vikalpa-beta systemetic risk

VIKALPA • VOLUME 39 • NO 1 • JANUARY - MARCH 2014 41

R E S E A R C H

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ExecutiveSummary

Instability and Time Scale Dependence ofBeta in an Emerging Market Economy:Evidence from India

Amlendu Kumar Dubey

KEY WORDS

Beta

CAPM

Time Scale Dependence

Wavelets

Indian Equity Market

This paper is an attempt in analysing time-scale dependence of systematic risk of

stocks for an emerging market economy. Financial markets all over the world are

characterized by heterogeneous investors. For example, different investors have differ-

ent time horizons of investment which in turn is highly related to perception of risk of

different investors in holding these stocks. Also, in emerging market economies, eco-

nomic conditions are very fluid. Not only new firms are joining the market but existing

firms themselves are changing rapidly; they are expanding into new markets, and at

times with different products. Therefore, assuming that the risk in holding a firm’s

stock will be constant over a longer period is rather a restrictive assumption. Also,

Indian equity markets are one of the most dynamic equity markets in the world today.

The last decade has been the most eventful period for the Indian securities market.

Resource mobilization in the primary market has increased dramatically, rising six-

fold between 2000 and 2010 (NSE, 2010), which is having a very significant impact on

the risk-return trade-off in the secondary market. Market capitalization has grown

substantially over the period indicating that not only more companies are using the

stock markets for resource mobilization today but overall market participation has

also increased considerably.

This paper tests for time-scale stability of beta of different trading stocks in the Indian

equity market, using wavelet filters following Gencay et al (2002; 2005) and Fernandez

(2006) and finds considerable instability in beta estimates. Based on this analysis,

time-scale dependent beta estimates are provided for all the stocks under considera-

tion.

Time-scale dependent estimates of systematic risk embedded in different stocks will

provide considerable information to practitioners in terms of benefits of diversifica-

tion while constructing different portfolios using different stocks traded in Indian

equity markets. Essentially, with the tools explained in this paper, practitioners will

be able to incorporate their horizons of investment while planning for portfolio diver-

sification. Also, the results emphasize the importance of a hedging strategy that varies

over different time horizons of investments over a strategy where the hedge ratio is

invariant to different time horizons.

42

Time scales of measurement are closely related with

the investment horizon of different classes of in-

vestors. Most of the financial markets are charac-

terized by heterogeneous investors, with different invest-

ment horizons. There are intraday traders, who carry out

trade only within a given trading day. Then, there are

traders with relatively shorter or longer horizons of in-

vestment. Consistent with their trading horizons, the be-

haviour of different trading class varies and may have

different risk perceptions.

Secondly, in such a heterogeneous market, a low fre-

quency or a systematic shock to the system penetrates

through all the layers. The high frequency shock would

be short-lived and may have no impact out of immediate

time span but a systematic shock may have long lasting

impact on the performance of the market. The varied re-

sponse to the different disturbances and the heterogene-

ous structure of the market is intimately related to the

risk-return trade-off, central to the portfolio allocation and

pricing of different financial instruments.

Also, in emerging markets, conditions themselves are very

fluid; today’s leading firm may well be tomorrow’s fol-

lower or vice-versa. New firms are joining the market and

even firms themselves are changing quite rapidly; they

are expanding into new markets, and at times with differ-

ent products. Therefore, assuming that the risk in hold-

ing a firm’s stock will be constant over a longer period,

especially in case of an emerging market economy, would

rather be a restrictive assumption.

This paper discusses the time scale dependence of betas

of different trading stocks listed in the Indian equity mar-

kets – one of the most dynamic equity markets in the world

today. The last decade has been the most eventful period

for the Indian securities market during which it took ma-

jor strides. Resource mobilization in the primary market

increased dramatically, rising six-fold between 2000 and

2010 (NSE, 2010), which had a very significant impact on

the risk-return trade-off in the secondary market. Market

capitalization also grew substantially over the period

indicating that not only more companies were using the

stock exchanges for resource mobilization but there was

considerable increase even in the overall market partici-

pation.

