We seek to compare this volatility with the volatility prevailing in the market before the index futures (i.e. Nifty futures) and check if it is statistically significant.

## 8. Data and period of study

To investigate the effect of the introduction of futures trading, the sample period of June 1995 to April 2010 is chosen. Index futures trading were officially introduced on the NSE on June 12, 2000. The sample period is divided in to two periods- period I being the pre event phase (from 7th June 1995 to 9th June 2000) consisting of 2489 trading days and period II being the post event phase ( from 13th June 2000 to 26th April 2010) consisting of 2475 trading days. The two phases are separated by the event day (t-day) i.e. 12th June. The study is entirely based on time series secondary data collected from website of National Stock Exchange (www.nse-india.com).

The NSE provides a fully automated and screen based trading system for futures and spot market transactions, on a nationwide basis and an online monitoring and surveillance mechanisms.

## 9.1 Model 1: Estimating volatility based on classical formulas given by Parkinson, Garman-Klass etc.

The various parameters used in estimating volatilities are given below:

σ= asset volatility, to be estimated;

Ci = closing price on day i;

Oi = opening price on day i;

Hi = high price on day i;

Li = low price on day i;

ci= lnCi – lnOi, the normalized close price;

oi = lnOi - lnCi-1, the normalized open price;

ui = lnHi – lnOi, the normalized high price;

di = lnLi – lnOi, the normalized low price;

n = number of daily periods.

## Parkinson’s Formula:

Garman-Klass Formula: Garman and Klass provide an estimator with superior efficiency, having minimum variance on the assumption that the process follows a geometric Brownian motion with zero drift.

## Rogers-Satchell Formula:

## Classical Formula:

## Pre Futures Volatility measures

## Variance

## Parkinson’s

0.000183702

## Garman-Klass

0.000158888

## Rogers-Satchell

0.000154812

## Classical Formula

0.000303709

## Post Futures Volatility measures

## Variance

## Parkinson’s

0.000256268

## Garman-Klass

0.000241063

## Rogers-Satchell

0.000243246

## Classical Formula

0.000298127

Conclusion: According to the classical definitions of variances and volatility, we see that there has been a considerable increase in volatility of spot market prices after the introduction of futures market. But this might be partly due to the fact that classical formulas don’t consider mean reversion, heteroskedasticity & autocorrelation. Also, the structural changes post liberalisation aren’t taken into consideration in classical models. We would try to analyse this phenomenon using a GARCH model.

## 9.2 Model 2: Using variances of NIFTY and NSE 500; conducting a statistical analysis like F-test to determine whether there has been a significant change in volatility due to futures

## Standard Deviation

## Variance

## NIFTY

0.113720524

0.012932357

## NSE 500

0.13269621

0.017608284

Standard Deviation measures the volatility of the data and would be the most appropriate to use for comparison. When we compare the Standard Deviation, it is higher in case of NIFTY JUNIOR, we can infer that NIFTY is less volatile than NIFTY JUNIOR. We can test it using F-statistic, test for variances. We get the following result from MS Excel.

Null Hypothesis:

There is no significant difference between the variances in price changes in NIFTY and Nifty Futures.

Alternate Hypothesis:

There is significant difference between the variances in price changes in NIFTY and Nifty Futures.

## F-Test Two-Sample for Variances

## NIFTY

Mean

1

Variance

0.012932

Observations

258

df

257

F

0.734447

P(F<=f) one-tail

## 0.006819

F Critical one-tail

0.81417

Statistical Result:

We tend to accept the Null Hypothesis at 95% Level of significance. Hence there is no significant difference in the variance of NIFTY.

Conclusion:

Since NSE 500 does not contain Futures. We are comparing it with NIFTY, which has futures and hence testing for any significant difference. With the F-test for variance, we conclude that there is no significant difference in NIFTY and Nifty futures. We can conclude that NIFTY Futures doesn’t contribute towards volatility of NIFTY.

## 9.3 Model 3 – Using Regression Analysis

Data and Methodology

We use a regression model to capture the volatility of NIFTY. The dependent variable, we take as the Volatility Index (VIX). The volatility in the market is generally due to the Macro-Economic Variables, Futures (We are interested in checking this), and stock volumes. Thus, when we regress this model using SPSS, we get the result.

Yt = b0 + b1Xt-1 + b2X2 + b3X3 + b4X4 + b5X5 + e where

Y = Volatility Index

ßi = regression coefficients

Xt-1= Volatility Index

X2 = Nifty 1 Month Futures

X3 = S&P CNX NIFTY 50

X4 = Nifty Volumes

X5 = NSE MIDCAP 500

e = random error term

Volatility Index – VIX

Volatility Index is the measure of market’s expectation of volatility on the near term. This is also defined as the “rate and magnitude of changes in prices” which is also a measure of risk in finance. Volatility index is a good indicator of the “risk perception” of the investor. During times of high market volatility, market fluctuates steeply in either dirction which causes the CIX to rise. When volatility stabilizes, option price tend to decline over time. This in turn draws down the VIX.

