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Stock Market Volatility in the Long Run, 1961-2005

The study measures the volatility of daily returns in the Indian stock market over the period 1961 to 2005. Volatility is analysed using the combined data set of the Economic Times Index and the S&P CNX Nifty together. The return series observes volatility clustering where tranquil periods of small returns are interspersed with volatility periods of large returns. The GARCH (1, 1) model is estimated and the result reports evidence of time varying volatility. The TARCH (1,1) model is also used to test the asymmetric volatility effect and the result suggests an asymmetry in volatility. The conditional volatility for the combined return series shows a clear evidence of volatility shifting over the period. Although the high price movement started in response to strong economic fundamentals, the real cause for abrupt movement appears to be the imperfection of the market.

Stock Market Volatility in the Long Run, 1961-2005

The study measures the volatility of daily returns in the Indian stock market over the period 1961 to 2005. Volatility is analysed using the combined data set of the Economic Times Index and the S&P CNX Nifty together. The return series observes volatility clustering where tranquil periods of small returns are interspersed with volatility periods of large returns. The GARCH (1, 1) model is estimated and the result reports evidence of time varying volatility. The TARCH (1,1) model is also used to test the asymmetric volatility effect and the result suggests an asymmetry in volatility. The conditional volatility for the combined return series shows a clear evidence of volatility shifting over the period. Although the high price movement started in response to strong economic fundamentals, the real cause for abrupt movement appears to be the imperfection of the market.

MADHUSUDAN KARMAKAR

O
ver the last two decades, considerable attention has been paid to estimating and predicting aggregate stock market volatility. It has been observed that many financial time series in developed as well as developing countries frequently exhibit volatility clustering, where tranquil periods of small returns are interspersed with volatility periods of large returns. In the finance literature, this is called time varying conditional volatility. Conditional volatility plays a key role in various financial activities. Many models of asset pricing predict that the expected return on any asset is directly related to its covariance with one or more pricing factors. Most portfolio diversification and risk hedging strategies are based on the ability to predict variances and covariances. Volatility is also an important element in the pricing of derivative securities.

The purpose of the present study is to characterise the time varying volatility of the Indian stock market in the long run. We focus our attention on the following questions. First, does stock return volatility change over time? If so, are volatility changes predictable? Second, does volatility responds symmetrically for positive and negative shocks? Third, has volatility increased over the period? If so, what is the explanation for higher volatility?

With these objectives we have measured volatility of daily stock returns in the Indian stock market over the period from 1961 to 2005. The study reports an evidence of time varying volatility, which exhibits clustering, high persistence and predictability and responds asymmetrically for positive and negative shocks. The conditional volatility also shows a clear evidence of volatility shifting over the period under study.

We proceed in steps. First, we discuss the models that measure volatility. Then, we discuss the data series and characteristics. Thereafter, we estimate an appropriate time varying model, which explains the data series. Finally, we summarise and conclude the study.

I Measurement Tools

“What is volatility?” Volatility can be defined as variability or randomness of asset prices. Theoretically, a change in the volatility of either future cash flows or discount rates causes a change in the volatility of share prices. “Fads” or “bubbles” introduce additional sources of volatility [Schwert 1989].

How to measure volatility? In the finance literature, there are a number of alternative methods to measure volatility [Beckers 1983]. In the following paragraphs, we introduce the widely used measures, which include the simple standard deviation as well as the complicated ARCH class of models.

Simple Standard Deviation

The most commonly used measure of volatility in financial analysis is standard deviation.1 Though financial economists find the standard deviation useful, it may not be the appropriate estimate. In this method, the volatility is estimated by the sample standard deviation of returns over a period. But what is the right period to use? If it is too long, then it will not be so relevant for today and if it is too short, it will be very noisy. Furthermore, it is really the volatility over a future period that should be considered the risk, hence a forecast of volatility is needed as well as a measure for today.

Rolling Standard Deviation

The econometric challenge is to specify how the information is used to forecast the volatility, conditional on past information. Virtually no standard methods were available for volatility forecasting before the introduction of ARCH models. The primary descriptive tool was the rolling standard deviation. This is the standard deviation calculated using a fixed number of the most recent observations. For example, this could be calculated every day using the most recent month (22 business days) of data. The rolling standard deviation of January 1 is calculated using 22 business days of last December. The start and end dates of the sample period is then rolled forward one business day and the standard deviation is re-estimated with the new sample to estimate the volatility for the second date, i e, January 2.