Market capitalization in the Indian markets was around

`61,704,205 million (US $1,366,952 million) at the end of

March 2010. Market capitalization ratio1 increased to

83.11 percent in 2009, substantially recovering from the

drop of 53.16 percent in 2008 (NSE, 2010).

Table 1: Comparison of Global Stock Markets

Country Market No. ofCapitalization Ratio Listed Companies

2007 2008 2009 2007 2008 2009

Australia 151.54 65 82.37 1,913 1,924 1,882

France 106.83 52.28 51.55 707 966 941

Germany 63.35 30.31 38.51 658 638 601

Japan 101.73 65.9 82.74 3,844 3,299 3,208

Singapore 199.98 93.11 138.43 472 455 459

UK 137.85 69.55 156.47 2,588 2,415 2,179

USA 142.37 81.69 327.83 5,130 5,603 4,401

China 177.61 61.63 179.67 1,530 1,604 1,700

India 147.56 53.16 83.11 4,887 4,921 4,955

Russia 115.61 23.82 55.46 328 314 279

Brazil 100.32 35.97 41.3 442 432 377

Indonesia 48.98 19.35 21.34 383 396 398

Korea 107.09 53.11 189.97 1,767 1,798 1,778

Malaysia 175.11 84.58 38.08 1,036 977 953

Mexico 38.78 21.34 8.81 125 125 125

Sources: S&P Global Stock Market Fact Book, 2009; World DevelopmentIndicators; World Bank and NSE (2010)

The Beta

For the sake of completeness, to provide a definition of

beta, here a heuristic description of the capital Asset Pric-

ing Model (CAPM) has been preset. Let us assume that an

individual plans to invest part of his wealth in a risk-free

asset and the remaining part in a risky asset. Let rf be the

expected returns to the risk-free asset and rm be the ex-

pected excess return to a portfolio of risky assets over rf.

Now, suppose ri is the expected excess return to the asset

i over rf , then CAPM may be written in a form that is

known as the single index market model:

ri= ai + βirm (1.1)

Here, ai represents that component of the return to asset i

that is independent of the return rm to the market portfo-

lio. Part of it is determined by the risk-free rate of return rf ,

but the other part may be thought of as a purely random

1 Market capitalization ratio is defined as total market capitaliza-tion of stocks divided by the GDP. It is used as a measure to denotethe importance of equity markets relative to the GDP and indi-cates the ability to mobilize capital and diversify risk.

INSTABILITY AND TIME SCALE DEPENDENCE OF BETA IN AN EMERGING MARKET ECONOMY...


phenomenon.

It is thus helpful to rewrite (1.1) as

ri = ai+ βirm + ε (1.2)

βi cannot be observed but may be estimated using ordi-

nary least square (OLS), defined as

(1.3)

In the above description, which follows the Sharpe-Linter

version of the CAPM, it has been assumed that a risk-free

asset exists in the economy with a sure return of rf . If there

is no risk-free asset, Black (1972) showed that it is still

possible to derive the CAPM. The following model is

known as the Black’s version of the CAPM.

(1.4)

where, rim is the return on a zero-beta portfolio, which is

defined as the minimum variance portfolio among all port-

folios uncorrelated with m.

TIME SCALE DEPENDENCE OF BETA

There are several plausible reasons (Shah & Moonis,

2003), apart from the ones listed earlier (different invest-

ment horizon of investors, varied response to different

shocks, and inherent nature of emerging market econo-

mies) which suggest that beta may be time varying:

• Beta is linked to the leverage of the firm. It can be shown

that the systematic risk of a stock can be split into two

components – operational risk and financial risk. Fi-

nancial risk is a function of the leverage of the firm

(Hamada, 1972; Mandelker & Rhee, 1984). Since lev-

erage can change with changes in stock prices, stock

price movement can generate changes in beta.

• Any news that does not affect market and stock re-

turns uniformly, will change the correlation between

the stock and market returns and hence the beta of the

stock (Rosenberg & Guy (1976)).

• There is considerable evidence that stock and index

returns have time-varying second moments (Bollerslev

et al., 1992). By the definition of beta, time-variation in

second moments of returns can generate time-varia-

tion in beta.