Computation methodology:

The generalized formula used in the India VIX calculation is:

## Durbin-Watson Statistic:

This is a test statistics used to detect the presence of autocorrelation in the residuals from a regression analysis. Its value lies between 0 and 4. A value of 2 indicates no statistical correlation. If the value of the test statistics is significantly lower than 2 it indicates a high correlation. If the Durbin-Watson statistics is less than 1, there is a reason for alarm while smaller values indicates that error terms are auto correlated; while large values suggests negative auto-correlation.

## Descriptive Statistics

Mean

Std. Deviation

VIX

32.43

10.93

MIDCAP

3840.20

509.58

NSE

4692.70

533.65

Volume

256310000.00

92515200.00

PREV

32.97

10.90

FUTURES

4694.70

533.53

Determine based on Eigen values: An Eigen value represents the amount of variance associated with the factor. Generally only factors with an Eigen value of >1.0 is included.

## Collinearity Diagnostics

Model

Dimension

Eigen value

Condition Index

Variance Proportions

(Constant)

NSE

Volume

FUTURES

1

1

4.8584

1

0.00015

7.88E-08

0.002

9E-08

2

0.13732

5.948082

7.8E-06

9.13E-07

0.34

1E-06

3

0.00413

34.30598

0.66748

1.56E-05

0.602

2E-05

4

0.00015

178.7676

0.2268

0.002127

0.039

0.0029

5

9.8E-07

2222.885

0.10557

0.997857

0.017

0.997

a. Dependent Variable: VIX

A Durbin-Watson Statistic below 1 is a cause of alarm. There is auto correlation between the variables in VIX. We go for Auto-Regressive model. Also as we see, in the later half of the report even the Augmented Dickey-Fuller test tells about the existence of a strong auto correlation between the variables. In the Auto-Regressive model, we even add the past values of the predicted index as we feel it has a strong relation with it as demonstrated by Durbin-Watson statistic and ADF test.

## Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

Change Statistics

R Square Change

F Change

df1

df2

Sig. F Change

1

0.842

0.708

0.704

5.9471

0.70847

153.707

4

253

1.74E-66

a. Predictors: (Constant), MIDCAP, Volume, FUTURES, NSE

b. Dependent Variable: VIX

## Auto-Regressive Models:

## Correlations

VIX

MIDCAP

NSE

Volume

PREV

Pearson Correlation

VIX

1

-0.835

-0.828

0.638

0.906

MIDCAP

-0.835

1

0.993

-0.674

-0.827

NSE

-0.828

0.993

1

-0.657

-0.821

Volume

0.638

-0.674

-0.657

1

0.64

PREV

0.906

-0.827

-0.821

0.64

1

FUTURES

-0.826

0.992

1

-0.654

-0.819

Sig. (1-tailed)

VIX

## .

0

0

0

0

MIDCAP

0

## .

0

0

0

NSE

0

0

## .

0

0

Volume

0

0

0

## .

0

PREV

0

0

0

0

## .

FUTURES

0

0

0

0

0

N

VIX

258

258

258

258

258

MIDCAP

258

258

258

258

258

NSE

258

258

258

258

258

Volume

258

258

258

258

258

PREV

258

258

258

258

258

FUTURES

258

258

258

258

258

Here we have included 2 models, both Auto-Regressive in nature and have a Durbin-Watson statistic > 2, which depicts the fact that this model is a good model.

## Model Summary

Model

R

R Square

Adjusted R Square

Std. Error

Change Statistics

R Square Change

F Change

df1

df2

Sig. F Change

1

0.9191

0.8448

0.8417

4.3482

0.8448

274.2774

5.0000

252.0000

0.0000

2

0.9185

0.8436

0.8411

4.3558

0.8436

341.1870

4.0000

253.0000

0.0000

a. Predictors: (Constant), FUTURES, Volume, PREV, MIDCAP, NSE

b. Predictors: (Constant), FUTURES, Volume, PREV, NSE

c. Dependent Variable: VIX

## Residuals Statistics

Minimum

Maximum

Mean

Model 1

Predicted Value

18.25634

69.22996

32.43411

Residual

-26.23

36.52602

1.42E-14

Std. Predicted Value

-1.41151

3.663313

-1.5E-15

Std. Residual

-6.03235

8.400228

3.29E-15

Model 2

Predicted Value

17.73563

69.46959

32.43411

Residual

-26.4696

36.64511

2.76E-14

Std. Predicted Value

-1.46435

3.689703

-2.80E-15

Std. Residual

-6.07687

8.412965

6.39E-15

a. Dependent Variable: VIX

## Collinearity Diagnostics

Model

Dimension

Eigen value

Condition Index

Variance Proportions

(Constant)

