Risk-return trade-off in Indian capital market during last two decades with special emphasis on crisis period.
Emerging stock markets are in developmental stage hence they need to determine cost of capital, evaluate portfolio investments, and make asset allocation decisions, for this understanding of volatility pattern is very important. Time-varying volatility is modeled using ARCH model proposed by Engle (1982) which was later generalized by Bollerslev (1986) as GARCH. These models consider non-linearity in the mean equation. They are able to explain the volatility clustering and persistence in the volatility. But some of the important properties of the financial data like asymmetric pattern of the volatility is not captured by them. Financial series shows asymmetric nature where the conditional variance tends to respond asymmetrically to positive and negative shocks in errors. This asymmetric nature of volatility can be explained through leverage effect (Black, 1976; Christie, 1982) and volatility feedback effect (French, Schwert and Stambaugh, 1987; Pindyck, 1986). To incorporate asymmetry in volatility, many nonlinear extensions of the GARCH model have been proposed. Nelson (1991) gave an exponential GARCH (EGARCH) model, based on a logarithmic expression of the conditional variability. Later, many modifications were derived from this method. The GJR-GARCH was given by Glosten, Jagannathan and Runkle (1993), Threshold ARCH method was introduced by Zakoian (1994) and Ding et al. (1993) proposed the Power-ARCH model.
The relationship between the return on an asset and its volatility as a proxy for risk has also been an important topic in financial research. Earlier, researchers used unconditional distribution of returns to investigate this relationship. Merton (1980), criticized the failure of researchers to account for the effect of changes in the level of risk when estimating expected returns. To handle this problem now we have GARCH-M model, a variation of GARCH model, to investigate the risk-return relationship. This model allows the conditional variance to affect the mean. In this way changing conditional variances directly affect the expected return on a portfolio. This variance is termed as risk and the profit gained through investments in securities is called return. The direct relationship between the two means that if an investor decides to invest in a security that has a relatively low risk, the potential return on that investment is typically fairly small. Conversely, an investment in a security that has a high risk factor also has the potential of higher returns. The relation between asymmetric volatility and return can be evaluated by Threshhold GARCH-in-mean model (TGARCH-M), Exponential GARCH-in-mean model (EGARCH-M) or Power-in-Mean GARCH model (PGARCH-M). Baillie and DeGennarro (1990) assert that most asset-pricing models postulate a positive relationship between a stock portfolio's expected returns and volatility. In reality there has been mixed results and the relationship has been found to be positive as well as negative by researchers.
The models mentioned above have been used in various foreign studies (Bali and Peng, 2006; French et al., 1987; Ghyselsa et al., 2005; Glosten et al., 1993; Guo & Whitelaw, 2006; and Harrison & Zhang, 1999) but there is less empirical research on risk-return relationship in emerging markets. In Indian context there are even lesser studies on the subject especially involving the crisis period. The only studies which have reported some result on risk-return trade-off, thus validating the CAPM theory in Indian stock market are (Dhankar and Kumar, 2006; Karmakar, 2007; Selvam & Jeyachitra, 2009).
In this paper we are also covering two important crisis that gripped the world namely: Asian crisis of 1997 and Sub-prime crisis of 2007. The US kick-started the build up of both Asian and Sub-prime crisis but the bank was the common source of contagion for the spread. Both crisis were the result of unchecked profit-seeking taking the form of high-risk lending; in both cases, the risks were extended across the financial community and, when the bubble burst, even parties not initially involved were affected because the entire lending/borrowing system was infected. The major difference between the two was that foreign investors played a major role in the East-Asian crisis, whereas in the sub-prime crisis it was mainly limited to American nationals. In Asian crisis it was the non-wealthy of Asia who suffered the most from the actions of their rich leaders and foreign lenders whereas in the sub-prime crisis all parties suffered. India experienced some effects of the Asian crisis but they were not substantive. This is partly attributed to the role of stabilization policy in India that included intervention in the foreign exchange market by the central bank, phased tightening of monetary policy and restrictions on capital flows. After Asian crisis Indian government initiated financial sector reforms as a result of which last decade witnessed major transformations and structural changes in the capital market. Derivatives were introduced in a phased manner at both National Stock Exchange (NSE) and Bombay StockExchange (BSE) in 2000 with a view to provide tools for risk management to investors. Despite these efforts India experienced heightened volatility during sub-prime crisis. The withdrawal of foreign institutional investors from Indian Stock Market and tightening of global credit markets brought about an intense liquidity crisis in the Indian economy. Major reason why India was hit by the crisis, despite mitigating factors, is India's rapid and growing integration with the global economy and the emergence of crisis in India at a time when Indian economy was already preoccupied with the adverse effects of inflationary pressures and depreciation of currency. Despite tremendous growth, the Indian market is still in a developmental stage. In this regard implications from a carefully designed and executed study on risk-return relationship will help in financial decision making and thereby help build a more effective market operation system in India.