• Beta is found to be correlated positively with growth,

leverage, and earning variability of the firm and nega-

tively with liquidity and size of the firm (Beaver et al.,

1970). This also induces time variation in beta.

• One reason suggested (Alexander & Chervany, 1980,

p.128) for beta instability is measurement error - theo-

retical beta relates ex ante expectations while estimated

beta relates ex post observations. Scott and Brown (1980)

claim that this type of error combined with auto corre-

lation in the residuals would result in unstable esti-

mates.

• Another reason for beta instability could be that mar-

ket reacts differently during bull and bear periods (bull

period is characterized by a sustained rise in the stock

prices signifying persistent demand for the stocks. In

the bear period, there is a sustained fall in the stock

prices). This would yield different betas for different

periods even if the beta coefficient had a stable bull

and bear value (Kon & Jen, 1978; 1979).

Country-specific studies providing evidence that betas

are time-varying in different economies include Fabozzi

and Francis (1978), Bos and Newbold (1984), Jagannathan

and Wang (1996), and Groenewold and Fraser (1999) for

the United States; Cheng (1997) for Hong Kong; Brooks et

al. (1998) for Australia; Wells (1996) for Sweden; Bucland

and Fraser (2001) for the United Kingdom, and Shah and

Moonis (2003) for India.

MODELS FOR UNSTABLE BETA ESTIMATION

If beta is unstable – which is a consensus now – then, it

raises several modeling issues for the estimation of beta.

It has often been modeled either as mean-reverting, ran-

dom coefficient or random walk beta (Schaefer, 1975;

Wells, 1996; Shah & Moonis (2003). But these specifica-

tions pose the problems related with the estimation of

beta. Beta is an unobservable variable. If it is assumed to

have different betas for each point in time, then OLS, which

is a standard method of estimating constant beta, cannot

be used for estimation as there is only one observation for

each point in time. One of the most widely used method

to estimate beta as a time series process is the Kalman

Filter (Kalman, 1960). It has been applied for the estima-

tion of betas and tests for beta constancy in a number of

studies (Kantor, 1971; Fisher, 1971; Szeto, 1973; Rosenberg,

1973; Garbade & aRentzler, 1981; Ohlson & Rosenberg,

1982; Bos & Newbold, 1984; Collins et al., 1987; Fisher &

Kamin, 1985; Shah & Moonis, 2003). The Kalman Filter

allows beta to be estimated as a time-varying stochastic

44

process. However, as is evident, the standard Kalman

filter estimates the market model under the assumption

of homoscedastic normally distributed errors. If the as-

sumption of normality of market model errors is not valid,

then the results from the Kalman filter methodology are

suspect. There exists compelling empirical evidence

against homoscedasticity and normality of financial re-

turns. Financial returns are known to show volatility clus-

tering and temporal dependence in the second moments

which may result in conditional or unconditional non-

normality (Bollerslev, 1986; Bollerselv et al., 1992). To the

extent the portfolio returns show volatility clustering and

are non-normal, the Gaussian Kalman filter is

misspecified and the results for tests of beta stability are

suspect (Shah & Moonis, 2003).

A totally alternative approach based on wavelet analy-

sis, which takes time-scale dependence explicitly into

account has been suggested by Gencay et al (2002; 2005)

and Fernandez (2006). This method allows for a time-

scale decomposition of financial data and provides a

natural method on which to investigate the time horizon

dependence of the beta behaviour.

Wavelet-based Beta Estimation

An important characteristic of the wavelet transform is

its ability to decompose the variance of a time series. If

one believes that the process under study is composed of

simple processes that move across different time scales,

this falls into the wavelet variance framework.

Let be a jth level MODWT (Maxi-

mum Overlap Discrete Wavelet Transform2) wavelet fil-

ter associated with scale λj = 2j-1, where Lj ≡ (2j–1)(L–1)+1,

is the width of the filter. Let Xt be a real valued stochastic

process with variance and let be the MODWT-wave-

let coefficient at level j. Then wavelet variance for scale

λj=2j-1, is defined as

(1.5)

and follows the relationship

(1.6)

Thus, the wavelet variance decomposes with

respect to different time scale. The unbiased MODWT es-

timator of the wavelet variance for scale , is given

by

(1.7)

where, 1 is the number of coefficients unaf-

fected by the boundary conditions.