NSE

Volume

PREV

1

1

5.764

1.000

0.000

5.5E-08

0.0016

0.0008

2

0.195

5.441

0.000

9.98E-07

0.1034

0.0463

3

0.039

12.189

0.000

3.4E-08

0.7363

0.3807

4

0.002

55.248

0.817

3.12E-05

0.1123

0.5622

5

0.000

195.068

0.096

0.002101

0.0337

0.0037

6

0.000

2428.978

0.086

0.997867

0.0127

0.0063

2

1

4.796

1.000

0.000

9.71E-08

0.0024

0.0012

2

0.164

5.411

0.000

2.66E-06

0.1159

0.0488

3

0.039

11.127

0.000

1.1E-07

0.7456

0.3905

4

0.002

53.736

0.961

0.000146

0.0993

0.5431

5

0.000

2035.159

0.038

0.999851

0.0369

0.0164

a. Dependent Variable: VIX

## ANOVA

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

25928.82

5

5185.763

274.2774

9.7E-100

Residual

4764.564

252

18.907

Total

30693.38

257

2

Regression

25893.23

4

6473.309

341.187

1.3E-100

Residual

4800.146

253

18.97291

Total

30693.38

257

a. Predictors: (Constant), FUTURES, Volume, PREV, MIDCAP, NSE

b. Predictors: (Constant), FUTURES, Volume, PREV, NSE

c. Dependent Variable: VIX

## Statistical Results:

Model 1:

An R-Square of 0.8448 indicates the degree to which volatility is explained by the independent variables, with the incremental part of it being highest for auto correlated variable, the volatility index. Durbin-Watson Statistic of 2.4675 indicates a low auto correlation, which is desirable.

The critical F value of 274.2774 indicates the strength of the strength of our regression model. The p value is also extremely low.

We get a regression model from the data:

Yt = 29.4559 + 0.6745Xt-1 + -.0007X2 + .0018X3 + 0X4 + -.0066X5 + e, where

Y = Volatility Index

ßi = regression coefficients

Xt-1= Volatility Index

X2 = Nifty 1 Month Futures

X3 = CNX NIFTY 50

X4 = Nifty Volumes

X5 = NSE Midcap

e = random error term

The p value is very low for b2; hence indicating the significant contribution of Nifty futures towards predicting Volatility, The predicted volatility value for VIX will lie in the range 18.2563 to 69.22996 with a mean of 32.43411 with a standard deviation of 10.044.

Model 2:

An R-Square of 0.8436 indicates the degree to which volatility is explained by the independent variables, with the incremental part of it being highest for auto correlated variable, the volatility index. Durbin-Watson Statistic of 2.4852 indicates a low auto correlation, which is desirable.

The critical F value of 341.187 indicates the strength of the strength of our regression model. The p value is also extremely low.

We get a regression model from the data:

Yt = 32.0728 + 0.6804Xt-1 +.0184X2 + -.02348X3 + 0X4 + 0X5 + e, where

Y = Volatility Index

ßi = regression coefficients

Xt-1= Volatility Index

X2 = Nifty 1 Month Futures

X3 = CNX NIFTY 50

X4 = Nifty Volumes

X5 = NSE Midcap

e = random error term

The p value is very low for b2; hence indicating the significant contribution of Nifty futures towards predicting Volatility, The predicted volatility value for VIX will lie in the range 17.73563 to 69.46959 with a mean of 32.43411 with a standard deviation of 10.0375.

## Conclusion from this model:

With the regression model we can see that the beta of futures i.e. b2 is -0.0007 & .0184. This beta value is significant. This implies that futures contribute towards stabilizing the market.

## 9.4 Model 4: GARCH Analysis of NSE to evaluate the conditional & unconditional volatility

## Introduction

The volatility of financial markets has been the object of numerous developments and applications over the past two decades, both theoretically and empirically. Financial economists are increasingly concerned with modelling volatility in asset returns. This is important as volatility is considered as a measure of risk, and investors want a premium for investing in risky assets. Banks and other financial institutions apply value-at-risk models to assess their risks. Modelling and forecasting volatility or, in other words, the covariance structure of asset returns, is therefore important.