ARCH/GARCH Models

The rolling standard deviation model in the previous example assumes that the variance of today’s return is an equally weighted average of the squared residuals from the last 22 days. The assumption of equal weights seems unattractive, as one would

Figure 1: Combined Market Index and Return fromMay 1961 to June 2005

.2

Market Return Market Index 2500 2000 1500 1000 500 0 .1 .0 –.1 –.2 65 68 72 76 80 84 89 92 94 98 02

think that the more recent events would be more relevant and therefore should have higher weights. Furthermore, the assumption of zero weights for observations more than one month old is also unattractive. The ARCH model proposed by Engle (1982) lets these weights to be parameters to be estimated.2 Thus, the model allows the data to determine the best weights to use in forecasting the variance.

A useful generalisation of this model is the GARCH parameterisation introduced by Bollerslev (1986), which is today the most widely used model. The GARCH model essentially generalises the purely autoregressive moving average model. The weights on past squared residuals are assumed to decline geometrically at a rate to be estimated from the data.

A second enormously important generalisation is the exponential GARCH of EGARCH model of Nelson (1991). The model recognises that volatility can respond asymmetrically to past forecast errors. In a financial context, negative returns seem to be more important predictors of volatility than positive returns. Large price declines forecast greater volatility than similarly large price increases. The simple GARCH model fails to capture the negative asymmetry, since its conditional variance depends on the magnitude of the disturbance term, but not its sign. The EGARCH model ameliorates this problem by allowing for standardised residual as a moving average regressor in the variance equation, while preserving the estimation of the magnitude effect. The tendency for negative shocks to be associated with increased volatility is captured in the EGARCH class of models.3 Later, a number of modifications were derived from the EGARCH of Nelson. One of them is the TARCH method (Threshold ARCH), which was introduced by Zakoian (1994). Another important model is the GJR GARCH model developed by Glosten, Jaganathan and Runkle (1993).

Further generalisations have been proposed by many researchers to better capture the stylised characteristics of the data. These models go by such exotic names as AARCH, NARCH, PARCH, PNP-PARCH, STARCH, and Component ARCH, among others. It is probably still too early to ascertain which will be the most useful models for which markets, and for which types of data.

II Data Set and its Properties

Data Description

The sample data to be used here consists of two sets. The first set comprises of the series of index number of share prices, namely, “The Economic Times Index Number of Ordinary Share Prices”, compiled and published by the Economic Times on daily basis for a period from May 1961 to June 1995. The second one is the S&P CNX Nifty compiled and published on a daily basis by the NSE India for the period from July 1990 to June 2005.

We have analysed volatility using the combined data set of the Economic Times Index and the Nifty together for a long period of time from 1961 to 2005. Choice of the combined data sets is primarily guided by the availability of the daily share price index. To the best of my knowledge, no reliable single daily share price index was readily available for the entire period under study. The S&P CNX Nifty is available only from July 1990. Similarly, The Economic Times Index is not available after 1995. Since none of the price indices was solely available for the entire period, the two series have been combined successively to cover a relatively longer period of time of nearly 45 years. The Economic Times Index is taken for the period from May 1961 to June 1990 and S&P CNX Nifty is taken for the period from July 1990 to June 2005.

The raw data are presented in Figure 1, where prices are shown on the left axis. The price curve shows what has happened to The Economic Times Index from May 1961 to June 1990 and to the S&P CNX Nifty from July 1990 to June 2005.4 It is easy to see that the price movement was more or less stable up to 1980. Almost from the beginning of 1980s, there was an indication of the change in the present mood of the market.

Bidding farewell to the “control regime”, the Indian economy gradually entered into an era of liberalisation from the early 1980s. In response to the liberalisation, the stock market started booming. The market buoyancy continued over the decade, with a few setbacks and gained momentum since 1990. But what happened after the presentation of the union budget of 1992-93, was a miracle in the Indian capital market. Share prices shot up almost vertically till April and thereafter, and descended sharply in May 1992, the downward journey continued up to 1993. In the following period, the share price moved up and down very much.

The daily return series (computed as the logarithm of the price today divided by the price yesterday) is shown at the top of Figure 1. This shows the daily price change on the right axis. This return series is centred around zero throughout the sample period, even though prices are sometimes increasing and sometimes decreasing. Now, the dramatic event was the crash of 1992, where return declines heavily and there is a subsequent partial recovery.