Similarly, the unbiased MODWT estimator of the wavelet

covariance for scale λj=2j-1,can be obtained as

(1.8)

In the CAPM, following (1.3), (1.7), and (1.8), a time-scale

dependent beta estimator for asset i at the scale λj=2j-1,

can be defined as

(1.9)

EMPIRICAL ANALYSIS

The data set consists of all the constituent stocks of the

NIFTY index as on March 31, 2010. Table 1 provides the

list of all these companies. The period of analysis is from

June 15, 2001 to March 31, 2010 to account for the most

dynamic decade in the Indian equity market’s history.

For the companies, which were listed after June 15, 2001,

the data has been taken from the date it has been first

made available. The risk-free rate of return is proxied by

the overnight FIMMDA-NSE-MIBOR on which daily data

is available.

Since daily data is employed in the analysis, wavelet

scales are such that scale 1 is associated with 2-4 days

dynamics, scale 2 with 4-8 day dynamics, scale 3 with 8-

16 days dynamics, scale 4 with 16-32 days dynamics,

scale 5 with 32-64 days dynamics, scale 6 with 64-128

days dynamics, and scale 7 with 128-256 days dynam-

ics, which is roughly of about one year.

A Test for Beta Stability

As has been already explained, the initial hypothesis is

that heterogeneous nature of investors, varied response

of the market to different shocks, and inherent nature of

2 For a complete description of wavelet analysis of time series, seePercival and Walden (2000).



emerging market economies, apart from other plausible

reasons listed earlier, will induce instability in the beta

estimates. Therefore, the study first tests for the stability

of beta following Yamada (2005). Let ri,t and rm,t be the

excess returns on the individual stock and market portfo-

lio respectively. Then, βi is estimated by the OLS estima-

tion of the following equation:

, (1.10)

Following wavelet filters, the market returns series can be

decomposed into two series, one representing the short

periodicities (corresponding to scale j) and other the long

periodicities.

(1.11)

Now, the following model is estimated,

(1.12)

where, is corresponding to the series representing short

periodicities and is corresponding to the series repre-

senting the long periodicities. The stability of β at the

scale j can be tested by F-test of the following null hypoth-

esis,

(1.13)

EMPIRICAL RESULTS

Figure 1 shows the time series plots of the excess returns

on the NIFTY index series as well as on its different con-

stituent stocks. Figure 2 shows the decomposition of the

excess returns on the NIFTY series according to different

time scales of measurement. Table 3 reports for different

trading stocks the results of the test of β stability at scales

j=1,2,.....,7, which correspond to different time horizons

of investment. Some of the important observations are as

the following.

For one group of stocks, null hypothesis is rejected at all

the scales which indicates that for these stocks, β changes

with changes in all the time horizons of investment, i.e.

short periodicity beta estimates are significantly different

from long periodicity beta estimates at all the scales. This

group includes ABB Ltd., ACC Ltd., Ambuja Cements Ltd.,

Cipla Ltd., HDFC Bank Ltd., Hindustan Unilever Ltd.,

Hero Honda Motors Ltd., Hindalco Industries Ltd., ITC

Ltd., Ranbaxy Laboratories Ltd., Reliance Capital Ltd.,

Reliance Infrastructure Ltd., Steel Authority of India Ltd.,

Siemens Ltd., Sun Pharmaceutical Inds. Ltd., DLF Ltd.,

Jaiprakash Associates Ltd., and Reliance Communica-

tions Ltd.

