volatility DefinitionThe relative rate at which the price of a security moves up and down. Volatility is found by calculating the annualized standard deviation of daily change in price. If the price of a stock moves up and down rapidly over short time periods, it has high volatility. If the price almost never changes, it has low volatility.

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Stock Valuation MethodsStocks have two types of valuations. One is a value created using some type of cash flow, sales or fundamental earnings analysis. The other value is dictated by how much an investor is willing to pay for a particular share of stock and by how much other investors are willing to sell a stock for (in other words, by supply and demand). Both of these values change over time as investors change the way they analyze stocks and as they become more or less confident in the future of stocks. Let me discuss both types of valuations. First, the fundamental valuation. This is the valuation that people use to justify stock prices. The most common example of this type of valuation methodology is P/E ratio, which stands for Price to Earnings Ratio. This form of valuation is based on historic ratios and statistics and aims to assign value to a stock based on measurable attributes. This form of valuation is typically what drives long-term stock prices. The other way stocks are valued is based on supply and demand. The more people that want to buy the stock, the higher its price will be. And conversely, the more people that want to sell the stock, the lower the price will be. This form of valuation is very hard to understand or predict, and is often drives the short-term stock market trends. In short, there are many different ways to value stocks. I will list several of them here. The key is to take each approach into account while formulating an overall opinion of the stock. Look at each valuation technique and ask yourself why the stock is valued this way. If it is lower or higher than other similar stocks, then try to determine why. And remember, a great company is not always a great investment. Here are the basic valuation techniques:Earnings Per Share (EPS). You've heard the term many times, but do you really know what it means. EPS is the total net income of the company divided by the number of shares outstanding. It sounds simple but unfortunately it gets quite a bit more complicated. Companies usually report many EPS numbers. They usually have a GAAP EPS number (which means that it is computed using all of mutually agreed upon accounting rules) and a Pro Forma EPS figure (which means that they have adjusted the income to exclude any one time items as well as some non-cash items like amortization of goodwill or stock option expenses). The most important thing to look for in the EPS figure is the overall quality of earnings. Make sure the company is not trying to manipulate their EPS numbers to make it look like they are more profitable. Also, look at the growth in EPS over the past several quarters / years to understand how volatile their EPS is, and to see if they are an underachiever or an overachiever. In other words, have they consistently beaten expectations or are they constantly restating and lowering their forecasts?The EPS number that most analysts use is the pro forma EPS. To compute this number, use the net income that excludes any one-time gains or losses and excludes any non-cash expenses like stock options or amortization of goodwill. Then divide this number by the number of fully diluted shares outstanding. You can easily find historical EPS figures and to see forecasts for the next 1-2 years by visiting free financial sites such as Yahoo Finance (enter the ticker and then click on "estimates").By doing your fundamental investment research you'll be able to arrive at your own EPS forecasts, which you can then apply to the other valuation techniques below.Price to Earnings (P/E). Now that you have several EPS figures (historical and forecasts), you'll be able to look at the most common valuation technique used by analysts, the price to earnings ratio, or P/E. To compute this figure, take the stock price and divide it by the annual EPS figure. For example, if the stock is trading at $10 and the EPS is $0.50, the P/E is 20 times. To get a good feeling of what P/E multiple a stock trades at, be sure to look at the historical and forward ratios.Historical P/Es are computed by taking the current price divided by the sum of the EPS for the last four quarters, or for the previous year. You should also look at the historical trends of the P/E by viewing a chart of its historical P/E over the last several years (you can find on most finance sites like Yahoo Finance). Specifically you want to find out what range the P/E has traded in so that you can determine if the current P/E is high or low versus its historical average.Forward P/Es are probably the single most important valuation method because they reflect the future growth of the company into the figure. And remember, all stocks are priced based on their future earnings, not on their past earnings. However, past earnings are sometimes a good indicator for future earnings. Forward P/Es are computed by taking the current stock price divided by the sum of the EPS estimates for the next four quarters, or for the EPS estimate for next calendar of fiscal year or two. I always use the Forward P/E for the next two calendar years to compute