Other important features of this data series can be seen best by looking at portions of the whole history. Figure 2 shows the same graph for the period 1961-90. It appears from the figure that there is low volatility of returns up to the beginning of the 1980s. This was accompanied by a slow and steady growth of equity prices. The volatility began to rise as stock prices started increasing at a higher rate since the beginning of 1980s. During 1986-87, there seems to be a bubble, but in reality it’s only a boom.5

Figure 3 shows the same graph for the period July 1990 to June 2005. It is very apparent that the amplitude of the return is changing. The magnitude of the changes is sometimes large and sometimes small. This is the effect that GARCH is designed to measure and that we have called volatility clustering.

There is however another interesting feature in these graphs. It is clear that the volatility is higher when prices are falling (see the periods around 1985 in Figure 2 and 1992 in Figure 3). It means that negative returns are more likely to be associated with greater volatility than positive returns. This is the

Economic and Political Weekly May 6, 2006

Figure 2: Economic Times Daily Prices and Returnsfrom May 1961 to June 1990

.

.08

EconomicTimesReturn

Economic Times Return

.

.04

..00

-

–.04

-–.08 500 Bubble

600

400 300

Economic Times Price

EconomicTimesPrice

200 100 0

61 65 68 72 76 80 84 89

Figure 4: Squared Return Autocorrelations(1961-1990)

R2

1.0

.5

0.0

–.5

CConfidence limits

Figure 3: Nifty Prices and Returns from July 1990 to June 2005

. .2
Ni fty Re tu r n Nifty Return . .1
. .0
-–.1
2500 -–.2
2000
1500 Ni fty P r i c e Nifty Price
1000
500
0
1992 1994 1996 1998 2000 2002 2004
Figure 5: Squared Return Autocorrelation (1990-2005)

R2

1.0

.5

0.0

–.5 CConfidence limits

ACF

–1.0

CCoefficient

ACF

–1.0 CCoefficient

1 5 9 13 17 21 25 29 33 3 7 11 15 19 23 27 31 35

Lag Number

asymmetric volatility effect that Nelson described with his EGARCH model.

Return Characteristics

We now show some statistics that illustrate the two stylised facts: fat tails and volatility clustering. Some features of returns are shown in Table 1. The mean is close to zero, relative to the standard deviation for both periods. It is 0.03 per cent per trading day or about 7.8 per cent per year for the period from 1961 to 1990. For the latter period, it is higher (0.057 per cent) per trading day. The standard deviation is also higher in last 15 years (Nifty). These standard deviations correspond to annualised volatilities of 11 per cent and 30 per cent. The returns are negatively skewed for both the sub-periods.

The most interesting feature is the kurtosis, which measures the magnitude of the extremes. If returns are normally distributed, then the kurtosis should be three. The kurtosis of the last 15 years is very high (8.81), while for the period up to 1990, it is substantial, at 14.28. The results thus suggest that the return series have fatter tails than the normal distribution. That is, the probability of extreme returns that has been observed empirically is higher than the probability of extreme returns under the normal distribution. This feature is referred to as lepto kurtosis, or simply “fat tails”.6 The daily stock returns are thus not normally distributed – a conclusion which is confirmed by the Jarque-Bera test for both the sub-periods.

Volatility clustering will show up as significant auto-correlation in squared returns. Figure 4 shows the plots of squared returns

1 5 9 13 17 21 25 29 33

3 7 11 15 19 23 27 31 35 Lag Number

for the period of 1961-90 and Figure 5 shows the plots of the same for the period of 1990-2005. Under conventional criteria, an auto-correlation bigger than 3 standard errors in absolute value would be significant at a 5 per cent level. Clearly, the square returns have all auto-correlation significant for both the pre-1990 period and the post-1990 period. Furthermore, the autocorrelations are all positive, which is highly unlikely to occur by chance. These two figures give powerful evidence for the volatility clustering for both the sub-periods.

