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M. T. Raju, Anirban Ghosh April 2004
Working Paper Series No. 8
Stock Market Volatility – An International Comparison M. T. Raju, Anirban Ghosh Working Paper Series No. 8 The views expressed in this paper are those of the authors and do not necessarily reflect those of the Securities and Exchange Board of India. We sincerely thank Shri G. N. Bajpai, Chairman, SEBI for his unlimited support and encouragement in conducting research work. But for him, it would not have been possible to bring out this paper timely. We also thank many of our colleagues for their comments and suggestions.
Foreword Acknowledgement SEBI Abstract 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Stock Market Volatility: An International Comparison Methodology Analysis of Results Inter and Intra-day Volatility Intra-day Volatility and Developed Capital Markets Emerging Capital Markets Indian Market High and Low Volatility (Volatility Transmission) Extreme Volatility Analysis (India) Return Squared Volatility Return Squared Analysis Conclusion and Recommendation References SEBI Working Paper Series (i) (iii) (v) (vii) 1 4 8 11 12 13 13 14 15 15 16 17 19
Foreword During the past few years Indian Capital Market has undergone metamorphic reforms. Every segment of Indian Capital Market viz primary and secondary markets, derivatives, institutional investment and market intermediation has experienced impact of these changes. Our market, today, is being recognized as one of the most transparent, efficient and clean markets. Several techniques /instruments are used by academicians, policy makers, practitioners and investors to test the extent of efficiency of the market. In this research paper, an attempt has been made to analyse distributional characteristics of stock indices in India and compare them with some of the mature as well as emerging capital markets around the globe. Return (Mean), Volatility (Standard Deviation), Skewness and Kurtosis are computed for various indices for different lengths of periods. These, known as first, second, third and fourth order moments of a distribution respectively, provide a picture of Indian stock price movements. In the recent past there have been perceptions that volatility in the market has gone up; Inter and Intra-day volatility. News items and some clinical research papers also provided figures to evidence this argument. SEBI undertook a comprehensive and deep analysis of volatility by using several statistical techniques to measure and analyse it. 18 countries covering almost all continents- developed as well as emerging markets and young and old markets- have been analysed. The results show that the volatility has not gone up much in the recent past as it has been perceived. Indian stock market provides a very high rate of return and comparatively moderate volatility. Efficiency of Indian market appear to have improved in the past few years owing to contraction in settlement cycles, introduction of derivative products, improvement in corporate governance practices etc,. Stock market return exhibit informational efficiency and approximates to normal distribution. I heartily extend my congratulations to the Research Department for bringing out this paper. I also expect it to conduct further study at individual stock level, to find out behaviour of idiosyncratic volatility which will be of great help to various policy makers.
G.N.Bajpai Chairman Securities and Exchange Board of India
April 19, 2004 Mumbai
The authors of the paper are immensely grateful to Shri G.N. Bajpai, Chairman, SEBI for his unstinting guidance and support throughout the project. He has been a great source of inspiration and motivation to all of us. Shri P. K. Mishra, Executive Director, Research Division, SEBI has provided considerable flexibility and freedom to complete this working paper timely. The entire team is thankful to Dr. Prabhakar Patil for his thoughtful inputs. Our sincere thanks are due to Ms. Jacinta Saldanha and Ms. Meenakshi Ramakrishnan for their sincere, adroit and untiring secretarial assistance to complete the paper in time. Shri. C. R. Unny, GM, Treasury and Accounts Division, SEBI provided all the necessary support in bringing out this publication and we thank him for the same.
SEBI was established as a statutory body on 21 February 1992. which was subsequently replaced by an Act of Parliament. 1992 enshrines the objectives of SEBI – to protect the interest of investors in securities market and to promote the development of and to regulate the securities market. The Ordinance was replaced by an Act of Parliament on 4 April 1992. The preamble of the SEBI Act. The statutory powers and functions of SEBI were strengthened through the promulgation of the Securities Laws (Amendment) Ordinance on 25 January 1995. SEBI was given statutory status and powers through an Ordinance promulgated on January 30 1992.Securities and Exchange Board of India
The Securities and Exchange Board of India (SEBI) was constituted on 12 April 1988 as a non-statutory body through an Administrative Resolution of the Government for dealing with all matters relating to development and regulation of the securities market and investor protection and to advise the government on all these matters.
Pricing of securities is supposed to be dependent on volatility of each asset. T. Indian market show less of skewness and Kurtosis.Stock Market Volatility – An International Comparison
M. Raju • Anirban Ghosh
Volatility estimation is important for several reasons and for different people in the market. volatility has not gone up. In this paper we not only extend the study period of the earlier paper but also expand coverage in terms of number of countries and statistical techniques. both provide as high a return as the US and the UK market could provide but the volatility in both countries is higher. Intra day volatility is also very much under control and has came down compared to past years. Comparatively. The third and fourth order moments exhibit large asymmetry in some of the developed markets. Amongst emerging markets except India and China. all other countries exhibited low returns (sometimes negative returns with high volatility). Indian markets have started becoming informationaly more efficient. Contrary to the popular perception in the recent past. Mature markets / Developed markets continue to provide over long period of time high return with low volatility. India with long history and China with short history.
These precipitous market wide price drops cannot always be traced to a specific news event. Amongst the main concerns. which will efficiently distribute risk? Has global financial integration led to faster transmission of volatility and risk across national frontiers? Can financial managers most efficiently manage risk under current circumstances? What role the regulators ought to play in the process? This paper would be useful in debating some/all of these issues. and the quasi-standardised status it holds in the field of finance. In segmented capital markets.
As a concept. there are some subtleties that make volatility challenging to analyse. Peters (1994) noted that stock prices and returns are cyclical. Despite the clear mental image of it. To be more meaningful. Greater this deviation.”
The issues of volatility and risk have become increasingly important in recent times to financial practitioners. which have now become endemic features of securities markets add to the concern. which are currently expressed include: . the term volatility is simply synonymous with risk: in their view high volatility is to be deplored. It measures variability or dispersion about a central tendency. Nor should th is lack of smoking gun be seen as in any way anomalous in market for assets like common stock whose value depends on subjective judgement about cash flow and resale prices in highly uncertain future. if the market crashes. The public takes a more deterministic view of stock prices.has the world’s financial system become more volatile in recent times? Has financial deregulation and innovation lead to an increase in financial volatility or has it successfully permitted its redistribution away from risk averse operators to more risk neutral market participants? Is the current wave of financial innovation leading to a complete set of financial markets.writes in his book Financial Innovation And Market Volatility …. volatility can indicate the strength or conviction behind a price move. there must be a specific reason. Merton Miller (1991) the winner of the 1990 Nobel Prize in economics . market participants. commodity and stock with world markets and existence of common players. because it means that security values are not dependable and the capital markets are not functioning as well as they should.Stock Market Volatility : An International Comparison
Peripatetic stock prices and their volatility. regulators and researchers.
To many among the general public. imperfectly predictable in the short run. particularly down moves. have given volatility a new property – that of its speedy transmissibility across markets. At a more fundamental level. The growing linkages of national markets in currency. occur. a country's volatility is a critical input in the cost of capital (Bekaert and Harvey 1995). volatility is simple and intuitive. greater is the volatility. it plays a key role in assessing the risk/return tradeoffs and forms an important input in asset allocation decisions.
. “By volatility public seems to mean days when large market movements. Since volatility is a standard measure of financial vulnerability. it is a measure of how far the current price of an asset deviates from its average past prices.
Third. especially with equity returns. behavior related to time-varying positive feedback. While idiosyncratic volatility can be eliminated in a well-diversified portfolio.and unpredictable in the long run and that they exhibit nonlinear. Typically. at the level of the investor. Those investors
. with other emerging and developed markets. many investors do not hold diversified portfolios. big up-moves. When the total volatility of individual stock is decomposed into systematic volatility and idiosyncratic volatility. it is clearly evident that idiosyncratic volatility has trended up. Return series may not be normally distributed and often tend to exhibit excess kurtosis. Nor does this paper seek to throw an insight into the existence of a possible s relationship between such variables which capture financial and economic integration as market capitalisation to GDP. It is also consistent that world factors could have an increased influence on volatility with increased market integration. Risk averse and risk neutral investors may shy away from the market with frequent and sharp price movements. Finally. individual investors may still care about the specific risk of the securities they hold. country credit risk ratings. so that extreme values are more likely than the normal distribution would suggest. frequent and wide stock market variations cause uncertainty about the value of an asset and affect the confidence of the investor. Volatility in national markets is determined by world factors and part determined by local market effects. and possibly chaotic. comparison of time-series volatility of Indian equity market. There are several reasons which prompted us to take up this study once again now. The distribution is centered at the mean and its width is determined by the standard deviation (volatility). of asymmetries in volatility under different market conditions (especially for India during pre and post reform) may shed interesting light on the evolving characteristics of Indian equity market. the normal distribution is used to characterise a series of returns. Research has also shown that capital market liberalisation policies too. It would be of interest to policy makers that the correlation between the two has been found to be positive in the case of some countries. distributional characteristics of the variance process and evidence if any. are likely to affect volatility.b). Because of wealth constraints or by choice. Bekaert and Harvey (1995) showed this using time-varying market integration parameter. This paper does not make an attempt to measure idiosyncratic volatility both at index as well as at stock levels. Such fat-tailed distributions are common with financial parameters. An understanding of the market volatility is thus important from the regulatory policy perspective. Skewness is also common. perceptions vary about the dispersions of Indian stock prices. there is a need for a comprehensive study on the volatility of Indian stock markets covering as long a period as 20 years along with intra-day volatility (to the extent data is available from a single source) and international comparison. assuming that the national markets are globally linked. Time-variation in market volatility can often be explained by macroeconomic and microstructural factors (Schwert 1989a. This paper does not reexamine any of these i sues. First. Crosssectional regressions that the volatility of individual stocks maybe related to the amount of institutional ownership. where big downmoves are typically more likely than comparable. Asset-return variability can be summarised by statistical distributions. Second.
The emerging market returns in the past have demonstrated certain distinguishing features. To some extent our choice and number of countries is limited to availability of data from the Bloomberg Service. Our research focuses particularly on return and volatilities behavior.
Existing studies of volatility across markets. have shown that the characteristics of emerging market equities are vastly different from those for developed markets’ equities.
. Moreover. correlation with developed market returns was low. Bloomberg database is used by us as the data source. Our research helps understand the time series variation and higher order moments in the volatility of equities in these markets.. whose total profits depend on total volatility instead of market volatility. average returns were higher. across markets. two popular indices viz.might feel that the risk of their portfolios has increased when idiosyncratic volatility is rising. We provide a detailed analysis of equity market volatility in 18 developed and emerging markets. while for all other countries single index is used for each country. including India. The names of the countries. Although it is important and necessary to understand and estimate volatility of individual stock level. We use the International Organisation of Securities Commission (IOSCO) classification to categorise countries into emerging and developed markets. There are six countries from developed capital markets and twelve from emerging markets including India. Idiosyncratic volatility is also important to arbitrageurs and option traders. indices and data periods are provided in the following Exhibit I. high idiosyncratic volatility could increase potential total transactions costs if investors with relatively limited means choose to achieve adequate diversification. investors looked to emerging markets for risk diversification. (Bekaert and Harvey 1995). As far as India. This is so because an increase in idiosyncratic volatility will have an important effect on increasing the number of securities one must hold to achieve reasonably “full” diversification. returns were more predictable and volatility was higher. it has not been carried out in this study owing to objectives set and time and space restrictions. BSE Sensex and S&P CNX Nifty are analysed.