my forward P/Es. That way I can easily compare the P/E of one company to that of it's competitors and to that of the market. For example, Cisco's fiscal year ends in July, so to compute the P/E for that calendar year, I would add together the quarterly EPS estimates (or actuals in some cases) for its quarters ended April, July, October and the next January. Use the current price divided by this number to arrive at the P/E.Also, it is important to remember that P/Es change constantly. If there is a large price change in a stock you are watching, or if the earnings (EPS) estimates change, be sure to recompute the ratio.Growth Rate. Valuations rely very heavily on the expected growth rate of a company. For starters, you can look at the historical growth rate of both sales and income to get a feeling for what type of future growth that you can expect. However, companies are constantly changing, as well as the economy, so don't rely on historical growth rates to predict the future, but instead use them as a guideline for what future growth could look like if similar circumstances are encountered by the company. To calculate your future growth rate, you'll need to do your own investment research. The easiest way to arrive at this forecast is to listen to the company's quarterly conference call, or if it has already happened, then read a press release or other company article that discusses the company's growth guidance. However, remember that although company's are in the best position to forecast their own growth, they are not very accurate, and things change rapidly in the economy and in their industry. So before you forecast a growth rate, try to take all of these factors into account. And for any valuation technique, you really want to look at a range of forecast values. For example, if the company you are valuing has been growing earnings between 5 and 10% each year for the last 5 years but suddenly thinks it will grow 15 - 20% this year, you may want to be a little more conservative than the company and use a growth rate of 10 - 15%. Another example would be for a company that has been going through restructuring. They may have been growing earnings at 10 - 15% over the past several quarters / years because of cost cutting, but their sales growth could be only 0 - 5%. This would signal that their earnings growth will probably slow when the cost cutting has fully taken effect. Therefore you would want to forecast earnings growth closer to the 0 - 5% rate than the 15 - 20%. The point I'm trying to make is that you really need to use a lot of gut feel to make a forecast. That is why the analysts are often inaccurate and that is why you should get as familiar with the company as you can before making these forecasts.PEG Ratio. This valuation technique has really become popular over the past decade or so. It is better than just looking at a P/E because it takes three factors into account; the price, earnings, and earnings growth rates. To compute the PEG ratio (a.k.a. Price Earnings to Growth ratio) divide the Forward P/E by the expected earnings growth rate (you can also use historical P/E and historical growth rate to see where it's traded in the past). This will yield a ratio that is usually expressed as a percentage. The theory goes that as the percentage rises over 100% the stock becomes more and more overvalued, and as the PEG ratio falls below 100% the stock becomes more and more undervalued. The theory is based on a belief that P/E ratios should approximate the long-term growth rate of a company's earnings. Whether or not this is true will never be proven and the theory is therefore just a rule of thumb to use in the overall valuation process.Here's an example of how to use the PEG ratio. Say you are comparing two stocks that you are thinking about buying. Stock A is trading at a forward P/E of 15 and expected to grow at 20%. Stock B is trading at a forward P/E of 30 and expected to grow at 25%. The PEG ratio for Stock A is 75% (15/20) and for Stock B is 120% (30/25). According to the PEG ratio, Stock A is a better purchase because it has a lower PEG ratio, or in other words, you can purchase it's future earnings growth for a lower relative price than that of Stock B.Return on Invested Capital (ROIC). This valuation technique measures how much money the company makes each year per dollar of invested capital. Invested Capital is the amount of money invested in the company by both stockholders and debtors. The ratio is expressed as a percent and you should look for a percent that approximates the level of growth that you expect. In it's simplest definition, this ratio measures the investment return that management is able to get for its capital. The higher the number, the better the return.To compute the ratio, take the pro forma net income (same one used in the EPS figure mentioned above) and divide it by the invested capital. Invested capital can be estimated by adding together the stockholders equity, the total long and short term debt and accounts payable, and then subtracting accounts receivable and cash (all of these numbers can be found on the company's latest quarterly balance sheet). This ratio is much more useful when you compare it to other companies that you are valuing.Return on Assets (ROA). Similar to ROIC, ROA, expressed as a percent, measures the company's ability to make money from its assets. To measure the ROA, take the pro forma net income divided by the total