III Estimation of Volatility

Now we turn to the problem of estimating volatility. We estimate volatility by using the ARCH class of models. The natural first model to estimate is the GARCH (1, 1). The GARCH

Table 1: Return Statistics Figure 6: Conditional Standard Deviation of the CombinedIndices of The Economic Times and S&P CNX Nifty(May 1961 to June 2005) Estimated on the Conditional VarianceEquation of TGARCH (1,1)

Sample May 1961-June 1990 July 1990-June 2005
Mean 0.000297 0.000574
Median 0.000000 0.000674
Maximum 0.061333 0.120861
Minimum -0.067101 -0.130539
Std Dev 0.006878 0.01838
Skewness -0.010369 -0.108677
Kurtosis 14.28494 8.818870
Jarque-Bera 38714.46 4984.254
Probability 0.000000 0.000000
Sum 2.169360 2.024293
Sum Sq Dev 0.345096 1.122319
Observations 7296 3528

.08

.07

.06

.05

.04

.03

.02

.01

.00 65 70 75 80 85 90 92 97 02

—— Conditional standard deviation

(1, 1) model for daily stock return is given below:

rt = a + brt-1 + εt,

where, ε/It -1 ~ N(0, ht ), where ht is the variance and the variance

tequation is given by

= ω+ α2 + β…(1)

ht1 εt-1 1ht-1 In equation (1) ω>0, α1 ≥0, β1 ≥0. The stationary condition for GARCH (1, 1) is α1+ β1< 1.

In the GARCH (1, 1) model, the effect of a return shock on current volatility declines geometrically over time. This model gives weights to the unconditional variance (σ2), the previous forecast (ht-1) and the news measured as the square of yesterday’s return (ε2). The weights are estimated to be (1 – α1 = 0.014682,

t-1 1– ββ1 = 0.859457, and α1 = 0.125861) for The Economic Times Index (1961-1990) and (1 – α1– β1 = 0.019246, β1 = 0.862213 and α1= 0.118541) for the Nifty (1990-2005) respectively.7 Clearly the bulk of the information comes from the previous days forecast (around 86 per cent). The new information changes this a little and the long run average variance has a very small effect.

We have observed in the data that the volatility appears to be more when price declines than that when price increases. Hence, we will use an asymmetric volatility model, namely, TARCH for Threshold ARCH, developed by Zakoian (1994). The specification for the conditional variance of the TARCH (1, 1) model is given by

= ω+ αε2 + ⏐γε...(2)

htt–1 t–12 dt-1 + β.ht 1 where dt = 1 if ε>0, and 0 otherwise. In this model good news

t(ε> 0 ), and bad news (ε< 0 ), have different effects on the

ttconditional variance – good news has an impact of α, while bad news has an impact of (α+ γ). If γ= 0, the volatility is symmetric and if γ≠0, the volatility is asymmetric.

The statistical results are given in Table 2. As is mentioned, there are two types of news. There is a squared return and there is a variable that is the squared return when returns are negative, and zero otherwise. On average, this is half as big as the variance, so it must be doubled, implying that the weights are half as big. The weights are now computed on the long run average, the previous forecast, the symmetric news and the negative news. These weights are estimated to be (0.015, 0.861, 0.135, -0.011) and (0.0213, 0.859, 0.103, 0.0167) for the two sub-periods respectively.8 The asymmetric effect term is significantly different from zero for both the periods. For the pre-1990 period, the effect is significantly negative, while for the post-1990 period it is significantly positive. The findings are interesting. While for the pre-1990 period, the bad news slightly reduces the volatility, for the post-1990 period, the bad news increases the volatility substantially.9 In fact, negative returns for the post-1990 period have 1.32 times the effect of positive returns on future variances. The explanation for the reverse effect of bad news on future volatility for the two sub-periods deserves careful investigation, which is kept for future research.

IV Volatility Shifting

Conditional volatility for the combined return series,10 generated by the TARCH (1,1) model, is given in Figure 6. The figure shows a clear evidence of volatility shifting over a period of 45 years. The level of volatility was modest for the first two decades of the 1960s and 1970s. Almost from the beginning of 1980, however, there were indications of change in the mood of the market. Volatility touched a new high from 1985, and in the year 1992, it surpassed all previous records. This period experienced the highest volatility in the history of the Indian stock market and this coincided with initial years of liberalisation of the Indian economy. Coming as it did, after a long era of control, experts and policy-makers were bewildered by this phenomenon. However, after the meteoric fall in share prices in 1992 when the largest ever security scam was unearthed in the Indian stock market, doubts were expressed about the capabilities of the market to support the liberalisation policy of the government. The violent fluctuation of 1992 was followed by a tranquil period of around four years, but volatility again continued to increase till the end of the decade (1996-1999) when a series of security scams were revealed once again in the Indian stock market. Only since last two/three years volatility has declined and this period is accompanied by increasing price rise.

Why Should Increased Volatility Matter?