The distinguishing factor of this study is that it evaluates the risk-return relationship during a long period of two decades around introduction of derivatives in India, paying special attention to impact of Asian crisis in pre-derivative period and Sub-prime crisis in post-derivative period. This has not been done in any of Indian studies.
The paper is organized as follows. In section II the available literature on asymmetric volatility and risk-return relationship is reviewed. Section III presents the research methodology which talks about usage of various techniques and models to establish the results. Subsequently, section IV has data and empirical results. Some concluding remarks are offered in the final section followed by references.
II. LITERATURE REVIEW
The GARCH-M model has been used in several U.S and U.K studies (Baillie and DeGennaro, 1990; Chou, 1988; French, Schwert and Stambaugh, 1987; and Poon and Taylor, 1992) to examine the relationship between risk and returns. The findings in the extant literature about the relationship are in general mixed. For example, French, Schwert and Stambaugh (1987), Chou (1988), Campbell and Hentschel (1992), Bansal and Lundblad (2002), Bali and Peng (2006), Yakob and Sarath Delpachitra (2006) and Leon et al. (2007) found a positive relationship between conditional excess returns and conditional variance. In contrast, Black (1976), Cox and Ross, (1976), Fama and Schwert (1977), Bree, Glosten and Jagannathan (1989), Nelson (1991), and Bekaert and Wu (2000) found a negative association. Glosten et al. (1993), Harvey (2001), and Turner et al. (1989) found both a positive and a negative relation depending on the method used. Baillie and DeGennaro (1990) found it to be insignificant in seven out of their eight specifications. Fraser and Power (1997) reported that in none of nine emerging markets were the coefficients significant, indicating the lack of a trade-off. Some researchers have tried to explain these mixed findings, they showed that the theoretical inter-temporal mean variance trade off is not necessarily positive (Abel, 1988; Backus and Gregory, 1993).
Apart from GARCH-M there are many alternative methods which have been used by researchers. Campbell (1987), Harvey (1991), and Whitelaw (1994) used instrumental variable specification for conditional moments and found mixed results on the risk-return trade off. Pagan and Hong (1991) used non-parametric techniques and found a weak negative relationship, but Harrison and Zhang (1999) found the relationship is significantly positive at longer horizons. Ghysels, Santa-Clara, and Valkanov (2005) employed a high-frequency measure of market volatility outside of the GARCH parametric setting, and uncovered a positive relationship. Whitelaw (2000) documented a negative unconditional link between the mean and variance using a regime-switching specification. Scruggs (1998) and Guo and Whitelaw (2003) documented a positive trade off within specifications that facilitate hedging demands. However, Scruggs and Glabadanidis (2003) found that this partial relationship is not robust across alternative volatility specifications.
There have been few studies in Indian context, some found significant risk-return trade-off and CAPM was applicable while others found it unsuitable. Dhankar and Kumar (2006) applied Market Index model and reported high positive correlation between portfolio return and risk, also signifying that portfolio non-market risk declines with diversification. Sihag (2008) explored the contributions of Kautilya, who wrote the Arthashastra during the fourth century BCE. Kautilya considered risk-return trade-offs in making choices involving risky situations. Although he was not aware of the terms, such as portfolio balancing, diversification, mean-variance approach, the relative-risk aversion, absolute risk-aversion, risk premium, and expected or unexpected utility theory but he did use some of these concepts in formulating various economic policies. Selvam & Jeyachitra (2009) measured the relationship between risk and returns by applying CAPM. The study found that there was high positive correlation between systematic risk and expected returns and CAPM is very much applicable to Indian Stock Market. Contrary to this, there are Indian studies which provide evidence against the CAPM hypothesis (Basu & Chawla, 2010; Choudhary & Choudhary, 2010; Peer Mohamed & Abirami Devi, 2004). (Karmakar, 2007) reported an evidence of time varying asymmetric volatility, however, he could not find significant relation between risk and return. Looking at the ambiguous results it is imperative to re-examine the issue.
III. RESEARCH METHODOLOGY
The Nifty return series is calculated as a log of first difference of daily closing price i.e.,
[R.sub.t] = ln([P.sub.t]/[P.sub.t-1])
Where, [R.sub.t] is the daily log return on Nifty index for time t. [P.sub.t] Refers to the closing price at 't' and [P.sub.t-1] refers to the corresponding price in the period t-1.