assets. However, because of very common irregularities in balance sheets (due to things like Goodwill, write-offs, discontinuations, etc.) this ratio is not always a good indicator of the company's potential. If the ratio is higher or lower than you expected, be sure to look closely at the assets to see what could be over or understating the figure.Price to Sales (P/S). This figure is useful because it compares the current stock price to the annual sales. In other words, it tells you how much the stock costs per dollar of sales earned. To compute it, take the current stock price divided by the annual sales per share. The annual sales per share should be calculated by taking the net sales for the last four quarters divided by the fully diluted shares outstanding (both of these figures can be found by looking at the press releases or quarterly reports). The price to sales ratio is useful, but it does not take into account any debt the company has. For example, if a company is heavily financed by debt instead of equity, then the sales per share will seem high (the P/S will be lower). All things equal, a lower P/S ratio is better. However, this ratio is best looked at when comparing more than one company.Market Cap. Market Cap, which is short for Market Capitalization, is the value of all of the company's stock. To measure it, multiply the current stock price by the fully diluted shares outstanding. Remember, the market cap is only the value of the stock. To get a more complete picture, you'll want to look at the Enterprise Value.Enterprise Value (EV). Enterprise Value is equal to the total value of the company, as it is trading for on the stock market. To compute it, add the market cap (see above) and the total net debt of the company. The total net debt is equal to total long and short term debt plus accounts payable, minus accounts receivable, minus cash. The Enterprise Value is the best approximation of what a company is worth at any point in time because it takes into account the actual stock price instead of balance sheet prices. When analysts say that a company is a "billion dollar" company, they are often referring to it's total enterprise value. Enterprise Value fluctuates rapidly based on stock price changes.EV to Sales. This ratio measures the total company value as compared to its annual sales. A high ratio means that the company's value is much more than its sales. To compute it, divide the EV by the net sales for the last four quarters. This ratio is especially useful when valuing companies that do not have earnings, or that are going through unusually rough times. For example, if a company is facing restructuring and it is currently losing money, then the P/E ratio would be irrelevant. However, by applying a EV to Sales ratio, you could compute what that company could trade for when it's restructuring is over and its earnings are back to normal.EBITDA. EBITDA stands for earnings before interest, taxes, depreciation and amortization. It is one of the best measures of a company's cash flow and is used for valuing both public and private companies. To compute EBITDA, use a companies income statement, take the net income and then add back interest, taxes, depreciation, amortization and any other non-cash or one-time charges. This leaves you with a number that approximates how much cash the company is producing. EBITDA is a very popular figure because it can easily be compared across companies, even if all of the companies are not profitable.EV to EBITDA. This is perhaps one of the best measurements of whether or not a company is cheap or expensive. To compute, divide the EV by EBITDA (see above for calculations). The higher the number, the more expensive the company is. However, remember that more expensive companies are often valued higher because they are growing faster or because they are a higher quality company. With that said, the best way to use EV/EBITDA is to compare it to that of other similar companies.Now that we've covered many of the stock valuation ratios, it's time to do your competitive analysis. MethodologyExisting studies of volatility across markets, (Bekaert and Harvey 1995), have shown that thecharacteristics of emerging market equities are vastly different from those for developed marketsequities. The emerging market returns in the past have demonstrated certain distinguishingfeatures; average returns were higher, correlation with developed market returns was low,investors looked to emerging markets for risk diversification, returns were more predictable andvolatility was higher. Our research focuses particularly on return and volatilities behavior, acrossmarkets.We provide a detailed analysis of equity market volatility in 18 developed and emergingmarkets, including India. Our research helps understand the time series variation and higherorder moments in the volatility of equities in these markets.We use the International Organisation of Securities Commission (IOSCO) classification tocategorise countries into emerging and developed markets. The names of the countries, indicesand data periods are provided in the following Exhibit I. There are six countries from developedcapital markets and twelve from emerging markets including India. Bloomberg database is usedby us as the data source. To some extent our choice and number of countries is limited toavailability of data from the Bloomberg Service. As far as India, two popular indices viz., BSESensex and S&P CNX Nifty are