Volatility is such a phenomenon that is really difficult to predict or forecast. Though one class of model has been successfully forecasted volatility in many situations is the GARCH models. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models were propounded by Engle (1982) and Bollerslev (1986). The distinctive feature of these models is that they recognize that volatilities and correlations are not constant. During some periods, a particular volatility or correlation may be relatively low, whereas during other periods it may be relatively high. The model attempts to keep track of the variations in the volatility or correlations through time. These models are discrete time models that have been used to estimate a variety of financial time series ranging from stock returns, interest rates to foreign exchange rates. GARCH modelling builds on advances in the understanding and modelling of volatility. GARCH models consider excess kurtosis (i.e., fat tail behaviour) and volatility clustering, which are two important aspects of financial time series. These models provides accurate forecasts of variances so these models are used in abundance in diversified arena such as risk management to portfolio management to option pricing to foreign exchange. The GARCH (p, q) model is formulated as:

Alexander and Leigh (1997) perform a statistical evaluation of the three types of statistical volatility forecasts that are in standard use: ‘historical’ (equally weighted moving averages), EWMAs and GARCH. Given the remarks just made, it is impossible to draw any firm conclusions about the relative effectiveness of any volatility forecasting method for an arbitrary portfolio. However, using data from the major equity indices and foreign exchange rates, some broad conclusions do appear. While EWMA methods perform well for predicting the centre of a normal distribution, the VaR model back-testing indicates that GARCH and equally weighted moving average methods are more accurate for the tails prediction required by VaR models. These results seem relatively independent of the data period used. GARCH forecasts are designed to capture the fat tails in return distributions, so VaR measures from GARCH models tend to be larger than those that assume normality.

The study uses a GARCH (1, 1) model to forecast underlying stock volatility, both the Conditional and unconditional variances.

ARCH (1) formula

GARCH (1, 1) Formula

## Augmented Dickey Fuller Test for Stationarity of NSE:

## Augmented Dickey-Fuller Unit Root Test on t-series

Null Hypothesis: t-series has a unit root

Exogenous: Constant

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

t-Statistic

Augmented Dickey-Fuller test statistic

-2.968882

Test critical values:

1% level

-3.455721

5% level

-2.872591

10% level

-2.572723

The test statistic is significant at 1% and we have to reject the hypothesis Ho of the distribution being stationary at 1% significance level. For rest all, the distribution of the t-stat tells that it is stationary.

## GARCH Findings:

## NSE Pre Futures

## NSE Post Futures

## Unconditional Volatility

0.01811623

0.01725441

## Omega

0.000042982683

0.000022178662

## Alpha

0.19649848612

0.30246304420

## Beta

0.66999424046

0.64998868438

## long run volatility (VL)

0.00032195

0.000466445

## conditional volatility

0.018150082

0.017914527

We see that the conditional and unconditional volatility post futures is lower compared to the pre futures period but the long run variance is on the higher side for post futures compared to pre futures.

The results of the study do confirm presence of asymmetric response in the case of most of the scrips analysed. Further, it was seen that subsequent to the introduction of derivatives trading, the relative importance of the ‘news coefficient’ in determining asset return volatility has increased. This result assumes greater importance when seen in light of the fact that post introduction of derivatives, the long run variance has increased, thus indicating an increase in the quantity of information flowing into the spot market. In other words, the ‘news coefficient’ has increased despite an increase in the overall quantum of information. On the whole, it is seen that introduction of derivative trading has resulted in a reduction in the spot market volatility of the underlying stock.

## 10. Conclusion:

The results of this study suggest that there is a trade-off between gains and costs associated with the introduction of derivatives trading at least on a short-term perspective. Governments and authorities planning to promote or facilitate futures and options trading would need to pay careful attention to the market restrictions they bring in for the purpose of market stabilization. The results suggest that the market would have to pay a certain price, such as a loss of market efficiency for the sake of market stabilization. Hence, a desirable market policy for derivatives trading would be one that would preserve market stabilization while still not damaging market efficiency in the underlying spot market. Derivative plays significant role in the process of price discovery and in completing the market. Derivative also contributed greatly towards the risk mitigation/management aspect for institutional investors and mutual funds. So it is clear that derivative contributes towards the risk management rather than increasing market volatility and thereby risk. Governments and authorities planning to promote or facilitate futures and options trading would need to pay careful attention to the market restrictions they bring in for the purpose of market stabilization.

Also, from the statistical analysis we have found the following conclusions.

Classical Volatility models state that the volatility has increased slightly in the post futures period.

F-test of variances of various indices proves that futures do not significantly contribute to the changing volatilities in stock market.

Both Model 1 and 2 of the regression analysis suggest that futures contribute towards stabilizing the market. Hence derivatives contribute towards stabilizing stock market.

GARCH analysis says that volatility hasn’t significantly increased post futures and the increased volatility is owing to the stupendously large amount of information that is being assimilated in the spot market.

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