A preliminary analysis is done by using descriptive statistics. Further, a time series graph of daily returns is plotted to see if there is any change in the behaviour of the return series. It may point to volatility clustering and the fact that the stock index returns distribution is not normally distributed. After confirming volatility clustering an Adf test is run on the series for presence of unit root. This is done to check if the series is stationary or not. The results of Adf test are shown in (table nr. 1)
Ordinary least-squares regression model assumes constant error variance called homoskedasticity. If the error variance is not constant, the data are said to be heteroskedastic which causes the OLS estimates to be inefficient. Models that take into account the changing variance can make more efficient use of the data. Hence ARCH/GARCH family of models are more suitable for studying the volatility. As variance (or standard deviation) is often used as a risk measure in risk management systems, the risk-return relationship in Indian capital market has been studied using GARCH-M, and three asymmetric models: TGARCH-M, EGARCH-M and PGARCH-M. First we have used the full period of two decades from 1990-2010 and then we have divided it into two sub-periods of a decade each around introduction of derivatives in India in 2000. The pre-derivative period runs from 1990-2000 and post-derivative period from 2000-2010. We have studied the effect of Asian crisis in pre-derivative period and that of Sub-prime crisis in post-derivative period using dummy variables. If the coefficient of the dummy variable is statistically significant then the crisis had an impact on return and volatility of the spot market.
In full period analysis we take a complete view of the environment by using lagged nifty return, lagged S&P500 return and dummyfut variable (it takes 0 value before derivatives and 1 value after derivatives) in the mean equation. The lagged S&P500 returns represent the impact of world wide price movements on volatility of Indian spot market. The dummyfut variable is used to study the impact of futures on volatility but here we have used it to get significant value of risk-return parameter. We saw that if this variable is not used we are not able to get significant value of the risk-return parameter even at higher lags. The variance equation also has the dummyfut variable. Hence following conditional mean and volatility equations of GARCH-M model are estimated
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
When r = 1, [[sigma].sup.2r.sub.t] denotes the conditional variance of the return [R.sub.t] given information up to time t-1, i.e., [[sigma].sub.t] = Var([R.sub.t]/[I.sub.t-1]). When r = 1/2, [[sigma].sup.2r.sub.t] becomes the conditional standard deviation. The term a in equation (8) is comparable to the risk-free return in the CAPM, and then f [[sigma].sup.2r.sub.t] represents the market risk premium for the expected volatility.
The trade-off parameter f is interpreted as the coefficient of relative risk aversion by Merton (1980) and Campbell and Hentschel (1992). Engle, Lilien and Robins (1987) show that the sign and the magnitude of this parameter depends on utility functions of the agents and the supply conditions of the assets. Hence, based on these characteristics, f can take a positive, a negative, or a zero value. The GARCH-M model has an advantage over the GARCH specification. The basic GARCH model is based on the implicit assumption that the average risk premium is constant for the sample period. The GARCH-M specification relaxes this restriction by allowing the velocity feedback effect to become operational. In this framework, when f is statistically significant, volatility [[sigma].sub.t] does contribute to the risk premium so that the premia may differ between periods of relative instability and periods of tranquility.
To assess the impact of Asian crisis in pre-derivative and that of Subprime crisis in post-derivative period we add their respective dummies in the return and volatility equation in place of dummyfut in equation (1) and (2).
To study the relation between asymmetric volatility and return we also use the EGARCH-M model which is a variation of EGARCH model proposed by Nelson (1991). This model is based on a logarithmic expression of the conditional variability. This implies that the leverage effect is exponential, rather than quadratic, and that forecasts of the conditional variance are guaranteed to be nonnegative. The mean equation of EGARCH-M is same as equation (1) and the variance equation augmented with dummyfut is as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
The presence of leverage effect can be tested by the hypothesis that [[gamma].sub.i] < 0. The impact is asymmetric if [[gamma].sub.t] <> 0.
TGARCH-M model is based on the Threshold ARCH (TARCH) method
introduced by Glosten, Jagannathan and Runkle (GJR, 1993) and Zakoian (1994). GJR-GARCH has been considered the best in estimating the impact of positive and negative shocks on volatility (Engle and Victor, 1993). For the TGARCH-M model the generalized specification for the conditional variance is given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
where [I.sub.t] = 1 if [[epsilon].sub.t] < 0 and 0 otherwise. In this model, good news, [[epsilon].sin.t-i] > 0, and bad news, [[epsilon].sub.t-i] < 0 , have differential effects on the conditional variance; good news has an impact of [[alpha].sub.t], while bad news has an impact of [[alpha].sub.i] + [[gamma].sub.i]. If [[gamma].sub.t] > 0, bad news increases volatility, and we say that there is a leverage effect for the i-th order. If [[gamma].sub.i] <> 0, the news impact is asymmetric.
Taylor (1986) and Schwert (1989) introduced the standard deviation GARCH model, where the standard deviation is modeled rather than the variance. This model, along with several other models, is generalized in Ding et al. (1993) with the Power ARCH specification. In the power ARCH model, the power parameter [delta] of the standard deviation can be estimated rather than imposed, and the optional parameter y is added to capture asymmetry of upto order r. The variance equation of Power-in-Mean GARCH model which is derived from this Power ARCH specification is as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
where [delta] > 0, [absolute value of [[gamma].sub.t] <=1 for i = 1, ..., r, [[gamma].sub.t] = 0 for all i > r, and r <= p.