analysed, while for all other countries single index is used foreach country.EXHIBIT - INAMES OF THE COUNTRIES, INDICES AND DATA PERIODCountry Index Period ObservationsUSA S&P 500 80:1 03:12 6061UK FTSE 100 84:1 03:12 4668France CAC 40 87:7 03:12 4133Germany DAX 30 Xetra 80:1 03:12 6023Australia All Ordinaries 84:1 03:12 5076Hong Kong, China Hang Seng 81:1 03:12 5685Singapore Straits Time 85:1 03:12 4755Malaysia Kuala Lumpur Composite 80:1 03:12 5905Thailand Stock Exchange of Thailand 87:7 03:12 4031China Shanghai Composite 95:1 03:12 2175Indonesia Jakarta Composite 91:11 03:12 2964Chile Chile Stock Market General 91:9 03:12 3079Brazil IBOV 92:1 03:12 2955Mexico MEXBOL 92:1 03:12 3005South Africa JALSH 95:6 03:12 2125Korea KOSPI 81:4 03:12 6373Taiwan TWSE 83:10 03:12 5630India BSE Sensex 85:1 03:12 4286India S&P CNX Nifty 95:1 03:12 2221Bloomberg usually chooses the most popular indices to describe the movements in stock pricesin the respective markets. Among these indices for each market, we choose the principallyrecognised stock price index of each country and obtain the time series data for a 24 year periodfrom 1980:1 2003:12. Index series are published in the currency of local markets. For crosscountrycomparisons, all indices are converted into one common currency, the US dollar, byusing a standard conversion method provided in the Bloomberg system. For some countries, thedata is not available for the entire period, either as the markets were not fully developed andhence there were no indices or the data had not been captured by Bloomberg. Consequently, thedata points are not uniform for all the countries. The analysis and conclusions are not affected bythis shortcoming as we study each country separately and on an annual basis.We use the standard indices with the limitation that the number of stocks in the national index,asset concentration, relative weights, and cross-sectional volatility of individual stocks couldhave an impact on the results. Despite this limitation, the study would still give a strong insightinto the volatility of the markets.We begin by analysing the time series of volatility. We use standard deviation as a proxy forvariability in stock prices. As a first step, we calculate returns using logarithmic method asfollows:rt = ln t 1tII(1)where rt and It indicate return and index value respectively at time t.Next, arithmetic mean, standard deviation, skewness and excess kurtosis are computed asdiscussed later. Past cross-country studies have indicated non-normality of stock returns. Wetherefore, go beyond the first and second order moments, and compute third and fourth ordermoments to infer more information about the patterns of price returns.VolatilityWe use the following standard formula for computing standard deviation.1 n 1r r 2 t s (2)We use Parkinsons (1980) model, which uses intra-day highs and lows, for estimation of intradayvolatility. Since, most asset pricing models are based on continuous time the extreme valueestimators are more efficient. We use the following Parkinson model to estimate intra-dayvolatility. This volatility measure is referred to as high-low volatility in our paper usage of factor0.601 scales down volatility although, statistically, it is correct. Therefore, in order to provideadditional information on intra-day (high-low) volatility we computed it K = 1 also.1 log2 t t s k n H L (3)where k = 0.601 and Ht and Lt denote intra-day high and low respectively.We also use the above formula i.e.1/ log( / ) 2 t t s k n H L (4)with k = 1 to measure high-low volatility.We calculated square root of the average r 2 for each year to capture the absolutechanges in volatility and this is called return squared volatility. Here r is thedaily log-normal return and is defined asrt = 1 ln / t tI I * 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. We then tookthe square root of this average r 2 to arrive at the volatility figure.After calculating the square root of the average r 2 in the method described abovewe sorted the top 5 percent of the same (i.e. square root of the average r 2 ) andcompared this top 5 percent of the observations of a particular year with thesquare root of the average r 2 calculated for the whole year.We use the Garman and Klass (1980) estimator which uses four intra-dayvariation statistics of open, high, low and close. This volatility measure isreferred to as open-close volatility in our paper. The following model is used forthis estimator.1 1 2log2 2 log( 2) 1log( / )2 t t t t s nH L C O (6)where Ht , Lt , Ct, and Ot denote intra-day high, low, close and open respectively.SkewnessAs stated previously, stock returns exhibit non-normality. If the returns arenormally distributed, then coefficients of skewness and excess kurtosis should beequal to zero. We use the following model to measure non-normality orasymmetry of equity returns.3 3Sk n 2 n 1 n 2 m s (7)where : n = sample size,m3 = third moment about the mean, ands = standard deviationExcess KurtosisWe measure the excess kurtosis by the following model244 2Ku n2 n 1 n 2 n 3 n 1 m 3 n 1 m s (8)where n = sample sizem4 = fourth moment about the mean,m2 = second moment about the mean, ands = standard deviationA comparison of a normal distribution with a distribution exhibiting positiveexcess kurtosis reveals the following points. For example, two distributions havethe same mean and variance, but the positive excess kurtosis distribution is morepeaked and has fatter tails. It is very