I NAMES OF THE COUNTRIES. the data is not available for the entire period. either as the markets were not fully developed and hence there were no indices or the data had not been captured by Bloomberg. and cross-sectional volatility of individual stocks could have an impact on the results.EXHIBIT . Despite this limitation. Consequently. We use the standard indices with the limitation that the number of stocks in the national index. China Singapore Malaysia Thailand China Indonesia Chile Brazil Mexico South Africa Korea Taiwan India India Index S&P 500 FTSE 100 CAC 40 DAX 30 Xetra All Ordinaries Hang Seng Straits Time Kuala Lumpur Composite Stock Exchange of Thailand Shanghai Composite Jakarta Composite Chile Stock Market General IBOV MEXBOL JALSH KOSPI TWSE BSE Sensex S&P CNX Nifty Period 80:1 – 03:12 84:1 – 03:12 87:7 – 03:12 80:1 – 03:12 84:1 – 03:12 81:1 – 03:12 85:1 – 03:12 80:1 – 03:12 87:7 – 03:12 95:1 – 03:12 91:11 –03:12 91:9 – 03:12 92:1 – 03:12 92:1 – 03:12 95:6 – 03:12 81:4 – 03:12 83:10 –03:12 85:1 – 03:12 95:1 –03:12 Observations 6061 4668 4133 6023 5076 5685 4755 5905 4031 2175 2964 3079 2955 3005 2125 6373 5630 4286 2221
Bloomberg usually chooses the most popular indices to describe the movements in stock prices in the respective markets. we choose the principally recognised stock price index of each country and obtain the time series data for a 24 year period from 1980:1 2003:12. relative weights. by using a standard conversion method provided in the Bloomberg system. the US dollar. Among these indices for each market. The analysis and conclusions are not affected by this shortcoming as we study each country separately and on an annual basis. INDICES AND DATA PERIOD
Country USA UK France Germany Australia Hong Kong. We begin by analysing the time series of volatility. For some countries. asset concentration. the data points are not uniform for all the countries. Index series are published in the currency of local markets. the study would still give a strong insight into the volatility of the markets. For crosscountry comparisons. As a first step. we calculate returns using logarithmic method as follows:
. all indices are converted into one common currency. We use standard deviation as a proxy for variability in stock prices.
and compute third and fourth order moments to infer more information about the patterns of price returns.e. arithmetic mean.
We also use the above formula i. We then took the square root of this average r 2 to arrive at the volatility figure. go beyond the first and second order moments. σ = k 1 / n∑ log( H t / Lt ) 2 (4)
. in order to provide additional information on intra-day (high-low) volatility we computed it K = 1 also. statistically. Therefore. for estimation of intraday volatility. After calculating the square root of the average r 2 in the method described above we sorted the top 5 percent of the same (i. We calculated square root of the average r 2 for each year to capture the absolute changes in volatility and this is called “return squared volatility”. square root of the average r 2 ) and compared this top 5 percent of the observations of a particular year with the square root of the average r 2 calculated for the whole year. which uses intra-day highs and lows.e. it is correct.601 scales down volatility although. skewness and excess kurtosis are computed as discussed later.601 and Ht and Lt denote intra-day high and low respectively. most asset pricing models are based on continuous time the extreme value estimators are more efficient.
We use the following standard formula for computing standard deviation. We therefore. Here r is the daily log-normal return and is defined as rt = ln ( I t / I t−1 ) * 100 (5) where It is the closing value of the index at time period t. We calculated daily r 2 and took an average of r 2 for the whole year. Past cross-country studies have indicated non-normality of stock returns. Next. standard deviation. with k = 1 to measure high-low volatility. Since.
(1 n − 1)∑ (rt
We use Parkinson’s (1980) model.
σ = k 1 n ∑ log (H t Lt )
where k = 0. This volatility measure is referred to as high-low volatility in our paper usage of factor 0. We use the following Parkinson model to estimate intra-day volatility.r t = ln
 It   I    t −1 
where rt and It indicate return and index value respectively at time ‘t’.
low. high. close and open respectively. σ = 1 n ∑ (1 2)[log ( H t Lt )]2 − [2 log( 2) − 1] [log( Ct / Ot ) ]2
where Ht . low and close. and Ot denote intra-day high. This volatility measure is referred to as open-close volatility in our paper. Ct .We use the Garman and Klass (1980) estimator which uses four intra-day variation statistics of open. (6)
. The following model is used for this estimator. Lt .
the starting year is not 1980 owing to non-availability of data for various reasons that include : a) The markets might have started stock exchanges in the later period. two distributions have the same mean and variance. and s = standard deviation
A comparison of a normal distribution with a distribution exhibiting positive excess kurtosis reveals the following points. Bloomberg. and s = standard deviation
Excess Kurtosis We measure the excess kurtosis by the following model 2 Ku = n 2 (n − 1)(n − 2)(n − 3) (n + 1)m4 − 3(n + 1)m2 s 4
n = sample size m 4 = fourth moment about the mean. m 3 = third moment about the mean. but the positive excess kurtosis distribution is more peaked and has fatter tails. m 2 = second moment about the mean. For example. At the same time.
Analysis of Results Table 1 provides details of daily mean return and daily standard deviations for the sample countries over 24 year period from 1980 to 2003. For certain countries. Probability mass is added to the central part of the distribution and to the tails of the distribution. and c) Any other reason. probability mass is taken from regions of the probability distribution that are intermediate between the tails and the centre. We use the following model to measure non-normality or asymmetry of equity returns.Skewness
As stated previously. It is very interesting to note what happens when we move from a normal distribution to a distribution with positive excess kurtosis. b) The source. stock returns exhibit non-normality. The effect of excess kurtosis is therefore to increase the probability of very large moves and very small moves in the value of the variable. while decreasing the probability of moderate moves. If the returns are normally distributed. might not have collected information for these countries even though stock exchanges existed. then coefficients of skewness and excess kurtosis should be equal to zero. Sk = (n 2 (n − 1)(n − 2 ))(m 3 s 3 ) (7)
where : n = sample size.
the volatility slowed down in almost all the countries which is analyzed in this sample.39 percent and France 2. Chile. This also provides evidence to indicate extent of globalization of markets. However. Indonesia.02 percent to 0.07 percent. Between the US and the UK. Germany and Australia.44 percent and 1. in fact. China. The UK provides equal average returns but high dispersion compared to the US with 0. The third largest equity market in the world reside in the UK (in terms of market capitalization).04 percent and 0.02 percent whereas the volatility was 1. in the long run daily retur n works out to 0.54 percent. both on high and low sides as well as average. From the Table 1 it is clear that these countries do exhibit low return and higher volatility compared to the US.03 percent.23 percent standard deviation.64 percent and 1. Malayasia. One significant observation is that all these countries including emerging markets countries experienced high volatility from 1997 to 2002 which indicates that there is a large co-movement in the prices of indices and in the underlaying stocks. 0.52 percent (1985) and 1.04 percent average daily returns and 1. 2001 and 2002 are the years in which many countries threw up negative returns and in these years by and large the volatilities have been higher than immediate preceding years with positive retur ns. South Korea and Taiwan all support this finding. 0. Other major markets analyzed include France. There is a large literature which corroborates evidence on longer persistence of negative volatility and the negative volatility being higher than the positive volatility. 2001 and 2002 experienced consistently high volatility when compared to preceding period as well as to the average.01 percent returns. 1993 and 1992 had low volatility of 0.04 percent and a volatility of 1. From the Table 1 it is clear that second part of the 1990s and 2000.49 percent.82 percent (1987). One more interesting finding is that 2000. A close look at the Table 1. It provides a daily average rate of return of 0. South Africa.61 respectively in t he USA. investors should enter and exit at appropriate time otherwise they would be losers.89 percent for a long period of time (Sensex) which is far better than the rest of the emerging market and many of the major markets. 0. Yet another observation is in 2003. USA experienced high daily volatility of 2.21 percent respectively. Mexico. the UK experienced higher volatility.81 percent volatility respectively.40 percent. Both returns and volatility exhibit high variation over a period and across countries. Brazil. Germany. For example Indonesia recorded -0. The years 1995. 1. 0.61 percent in 1987 followed by Germany at 2. The volatility was at its peak in 1984 with 2. and Australia were 0.12 percent compared to average of 1.29 percent in1987. further reveals that emerging markets experienced higher volatility accompanied by lower or negative return. Among these countries. and for many other developed countries it varies from 0. have negative returns even over a very long period of time. Australia had highest volatility of 2. Fund Managers and others investors have a lesson here. Some of the emerging markets. In 1987. 1995 and 1994 were relatively calm years with 0. The experience of India tells a different story.04 percent for USA. Again in 2002 and 2000 the volatility in the US was 1. Emerging markets exhibit bouts of return and volatility patterns.63 percent.40 percent respectively. China and India are to
. Thailand. One interesting observation is that many emerging markets witnessed almost zero returns and high volatility which implies that these markets provide low or negative rate of returns with high volatility. Therefore. The average return in France.72 percent followed by 2.04 percent. 1996.74 percent and 0.Daily mean return and volatility (standard deviation) are calculated for each country.
its volatility is almost twice as much of USA.96 percent (1995). the same as of USA.27 percent (2001). The late 1980’s and the late 1990’s exhibited asymmetry in return distributions.93 percent (1994).11 percent followed by 1. USA. in the recent times.49 percent (1998) followed by 7. 3. The UK.64 percent (1994). There is a clear patterns available between developed capital markets and emerging capital markets overtime. Countries like Hongkong. 7. The daily average return and average volatility are useful to the policy makers.68 percent(1995). In the years. Developed markets experienced very high negative skewness and high kurtosis in 1987 which was extremely undesirable because all the returns earned by investors previously were erased. apart from negative skewness.45 percent followed by 2. China has a short history of capital market and in this short history it provided daily average returns of 0. provides statistics pertaining to asymmetrics such as skewness and kurtosis (higher order moments). Brazil with 6. Higher order moments for sensex and Nifty are calculated from 1985 and 1995 respectively.18 percent (2003) 1.32 percent (1995). India also followed quieter moments from 1999 to 2003. market participant and even investors. the third and fourth order moments are comparatively low. Reasons for this behavior include 1987 great fall in the US stock market and its contagion effect on some of the markets.50 percent (1990) and 2. Countries like Indonesia. Brazil and Mexico have had very high volatility of 10. Indian market indices showed very high stability and normality. 1987. 1997.some extent exceptional. Australia. The highest was in 1992 at 3. in that order.23 percent (1991). intra-day volatility has assumed considerable significance because of its influence on the decision of the market participants and its impact on other instruments such as derivatives. Surprisingly. 2. investors. Table 2. regulators and policy makers. Though India did show some amount of high volatility but it is low compared to any of these emerging countries. For many fund managers.97 percent (1992).04 percent. Stock markets were relatively stable and returns followed near normal distribution for the past five years (1999 to 03). regulators.97 and 3. 6. (China). Volatility f gures are also important for derivative i traders. Still many traders continue to use realized volatility as opposed to implied volatility.38 percent (2000). India recorded lowest volatility in 2002 at 1. Indonesia had the highest volatility of 10. Like other markets. The East Asian crisis could be one of the reasons for the negative skewness and high kurtosis. 3.04 percent with a low volatility compared to China but higher than America. India with its long history provides higher return of 0. among developed markets have had very high kurtosis. Several metrics are employed to estimate intra-day volatility : (a) open-close index level (b) high low index level and (c) open to open index levels
. Mexico with 3. However. and 1998.96 respectively in certain years. it may be possible to conclude that Indian market exhibited less asymmetry in the entire period. Inter and Intra-day volatility So far we have discussed inter-day volatility by computing close to close index level on daily basis. Both skewness and kurtosis are relatively low. Emerging markets also recorded very high volatility in several years.49.72 percent (1998) and 2.