Investors are always concerned about the present and future value of their investments. Greater volatility leads to a perception of greater risk, which threatens investors’ assets and wealth. When the stock market takes a sharp nose-dive, investors see the value of their assets rapidly dissipating. When the asset price exhibits significant volatility over very short periods of time (such a day), investors “lose confidence in the market”. They began to see financial markets as the province of the speculator and the insider, not of the rational long-term investor. If this view becomes pervasive, investors may simply withdraw from the market.

Table 2: TARCH Estimates of Return Data

Coefficient Std Error z-Statistic Prob

Economic Times Index (1961-1990) C 0.0000012 0.0000000621 19.29544 0.0000 ARCH (1) 0.135161 0.005266 25.66488 0.0000 γ -0.022885 0.005571 -4.107976 0.0000 GARCH (1) 0.861139 0.004262 202.0702 0.0000

S&P CNX Nifty (1990-2005) C 0.00000779 0.00000095 8.200486 0.0000 ARCH (1) 0.103865 0.009803 10.59573 0.0000 γ 0.033331 0.011765 2.833078 0.0000 GARCH (1) 0.859398 0.006823 125.9477 0.0000

Economic and Political Weekly May 6, 2006

While there is an obvious public perception that increases in volatility are bad, it is difficult to establish concrete links between volatility and either economic activity or economic welfare. Increased volatility may simply reflect fundamental economic factors, or information and expectations about them. In that case, there is no apparent social cost associated with such volatility. In fact, the more quickly and accurately prices reflect new information, the more efficient the allocation of resources will be. If volatility either exceeds or falls short of the level indicated by fundamental economic factors, however, the result is mispricing, and as a consequence, misallocation of resources.

Explanation of Higher Volatility

What are the factors that contributed to the gradual rise in volatility since the beginning of the second half of 1980s and the highest volatility in 1992? Are they simply fundamental economic factors or a number of imperfections that are responsible for the vociferous movement in share prices?

One of the intuitively appealing explanations combines both fundamental factors and irrational behaviour of investors while interpreting the gradual rise in volatility. The initial boost up of share prices and fluctuations apparently owed much to the strong fundamentals11 of the decade of the 1980s, which were supplemented by a number of liberalising policies and procedures in the financial sector when the new economic policy was launched in July 1991. During this phase, “trend chasing” investors seemed to be further encouraged by the optimism expressed by the government, the media, and leading financial advisers12 and the general public entered the market in herds. Obviously, they joined in clusters, which resulted in a gradual shift in the demand for shares in a basically thin market.13 When investors were in a frenzy, speculators,14 armed with outside money,15 entered the market, adding fuel to the fire. Price started moving undeviatingly, fluctuations were high, and it culminated in a record high in March 1992, the year when the Indian economy was in deep crisis.16 Following the rule of the market, eclipse followed illumination, and in April 1992, the “bubbles” burst and price started its downward journey. The formation and eventual burst of the bubble was a period of extreme volatility of the Indian stock market. Doubts were raised regarding whether stock price movement can be justified by fundamental economic factors. Roy and Karmakar (1994) have attempted to test this hypothesis and the findings reveal that stock price volatility over the period (1968-91) appears to be far too high to be attributed to new information about future real dividends. The actual price volatility exceeds the level indicated by new information about the fundamental determinants of price in general during the whole period and more particularly from 1985 to 1991. Since price movement exceeds the level indicated by fundamental economic factors, the existence of “fad” or “bubbles” cannot be ignored.17

After a stable period of four years, the stock market again witnessed excessive fluctuation of share price at the end of the last decade. Scandal once again unveiled the shady nexus between speculators and outside money, particularly public money to strengthen the activities of noisy traders. The market was still dominated by the speculators and noise traders, who often manipulated the prices at the cost of general investors, and did drive the price away from the fundamental level, causing excessive movement in share prices.

The social cost associated with high volatility was heavy. Investors aptly thought that the security market was the province of speculators and insiders only. They had got duped and withdrew en masse from the market. In many stock exchanges, including the Calcutta Stock Exchange, the second largest exchange in the country, trading almost stopped. As reflected in the primary market, the fund mobilisation through IPOs almost dried up. The situation continued till the recent past.

Only over the last two or three years, the market buoyancy has started again following the improved economic condition of the country. But still, equity participation has failed to catch up among retail investors. Very recently, FIIs have pumped huge money into the markets as they see a bright future for the country. But the investment made by the FIIs is hot money and hence excessive reliance on them poses a risk to the economy.