interesting to note what happens when wemove from a normal distribution to a distribution with positive excess kurtosis.Probability mass is added to the central part of the distribution and to the tails ofthe distribution. At the same time, probability mass is taken from regions of theprobability distribution that are intermediate between the tails and the centre.The effect of excess kurtosis is therefore to increase the probability of very largemoves and very small moves in the value of the variable, while decreasing theprobability of moderate moves.Analysis of ResultsTable 1 provides details of daily mean return and daily standard deviations for the samplecountries over 24 year period from 1980 to 2003. For certain countries, the starting year is not1980 owing to non-availability of data for various reasons that include :a) The markets might have started stock exchanges in the later period;b) The source, Bloomberg, might not have collected information for these countries even thoughstock exchanges existed; andc) Any other reason.Daily mean return and volatility (standard deviation) are calculated for each country. However,in the long run daily retur n works out to 0.04 percent for USA, and for many other developedcountries it varies from 0.02 percent to 0.04 percent. Some of the emerging markets, in fact, havenegative returns even over a very long period of time. For example Indonesia recorded -0.01percent returns. One interesting observation is that many emerging markets witnessed almostzero returns and high volatility which implies that these markets provide low or negative rate ofreturns with high volatility. Fund Managers and others investors have a lesson here. Emergingmarkets exhibit bouts of return and volatility patterns. Therefore, investors should enter and exitat appropriate time otherwise they would be losers. The experience of India tells a differentstory. It provides a daily average rate of return of 0.04 percent and a volatility of 1.89 percent fora long period of time (Sensex) which is far better than the rest of the emerging market and manyof the major markets.Both returns and volatility exhibit high variation over a period and across countries. In 1987,USA experienced high daily volatility of 2.12 percent compared to average of 1.07 percent. Againin 2002 and 2000 the volatility in the US was 1.64 percent and 1.40 percent respectively. From theTable 1 it is clear that second part of the 1990s and 2000, 2001 and 2002 experienced consistentlyhigh volatility when compared to preceding period as well as to the average. The years 1995,1993 and 1992 had low volatility of 0.49 percent, 0.54 percent, 0.61 respectively in t he USA.The third largest equity market in the world reside in the UK (in terms of market capitalization).The UK provides equal average returns but high dispersion compared to the US with 0.04 percentaverage daily returns and 1.23 percent standard deviation. The volatility was at its peak in 1984with 2.72 percent followed by 2.52 percent (1985) and 1.82 percent (1987). 1996, 1995 and 1994were relatively calm years with 0.63 percent, 0.74 percent and 0.81 percent volatility respectively.Between the US and the UK, the UK experienced higher volatility, both on high and low sides aswell as average.Other major markets analyzed include France, Germany and Australia. From the Table 1 it isclear that these countries do exhibit low return and higher volatility compared to the US. Theaverage return in France, Germany, and Australia were 0.03 percent, 0.04 percent and 0.02percent whereas the volatility was 1.40 percent, 1.44 percent and 1.21 percent respectively.Among these countries, Australia had highest volatility of 2.61 percent in 1987 followed byGermany at 2.39 percent and France 2.29 percent in1987. One significant observation is that allthese countries including emerging markets countries experienced high volatility from 1997 to2002 which indicates that there is a large co-movement in the prices of indices and in theunderlaying stocks. This also provides evidence to indicate extent of globalization of markets.Yet another observation is in 2003, the volatility slowed down in almost all the countries which isanalyzed in this sample. One more interesting finding is that 2000, 2001 and 2002 are the years inwhich many countries threw up negative returns and in these years by and large the volatilitieshave been higher than immediate preceding years with positive retur ns. There is a largeliterature which corroborates evidence on longer persistence of negative volatility and thenegative volatility being higher than the positive volatility.A close look at the Table 1, further reveals that emerging markets experienced higher volatilityaccompanied by lower or negative return. Malayasia, Thailand, China, Indonesia, Chile, Brazil,Mexico, South Africa, South Korea and Taiwan all support this finding. China and India are tosome extent exceptional. China has a short history of capital market and in this short history itprovided daily average returns of 0.04 percent, the same as of USA. However, its volatility isalmost twice as much of USA. India with its long history provides higher return of 0.04 percentwith a low volatility compared to China but higher than America. Countries like Indonesia,Brazil and Mexico have had very high volatility of 10.49, 6.97 and 3.96 respectively in certainyears.Emerging markets also recorded very high volatility in several years. Indonesia had the