The symmetry model sets [[gamma].sub.t] = 0 for all i. If [delta] = 2 and [[gamma].sub.t] = 0 for all i, the PARCH model is simply a standard GARCH specification. The asymmetric effect is present if [gamma] <> 0.
IV. DATA AND EMPIRICAL RESULTS
We have taken daily closing prices of S&P CNX Nifty index from the website of National stock exchange of India www.nseindia.com. The total period of two decades runs from July 3, 1990 to November 30, 2010, the prederivative period from July 3, 1990 to June 9, 2000 and the post-derivative period goes from June 12, 2000 to November 30, 2010. S&P500 is widely regarded as the best single gauge of the US equities market, this world-renowned index includes a representative sample of 500 leading companies in leading industries of the US economy. The daily data on S&P 500 index of US have been obtained from yahoo finance website. Eviews 7 econometrics package is used for analysis of data.
The distribution for the total period of two decades show that mean of return is positive that means the price series has increased over the period. The returns are negatively skewed indicating that there is higher probability of earning returns greater than the mean. The kurtosis is higher than 3 so returns are leptokurtic and distribution is not normal. This is further confirmed by Jarque Bera test. The values of Q(36) and [Q.sup.2](36) test statistic show that there is serial correlation in both Nifty returns and the squared returns at all lags suggesting the presence of volatility clustering in the return series.
[FIGURE 1 OMITTED]
(Fig. no. 1) shows volatility clustering in daily Nifty returns. In volatility clustering, large changes tend to follow large changes, and small changes tend to follow small changes. The changes from one period to the next are typically of unpredictable sign.
The least square test was performed to check for ARCH effect in residuals. The null of No ARCH effect was strongly rejected at 1%. Based on this the risk-return parameter was evaluated first using the GARCH-M model. Next we examined the relation between asymmetric volatility and the returns using three models: TGARCH-M, EGARCH-M and PGARCH-M.
Risk-return relationship during full period of 20 years.
The results of applying all the four models are as follows:
We have used GED distribution as the risk-return parameter and other variables are significant under this distribution, likelihood ratios are very high. This all shows that GARCH and the three asymmetric models are a good fit for this data series. The [alpha] and [beta] parameters determine the short-run dynamics of the resulting volatility time series, if [alpha] + [beta] < 1, the GARCH process is stationary. We can see from the results in (table nr. 2) that risk-return parameter is insignificant at lag 1 for all the models and only at higher lags this value becomes significant. We also had to reduce the observations from 4720 to 4665 to obtain this value. Effectively a period of 2 and half months from September 15 to November 30, 2011 is not taken.
Mean Equation: The risk-return parameter is positive and significant at higher lags, this indicates that there is positive relation between risk and return as postulated by CAPM theory. The coefficient of lagged Nifty and lagged S&P500 returns are positive which shows that impact of both on returns is positive with S&P500 being more forceful. Dummyfut is also positive here indicating that introduction of future had a positive effect on returns.
Variance Equation: [alpha] < [beta] which implies that impact of old news is much more than recent news, i.e., volatility is persistent in nature. [gamma], the leverage coefficient efficiently captures the asymmetric effect in all the three models. Dummyfut is showing negative values implying that future trading has led to a decrease in volatility. Likelihood ratios are highest and AIC, SC and H-QC values are minimum in case of TGARCH-M and PGARCH-M models. The power parameter in PGARCH-M model has been set to be 2.
Risk-return relationship during pre-derivative period of 10 years.
The results of applying all the four models in this period are as follows:
Here we have used T distribution to obtain significant values of risk-return parameter. In this period also risk-return parameter is insignificant at lag 1 for all the models and only at higher lags this value becomes significant. Again we had to take the observations from 13 to 2156 out of a total of 2195 to obtain significant value of risk-return parameter. Effectively a period of 2 months is reduced before introduction of derivatives in 2000.
Mean Equation: The risk-return parameter is positive and significant at higher lags. The coefficient of lagged Nifty and lagged S&P500 returns are positive which show that both are increasing the current Nifty return with Nifty having more impact. DummyAsianCrisis is negative indicating that the crisis reduced the returns but the p-values show that it is insignificant.
Variance Equation: [alpha] < [beta] implies that old news has much more effect than recent news, i.e., volatility is highly persistent in nature. We can see from above results that [gamma], the leverage coefficient, is significant at higher lags only that too with TGARCH-M and PGARCH-M models, it is insignificant with EGARCHM model. The positive value of [gamma] in the two models shows presence of leverage effect in the market during this period. DummyAsianCrisis is positive and significant implying that crisis increased the volatility of Nifty returns. Likelihood ratios are again highest and AIC, SC and H-QC values are minimum in case of TGARCH-M and PGARCH-M models. The power parameter in PGARCH-M model has been set to be 2.