number of trading hours have been enhanced. these metrics are computed. It appears that the US also scores over other developed markets in terms of intra-day volatility. With the implementation of computer screen based trading. Even the high and low price movement variation is also low. is expected to get reflected in the opening prices of shares and on the index. in the UK also. it almost touched 3 percentage points and peaked at 3. The volatility is on the rise for the past five years. exposure limit. This is important mainly for India as the trading hours increased over a period of time. It is a sign of an emerging market owing to economic and socio-political variations. policy makers and SROs strive to implement policies that smoothen information flow and they also ensure certain measures which ensure bounded extremes with the help of circuit breakers. Intra-day dispersion is also high. longer the trading hours higher is the expected volatility. In the UK. Australia appears to have comparatively quieter markets. in case of France. open to open. The UK and USA. open to open and close to close volatility appears to be neck to neck. Brazil
. Any positive or negative information that comes after the close of the market and before the start of the next day’s trading. Emerging capital markets Emerging markets exhibited higher intra-day volatility compared to developed markets. 2001 and 2003. Significant economic and sociopolitical developments induce price movements and the extent of price movement depend on severity of information. Open to close volatility. Brazil and South Korea. Among all the emerging countries studied.For all the sample countries and for India. High open to open volatility reveals informational asymmetry and also overflow of information. Intra-day and inter -day movements in stock prices are considerably stable in Australia. the market was open for about two hours. In the open-out-cry system. one has to keep this in mind while interpreting the results.79 percent in 2002 and it appears to be highest among all the developed markets in that year. Inter -day volatility has been consistently lower than 1 percent and it is half of it in 2002 and 2003. Open to open volatility is very important for several of the participants. is the highest among all volatility. High-low volatility. Highlow volatility appears to be very high in Germany. Therefore. margin etc. Extreme volatility. the volatility in the emerging markets is generally on the high side. Now the market is open for almost 6 ½ hours. Later on number of trading hours were extended. Intra-day volatility and developed capital markets In the US. Countries like Indonesia. intra-day volatility. regulators. high-low is the highest among the four types of volatility measured as was the case with inter -day volatility. There is an elaborate literature to show that volatility is a function of length of time that means. is lower than open to open and close to close. High-low volatility conveys extreme movements and dispersion during the trade time. France scored higher volatility compared to the UK and USA. The volatility in Germany is higher than France. did show higher intra-day volatility. Open to close volatility provide information on change of the prices during the day. A very high high-low volatility is likely to scare investors and lead sometimes to panic conditions in the market place. Therefore. In the year 2002. This indicates smooth flow of information during the day as well as over -night. is slightly higher than inter-day volatility and lower than open to close volatilit ies.
69 percent in 2003. mostly in the popular press. An attempt has been made to calculate inter and intra-day volatility for both Sensex and Nifty with reference to these periods also. From 1998 the indicators traveled nearly together. If one country (mainly the dominant market) experiences extreme volatility in any given date/given
. Nifty. The tables and charts evidently exhibit a close relationship between inter and intraday relationship. High and low volatility ( Volatility Transmission) With a view to finding out the extent of integration and segmentation of market it was decided to identify the top three and bottom three volatility years for each country in the sample. Intra-day volatility in 2003 has been very slightly higher than the immediate preceding years though nothing disturbing is evidenced. This observation holds true to both the major exchanges. South Korea and Mexico. Intra-day volatility parameters : open-close and high-low also experienced close togetherness excepting for 1991. citing that the intra-day volatility in particular and volatility in general went up in 2003 and more so in the first three months of 2004. Open close volatility however. In fact. In the first 3 months of 2004 volatility calculation reveals that high low volatility slightly went up in January 2004 to 2. the divergence was little higher and it was highest in 1997. in an efficient market both are supposed to be almost the same because the time length is identical and if there are no informational asymmetry then these two parameters converge and have identical volatility. This is something very intriguing and deserves micro investigation for the purpose of effective dissemination of information. although the parameters registered their peak in 2000. Nifty appears to be more volatile both in terms of open to close and high low dispersions. Extreme value volatility touched its peak in 2000 at 3.experienced very high intra-day volatility and also extreme value volatility followed by Indonesia. Only Nifty showed a little more intra-day volatility compared to the previous year and to the Sensex. they fell down further in 2001 and 2002. This little divergence was evident from 1997 to 2002. Compared to most of the emerging markets sampled here. The divergence. Indian Market There have been reports. volatility is always higher than close to close volatility and many a times higher than open to close. A close examination of the Tables 4. 5 and 6 with regard to open to close volatility and high low volatility reveals that the perceptions are not altogether correct. The integration between these two parameters is higher in case of Sensex. Tables 8 and 9.10 percent but it is much lower than what was recorded in 2000 and 2001. In India open to open. prevailed for the entire period from 1995 to 2003 and they never crossed. Between BSE Sensex and S&P. the volatility as per these two parameters in 2003 is only slightly higher compared to 2002. continuous to be low and although the parameters further receded in February and March 2004.17 percent and it continuously slided in the following years and marginally increased to 1. Only in case of Nifty. The results are more or less the same for both the Indian indices. intra-day volatility in India is low. compared to Nifty. Intra-day volatility for India has been computed for 13 years. Nifty. Charts 3 and 4 provide information on inter and intra-day volatility for both Sensex and Nifty in terms of Indian rupees (not adjusted for $ terms). but when compared to 2001 and 2000 this is much lower and about 50 percent of what it was in 2000. The volatility levels are almost identical. As per finance theory. Close to close and open to open volatility moved in tandem with little divergence in a few periods. However. CNX.
Extreme volatility analysis (India) Charts for BSE Sensex and NSE Nifty and tables for both the indices are drawn separately with extreme positive and negative price movements. When the volatility is stable. here we used a new measurement to compute volatility. The relative or returns are squared and converted into percentage. also witnessed higher positive variation and the years are relatively more stable. Return squared volatility As far as India is concerned. Malaysia and Thailand. France. it is found that they have used high-low index levels of the day to compute dispersion and call it volatility. As a fist step. one more different metric has been computed to measure volatility. due to globalization. As a next step. It also demands high level of information sharing and also co-ordination so that markets across the globe will have less of volatility or sudden bouts of volatility which is likely to affect investor sentiments. In 1987. Here one significant assumption is that daily average return is expected to be zero which is by and large true if we examine closely all the data provided in Table 1 for various countries. 1992 and 1993. SEBI for obtaining tables and charts. Negative price movements crossed 15 percent in 1993 and it was about 15 percent and 10 percent in 1991 a 1992 respectively. From the charts and the tables1. the positive volatility is higher than the negative volatility.
. sudden change in volatility will affect the sentiments of investors and it will have impact on other markets also.period and if markets are integrated then. Following 10 day price movement have been analyzed to find out the extent of persistence in volatility. USA had the lowest volatility in 1995 which is felt in other countries. USA exhibited highest v olatility which is also seen in the UK. Singapore. From the data it is clear that negative variation persist for longer period compared to positive volatility. Germany. policy makers and regulators have to be extremely cautious while initiating measures that affects stock prices. Even 2002 and 2003. the volatility is expected to get transmitted from one market to another. For example in 1994. Australia. many a times.
Owing to space restrictions and with a view to providing smooth reading through the article some of the tables and charts are not included in the paper. it is clear that the negative volatility is highest in 1991. Australia. it was negative volatility. 1995 and 1996. average volatility for the entire year is calculated and top 5 percent of the returns (in absolute terms) are computed to see the difference between the average and extremes. it may be reasonable to conclude that volatility transmits across countries if there is a financial market integration. Thailand and Korea. In this analysis highest index movement on any day in a year has been identified. Indonesia. In the popular press. Many institutional investors are common throughout the world. while rest of the countries did not feel it. In other words. However. the volatility was higher. the interested readers are most welcome to contact the authors and/or Research Department. relative logarithamic return on close index value are used f computing relative return. In this procedure there are several pitfalls. Therefore. did not have markets. such as the UK. Therefore. they were basically closed or semi-closed markets in 1987 and in some countries such as China. Germany. the price variation is higher on positive side compared to negative side. The depth also is higher for negative volatility. Hong Kong. mainly major markets. nd Whenever. If we look at the non-affected countries. Therefore.
From Table 1 we can observe that the broad contours of this table across that of overall 0. The data has been looked at from different angle without using the traditional method of using standard deviation. The stock market volatility in India has a lot to do with domestic market related developments. and becoming more loss averse as downward movements in the value of their portfolios remind them of their incomplete personal control. 1997 to 2000. Conclusion & Recommendation : § As expected daily average return and daily volatility across markets vary over time and space. Thereafter. The year 2002 is a relatively stable year. on a daily basis they have been usually stable. arbitrage and all kinds of market making. Some countries (US) provide as high as 0.01 percentage.04 percentage return while some of the emerging markets s uch as Indonesia recorded negative returns of -0.34 percent in 1992 and second highest in 1999 at 8. Neoclassical economic models assume that negative feedback always dominates. the volatility continued to fall till 1996. Return squared analysis The observation that stock-price breaks (negative) are more severe than upward variation is also consistent with investors being loss averse. average volatility came down between 1997–1999.