V Summary and Conclusion

The study measures the volatility of daily stock return in the Indian stock market over the period from 1961 to 2005. We have analysed volatility using the combined data set of the Economic Times Index and the S&P CNX Nifty together. While studying the daily logarithmic return series, we observed that the market is tranquil and volatile, volatile and tranquil. This is the effect that we have called volatility clustering. It tells us something about the predictability of volatility. The GARCH (1, 1) model is estimated to see whether volatility is predictable. We find strong evidence of time varying volatility. We also find that periods of high and low volatility tend to cluster. Also, volatility shows high persistence and is predictable. The TARCH model is also used to test the asymmetric volatility effect and the result suggests the asymmetry in volatility.

The conditional volatility for the combined series has been plotted in Figure 6 over the period from May 1961 to June 2005. From the figure, it appears that the level of volatility was modest for the first two decades of the 1960s and 1970s. Almost from the beginning of 1980, however, there were indications of change in the mood of the market. Volatility touched a new high from 1985, and in the year 1992, it surpassed all previous records. Truly, higher price movement started in response to strong economic fundamentals. But the real cause for abrupt movement appears to be the imperfection of the market. Information that is available particularly after unearthing of a series of security scams reveals that, blessed with public money, the noise traders simply destabilised the market and moved security prices away from fundamentals, resulting in “fads” or “bubbles” as the natural outcomes in the price formation process. The irrational behaviour of the market made the year 1992 as the year of highest volatility in the history of the Indian stock market. The violent fluctuations of 1992 were followed by a tranquil period of around four years, but volatility again continued to increase till the end of the decade when a series of security scams were revealed once again in the Indian stock market. The social cost associated with high volatility was heavy. Genuine investors lost confidence and withdrew from the market en masse. For last two or three years, volatility has declined and this period is accompanied by increasing price rise, mainly fuelled by the investment made by the FIIs.

Instead of a microscope, the plots of volatility in this article can be thought of as an electrocardiogram. They reflect the pulse of financial markets by measuring the rate of price changes over a long period of time from 1961 to 2005. They show the risk borne by investors in the stock market, and where stock volatility reflects uncertainty about more fundamental economic aggregates [e g, Schwert 1989], they provide information about the health of the economy in a historical perspective.

m

Email: madhu@iiml.ac.in

Notes

1 The standard deviation ó of returns Rt from a sample of N observation is the square root of the average squared deviation of returns from the

average return in the sample: ó = N , where E (R)

∑{(Rt − E(R )} /(N − 1)is the sample average return. t =1 2 The ARCH (q) process captures the conditional heteroskedasticity of financial returns by assuming that today’s conditional variance is a weighted average of past squared unexpected returns: h = α0 + α1 2 + α2 2 +

tεt-1 εt-2 ………..+ αε2, where α0 > 0, α1, α2, α≥ 0 and e~ N (0, h)

q t-q ……….., q t/It -1 t

3 The conditional variance equation in the EGARCH model is defined in terms of a standard normal variate Zt: In h2t = g(Zt-1) + β In ht-1 Where g(.) is an asymmetric response function defined by g (Zt) = λZt +

ϕ(IZtI–

2/∏ ).

The standard normal variate Zt is the standardised unexpected return /h1/2

εtt. When ϕ > 0, and λ < 0 negative shocks to return (Zt-1 < 0) induce larger conditional variance responses than positive shocks [Carol Alexander 2001].

4 A minute observation of Figure 1 can identify a sharp price decline in between 1989 and 1992. In fact, it is a point where the ET index ends and the Nifty starts. The ET Index at the last day (last trading day of June 1990) is 452.4 and the S&P CNX Nifty at the first day (the first trading day of July 1990) is 284.04, which can be observed in Figures 2 and 3 respectively. But the spike change in price due to the change in index has no effect on the return series in Figure 1 since the daily return on Nifty on the first trading day of July 1990 calculated as [In

(ETI)}] = In (284.04 /452.4) = -0.4654167

{Pfirst trading day (Nifty}/P last trading day

(which is not the actual return) has been dropped from the series.

5 During 1986-87, there seems to be a bubble but in reality it’s a boom only. The ET Index was revised to 244.6 on January 1, 1987 from 466 on December 24, 1986 (the last trading day of December) by changing the base year. The price change due to the revision of the index from December 24, 1986 to January 1, 1987 appears to be a sharp decline. But the change in price due to the revision has not any effect on the return series since the daily return on January 1, 1987 calculated

) = In (244.6/466) = -0.64456 (which is not

as In (P Jan 1, 1987/P Dec. 24, 1986

the actual return) has been dropped from the series.