Risk-return relationship during post-derivative period of 10 years.
The results of applying all the four models in this period are as follows:
We can see from results shown in (table nr. 4) that the risk-return parameter is significant at lag 1 under GED distribution. This time we had to take observations from 91 to 2516 out of 2526, this means we reduced a period of approximately 4 months immediately after introduction of derivatives. This implies that market needed some time to mature after future trading started in India to give a significant risk-return parameter.
Mean Equation: The risk-return parameter is positive and significant at lag 1 only showing a positive relation between risk and return. The coefficient of lagged Nifty and lagged S&P500 returns are positive which show that both are increasing the current Nifty return with S&P500 having more impact in this period. DummySubprimeCrisis is negative and highly significant indicating that the crisis reduced the returns.
Variance Equation: [alpha] < [beta] implies that old news has much more effect than recent news, i.e., volatility is highly persistent in nature. [gamma], the leverage coefficient, is significant with all the three asymmetric models showing presence of leverage effect in the market during this period. DummySubprimeCrisis is positive and highly significant implying that crisis increased the volatility of Nifty returns. Likelihood ratios are again highest and AIC, SC and H-QC values are minimum in case of TGARCH-M and PGARCH-M models. The power parameter in PGARCH-M model has been set to be 2.
Comparison of Pre-derivative period with post-derivative period.
The risk-return parameter is higher in pre-derivative period compared to post-derivative period. This means for a fixed amount of risk the return was slightly more before future trading started in India. As indicated by dummies the impact of Sub-prime crisis was more severe than Asian crisis. Decrease in return and rise in volatility is much sharper during Sub-prime crisis.
We estimated the standardized residuals and the squared standardized residuals and computed the Ljung-Box (Q) statistic to test the null hypothesis of no autocorrelation up to order 36 for all the three periods. In all periods the Q statistics indicated serial correlation at some lags in the standardized residuals but the [Q.sup.2] statistics suggested no serial correlation in the squared standardized residuals at any lag for all the models. Only in pre-derivative period in case of EGARCH-M model there is serial correlation in squared residuals after lag 10. This means that all the models are adequately describing the volatility process and higher lags are not needed to capture the autocorrelation.
In this study we investigated whether there is asymmetric volatility in Indian stock market and with this what is the relation between risk and return. We found evidence of time-varying volatility which exhibits clustering and high persistence. During full period of two decades, the results showed that the symmetric GARCH-M and the three asymmetric models do not give significant value of risk-return parameter at lag 1. The GARCH-M(1,5), TGARCH-M(1,7) and PGARCH-M(1,7) models give positive value of risk-return parameter at a significance of 10% under GED distribution. However, the parameter is not significant with EGARCH(3,7) model. Since the volatility is asymmetric the TGARCH-M(1,7) and PGARCH-M(1,7) models are the best fitted models.
During pre-derivative period again the models do not give significant value at lag 1. GARCH-M(1,5) and EGARCH-M(1,9) give positive value at a significance of 10% and TGARCH-M(1,7) and PGARCH(1,7) give positive value at a significance of 5%. Since we will consider asymmetric volatility and likelihood ratios as the model selection criteria so TGARCH(1,7) and PGARCH(1,7) models are the best fitted models. DummyAsianCrisis evaluated during this period shows that it decreased the return and increased the volatility.
Finally during the post-derivative period the models gave significant value of risk-return parameter at lag 1 and the value is positive and significant at 10% in all cases. The TGARCH-M(1,1) and PGARCH-M(1,1) are best fitted models based on highest likelihood ratios and minimum AIC, SC and HQ-C criteria. DummySubprimeCrisis evaluated during this period decreased the return and increased the volatility.
The findings of the study are that volatility is time-varying and is an asymmetric function of past innovations, rising sharply during crisis period. We get evidence of positive and significant risk-return trade-off. This implies that CAPM holds in explaining the risk-return relationship in India. The positive values indicate that investors are compensated for assuming high risk. In last few decades there has been substantial change in market environment in India as a result of financial liberalization, introduction of futures trading, financial and technical innovations and integration with global market. Hence these findings are useful for financial decision making and thereby help build a more effective market operation system in India. Since no work has been done on this subject on individual stocks, the work in this paper can be extended to individual stocks.
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SUNITA NARANG *
University of Delhi, India
Prof. V. K. BHALLA **
University of Delhi, India
* Correspondence to: Sunita Narang, Department of Computer Science, Acharya Narendra Dev College, University of Delhi, Delhi - 110019, India.