highestvolatility of 10.49 percent (1998) followed by 7.38 percent (2000), 7.27 percent (2001), Brazil with6.97 percent (1992), 3.93 percent (1994), 3.68 percent(1995), Mexico with 3.96 percent (1995), 2.72percent (1998) and 2.64 percent (1994). Though India did show some amount of high volatilitybut it is low compared to any of these emerging countries. The highest was in 1992 at 3.45percent followed by 2.50 percent (1990) and 2.23 percent (1991). India recorded lowest volatilityin 2002 at 1.11 percent followed by 1.18 percent (2003) 1.32 percent (1995).The daily average return and average volatility are useful to the policy makers, regulators,market participant and even investors. Volatility figures are also important for derivativetraders. Still many traders continue to use realized volatility as opposed to implied volatility.Table 2, provides statistics pertaining to asymmetrics such as skewness and kurtosis (higherorder moments). There is a clear patterns available between developed capital markets andemerging capital markets overtime. Developed markets experienced very high negativeskewness and high kurtosis in 1987 which was extremely undesirable because all the returnsearned by investors previously were erased. Countries like Hongkong, (China), Australia, USA,The UK, among developed markets have had very high kurtosis, in that order, apart fromnegative skewness. The late 1980s and the late 1990s exhibited asymmetry in returndistributions. Reasons for this behavior include 1987 great fall in the US stock market and itscontagion effect on some of the markets. The East Asian crisis could be one of the reasons for thenegative skewness and high kurtosis. Stock markets were relatively stable and returns followednear normal distribution for the past five years (1999 to 03).Higher order moments for sensex and Nifty are calculated from 1985 and 1995 respectively.Surprisingly, Indian market indices showed very high stability and normality. Both skewnessand kurtosis are relatively low. In the years, 1987, 1997, and 1998, the third and fourth ordermoments are comparatively low. Like other markets, India also followed quieter moments from1999 to 2003. it may be possible to conclude that Indian market exhibited less asymmetry in theentire period.Inter and Intra-day volatilitySo far we have discussed inter-day volatility by computing close to close index level on dailybasis. For many fund managers, investors, regulators and policy makers, in the recent times,intra-day volatility has assumed considerable significance because of its influence on the decisionof the market participants and its impact on other instruments such as derivatives. Severalmetrics are employed to estimate intra-day volatility :(a) open-close index level(b) high low index level and(c) open to open index levelsFor all the sample countries and for India, these metrics are computed. Open to close volatilityprovide information on change of the prices during the day. There is an elaborate literature toshow that volatility is a function of length of time that means, longer the trading hours higher isthe expected volatility. This is important mainly for India as the trading hours increased over aperiod of time. In the open-out-cry system, the market was open for about two hours. Later onnumber of trading hours were extended. With the implementation of computer screen basedtrading, number of trading hours have been enhanced. Now the market is open for almost 6 hours. Therefore, one has to keep this in mind while interpreting the results.High-low volatility conveys extreme movements and dispersion during the trade time. A veryhigh high-low volatility is likely to scare investors and lead sometimes to panic conditions in themarket place. Therefore, regulators, policy makers and SROs strive to implement policies thatsmoothen information flow and they also ensure certain measures which ensure boundedextremes with the help of circuit breakers, exposure limit, margin etc. Open to open volatility isvery important for several of the participants. High open to open volatility reveals informationalasymmetry and also overflow of information. Any positive or negative information that comesafter the close of the market and before the start of the next days trading, is expected to getreflected in the opening prices of shares and on the index. Significant economic and sociopoliticaldevelopments induce price movements and the extent of price movement depend onseverity of information.Intra-day volatility and developed capital marketsIn the US, open to open and close to close volatility appears to be neck to neck. This indicatessmooth flow of information during the day as well as over -night. Extreme volatility, high-low isthe highest among the four types of volatility measured as was the case with inter -day volatility.It appears that the US also scores over other developed markets in terms of intra-day volatility.In the UK, intra-day volatility, open to open, is slightly higher than inter-day volatility and lowerthan open to close volatilit ies. High-low volatility, in the UK also, is the highest among allvolatility. The volatility is on the rise for the past five years. France scored higher volatilitycompared to the UK and USA. Open to close volatility, in case of France, is lower than open toopen and close to close. The volatility in Germany is higher than France, The UK and USA. Highlowvolatility appears to be very high in Germany. In the year 2002, 