For the second group of stocks, null hypothesis is not

rejected at any of the scales, i.e. for these stocks, short

periodicity beta estimates are not significantly different

from long periodicity beta estimates at any of the scales

indicating that β is not unstable for these stocks. This

group includes Axis Bank Ltd., Bharat Heavy Electricals

Ltd., GAIL (India) Ltd., HCL Technologies Ltd., Housing

Development Finance Corpn. Ltd., Jindal Steel & Power

Ltd., Kotak Mahindra Bank Ltd., Larsen & Toubro Ltd.,

Oil & Natural Gas Corpn. Ltd., State Bank of India, Tata

Motors Ltd., Tata Power Co. Ltd., Tata Steel Ltd., Unitech

Ltd., Bharti Airtel Ltd., Cairn India Ltd., Idea Cellular Ltd.,

Maruti Suzuki Ltd., NTPC Ltd., Punjab National Bank

Ltd., Power Grid Corpn. of India Ltd., Reliance Power

Ltd., and Suzlon Energy Ltd.

Table 2: List of all the NIFTY Constituent Companies as onMarch 31, 2010

Company Name Company Name

ABB Ltd. Larsen & Toubro Ltd.ACC Ltd. Mahindra & Mahindra Ltd.Ambuja Cements Ltd. Maruti Suzuki India Ltd.Axis Bank Ltd. NTPC Ltd.Bharat Heavy Electricals Ltd. Oil & Natural Gas Corpn. Ltd.Bharat Petroleum Corpn. Ltd. Power Grid Corpn. Of India Ltd.Bharti Airtel Ltd. Punjab National BankCairn India Ltd. Ranbaxy Laboratories Ltd.Cipla Ltd. Reliance Capital Ltd.DLF Ltd. Reliance Communications Ltd.GAIL (India) Ltd. Reliance Industries Ltd.HCL Technologies Ltd. Reliance Infrastructure Ltd.HDFC Bank Ltd. Reliance Power Ltd.Hero Honda Motors Ltd. Siemens Ltd.Hindalco Industries Ltd. State Bank Of IndiaHindustan Unilever Ltd. Steel Authority Of India Ltd.Housing Development Finance Corpn. Ltd. Sterlite Industries (India) Ltd.ICICI Bank Ltd. Sun Pharmaceutical Inds. Ltd.ITC Ltd. Suzlon Energy Ltd.Idea Cellular Ltd. Tata Consultancy Services Ltd.Infosys Technologies Ltd. Tata Motors Ltd.Infrastructure Development Finance Co. Ltd. Tata Power Co. Ltd.Jaiprakash Associates Ltd. Tata Steel Ltd.Jindal Steel & Power Ltd. Unitech Ltd.Kotak Mahindra Bank Ltd. Wipro Ltd.

Source: National Stock Exchange of India

46

For the third group of stocks consisting of Bharat Petro-

leum Corpn. Ltd., ICICI Bank Ltd., Infosys Technologies

Ltd., Mahindra & Mahindra Ltd., Reliance Industries Ltd.,

Sterlite Industries (India) Ltd., Wipro Ltd., Infrastructure

Development Finance Co. Ltd., and Tata Consultancy

Services Ltd., the complexity of time-scale dependence of

β comes out quite clearly. For these stocks, null hypoth-

esis is rejected at some of the scales and not rejected at

some other scales. For example, for Wipro Ltd., β shows

instability only at the time-scale of 8 days; otherwise it is

not unstable for other time- scales considered. On the other

hand, for Infosys Technologies Ltd., β is not unstable for

the time-scales of 8 days, 64 days, 128 days, and 256 days

but shows instability when time-scales of 16 days and 32

days are considered.

These results confirm that β estimates for different trad-

ing stocks in the Indian equity markets show consider-

able instability. These results suggest that the perception

of risk in holding any particular stock varies with the

horizon of investment. Also, in emerging markets, condi-

tions are very fluid and firms themselves are changing

rapidly but a priori, it is difficult to ascertain whether β for

any particular stock at any particular time-scale would

be unstable or not, as it has been demonstrated by several

firms showing considerable stability in their β estimates.

Therefore, it is prudent that instead of relying on a single

OLS β for the entire period, betas must be calculated tak-

ing into account different horizons of investment. There-

fore in Table 4, the values of time-scale dependent betas

are provided, which have been estimated following equa-

tion (1.9).

CONCLUSIONS

The results of this study show that in the Indian equity

markets, different trading stocks exhibit considerable in-

stability in their beta estimates as far as different invest-

ment horizons are concerned.