. For each year. Maximum volatility was recorded at 12. Volatility or rather the lack of it. yearly average on top 5 percent were high in 1992 followed by 1991. India is a bright spot. 1997 to 2000 the volatility again went up. it fell down and fell down sharply by almost 50 p ercent in 2002 compared to 2000. For this process daily returns are calculated which are squared and converted into percentage. volatility figures in other tables. In the sample period Indian investors could obtain as high as 0. The lowest volatility is in 2003. On both the exchanges. this new measurement also throws up that volatility in 2003 is slightly higher than the preceding years. Their divergencies are highly demonstrable. The average is calculated which is necessary to give a summary statistic. 10 it is clear that volatility measured by this way also confirms that the broad finding of standard measurement such as standard deviation. however. While stock prices have risen sharply over the last year. High volatility periods of 1990’s and also part of 2000 can be clubbed into 3 periods. tending to focus on negative information when under stress overweighting the probability of negative events. But for these irregularities. Firms such as Bear Stearns make a good deal of their money from exploiting the bumps and wrinkles in markets. employed previously. This will help to identify the pattern of extreme volatility and its behavior. top 5 percent (ignoring sign) of the observations are separated to calculate average of 5 percent. All the banks with big equities business have moaned that the low volatility of stock prices over the past few months has been making life difficult. Most of the high volatility can be attributed to some of the irregularities that occurred on the Indian stock exchanges in 1991-92 and 1997-98 and again in 2000-01. thereafter. Thereafter square root is taken.From the Table No. and that prices tend toward stability. Although.66 percent. Indian stock markets are by and large stable and volatility has been under control. which drive profits in derivatives. Yearly average as well as top 5 per cent attained high in 1992. Extreme volatility has been high although.04 percentage return with a moderate volatility of 1.89 percent.
Traditionally. Return distributions have been relatively stable for the past five years (1999-2003) that perhaps.). showed both negative third and large fourth order movement. The discovery of nonlinearity in security prices and the fact that outcomes can be predicted only within wide limits also have normative implications for financial decision making. Many of the developed markets and all emerging markets experienced high volatility during 1997 to 2002 indicating convergence of markets. The years 2000. bullish. Financial Times 20-21 March 2004) Some of the countries such as the UK. Brazil. while a kurtosis higher than 3 indicates gain. A normal distribution has a kurtosis of 3. Australia. experienced lower open to close volatility than open to open and close to close. Hong Kong (China). The returns on portfolio of stocks (index) are more or less normally distributed. Markets considerably expanded during these years. Countries like France.S. is. as measured by the distributions. as measured by its so-called ‘skewness’. The volatility is higher in Germany than in France. it is no longer appropriate to use the standard deviation as the sole measure of risk. `kurtosis’. provide additional information about he nature of return distribution. the risk of such portfolios can indeed be measured with one number. provided less variant in return and positive returns. 1987. Among these countries. the UK and USA.
. France. South Korea exhibited high intra-day volatility. of course. France. As far as the US market is concerned both open to open and close to close volatility appears to be almost identical. market watchers see high volatility as a sign of investor nervousness which. Brazil had higher intra-day volatility. Germany and Australia provide low return and higher volatility (compared to the U. Volatility was low in 2003 in almost all the countries. Since most investors are in it for the longer run. Indeed. and the probability of extreme positive or negative outcomes. The UK and Germany had negative skewness and large kurtosis. Negative skewness and high kurtosis are extremely harmful to investors (long only). low volatility is viewed as a sign of investor confidence or even complacency and a warning of a market downturn. in the counter-intuitive world of markets. they strongly rely on compounding effects. Emerging market countries like Indonesia. The late 1980s and a part of the late 1997’s across markets. In that case investors should also look at the degree of symmetry of the distribution. however. Higher order movements. 2001 and 2002 were bad for investors with very low or negative returns and high volatility. Surprisingly and unexpectedly. Indian stock market stood out as a normally distributed market. Close approximation signals smooth flow of information during and after the market hours. This means that negative skewness and high kurtosis are extremely undesirable features as one big loss may destroy years of careful compounding. the stock markets of the US. A symmetrical distribution will have a skewness equal to zero. Conversely. Confronted with non-normal distributions. Because normal distributions are fully described by their mean and standard deviation.§
Views differ on what has been behind the decline and what it means for the future. it is a very positive indicator as far as India and Indian regulator are concerned. while a distribution that implies a relatively high possibility of a large loss (gain) is said to exhibit negative (positive) skewness. (David Wighton. skewness and kurtosis.
“Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test. G and G. Geert and Campbell. France. National Bureau of Economic Research (NBER). Germany. G. pp 41-66 Miller. Harvey (1995). financial crises and stock volatility. Australia. pages 1115 – 1154 Schwert. pages 1 – 77
Garman. Merton H.” Review of Financial Studies. “Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models. Vol 65.126
. Financial Innovations and Market Volatility. pp 61-65 Schwert. Pierce. CarnegieRochester Conference Series on Public Policy. Vol 53. pages 1 . MacKinlay. Emerging Equity Market Volatility. 1978.” Journal of Business. Box. 44. Blackwell. pp 1509-1526 Bekaert. pp 67-72 Lo and A. Why does stock market volatility change over time. G. “On a Measure of Lack of Fit in Time Series Models. pp 67-78 Ljung. 1980. 31.
Box.17 per cent and continuously slided thereafter.§
Compared to emerging markets and some of the developed markets – India experienced low intra-day volatility. Australia. Vol 66. in 1987. Thailand and Korean markets. USA recorded highest volatility which was also seen in other countries like the UK. M and M. 1970. Working Paper 5307.C. 1988. 1980. Volatility transmission appears to be strong For eg. William (1989a). Extreme value volatility. Germany. M “The Extreme Value Method for Estimating the Variance of the Rate of Return”. Journal of Finance. Vol 53. Vol 1. “On the Estimation of Security Price Volatilities from Historical Data. Hong Kong. in India. G and D. R. pages 83 .288 Parkinson. (1991). And in 1995. Business cycles. William (1989b). the US markets recorded low volatility which is again observed in the UK. touched its peak in 2000 at 3. Singapore and Thailand. Journal of Business. Klass.” Journal of the American Statistical Association.” Biometrika.
03) H2 2.22 (00) L 3 0.96 (95) L 1 1.39 (02) L 1 0.73 (03) H2 2.61 (87) L1 0.54 (93) H3 1.12 (87) L1 0.64 (95)
H1 1.75 (96) H2 2.53 (97) L3 1.07 (89.57 (98) L1 1.65 (87) L3 1.51 (91) L 1 0.74 (95) H3 1.03 (98) L 1 1.20 (98) L 3 0.72 (96) L 2 1.14 (03) H2 2.97 (92) L 1 1.50 (90) L2 1.52 (02) L3 1.62 (93) H3 7.23 (97) L 3 1.93 (94) L2 2.90 (96)
H1 3.Table 3 : Top Three and bottom three volatility figures
H1 2.21 (87) L1 1.11 (02) H2 2.11 (86) H3 2.15 (94)
H1 3.29 (03)
H1 2.19 (89) H2 3.61 (00) L 3 0.18 (03) H3 2.80(87.64 (94) L 3 1. 95) H3 2.46 (96) H 2 3.91 (92)
H1 4.63 (96) H2 2.32 (95)
.88 (92) H2 1.45 (92) L1 1.13 (91)
H1 2.68 (95) L 3 2.29 (98) L1 0.33 (98) H3 2.64 (91) L3 1.72 (98) L 2 1.77 (96) H2 1.82 (02)
H1 3.11 (95) H3 3.81 (94)
H1 2.11 (96) H3 1.20 (00) L3 1.27 (93) H3 2.74 (90) L 1 0.82 (85) H2 2.06 (03) H3 3.82 (98) L1 0.25 (89) L 3 0.29 (87) L1 0.09 (88.28 (97) L2 1.11 (02) L2 1.78 (98) L2 1.61 (92)
H1 2.76 (93) H3 1.81 (92) H3 2.43 (96)
H1 2.89 (98) L 1 0.40 (00) L3 0.97 (84)
H1 3.19 (03)
H1 4.64 (02) L2 0.74 (01) L 3 1.86 (87) L 2 0.37 (00)
H1 10.45 (91) L 2 0.07 (96.82 (03)
H1 6.49 (98) L 1 1.88 (86) H3 2.08 (93)
H1 2.85 (96) H3 1.27 (01) L3 1.87 (97) L2 0.33 (00)
H1 3.95) H3 1.97(95) L1 1.27 (93.53 (01) L2 1.31 (85) L 2 0.82 (87) L 3 0.54 (95) H2 1.75 (97) L 2 1.69 (87) L3 0.98) L2 1.84 (93) H2 2.05 (84.23 (91) L3 1.72 (84) L1 0. 93)
H1 2.24 (95) L 2 0.32 (03) H2 7.49 (95) H2 1.38 (00) L2 1.52 (85) L2 0.72 (97) H2 1.03 (90) H2 3.89 (95) H3 1.67 (03) H2 2. 94) H3 1.
Raju Neelam Bharadwaj Kiran Karande Shikha Taneja Dr. Raju Kiran Karande Shikha Taneja Dr.T.Raju Dr. Patil Dr. Raju Prabhakar R. M. Raju Kiran Karande
Stock Market of Volatility – A Comparative Study of Selected Markets
Transaction Cost for Equity Shares in India (Revised) Dematerialisation: A Silent Revolution in the Indian Capital Market Impact of Takeover Regulations on Corporate Sector in India – A Critical Appraisal (June 2001)
Trade Execution Cost of Equity Shares in India (January 2002) Price Discovery and Volatility on NSE Futures Market (March 2003)
. M. T. T. M. T.Raju Varsha Marathe Pratip Kar M.T. Patil Kiran Karande Dr. M.T.SEBI Working Paper Series
1 Transaction Cost for Equity Shares in India Dr. M. T. M.Raju Prabhakar R.
Request for individual copies may be sent to the Research Department.gov. Phone : +91-22-22850451 – 56 Fax : +91-22-22831949 Web site : http://www. Mumbai – 400 021.sebi.in
. First Floor 224. Nariman Point. Securities and Exchange Board of India. ‘B’ Wing. Securities and Exchange Board of India Mittal Court.