6 In fact, leptokurtic literally means “thin-arched” or “thin-centred”. Fattailed distributions have thin centres. Literally translated to Greek, “fattailed” would be “platyeschatic”.

7 For a conventional GARCH (1, 1) model defined in the text, the weight to the unconditional variance [var(εt )=σ2] is (1 – α1– β1), the weight to the previous forecast (ht-1) is β1 and the weight to the news measured as the square of yesterday’s return (ε2t-1) is α1.

8 The respective weights are (1 – α – β – γ / 2, β, α , γ / 2).

9 As already mentioned in the text, good news has an impact of α, while bad news has an impact of (α + β). For the pre-1990 period, it is observed, γ = –0.022885 < 0, hence (α + β) < α , i e, bad news slightly reduces the volatility from α = 0.135161 to (α + β) = 0.135161 – 0.022885 = 0.112276. For the post-1990 period γ = 0.033331>0, hence (α + β) > α, i e, bad news increases the volatility from α = 0.103865 to (α + β) = 0.103865

+ 0.033331 = 0.137195.

10 Figure 6 shows the conditional volatility for the combined return series that is used for descriptive analysis of volatility shifting. The validity of using two indices comprising of different portfolios may be questioned. There are two points to defend the approach of using two indices for the purposes. First, no index maintains the same portfolio for a longer

Economic and Political Weekly May 6, 2006

period of time. The portfolio is often reshuffled, replacing inactive by active shares. Hence, even the use of a single index provides no guarantee that the volatility estimate would be based on the same set of shares for the entire period. Second, there is no evidence of significant variation in volatility estimates even when several alternative indices comprising different portfolios have been used simultaneously to measure it [Schwert 1989 and Karmakar 2003].

11 Some evidence of encouraging performance of the Indian corporate sector (1980-81 to 1989-90) is as follows:

Year Industrial Growth Rate Equity Dividend as (Per Cent) Percentage of Paid upEquity Capital

1980-81 4.0 12.7 1981-82 8.6 13.1 1982-83 3.9 12.6 1983-84 5.5 13.0 1984-85 5.6 14.3 1985-86 8.7 13.5 1986-87 9.1 14.9 1987-88 7.3 15.7 1988-89 8.7 18.3 1989-90 8.3 15.95

Source: Different Issues of RBI Bulletin.

12 The professionals of financial institutions opined: “Industry turns the corner and the share market matures”, “The present boom in the market is the beginning of an economic miracle in the country”’, etc (widely quoted remarks in different financial weeklies at that time).

13 The Indian stock market was extremely narrow and limited and lacked substantial breadth. A large percentage of listed securities are either traded infrequently, or not at all, with volumes concentrated on a relatively few number of scripts, particularly of the long established and well managed companies. This is evident from Table A.

(April 1988-March 1989)

Table A: Frequency Distribution of BSE-listed Companies by Percentage of Days Traded

Sl Percentage of No Trading Days No of Companies Percentage to Column Total
1 More than 90 per cent of days 456 20.0
2 More than 80 per cent and up to
90 per cent 152 6.7
3 More than 70 per cent and up to
80 per cent 94 4.1
4 More than 60 per cent and up to
70 per cent 57 2.5
5 More than 50 per cent and up to
60 per cent 72 3.2
Sub total (1 to 5) 831 36.5
6 More than 40 per cent and up to
50 per cent 66 2.9
7 More than 30 per cent and up to
40 per cent 51 2.2
8 More than 20 per cent and up to
30 per cent 79 3.5
9 More than 10 per cent and up to
20 per cent 93 4.1
10 Up to 10 per cent 1155 50.8
Sub total (6 to 10) 1444 63.5
Grand total 2275 100.0

Source:L C Gupta (1992): ‘Stock Exchange Trading in India: Agenda for Reform’, p 56.

14 Speculators dominated the Indian stock market during 1980s and early 1990s. The overspeculative characteristics of the market is reflected from the fact of “share trading velocity”, which states the ratio of shares traded in the market to all shares outstanding. The trading velocity of individual shares in BSE were much higher than that of NYSE (Table B). An examination of trading concentration in terms of percentage of trading volume also points to the speculative dominance of the Indian stock market.