2001 and 2003, it almosttouched 3 percentage points and peaked at 3.79 percent in 2002 and it appears to be highestamong all the developed markets in that year. Intra-day dispersion is also high. Australiaappears to have comparatively quieter markets. Intra-day and inter -day movements in stockprices are considerably stable in Australia. Inter -day volatility has been consistently lower than 1percent and it is half of it in 2002 and 2003. Even the high and low price movement variation isalso low.Emerging capital marketsEmerging markets exhibited higher intra-day volatility compared to developed markets. It is asign of an emerging market owing to economic and socio-political variations, the volatility in theemerging markets is generally on the high side. Countries like Indonesia, Brazil and SouthKorea, did show higher intra-day volatility. Among all the emerging countries studied, Brazilexperienced very high intra-day volatility and also extreme value volatility followed byIndonesia, South Korea and Mexico.Intra-day volatility for India has been computed for 13 years. Compared to most of the emergingmarkets sampled here, intra-day volatility in India is low. Extreme value volatility touched itspeak in 2000 at 3.17 percent and it continuously slided in the following years and marginallyincreased to 1.69 percent in 2003. Between BSE Sensex and S&P, CNX, Nifty, Nifty appears to bemore volatile both in terms of open to close and high low dispersions. In India open to open,volatility is always higher than close to close volatility and many a times higher than open toclose. This observation holds true to both the major exchanges. Intra-day volatility in 2003 hasbeen very slightly higher than the immediate preceding years though nothing disturbing isevidenced. Only Nifty showed a little more intra-day volatility compared to the previous yearand to the Sensex.Indian MarketThere have been reports, mostly in the popular press, citing that the intra-day volatility inparticular and volatility in general went up in 2003 and more so in the first three months of 2004.An attempt has been made to calculate inter and intra-day volatility for both Sensex and Niftywith reference to these periods also. A close examination of the Tables 4, 5 and 6 with regard toopen to close volatility and high low volatility reveals that the perceptions are not altogethercorrect. In fact, although the parameters registered their peak in 2000, they fell down further in2001 and 2002. However, the volatility as per these two parameters in 2003 is only slightly highercompared to 2002, but when compared to 2001 and 2000 this is much lower and about 50 percentof what it was in 2000. In the first 3 months of 2004 volatility calculation reveals that high lowvolatility slightly went up in January 2004 to 2.10 percent but it is much lower than what wasrecorded in 2000 and 2001. Open close volatility however, continuous to be low and although theparameters further receded in February and March 2004. The results are more or less the samefor both the Indian indices.Tables 8 and 9, Charts 3 and 4 provide information on inter and intra-day volatility for bothSensex and Nifty in terms of Indian rupees (not adjusted for $ terms). The tables and chartsevidently exhibit a close relationship between inter and intraday relationship. Close to close andopen to open volatility moved in tandem with little divergence in a few periods. This littledivergence was evident from 1997 to 2002. The volatility levels are almost identical. As perfinance theory, in an efficient market both are supposed to be almost the same because the timelength is identical and if there are no informational asymmetry then these two parametersconverge and have identical volatility. Only in case of Nifty, the divergence was little higher andit was highest in 1997. From 1998 the indicators traveled nearly together. Intra-day volatilityparameters : open-close and high-low also experienced close togetherness excepting for 1991. Theintegration between these two parameters is higher in case of Sensex, compared to Nifty. Thedivergence, Nifty, prevailed for the entire period from 1995 to 2003 and they never crossed. Thisis something very intriguing and deserves micro investigation for the purpose of effectivedissemination of information.High and low volatility ( Volatility Transmission)With a view to finding out the extent of integration and segmentation of market it was decided toidentify the top three and bottom three volatility years for each country in the sample. If onecountry (mainly the dominant market) experiences extreme volatility in any given date/givenperiod and if markets are integrated then, the volatility is expected to get transmitted from onemarket to another. Many institutional investors are common throughout the world, due toglobalization. Therefore, sudden change in volatility will affect the sentiments of investors and itwill have impact on other markets also.In 1987, USA exhibited highest volatility which is also seen in the UK, France, Germany,Australia, Hong Kong, Singapore, Malaysia and Thailand, while rest of the countries did not feelit. If we look at the non-affected countries, they were basically closed or semi-closed markets in1987 and in some countries such as China, Indonesia, did not have markets. USA had the lowestvolatility in 1995 which is felt in other countries, mainly major markets, such as the UK,Germany, Australia, Thailand and Korea. In other words, it