97 1.60 2.83 1.16 0.42 1.23 1.01 -0.85 1.09 0.16 1.94 1.65 Thailand MEAN NA NA NA NA NA NA NA -0.14 1.02 0.14 1.03 -0.21 0.06 0.08 -0.09 1.06 0.43 Malaysia MEAN 0.96 1.07 0.35 1.05 0.10 0.02 0.01 0.02 1.03 STDEV NA 2.17 -0.80 0.86 1.69 1.13 0.35 1.36 1.11 -0.76 1.06 0.14 -0.96 1.37 1.78 1.03 0.03 0.08 1.06 0.03 0.Tabel 1 : Stock Index Daily Return Average and Volatility (Percentage) Year 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 1980-1991 1992-2003 1980-2003 0.35 1.07 2.53 2.03 0.10 -0.28 1.80 1.86
Stock Index Daily Return Aveage and Volatility (Percentage) Year 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 Singapore MEAN NA NA NA NA NA -0.12 0.13 1.07 1.08 0.18 1.21 1.89 1.02 0.29 1.06 -0.10 1.03 0.28 1.07 -0.07 1.16 1.05 0.14 -0.12 -0.12 -0.12 1.47 1.09 -0.06 0.03 0.23 NA NA NA NA NA NA NA -0.50 1.71 1.40 1.17 1.23 1.14 -0.10 0.16 1.07 1.02 0.88 1.07 0.03 0.07 -0.40 1.20 1.19 -0.04 UK STDEV NA NA NA NA 2.03 0.29 1.22 1.19 2.21 Hongkong MEAN NA -0.12 0.81 0.02 0.05 STDEV NA NA NA NA NA 1.28 1.54 0.07 -0.37 1.11 0.75 1.02 0.12 1.18 1.31 1.12 -0.62 0.10 0.08 0.06 -0.62 0.80 1.25 1.13 -0.94 0.06 -0.75 1.11 1.09 0.28 1.52 1.43 1.09 0.07 MEAN NA NA NA NA -0.03 0.32 -0.06 0.11 0.03 0.03 0.48 1.05 -0.09 0.09 0.08 0.59 2.14 STDEV NA NA NA NA NA NA NA 2.01 -0.09 0.06 -0.43 1.07 1.32 1.22 1.96 1.11 3.65 1.10 -0.07 2.01 0.15 0.01 0.04 1.05 -0.11 2.01 0.04 0.09 1.03 0.03 0.04 0.12 0.08 0.18 1.89 0.04 USA MEAN STDEV 1.07 0.20 0.22 1.03 0.10 -0.02 0.05 -0.04 STDEV 1.06 -0.07 0.02 0.10 -0.03 0.98 0.12 0.12 0.05 0.14 0.63 1.08 1.07 0.30 1.20 1.16 -0.05 0.06 0.23 2.16 0.05 -0.21 -0.07 1.04 -0.61 1.46 2.13 -0.08 0.64 0.43 1.05 0.11 -0.00 0.64 1.02 1.64 1.30 0.11 0.09 0.41 1.03 0.03 0.13 0.82 0.07 0.72 2.52 1.90 0.08 0.00 0.01 -0.11 0.04 0.07 0.01 0.99 0.10 0.74 0.20 1.58 1.03 0.44 Australia MEAN NA NA NA NA -0.93 1.15 0.04 -0.36 1.58 1.61 0.00 0.26 0.93 2.93 1.01 0.15 1.02 0.27 1.13 1.08 1.16 0.02 0.63 0.32 1.74 1.31 -0.05 0.88 1.68 1.13 0.06 0.04 0.03 France MEAN STDEV NA NA NA NA NA NA NA 2.59 MEAN NA NA NA NA NA NA NA NA NA NA NA China STDEV NA NA NA NA NA NA NA NA NA NA NA Indonesia MEAN NA NA NA NA NA NA NA NA NA NA NA STDEV NA NA NA NA NA NA NA NA NA NA NA MEAN NA NA NA NA NA NA NA NA NA NA NA Chile STDEV NA NA NA NA NA NA NA NA NA NA NA
.03 0.02 0.04 0.02 0.13 0.05 1.32 1.38 1.22 0.49 0.06 -0.90 1.04 0.06 0.46 1.95 1.29 -0.05 0.14 0.24 0.02 STDEV NA NA NA NA 1.84 0.11 0.01 0.00 0.68 1.15 0.12 1.77 1.38 1.74 2.08 0.07 -0.06 0.54 1.02 0.10 -0.08 -0.17 1.40 Germany MEAN -0.12 -0.42 1.14 1.39 1.06 0.22 1.20 1.03 -0.04 STDEV 1.05 0.24 2.09 0.
17 0.52 1.01
1.04 0.23 -0.21 -0.03 0.18 1.72 1.07
-0.35 NA
0.04 -0.09 -0.66
0.19 1.10 2.25 -0.49 6.00
-0.14 -0.04 -0.22 2.93 3.88 2.21 -0.50 1.04 0.01
3.08 -0.10 -0.24 0.01
0.05 -0.24 0.29 2.20 0.00 0.23 -0.82 1.54 1.05 1.68 1.02 -0.82 0.61 7.23 0.10 0.31 1.06 1.25 0.10 1.61 1.07 0.28 3.51
0.04 0.22 0.29 0.14 0.09 5.96 2.91 0.07 0.89 1.38 1.00 -0.38 7.97 0.03 0.07 0.07 0.09 -0.23 1.25 -0.49 1.04 NA 0.43 2.26 -0.25 1.58 1.72 2.15 0.54 1.11 -0.09 -0.96 1.16 -0.63 1.31 0.08 -0.12 -0.49 1.29
NA NA NA NA -0.10 0.29 1.20 0.01 -0.93 2.13 0.15 0.05 -0.14 NA 0.06 -0.77 1.26 -0.18
South Africa MEAN NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.93
1980-1991 0.19 -0.01 -0.15 1.17 -0.02 0.49 -0.06 1992-2003 0.39 0.66 1.21 0.60 1.84 0.10 0.57 2.38 1.32 -0.21 0.11 0.18 -0.91 0.08 -0.52 NA NA NA NA NA NA NA NA NA NA NA NA
Mexico MEAN STDEV NA NA NA NA NA NA NA NA NA NA NA NA 1.06 2.07 0.36 3.47 1.34 0.07 0.01 0.09
1.96 0.10 0.06 NA 3.76 1.46 1.46 2.15 3.63 1.91 0.08 0.32 NA 5.03 -0.29 1.27 1.27 0.76 1.97 3.90 0.13 0.02 -0.26 -0.94 1.11 1.87 4.07 0.72 1.93 1.00 0.02
1992-2003 0.04 -0.01
1.72 2.10 -0.97 3.10 0.97 1.08 0.31 1.01 STDEV NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.08 -0.04 -0.05
.25 0.07 -0.69 1.41 2.05 0.78 1.05 -0.00 1.02 0.07 -0.66 1.51 0.03
Stock Index Daily Return Aveage and Volatility (Percentage)
Year MEAN 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 1980-1991 NA NA NA NA NA NA NA NA NA NA NA NA
Brazil STDEV NA NA NA NA NA NA NA NA NA NA NA NA 6.08 0.04 0.15 1.85 1.10 0.41 2.38 0.04
NA NA NA NA 2.43 2.17 1.64 1.08 0.09 0.11 10.06 0.81 1.12 -0.62 2.49 0.09 0.20 2.48 MEAN NA
Korea STDEV NA 2.00 0.28 -0.01 -0.47 0.75 4.07 0.17 -0.07 0.36 0.24 0.83 0.34 2.53 1.19 NA 1.00 0.73 1.74 2.33 2.60 2.14 NA 1.57 1.84 1.14 1.12 -0.05 1.77
0.02 0.17 1.10 0.10 0.03 0.02 0.72 1.06 0.19 0.11 -0.02 1.70 3.28 0.45 1.38 1.43 NA NA NA
Taiwan MEAN STDEV NA NA NA 1.01 1980-2003 0.83 2.57 2.28 0.07 0.02 0.43 1.52 1.72 2.01 1.11 0.37 1.04 0.53 0.22 NA -0.12 0.10 0.12 -0.37 1.54 1.11 -0.02 0.01 0.89 1.59 1.27 2.08 -0.15 2.01 0.03 2.02 0.82 0.01 0.07 NA 2.03 1.78 4.02 0.35 0.64 3.38 0.19 0.65 1.18 -0.08 -0.05 0.27 1.11 1.20 3.73 1.57 0.03 0.07 0.66 1.62 1.56 1.69 1.08 0.01 0.07 0.61 1.19 -0.03 -0.64 3.11 NA 0.09 0.21 0.12 0.23 -0.94
0.63 2.37 3.27 3.10 0.82 1.02 -0.03 1.06 0.84 0.01 -0.02
1.33 1.11 -0.1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
0.00 0.12 0.13 -0.65 1.05 2.81 1.20 0.97 2.05 -0.19 0.
0.01 0.08 0.04 -0.90 2.71 1.02
2.01 1.86
Stock Index Daily Re turn Average and Volatility (Percentage) Year 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 Sensex MEAN NA NA NA NA NA 0.11 0.07 -0.11 0.99 1.09 0.20 -0.25 -
1980-1991 0.11 1.01 0.78 1.05
3.82 2.02 1980-2003 0.66 1.32 1.11 0.24 STDEV NA NA NA NA NA 1.11 1.86 2.08 0.12 -0.04
1.31 1.11 0.48
0.68 1.44 1.04
.23 STDEV NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 1.75 1.01
1.1980-2003 0.80 1.01 0.08 1992-2003 0.19 -0.97 1.02 0.40 1.04 -0.15 -0.59 1.45 2.00 1.18
0.23 3.85 1.22 1.09 -0.33 -0.16 -0.59 1.12 0.54 2.03 -0.18 1.02 0.11 1.89 S&P CNX Nifty MEAN NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.13 0.02
04 -0.27 -0.68 0.50 0.26 1.29 -0.05 0.49 0.50 72.54 51.45 -0.40 0.30 0.62 0.65 0.40 -0.31 0.70 0.03 -0.81 0.43 0.95 8.13 France SKEW NA NA NA NA NA NA NA -0.15 3.06 -0.04 -2.33 Germany SKEW -0.02 -0.28 0.58 UK SKEW KURT NA NA NA NA 0.11 -0.11 2.25 -0.90 77.04 0.60 0.16 3.84 -0.48 53.01 0.43 0.22 0.90 0.63 0.06 0.53 -0.70 -0.28 16.34 -0.08 -0.82 0.44 -0.15 -0.81 6.78 0.29 1.43 0.23 0.49 1.24 -1.93 1.85 -0.09 68.68 0.13 1.44 2.09 -0.11 1.58 -0.12 -1.74 KURT 0.07 -0.36 -0.89 1.24 -0.10 0.30 0.33 1.02 0.25 1.13 -0.30 -0.66 -0.33 1.35 104.06 0.03 0.31 1.34 -0.66 4.13 -0.79 -0.32 -0.45 -0.18 0.22 2.27 2.93 0.74 8.88 0.13 0.53 KURT NA NA NA NA 1.16 2.79 8.16 8.82 6.02 2.08 -0.28 -3.22 -0.18 -5.27 KURT NA NA NA NA NA NA NA 5.96 -0.27 0.24 -0.17 0.14 0.12 0.80 38.14
.45 0.39 2.68 -0.56 2.71 -1.80 4.13 1.23 0.51 -0.42 -0.11 0.37 0.00 0.12 -0.91 0.54 1.17 -0.19 2.51 0.37 0.72 2.88 Hongkong SKEW NA -0.14 2.60 9.86 -0.97 3.32 1.17 -0.07 -0.34 -3.17 -0.31 3.13 3.02 1.07 -0.36 0.26 -0.35 1.40 1.16 0.36 -0.00 -0.82 -0.02 -0.16 -0.02 -0.98 -5.34 0.09 -0.13 -0.06 -0.27 79.21 -0.78 2.81 -0.38 0.77 0.66 -0.35 0.18 -0.22 -0.02 -8.90 -0.10 1.82 0.06 0.90 100.00 0.29 0.25 0.08 1.04 -0.34 -2.79 -0.18 10.03 -1.68 0.90 21.20 1.09 -0.46 NA NA NA NA -0.06 1.26 0.62 0.27 -0.05 21.26 5.00 0.39 -0.43 0.97 14.04 -1.06 4.02 -1.16 0.06 13.78 2.45 14.31 0.04 -0.20 -5.12 -0.11 1.40 2.32 1.06 -0.92 2.55 2.05 6.05 -0.38 2.11 -1.16 0.09 0.18 0.05 0.33 3.48 5.34 -0.57 1.39 -2.39 0.81 -0.04 0.25 KURT 0.83 Australia SKEW NA NA NA NA 0.77 -0.20 -0.72 -1.01 0.70 -0.04 -0.23 14.28 0.27 -0.14 1.58 54.11 0.44 1.06 3.06 1.95 3.04 -4.16 -0.61 -1.84 -6.02 -0.17 -0.22 0.58 -0.53 1.52 KURT NA 1.17 2.47 10.01 0.92 0.Table 2 : Higher Order Moments of Stock Index Daily Returns Year 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 1980-1991 1992-2003 1980-2003 USA SKEW -0.19 0.64 2.02 0.23 0.49 1.34 -0.79 2.18 0.95 10.20 0.21 11.66 1.35 0.63 2.62 -0.14 2.