** Correspondence to: Prof. V. K. Bhalla, Faculty of Management, North Campus, University of Delhi, Delhi-110007, India.
Table 1: Descriptive statistics Total Period (1990-2010) Mean 0.000641 Std. Dev. 0.018698 Skewness -0.156502 Kurtosis 12.750760 Jarque-Bera 18721.75 (0.00) Q(36) 102.64 (0.00) [Q.sup.2] (36) 1146.5 (0.00) Unit Root Test ADF t-stat: Constant, no trend -63.53590 (0.00) Constant, trend -63.53172 (0.00) PP t-stat: Constant, no trend -63.55148 (0.0001) Constant, trend -63.54657 (0.00) Observations 4721 Authors calculations with p-values in brackets. Table 2: Risk-return trade-off during full period 1990-2010-20 year data (No. of obs = 4720) GARCH- GARCH- TGARCH- TGARCH- M(1,1) M(1,5) M(1,1) M(1,7) Distribution GED dist. GED dist. GED dist. GED dist. used Obs. used 4665 4665 4665 4665 Mean Eq. Sqrt(GARCH) 0.068693 0.089835 0.062270 0.077237 (0.1478) (0.0565) (0.1870) (0.0925) C -0.000915 -0.001246 -0.000983 -0.001243 (0.2694) (0.1281) (0.2383) (0.1218) Nifty(-1) 0.089513 0.088478 0.093278 0.090820 (0.00) (0.00) (0.00) (0.00) Snp500(-1) 0.190466 0.191400 0.188675 0.191309 (0.00) (0.00) (0.00) (0.00) Dummyfut 0.001290 0.001382 0.001309 0.001380 (0.0021) (0.00) (0.0021) (0.0011) Variance Eq. C 1.31E-05 1.31E-05 1.69E-05 1.48E-05 (0.00) (0.00) (0.00) (0.00) Alpha 1 0.114802 0.124146 0.079927 0.073830 (0.00) (0.00) (0.00) (0.00) Alpha 2 Alpha 3 Beta 1 0.855643 0.636557 0.839138 0.578637 (0.00) (0.00) (0.00) (0.00) Beta 2 0.770270 1.050344 (0.00) (0.00) Beta 3 -0.659677 -0.699133 (0.00) (0.00) Beta 4 -0.354649 -0.824443 (0.0026) (0.00) Beta 5 0.454101 0.709612 (0.00) (0.00) Beta 6 0.289734 (0.0285) Beta 7 -0.251430 (0.0002) Gamma 0.087679 0.082580 (0.00) (0.00) Dummyfut -4.29E-006 -4.32E-006 -6.85E-06 -5.98E-006 (0.0190) (0.0251) (0.0012) (0.0022) Dist. DOF 1.267841 1.278648 1.270541 1.293551 (0.00) (0.00) (0.00) (0.00) Log likelihood 12750.25 12757.81 12759.81 12769.72 AIC -5.463227 -5.464757 -5.466899 -5.468577 SC -5.449403 -5.445403 -5.451692 -5.445076 H-QC -5.458365 -5.457950 -5.461550 -5.460311 Q(36) 55.978 55.648 60.986 60.257 (0.018) (0.019) (0.006) (0.007) [Q.square.2) 2.7 2.391 2.851 2.808 (36 (1.00) (1.00) (1.00) (1.00) 1990-2010-20 year data (No. of obs = 4720) EGARCH- EGARCH- PGARCH- PGARCH- M(1,1) M(3,7) M(1,1) M(1,7) Distribution GED dist. GED dist. GED dist. GED dist. used P = 2 P = 2 Obs. used 4665 4665 4665 4665 Mean Eq. Sqrt(GARCH) 0.045929 0.064825 0.062341 0.079478 (0.3233) (0.1237) (0.1865) (0.0810) C -0.000803 -0.000836 -0.000984 -0.001283 (0.3326) (0.2566) (0.2376) (0.1089) Nifty(-1) 0.088743 0.081257 0.093279 0.090795 (0.00) (0.00) (0.00) (0.00) Snp500(-1) 0.189948 0.198191 0.188680 0.191457 (0.00) (0.00) (0.00) (0.00) Dummyfut 0.001422 0.001363 0.001309 0.001375 (0.0007) (0.0008) (0.0021) (0.0011) Variance Eq. C -0.529137 -1.328677 1.69E-05 1.47E-05 (0.00) (0.00) (0.00) Alpha 1 0.219823 0.255608 0.119716 0.110903 (0.00) (0.00) (0.00) Alpha 2 0.307525 (0.00) Alpha 3 0.238584 (0.00) Beta 1 0.954330 -0.455604 0.839170 0.548296 (0.00) (0.00) (0.00) (0.00) Beta 2 0.434228 1.094302 (0.00) (0.00) Beta 3 0.972035 -0.684751 (0.00) (0.00) Beta 4 0.012702 -0.867084 (0.8408) (0.00) Beta 