may be reasonable to conclude thatvolatility transmits across countries if there is a financial market integration. Therefore, policymakers and regulators have to be extremely cautious while initiating measures that affects stockprices. It also demands high level of information sharing and also co-ordination so that marketsacross the globe will have less of volatility or sudden bouts of volatility which is likely to affectinvestor sentiments.Extreme volatility analysis (India)Charts for BSE Sensex and NSE Nifty and tables for both the indices are drawn separately withextreme positive and negative price movements. In this analysis highest index movement on anyday in a year has been identified. Following 10 day price movement have been analyzed to findout the extent of persistence in volatility. From the charts and the tables1, it is clear that thenegative volatility is highest in 1991, 1992 and 1993. Negative price movements crossed 15percent in 1993 and it was about 15 percent and 10 percent in 1991 and 1992 respectively.Whenever, the volatility was higher, it was negative volatility. When the volatility is stable, thepositive volatility is higher than the negative volatility. For example in 1994, 1995 and 1996, theprice variation is higher on positive side compared to negative side. Even 2002 and 2003, alsowitnessed higher positive variation and the years are relatively more stable. From the data it isclear that negative variation persist for longer period compared to positive volatility. The depthalso is higher for negative volatility.Return squared volatilityAs far as India is concerned, one more different metric has been computed to measure volatility.In the popular press, many a times, it is found that they have used high-low index levels of theday to compute dispersion and call it volatility. In this procedure there are several pitfalls.Therefore, here we used a new measurement to compute volatility. As a fist step, relativelogarithamic return on close index value are used for computing relative return. The relativereturns are squared and converted into percentage. Here one significant assumption is that dailyaverage return is expected to be zero which is by and large true if we examine closely all the dataprovided in Table 1 for various countries. As a next step, average volatility for the entire year iscalculated and top 5 percent of the returns (in absolute terms) are computed to see the differencebetween the average and extremes.1 Owing to space restrictions and with a view to providing smooth reading through the article some of thetables and charts are not included in the paper. However, the interested readers are most welcome tocontact the authors and/or Research Department, SEBI for obtaining tables and charts.From the Table No. 10 it is clear that volatility measured by this way also confirms that the broadfinding of standard measurement such as standard deviation, employed previously. Yearlyaverage as well as top 5 per cent attained high in 1992, 1997 to 2000. Extreme volatility has beenhigh although, average volatility came down between 19971999. The year 2002 is a relativelystable year. On both the exchanges, this new measurement also throws up that volatility in 2003is slightly higher than the preceding years. Maximum volatility was recorded at 12.34 percent in1992 and second highest in 1999 at 8.66 percent. The lowest volatility is in 2003.Return squared analysisThe observation that stock-price breaks (negative) are more severe than upward variation is alsoconsistent with investors being loss averse, tending to focus on negative information when understress overweighting the probability of negative events, and becoming more loss averse asdownward movements in the value of their portfolios remind them of their incomplete personalcontrol.Neoclassical economic models assume that negative feedback always dominates, however, andthat prices tend toward stability.The data has been looked at from different angle without using the traditional method of usingstandard deviation. For this process daily returns are calculated which are squared andconverted into percentage. Thereafter square root is taken. The average is calculated which isnecessary to give a summary statistic. For each year, top 5 percent (ignoring sign) of theobservations are separated to calculate average of 5 percent. This will help to identify the patternof extreme volatility and its behavior.From Table 10, we can observe that the broad contours of this table across that of overallvolatility figures in other tables. Although, yearly average on top 5 percent were high in 1992followed by 1991, thereafter, the volatility continued to fall till 1996. 1997 to 2000 the volatilityagain went up. Thereafter, it fell down and fell down sharply by almost 50 percent in 2002compared to 2000. The stock market volatility in India has a lot to do with domestic marketrelated developments. High volatility periods of 1990s and also part of 2000 can be clubbed into3 periods. Most of the high volatility can be attributed to some of the irregularities that occurredon the Indian stock exchanges in 1991-92 and 1997-98 and again in 2000-01. But for theseirregularities, Indian stock markets are by and large stable and volatility has been under control.

1 Transaction Cost for Equity Shares in India Dr. M.T.RajuVarsha Marathe2 Stock Market of Volatility A Comparative Study of SelectedMarketsPratip KarM.T.RajuPrabhakar R. PatilKiran Karande