74 -0.24 0.34 3.89 3.15 1.89 10.35 2.31 China SKEW NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 2.58 15.05 -0.61 43.11 0.30 2.59 0.36 1.01 0.14 0.34 -1.58 -0.19 0.11 1.05 -4.57 0.53 40.79 -0.Higher Order Moments of Stock Index Daily Returns Year 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 1980-1991 1992-2003 1980-2003 Singapore SKEW NA NA NA NA NA -2.20 -1.14 2.14 36.29 2.09 0.84 9.47 -0.69 0.21 -0.41 -0.58 -0.70 1.90 6.67 1.67 1.82 1.98 13.10 -0.51 10.57 2.60 -0.00 0.39 -1.09 0.25 0.35 0.88 KURT NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 32.10 -0.40 0.98 0.92 5.03 48.88 0.85 -0.72 6.15 3.35 -1.32 1.81 KURT 3.20 2.53 2.08 -0.38 1.43 0.42 -0.24 0.17 4.70 -0.91 8.20 3.22 16.94 3.44 -1.75 2.28 6.66 1.11 0.33 0.39 11.14 -0.04 Chile SKEW KURT NA NA NA NA NA NA NA NA NA NA NA 0.43 -0.38 2.09 NA 0.12 9.00 KURT NA NA NA NA NA NA NA NA NA NA NA 3.37 6.00 0.88 0.15 -0.25 -0.95 0.75 -0.31 77.87 3.84 2.62 KURT NA NA NA NA NA 30.08 0.13 0.76 -0.18 0.66 -1.62 -0.20 Indonesia SKEW NA NA NA NA NA NA NA NA NA NA NA 0.28 -0.19 -0.59 -0.32 0.01 -0.60 -0.26 -0.07
.95 NA 19.95 3.28 50.24 -0.46 2.40 0.88 0.35 0.25 0.88 -0.50 1.98 2.29 13.01 KURT NA NA NA NA NA NA NA 2.82 0.01 -2.02 0.04 -0.76 Malaysia SKEW -0.69 8.81 41.30 1.21 -0.16 7.60 0.13 5.23 1.76 7.06 3.73 2.46 3.16 10.53 1.44 7.03 0.74 19.14 1.19 0.85 2.32 -0.20 8.01 -0.98 -0.19 5.06 0.79 3.00 0.31 0.60 Thailand SKEW NA NA NA NA NA NA NA -1.08 -0.69 7.64 3.77 1.31 -1.24 5.26 0.18 0.80 0.23 8.20 24.12 -0.61 0.82 1.53 0.66 3.54 6.78 NA NA NA NA NA NA NA NA NA NA NA -0.37 0.06 3.89 4.21 6.81 1.70 NA 24.86 NA 0.12 0.10 7.05 0.00 3.40 -4.52 0.68 0.32 0.48 2.28 -3.90 -0.34 26.12 0.73 0.04 -1.94 -0.73 8.72 0.70 -0.10 1.38 4.16 1.54 10.17 -0.31 4.61 1.01 -1.09 9.53 -0.38 0.00 1.
33 6.07 -0.87 KURT NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.87 -0.11 -0.79 -0.20 -0.00 0.23 KURT NA NA NA 4.37 -0.25 3.18 1.05 0.67 -0.50 7.56 -0.20 -0.86 1.69 2.12 KURT NA 2.28 5.19 S&P CNX Nifty SKEW NA NA NA NA NA NA NA NA NA NA NA NA KURT NA NA NA NA NA NA NA NA NA NA NA NA
.15 -0.68 9.59 0.57 0.16 0.65 -0.17 -0.24 0.15 -0.89 3.19 -0.21 0.05 0.23 0.37 -0.80 0.88 12.11 0.05 5.11 -0.14 0.44 0.15 17.07 -0.40 -0.34 -0.33 Korea SKEW NA 0.42 0.76 1.49 -0.04 -0.04 0.00 NA -0.62 0.30 17.88 2.90 28.44 1.33 NA -0.07 1.76 1.43 0.47 2.47 0.37 0.94 35.81 0.21 0.87 1.90 34.38 NA -0.12 0.Higher Order Moments of Stock Index Daily Returns
Year 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 1980-1991 1992-2003 1980-2003 Brazil SKEW NA NA NA NA NA NA NA NA NA NA NA NA -0.88 South Africa SKEW NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.62 0.27 1.14 0.31 2.26 -0.30 1.72 4.14 0.71 5.80 1.06 0.83 0.39 -3.57 0.16 0.38 2.16 8.34 0.33 -0.42 -0.08 0.63 NA 15.22 0.30 1.67 0.97 1.08 -1.20 -0.14 -0.21 0.17 0.10 -0.10 -0.31 -0.13 0.04 -0.04 -2.25 0.71 1.46 0.09 KURT NA NA NA NA NA 1.62 0.92 0.26 -0.33 0.86 3.51 0.68 1.49 1.09 -1.41 -1.20 -0.41 0.02 -0.37 NA 7.21 -0.37 19.07 0.06 -0.33 4.57 -0.63 5.13 -0.92 1.10 0.08 9.48 1.01 12.10 -0.30 1.21 0.37 Mexico SKEW NA NA NA NA NA NA NA NA NA NA NA NA -0.34 -0.53 2.46 12.11 0.97 Taiwan SKEW NA NA NA -0.30 -0.64 1.21 2.51 -0.62 0.37 -0.44 0.40 0.33 7.26 2.70 0.07 -0.81 0.89 -0.30 1.57 -0.04 0.14 KURT NA NA NA NA NA NA NA NA NA NA NA NA 1.56 1.28 -0.69 0.24 0.82 1.37 -0.88 15.71 2.46 0.49 KURT NA NA NA NA NA NA NA NA NA NA NA NA 12.05
Higher Order Moments of Stock Index Daily Returns
Year 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 Sensex SKEW NA NA NA NA NA -0.13 0.25 0.84 2.42 -2.16 0.37 NA 19.96 8.04 -0.01 0.37 1.96 -0.
92 1.12 0.24 0.57 0.42 -0.51 -0.57 0.54 2.97 2.58 -0.11 -0.00 0.05
NA NA NA 0.01 -1.86
NA NA NA -0.79 1.05 3.21 1.28 0.50 0.81 4.05 1.18 -0.60 1980-2003
.35 0.26 11.51 0.93 4.15 0.67 0.60 -0.40 NA 2.76 1.35 1.19 -0.32 1.39 -0.16 5.12 0.1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 1980-1991 1992-2003
2.25 -0.99 0.16 -0.72
-0.49 2.50 0.33 NA -0.42 0.
99 1.06 1.93 1.25 1.30 1.68
1.97 2.74 2.92 2.08 1.30 2.39 1.72 2.08 1.601 factor for H-L Volty.77 1.64 1.93 3.77 1.07 1.20 1.43 1.71 1.29 1.62 2.01 0.01
0.01 0.80 1.40
1.CloseOpenHighOpenClose.39 1.29 1.52 1.34 1.36 1.00 0.95 2.03 1.33 1.18 1.84 1.97 2.14 1.79 2.61 2.91 1.62 1.01 0.38 1.38 1.06
1.33 1.74 1.83 1.08 0.31 1.84 1.51 1.41
0.79 1.16 1.87 0.15 1.45 0.00 0.19 2.32 0.10 1.07 1.85 0.64 1.84 2.26 1.00 0.20 1.49 0.40 2.11 1.58 1.75 1.01 1.59 1.14 1.05 2.19 1.68 1.46 1.08 2.68 2.28 1.96 1.33 2.39
0.40 1.47 1.01 1.)
USA Year UK France Germany CloseOpenHighOpen.95 2.71 1.33 1.52 1.05 0.75 1.01 0.60
1.15 1.27 2.11 1.64 0.19 1.20 1.88 1.88 1.55 1.07 1.27 1.00 2.36 1.72 1.42
0.HighOpenClose Close Low Open Close Close Low Open Close Close Low Open Close Close Low Open Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%)
1995 1996 1997 1998 1999 2000 2001 2002 2003 1995-2003 2000-01 2002-03
0.34 1.98
0.37 1.63 1.65 1.55 1.27 2.45 1.07 1.38 1.71 1.16 0.63 1.28 1.86 1.73 1.35 1.66 2.58
1.33 1.16 1.Table 4 : Inter and Intra Day Volatility (without 0.55 0.40 1.28 1.79 1.74 1.54 1.98 1.40 1.71 1.66 2.20
0.38 1.55 1.07 1.12 2.15 1.65 3.04 2.51 1.43 1.15 1.14 1.37
.75 2.74 0.55 0.78
0.60 2.42 1.11 1.39 1.33 1.29 1.19 1.14 1.26
0.64 1.23 1.74 2.91 2.OpenHighOpenCloseOpen.99 2.49 0.48 0.97 2.75 2.52 0.56 1.82 1.68 0.15 1.95 0.
26 0.96 1.62 2.74 2.27 2.94 0.07 1.82 1.83 1.79 0.34 1.68 3.01 1.69 0.59 1.17 1.13 1.43 1.68 1.88 2.49 2.93 1.58 0.OpenClose.73 2.05 1.18 0.93 0.82 1.48 4.09
1.58 2.04 1.16 1.21 1.12 1.90 0.56 1.44 1.26 1.45 1.38 1.21 1.87 1.87 4.52 1.80 1.11 1.02 0.76 0.65 1.36 1.34
1.34 0.05 1.76 2.46 3.38 1.45 1.30
1.57 0.81 1.82 1.29 2.49 1.88
0.73 0.73 1.70 0.36 3.23 1.90 1.54 1.70 0.04
1.91 1.55
0.80 2.28 3.83 2.83 3.67 0.33 0.52 1.35
.97 4.09 0.78 0.20 1.OpenHigh.61 1.98
0.29 0.33 3.88 2.46
1.58 1.66 1.23 1.55 1.15 0.08 0.54 1.86 1.42 1.14 0.73 1.89 0.93 0.22 0.76 1.23 1.58 1.96 0.50 1.05 1.24 0.15 0.Australia Year
Close.08 1.28 0.OpenCloseOpenHighOpenCloseOpenHighOpenClose Close Low Open Close Close Low Open Close Close Low Open Close Close Low Open VolatilityVolatility Volatility Volatility VolatilityVolatility VolatilityVolatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%)
1.58 1.38 1.56 1.37 1.81 1.84 1.55 2.OpenHigh.19 1.96 1.43 1.59 0.66 1.06 2.58 1.02 3.87 0.16 1.26 1.03 1.82 2.02 2.72 0.90 1.95 0.17 0.89 1.85 1.14 1.88 1.35 1.09 1.91 1.82 0.23 1.05 1.52 0.82 1.56 1.91 1.48 2.15 1.17 1.92
0.47 1.83 0.66
1.65 1.40 2.78
0.37 1.05 1.27 1.93
1.27 1.91 2.34 0.93 1.16 1.96 1.65 1.47 1.13 1.07 0.97 1.99 1.47 2.24 0.46 2.71
1.36 1.22 1.