Table B: Comparative Analysis of Share Trading Velocityand Share Trading Volume of Certain Groups of Sharesof BSE, 1989-90 and New York Stock Exchange, 1989

Groups of Shares Top 5 by Trading Volume BSE NYSE Percentage of Trading Volume BSE NYSE Trading Velocity BSE NYSE
Tata Steel ATT ACC IBM Tata Engineering Texaco Reliance Industries Gen Elec Bombay Dyeing Exxon Sub total of top 5Top 50 by trading volumeShares other than the top 50All shares 13.8 9.6 7.0 6.8 3.7 40.9 82.1 17.9 100.0 0.93 0.81 0.73 0.730.65 3.9 21.00 79.00 100.0 1.41 12.30 0.91 1.94 4.68 1.81 na na 0.52 0.36 0.58 1.11 0.33 0.15 0.34 1.04 0.19 0.57

Source: L C Gupta (1992): ‘Stock Exchange Trading in India: Agendafor Reform’, pp 7, 9.

15 Outside finance often used by the noise traders for speculative business,played a significant role in the excessive price movement. It is observedthat the main attraction in providing such finance for speculative transactionsin shares is the lucrative rate of interest which was about 35-40 per cent,in contrast to 18-20 per cent interest in formal money market [Barua andVarma 1993] and availability of better margin of easily realisable securities.Such finance, being of a short-term nature, while enabling the operatorsto take temporary delivery of shares from the markets, often lands theoperators into serious financial difficulties if it is withdrawn suddenlyfor any reason, obliging the operators to liquidate their position prematurely.Hence, provision of outside finance by giving impetus to excessivespeculative activity in some of the leading stock exchanges, exercisesa baneful and destabilising influence on the trading activity in the stockexchanges [Karmakar 1999:100].

16 During the period, the Indian economy had almost collapsed on accountof a balance of payments crisis and industry had been in the midst ofa deep recession [Roy and Karmakar 1995].

17 In another study [Roy and Karmakar 1995], the authors identified theassociated news events released in the vicinity of large price swings duringthe period of 1985-1992. Curiously enough, for many days, particularlyduring the years 1991 and 1992, there were no well-defined economicevents associated with abnormal price changes. The abnormal oscillationof share prices not justified by fundamentals during those days, implythat the changes could be attributed simply to private information, rumours,occasional “frenzy” of investors, etc.

References

Barua, S K and Jayanth R Varma (1993): ‘Securities Scam: Genesis, Mechanics,and Impact’, Vikalpa, Vol 18, No 1, pp 3-12.

Beckers, S (1983): ‘Variances of Security Price Returns Based on High, Low,and Closing Prices’, Journal of Business, Vol 56, No 1, pp 97-112.

Bollerslev, T (1986): ‘Generalised Autoregressive ConditionalHeteroskedasticity’, Journal of Econometrics, 31, pp 307-27.

Engle, R (1982): ‘Autoregressive Conditional Heteroskedasticity with Estimatesof the Variance of UK Inflation’, Econometrica, 50, pp 987-1008.

Friedman, M (1953): ‘The Case of Flexible Exchange Rates’ in Essays inPositive Economics, University of Chicago Press, Chicago.

Glosten, Lawrence R, Ravi Jagannathan and David E Runkle (1993): ‘Onthe Relation between the Expected Value and the Volatility of the NominalExcess Returns on Stocks’, Journal of Finance, 48, pp 1791-1801.

Gupta, L C (1992): ‘Stock Exchange Trading in India: Agenda for Reform’,Society for Capital Market Research and Development, New Delhi.

Karmakar, M (1999): ‘Bubble: A Study of Scam, Scandal and Corruptionin Indian Stock Market’, Regency Publications, New Delhi.

– (2003): ‘Heteroskedastic Behaviour of the Indian Stock Market: Evidenceand Explanation’, Journal of Academy of Business and Economics, Vol 1, No 1, pp 27-36.

Nelson, D B (1991): ‘Conditional Heteroscadasticity in Asset Returns: ANew Approach’, Econometrica, 59:2, pp 347-70.

Roy, M K and M Karmakar (1994): ‘Irrational Movement of Share Prices:Evidences and Implications’,Journal of Indian School of Political Economy,Vol 6, No 3, July-September.

– (1995): ‘Stock Market Volatility: Roots and Results’, Vikalpa, Vol 20, No 1, January-March.Schwert, G W (1989): ‘Why Does Stock Market Volatility Change OverTime?’ Journal of Finance, 44, pp 1115-53.

Zakoian, J M (1994): ‘Threshold Heteroskedastic Models’,Journal of Economic Dynamics and Control, 18, pp 931-55.

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