5 -0.319435 0.695261 (0.00) (0.00) Beta 6 0.132980 0.343995 (0.0947) (0.0022) Beta 7 0.131699 -0.276218 (0.00) (0.00) Gamma -0.054354 -0.006913 0.183307 0.187092 (0.00) (0.0024) (0.00) (0.00) Dummyfut -0.023566 -0.042848 -6.85E-06 -5.98E-06 (0.0022) (0.0391) (0.0012) (0.0021) Dist. DOF 1.254341 1.262301 1.270425 1.294885 (0.00) (0.00) (0.00) (0.00) Log likelihood 12749.66 12757.91 12759.83 12769.54 AIC -5.462548 -5.462652 -5.466910 -5.468499 SC -5.447341 -5.436386 -5.451704 -5.444998 H-QC -5.457199 -5.453414 -5.461562 -5.460233 Q(36) 59.985 55.66 60.971 60.248 (0.007) (0.019) (0.006) (0.007) [Q.square.2) 2.172 6.385 2.853 2.833 (36 (1.00) (1.00) (1.00) (1.00) Table 2: Authors calculations with p-values in brackets Table 3: Risk-return trade-off during pre-derivative period 1990-2000-10 year data (No. of obs. = 2195) GARCH(1,1) GARCH(1,5) TGARCH(1,1) TGARCH(1,7) T dist. T dist. T dist. T dist. Distribution 13 2156 13 2156 6 2156 6 2156 used Obs. used Mean Eq. Sqrt 0.095561 0.137575 0.084537 0.168483 (GARCH) (0.2279) (0.0743) (0.2866) (0.0275) C -0.001080 -0.001729 -0.000926 -0.002298 (0.3935) (0.1592) (0.4661) (0.0595) Nifty(-1) 0.154844 0.156111 0.155719 0.155456 (0.00) (0.00) (0.00) (0.00) Snp500(-1) 0.105588 0.105682 0.105211 0.099962 (0.0032) (0.0029) (0.0032) (0.0040) DummyAsian -0.001036 -0.001312 -0.001033 -0.001381 Crisis (0.2444) (0.1406) (0.2438) (0.1156) Variance Eq. C 7.57E-06 9.10E-06 8.11E-06 9.79E-06 (0.0011) (0.0012) (0.0014) (0.0004) Alpha 1 0.078646 0.097813 0.080178 0.077846 (0.00) (0.00) (0.00) (0.00) Alpha 2 Alpha 3 Alpha 4 Beta 1 0.897737 0.622376 0.890765 0.560095 (0.00) (0.00) (0.00) (0.00) Beta 2 0.865483 1.210416 (0.00) (0.00) Beta 3 -0.745608 -0.871198 (0.00) (0.00) Beta 4 -0.524452 -0.958963 (0.00) (0.00) Beta 5 0.655316 0.927076 (0.00) (0.00) Beta 6 0.315280 (0.0666) Beta 7 -0.304436 (0.0007) Beta 8 Beta 9 Gamma 0.011802 0.035114 (0.5922) (0.0995) DummyAsian 5.28E-06 7.55E-06 5.44E-06 6.67E-06 Crisis (0.0979) (0.0577) (0.1114) (0.0783) 5.836781 5.912687 5.762051 5.841645 Dist. DOF (0.00) (0.00) (0.00) (0.00) Log likelihood 5697.16 5703.12 5712.75 5720.02 AIC -5.305182 -5.307016 -5.301486 -5.302668 SC -5.278734 -5.269989 -5.272472 -5.257828 H-QC -5.295505 -5.293468 -5.290872 -5.286264 Q(36) 46.238 47.44 48.563 50.529 (0.118) (0.096) (0.079) (0.055) [Q.sup.2](36) 41.201 41.806 40.806 41.641 (0.254) (0.233) (0.267) (0.239) [Q.sup.2](10) 1990-2000-10 year data (No. of obs. = 2195) EGARCH(1,9) EGARCH(1,9) PGARCH(1,1) PGARCH(1,7) T dist. T dist. T dist. T dist. P = 2 P = 2 Distribution 13 2156 13 2156 13 2156 6 2156 used Obs. used Mean Eq. Sqrt 0.086481 0.134161 0.094406 0.156936 (GARCH) (0.2428) (0.0606) (0.2350) (0.0319) C -0.001013 -0.001701 -0.001097 -0.002094 (0.3959) (0.1343) (0.3880) (0.0700) Nifty(-1) 0.153483 0.158198 0.155776 0.156393 (0.00) (0.00) (0.00) (0.00) Snp500(-1) 0.099650 0.103569 0.106126 0.100027 (0.0049) (0.0031) (0.0030) (0.0035) DummyAsian -0.000861 -0.001043 -0.001060 -0.001387 Crisis (0.3110) (0.2155) (0.2326) (0.1130) Variance Eq. C -0.334897 -0.533106 8.12E-06 1.02E-05 (0.00) (0.00) (0.0009) (0.0005) Alpha 1 0.178901 0.297157 0.082529 0.100158 (0.00) (0.00) (0.00) (0.00) Alpha 2 Alpha 3 Alpha 4 Beta 1 0.975513 0.629110 0.892608 0.554867 (0.00) (0.00) (0.00) (0.0001) Beta 2 0.184404 1.193991 (0.00) (0.00) Beta 3 -0.096765 -0.848143 (0.1182) (0.00) Beta 4 0.300977 -0.936084 (0.00) (0.00) Beta 5 -0.129658 0.883798 (0.0618) (0.00) Beta 6 0.184771 0.298058 (0.00) (0.0856) Beta 7 0.057567 -0.275350 (0.3769) (0.0101) Beta 8 -0.723149 (0.00) Beta 9 0.555219 (0.00) Gamma -0.004213 -0.023323 0.047259 0.085688 (0.7780) (0.2122) (0.4644) (0.1011) DummyAsian 0.008873 0.018593 5.53E-06 7.41E-06 Crisis (0.3241) (0.2115) (0.0986) (0.0685) 5.744201 5.889829 5.806580 5.790566 Dist. DOF (0.00) (0.00) (0.00) (0.00) Log likelihood 5697.52 5711.13 5697.43 5720.23 AIC -5.304587 -5.309822 -5.304501 -5.302867 SC -5.275495 -5.259571 -5.275408 -5.258026 H-QC -5.293943 -5.291436 -5.293856 -5.286463 Q(36) 45.653 45.289 46.773 50.791 (0.130) (0.138) (0.108) (0.052) [Q.sup.2](36) 55.255 55.189 42.499 41.73 (0.021) (0.021) (0.211) (0.236) [Q.sup.2](10) [Q.sup.2] 6.0759 (15)-24.117 (0.809) (0.063) Table 3: Authors calculations with p-values in brackets. Table 4: Risk-return trade-off during post-derivative period 2000-2010-10 year data (No. of obs. = 2526) GARCH(1,1) TGARCH(1,1) Distribution used GED dist. GED dist. Obs. used 91-2519 91-2519 Mean Eq. Sqrt(GARCH) 0.120127 (0.0840) 0.124848 (0.0653) C -9.17E-05 (0.9194) -0.000385 (0.6593) Nifty(-1) 0.031736 (0.1097) 0.040041 (0.0516) Snp500(-1) 0.212698 (0.00) 0.213748 (0.00) Dummy Subprime Crisis -0.007804 (0.0038) -0.008175 (0.0021) Variance Eq. C 1.27E-05 (0.00) 1.69E-05 (0.00) Alpha 1 0.136328 (0.00) 0.031709 (0.0784) Beta 1 0.814455 (0.00) 0.784666 (0.00) Gamma 0.216836 (0.00) Dummy Sub-prime Crisis 6.67E-05 (0.0839) 9.97E-05 (0.0246) Dist. DOF 1.224139 (0.00) 1.247045 (0.00) Log likelihood 6897.7 6916.36 AIC -5.671220 -5.685764 SC -5.647362 -5.659519 H-QC -5.662546 -5.676222 Q(36) 40.852 (0.266) 47.17 (0.101) [Q.sup.2](36) 1.3247 (1.00) 1.607 (1.00) 2000-2010-10 year data (No. of obs. = 2526) EGARCH(1,1) PGARCH(1,1) Distribution used GED dist. GED dist. P = 2 Obs. used 91-2519 91-2519 Mean Eq. Sqrt(GARCH) 0.111627 (0.1090) 0.124770 (0.0654) C -0.000236 (0.7961) -0.000384 (0.6597) Nifty(-1) 0.037239 (0.0630) 0.040078 (0.0514) Snp500(-1) 0.213958 (0.00) 0.213806 (0.00) Dummy Subprime Crisis -0.008333 (0.0012) -0.008171 (0.0021) Variance Eq. C -0.900265 (0.00) 1.69E-05 (0.00) Alpha 1 0.206713 (0.00) 0.114499 (0.00) Beta 1 0.913407 (0.00) 0.784493 (0.00) Gamma -0.142932 (0.00) 0.474142 (0.00) Dummy Sub-prime Crisis 0.163114 (0.00) 9.98E-05 (0.0246) Dist. DOF 1.246630 (0.00) 1.247556 (0.00) Log likelihood 6913.13 6916.41 AIC -5.683103 -5.685801 SC -5.656858 -5.659556 H-QC -5.673561 -5.676259 Q(36) 48.074 (0.086) 47.180 (0.101) [Q.sup.2](36) 1.5190 (1.00) 1.6069 (1.00) Table 4: Authors calculations with p-values in brackets.
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|Title Annotation:||National Stock Exchange, India|
|Author:||Narang, Sunita; Bhalla, V.K.|
|Publication:||Annals of the University of Bucharest, Economic and Administrative Series|
|Date:||Jan 1, 2011|
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