75 1.31 2.86 2.98 2.87 1.03 1.66 2.14 2.43 0.81 1.59 0.29 1.66 6.56 3.78
2.60 1.05 1.OpenCloseOpenHighOpenCloseOpenHighOpenClose Close Low Open Close Close Low Open Close Close Low Open Close Close Low Open VolatilityVolatility Volatility Volatility VolatilityVolatility VolatilityVolatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%)
2.69 1.79 0.76 2.07 3.46
0.39 1.60 2.04 2.77 1.72 2.03 2.88 1.85 1.40 2.20 0.42 0.05 1.69
1.04 4.84 2.56 1.23 2.82 1.53 2.94 1.53 0.68 1.58 1.18 0.21 3.72 1.00 1.52 0.74 0.15 3.63 0.39 0.15 2.79 0.OpenHigh.94 1.16 1.84 0.33 2.96 2.89 1.40 1.80 0.94 1.23 1.48 0.60
3.14 1.18
0.70 3.42 2.19 2.36 0.64 3.69 1.68 1.46 2.54 1.82 0.13 1.88 1.32 2.42 2.46
.54 1.68 4.56
1.13 1.90 0.17 1.34 2.35
0.70 1.60 2.92 1.China Year
Close.46 6.72 1.57 1.39 1.04 1.63 0.45 0.22 1.81 1.49 0.48 2.OpenClose.87 0.12 1.84
0.80 0.65 3.44 1.14 1.06 2.81
3.01 2.88 3.53 1.69 0.OpenHigh.62 1.96 3.26 2.94 1.75 0.56
2.47 2.24 0.99 4.98 2.85 0.92 0.20 0.88 2.67 2.85 1.00 2.82 0.76 0.89 1.13
0.86 0.28 1.77 1.29 3.90 0.13 1.54 0.36 1.72 2.84 1.78 3.07 1.88 2.43
0.27 0.79 1.95 1.94 2.23 1.00 0.94 2.47 2.12 1.67 1.19 1.57 3.33 1.78 0.00 0.87
0.91 1.53 0.06 2.11 4.00 0.25 1.46 0.97 3.03 2.37 1.82 0.30 3.33 1.16 2.81 0.01 1.35 2.00 3.91 0.
38 1.60 3.58 1.50 1.47 1.51 2.61
0.20 3.31 2.93 1.42 0.44
1.69 2.39 1.22 2.OpenHigh.00 2.00 0.14 1.37 1.25 1.50 1.62
1.50 2.63 1.11 2.80
.60 3.45 1.51 1.49 2.25 1.51 1.14 3.73 1.71 1.87
0.86 2.19 1.23
0.07 2.00 1.00 0.50 1.96 1.10 1.00 1.15 2.43 2.25 2.19 1.10 2.25 1.07 1.81 1.05 1.65 1.50 2.95 1.00 0.OpenClose.38
4.52 1.10 2.62 1.80 2.57 1.23 1.00 0.60 2.36 2.08 2.96 1.93
1.53 1.71 2.43 1.66 1.65 2.33 1.43 2.57 0.00 1.OpenCloseOpenHighOpenCloseOpenHighOpenClose Close Low Open Close Close Low Open Close Close Low Open Close Close Low Open VolatilityVolatility Volatility Volatility VolatilityVolatility VolatilityVolatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%)
3.28 1.46 2.29 1.53 1.63 1.52 2.72 2.79 0.61 1.77 1.64 3.00 0.34 3.28 1.49 3.32 1.85 2.46 2.00 0.34 2.27
0.13 1.54 2.67 0.60 1.00 0.39 2.54 1.00 0.51 1.43 1.59 1.29 1.00 0.72 2.11 0.93
3.81 3.90 2.Mexico Year
Close.85 1.00 0.14 1.07 2.99 2.00 0.93 1.23
1.54 1.40 1.48 1.28 1.58 1.35
1.78 1.80 1.38 2.37 3.96 1.29 1.81 1.54 1.73 3.72 1.07 1.54 1.12 2.69 2.57 0.79 1.66 2.19 1.66 1.80 2.49 1.00 0.05 1.48 1.96 1.37
0.00 0.15 1.90 2.00 0.73 1.98 2.18 2.60 1.59 2.81 2.07 1.43 2.OpenHigh.22 1.94
0.71 2.11 1.43 2.22 2.00 0.07 1.23 1.00 0.08 1.04 1.05 2.21 1.11 1.11 1.53 1.
72 1.89 1.6 1.06 1.07 1.86 1.18 1.38 3.21
NA NA NA NA 1.High.15
0.26 2.42 2.80 1.70 1.21 1.64
2.91 2.85
NA NA NA NA 1.84 1.66 1.18 1.47 1.94 2.04 2.3 2.67 1.26 1.39 2.14 0.04 1.22 1.1 3.11 2.1 1.21 1.9 2.60 1.22 1.89 2.High.68 0.26 1.30 1.64 1.19 2.50 1.86 1.48 1.10 1.63 1.24 1.33 1.11 1.17
.88 1.47 1.57 1.OpenClose Close Low Open Close Close Low Open Volatility VolatilityVolatility Volatility VolatilityVolatility Volatility Volatility (%) (%) (%) (%) (%) (%) (%) (%)
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 1991-2003 1995-2003 2000-01 2002-03
1.2 2.02 1.00 2.85 1.5 1.03 1.52 1.63 1.33 1.83 1.25 1.43 1.36 2.29 1.01 2.70 2.74 1.13 2.36 1.Open.00 1.4 2.Open.42 3.17 2.52 1.23
NA NA NA NA 1.77 2.01 1.08 1.35 1.01 1.7 2 2.68 1.56 1.86 1.92 2.57 1.65 2.17
NA NA NA NA 0.56 1.08 1.41 1.81 1.72 1.69 2.59
1.01 1.26 2.97 1.71 2.Close.Sensex Year
Close.61 1.69 2.49 2.68 1.80 1.07 1.7 1.1 3.54 3.62 1.Open.77 1.75 1.89 3.22 1.
61 2.11 1.14 1.71 1.39 1.25 1.04
1.OpenHigh.Close.35 1.99 2.19
0.75 1.64 1.High.28 1.41
0.18 1.78
0.38 1.52 0.45 0.17 1.32 0.74 1.95 0.54 1.601 factor for H-L Volty.19 1.39
0.Open.33 1.11 1.60 2.Close.05 1.20 1.68
0.14 1.15 1.15 1.63 1.28 1.15 1.93 1.08 1.08 1.64 1.Open.34 1.74 1.88 0.28 1.69 0.48 0.73 1.19 1.80 1.91 1.84 1.01 0.33 1.52 0.40 1.06 1.19 1.76 2.27 1.01 1.15 1.37 1.64 0.Open.32 1.25 1.64 1.01 0.74 2.05 0.07 1.08 0.82 1.42
0.30 1.38 1.58
1.97 1.20 1.OpenHigh.33 0.38 1.05 1.20 1.11 1.23 1.29 1.93 1.01 0.62 2.68 1.06
1.63 1.36 1.01
1.45 1.36 1.03 1.42 1.06 1.55 0.33 1.43 1.33 1.00 0.74 0.16 0.65 1.03 1.13 1.53 1.55 0.52 1.OpenHigh.92 2.40 1.26 1.14 1.32
0.52 1.28 1.71 1.01 0.71 1.31 1.31 1.44 1.38 1.83 1.49 0.19 1.07 1.07 1.04 2.23 1.74 2.18 1.36 1.68 2.27 1.98 1.56 1.84 1.37
.29 1.78 1.38 1.85 0.40 1.41 0.16 1.66 2.47 1.07 1.40 0.49 0.Table 5 : Inter and Intra Day Volatility (with 0.Open.16 1.59 1.24 1.34 1.08
0.Close.60 1.00 0.21 1.91 2.40 1.77 1.48 0.00 0.04 1.88 1.27 2.43 1.52 0.00 1.39 1.39 1.51 1.71 1.29 1.75 1.58 1.OpenClose Close Low Open Close Close Low Open Close Close Low Open Close Close Low Open Volatility Volatility Volatility Volatility Volatility Volatility Volatilit y Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%)
1995 1996 1997 1998 1999 2000 2001 2002 2003 19952003 2000-01 2002-03
0.14 1.)
Year USA UK France Germany Close.91 1.59 2.28 1.77 1.99 1.65 1.
24 0.67 0.65 1.23 1.91 2.88 1.73 1.66
0.70 1.17
0.96 0.87 0.96 1.76
1.34 0.Year
Australia Singapore Malaysia Thailand Close.High.96 1.34 1.91 1.78
0.17 0.42 1.69 0.59 1.62 2.33 0.10 1.48 4.50 1.82 0.34 0.Open.13 1.46 2.78 0.09 0.15 1.87 0.23 1.47 1.73 0.70 0.26 1.88 2.76 1.93 0.56 0.80 2.OpenHigh.56 1.07 0.87 1.58 1.15 0.04 0.61 1.08 0.45 1.01 1.42 1.94 0.Open.43 1.Close.03
1.49 1.81 1.57 0.66 0.83 2.Close.22 1.74 2.93 1.15 1.90 1.89 0.37 1.34 1.16 1.36 1.82 1.27 1.05 1.38 1.67 0.66 1.Close.49 1.23 1.79 0.99 1.97 1.64 0.58 2.55
0.43 1.58 1.High.59 0.35
.27 2.65 1.08 1.50 0.06 1.88 0.81 2.58 1.93
1.29 2.14 1.54 1.58 1.87 1.81 0.38 1.88
1.73 2.17 1.05 1.01 1.15 1.46 3.40 2.93 1.61 1.69 0.72 0.89 1.85 1.00 1.49 1.08 0.54 1.58 0.22 0.24 0.54 0.Open.87 4.95 0.21 1.90 1.05 1.98
0.78 2.73 1.70 0.26 0.28 0.52 0.OpenClose Close Low Open Close Close Low Open Close Close Low Open Close Close Low Open Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%)
0.52 1.29 0.70 0.19 1.12 1.36 3.72 0.Open.OpenHigh.05 1.09 1.28 3.30
1.14 1.82 0.83 0.55 1.76 0.21 1.56 1.82 1.82 1.05 1.55 2.66 0.62 1.38 1.03 1.15 0.99 1.26 1.Open.09
0.02 0.84 1.63 1.33 3.42 1.86 1.01 0.30 1.52 1.17 1.57 0.13 1.56 1.11 0.
07 1.65 3.37 1.High.82 0.86 0.53 0.01 1.13 1.48 0.94 1.84
0.20 0.04 2.OpenClose Close Low Open Close Close Low Open Close Close Low Open Close Close Low Open Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%)
2.39 0.27 2.75 1.60
0.92 1.78 3.29 1.70 3.54 0.57 3.43 0.03 1.79 1.12 1.82 1.82 1.35 0.20 0.42 0.44 1.20 1.13 1.61 2.39 1.36 1.14 1.94 1.44 0.67 1.84 1.82 0.07 1.69 1.88 2.46 0.06 1.82 0.94 2.42 2.Open.53 1.13
0.45 0.76 0.00 2.19 1.72 1.30 2.Open.Close.13
0.28 1.17 1.95 1.79 0.88 3.97 1.41 0.02 1.06 2.42
1.81 0.Close.28 1.33 2.88 2.96 2.01 1.23 1.56
2.29 2.20 2.33 1.18 0.84 2.84 1.64 3.High.Year
China Indonesia Chile Brazil Close.24 0.81 1.54 1.22 1.77 1.90 1.66 2.96 3.43 3.72 1.66
2.00 0.90 0.77 1.66 6.46 1.27 0.00 0.80 1.60 1.34 1.49 1.90 0.87 1.15 2.89 1.Close.40 1.97 3.01 2.34 2.OpenHigh.36 0.12 1.89 1.39 1.Open.80 0.57 1.18 1.56
1.23 2.53 0.16 1.49 0.68 1.69 1.84 0.51 0.Open.81
3.52 0.Open.43
0.60 2.72 2.80 0.70 1.45 0.48 0.23 1.03 2.19 2.12 1.79 0.35 2.75 1.38 0.33 2.76 2.79 1.46
.11 1.87 0.51 0.56 1.47 2.41 0.47 0.46 6.40 2.58 1.88 1.54 1.14 1.60 2.60 0.98 2.98 2.91 0.92 0.05 1.OpenHigh.36 1.72 2.04 1.45 1.88 1.94 1.53 2.18
0.09 1.46
0.14 1.63 0.47 2.25 1.46 2.56
00 0.18 1.00 0.19 1.13 1.Open.22 2.51 1.00 2.02 1.96 1.51 0.Open.11 1.53 1.32 0.52 2.20 1.91 1.81 1.62 1.57 1.47 1.00 0.34 2.47 1.60 2.60 1.00 0.00 0.00 0.43 1.80 1.74 0.38 1.40 1.03 2.81 2.00 0.43 2.54 1.69 0.58 1.14 1.66 2.57 0.59 1.Open.11 1.73 1.65 1.79 0.03 1.22 2.09 1.33 1.32 1.27
0.08 1.73 3.10 1.44 1.29 1.69 2.50 1.42 1.10 2.78 1.72 1.21 1.07 1.83
0.19 1.94 0.Close.66 1.53 1.85 1.72 2.93 1.50 1.00 0.00 0.77 1.77 1.16 2.87
0.40 0.29 1.53 1.71 1.60 3.05 2.73 1.34 3.50 1.66 1.08 2.57 1.11 1.28 1.38 2.04
1.59 1.80
.63 1.80 2.43 2.11 1.72 2.48 1.High.50 1.28 1.25 1.54 1.54 1.35
1.14 1.64 3.00 0.48 1.23 1.25 1.51 1.12 2.85 1.00 0.10 2.Open.OpenHigh.85 2.93 1.Close.00 0.79 1.43 2.Close.31 2.00 0.15 0.24 1.61
0.14 1.50 1.29 1.High.50 2.43 1.58 1.90 2.20 3.07 1.16
1.43 2.46 2.48 1.44
0.39 1.Open.96 1.80 2.Year
Mexico South Africa Korea Taiwan Close.91
4.69 1.49 1.54 1.63 1.93
1.77 1.04 1.07 2.00 0.00 0.00 0.18 2.34
1.05 1.54 2.69 2.00 0.42 0.60 1.00 0.08 0.OpenClose Close Low Open Close Close Low Open Close Close Low Open Close Close Low Open Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%)
3.87 1.86 2.11 0.98 1.25 2.37
0.14 3.94
0.71 1.52 1.37 1.96 1.05 1.OpenHigh.07 1.00 1.22 1.62
1.59 2.
72 0.26 1.99
2.25 NA 1.56 1.3 1.84 1.06 1.67 1.2 2.57 1.7 1.22 1.02 1.Close.08 1.Year
Sensex S & P CNX Nity Close.2 1.68 1.07 1.22 1.17
.04 1.1 3.52 1.77 1.9 2.72 1.66 1.96 1.22 1.36 1.70 1.75 1.90 1.11 1.18 1.58 2.33 1.12 3.2 0.02 1.81 1.32 1.12 1.21 1.80 1.7 1.96 2.26 2.Open.45 1.01 1.83 1.41 1.26 1.98 1.52 1.12 1.31 1.43 1.26 NA 1.86 1.89 2.52 1.33 1.8 0.4 2.48 1.5 1.01 1.68 0.4 1.10 1.57 1.68 1.00 1.15
1 1.77 1.62 1.23
NA NA NA NA 1.89 3.63 1.03 1.21
NA NA NA NA 0.High.OpenClose Close Low Open Close Close Low Open Volatility Volatility Volatility Volatility Volatility Volatility Volatility Volatility (%) (%) (%) (%) (%) (%) (%) (%)
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 1991-99 1996-99 1991-2003 1995-2003 2000-01 2002-03
1.08 1.72 1.OpenHigh.24 1.01 1.50 0.20 NA 1.66 1.39 1.28 1.2 1.15 1.Open.68 1.3 1.47 1.25 2.56 1.01 2.81 1.64 1.72 1.89 1.18 1.01 1.01 1.84 1.07 1.30 NA 1.91 1.04 2.49 2.88 1.47 1.69 2.74 1.86 1.77 2.45 1.91 2.30 1.17
NA NA NA NA 0.57 1.11
NA NA NA NA 1.97 1.45 1.14 0.57 1.82 1.82 2.
52 1.21
0.07 1.97 1.08 1.90 0.15 1.89 2.49 2.45 0.56 1.68 1.30 1.52 1.67 1.47 1.57 1.82 1.10 1.66 1.74 1.31 1.04 1.17
.07 1.72 1.48 1.02 1.39 1.25 1.21 1.India S & P CNX Nifty (in Dollar terms) Year CloseOpenClose Close Volatility Volatility (%) (%) High-Low Open-Open Volatility Volatility (%) (%)
1995 1996 1997 1998 1999 2000 2001 2002 2003 1996-99 1995-2003 2000-01 2002-03
0.Table 6: Inter and Intra Day Volatility .56
1.77 1.72 1.81 1.77 2.33 1.58 2.98 1.30 1.2 2.01 1.57 1.86 1.02 1.22 1.70 1.86 1.20 1.26 1.84 1.
16 1.68 1.26 2.23
.12 3.03 1.01 1.01 2.47 1.62 1.75 1.14 0.High-Low OpenClose Close Volatility Open Volatility Volatility (%) Volatility (%) (%) (%)
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 1991-99 1996-99 1991-2003 2000-01 2002-03
0.18 1.56 1.77 1.91 1.29 1.89 3.82 2.68 1.1 3.99
2.74 1.08 1.India Sensex (in Dollar terms)
CloseOpen.43 1.00 1.50 0.11 1.4 2.59
1.02 1.12 1.04 2.24 1.96 2.01 1.06 1.45 1.12 1.01 1.90 1.33 1.88 1.81 0.Table 7 :Inter and Intra Day Volatility .90 2.52 1.22 1.29 1.42 1.52 1.26 1.66 1.80 2.89 2.03 1.64 1.25 2.26 1.68 0.36 1.83 1.18 0.96 1.72 0.34 1.57 1.18 1.28 1.63 1.23 1.22 1.
66 2.83 0.10
0.68 1.74 1.27 1.02 1.13 2.80 3.94 1.01 1.00 1.27 1.19 0.70 3.87 1.50 1.63 1.00 1.79 1.75 1.63 1.22 1.11 0.72 0.03 1.99
7.17 1.62 1.India Sensex (in Rupee terms) Year CloseOpenHigh-Low Close Close Volatility Volatility Volatility (%) (%) (%) Open-Open Volatility (%)
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 1991-2003 2000-01 2002-03
7.43 1.36 1.73 1.56 1.62 2.50 0.90 1.66 2.44 1.43 1.28 1.08 1.49 2.96 1.39 1.22 1.Table 8 : Inter and Intra Day Volatility .76 2.00
.00 0.06 1.81 0.80 1.54 1.98 2.06
1.84 1.54 2.82 2.23 1.50 1.01 1.38 1.47 1.17 1.17 1.
60 1.57 2.High-Low Open-Open Close Close Volatility Volatility Volatility Volatility (%) (%) (%) (%)
1.23 1.07 1.07 1.48 1.53 2.84 1.63 1.52 1.India S & P CNX Nifty (in Rupee terms) Year CloseOpen.98 1.57 1.02 1.11
1.82 1.17
.43 1.33 1.45 1.01 1.64 1.70 1.21
0.10 1.00 1.21 1.75 1.01 1.02 1.15
1.84 2.03 1.88 1.79 1.Table 9 : Inter and Intra Day Volatility .23 1.30 1.20 1.66 2.69 1.87 2.36 1.64 1.81 1.89 1.97 1.25 1.15 1.57 1.
36 1.45 5.87 2.58 1.39 2.27 5.90 2.Table 10 : DailyAverage Square Root of Return Squared (percentage) Year BSE NSE
Yearly Avg.00 5.33 5.58 4.04
.71 2.86 4.42 4.01 1.34 5.58 3.79 3.89 2.02 5.85 2.92 4.91 5.07 1.78 9.89 NA NA NA NA 1.50 1.60 1.19 1.96 1.02 5. Yearly Avg. Top 5% Avg. Top 5% Avg 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2.91 2.01 1.82 1.75 1.27 NA NA NA NA 2.20 6.11 1.24 5.40 1.22 1.27 3.66 1.71 3.
5 199 6 199 7 199 8 199 9 199 0 200 1 200 2 200 3 200
.Chart 1 : Inter and Intra-day Volatility (S&P CNX Nifty.5
1. in Dollars)
Chart 2 : Inter.5 3 2.5 1 0.5 2 1.and Intra-day Volatility (Sensex. in Dollars)
3.5 0 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 CC OC HL OO
Chart 3 : Inter and Intra-day Volatility Sensex (in Rupees)
0 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 C-C O-C H-L O-O
0 1995 1996 1997 1998 C-C 1999 O-C 2000 H-L 2001 O-O 2002 2003
.Chart 4 : Inter and Intra-day Volatility S&P CNX Nifty (in Rupees)
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