It has been argued that financial markets are character-

ized by heterogeneous investors, with different invest-

ment horizons. Consistent with the time horizon of

investment, the perception of risk, in holding different

stocks by different trading classes varies. It is also argued

that in emerging market economies, conditions are very

fluid; today’s leading firm may well be tomorrow’s fol-

lower or vice-versa. Moreover, firms themselves are chang-

ing: they are expanding into new markets, at times with

different products. Therefore, the assumption that the risk

in holding a firm’s stock will be constant over a longer

period, especially in the case of an emerging market

economy, is restrictive. The stability of beta estimates of

different trading stocks in the Indian equity markets was

tested during the period 2001-2010. Considerable insta-

bility was found in beta estimates of different stocks across

different horizons of investment during this period. Time-

scale dependent beta estimates for all these stocks were

also provided.

The results have important implications for practitioners

who are planning portfolio diversification, or construct-

ing different strategies for hedging risk in the Indian eq-

uity markets.

Time-scale dependent estimates of systematic risk embed-

ded in different stocks will provide considerable infor-

mation to practitioners in terms of benefits of diversi-

fication while constructing different portfolios using dif-

ferent stocks traded in the Indian equity markets. As has

been shown in Figure 3, the results show that conven-

tional OLS estimates of beta underestimates the extent of

systematic risk embedded in some stocks, thus overstat-

ing the potential gains from diversification whereas for

some other stocks, conventional OLS estimates of beta

overstates the extent of systematic risk embedded, thus

underestimating the potential gains from diversification.

Essentially, with the tools explained in this paper, practi-

tioners will be able to incorporate their horizons of in-

vestment while planning for portfolio diversification.

Also, the results emphasize the importance of a hedging

strategy that varies for different time horizons of invest-

ments over a static strategy where the hedge ratio is in-

variant to different horizons of investment. The basic

concept of hedging involves reduction of volatility in the

value of a spot position by including futures contracts in

the portfolio. Most of the empirical studies ignore the de-

pendence of the optimal hedge ratio on the hedging hori-

zon even though individuals and institutions, which use

futures contracts for hedging purposes, do not have the

same hedging horizon (Lien & Shrestha, 2007).



Figure1: Plots of the Excess Returns on NIFTY Index and its Constituent Firms

NIFTY ABB Ltd. ACC Ltd.

Ambuja Cements Ltd. Axis Bank Ltd. Bharat Heavy Electricals Ltd.

Bharat Petroleum Corpn. Ltd. Bharti Airtel Ltd. Cairn India Ltd.

Cipla Ltd. DLF Ltd. GAIL (India) Ltd.

HCL Technologies Ltd. HDFC Bank Ltd. Hero Honda Motors Ltd.

48 INSTABILITY AND TIME SCALE DEPENDENCE OF BETA IN AN EMERGING MARKET ECONOMY...

Hindalco Industries Ltd. Hindustan Unilever Ltd. Housing Development Finance Corpn. Ltd.

ICICI Bank Ltd. ITC Ltd. Idea Cellular Ltd.

Infosys Technologies Ltd. Infrastructure Development Finance Co. Ltd. Jaiprakash Associates Ltd.

Jindal Steel & Power Ltd. Kotak Mahindra Bank Ltd. Larsen & Toubro Ltd.

Mahindra & Mahindra Ltd. Maruti Suzuki Ltd. NTPC Ltd.

Oil & Natural Gas Corpn. Ltd. Power Grid Corpn. of India Ltd. Punjab National Bank


Ranbaxy Laboratories Ltd. Reliance Capital Ltd. Reliance Communications Ltd.

Reliance Industries Ltd. Reliance Infrastructure Ltd. Reliance Power Ltd.

Siemens Ltd. State Bank of India Steel Authority of India Ltd.

Sterlite Industries (India) Ltd. Sun Pharmaceutical Inds. Ltd. Suzlon Energy Ltd.

Tata Consultancy Services Ltd. Tata Motors Ltd. Tata Power Co. Ltd.

Tata Steel Ltd. Unitech Ltd. Wipro Ltd.

50

Note: “SP series 8 days” stands for short periodicity series corresponding to time scale of 8 days and “LP series 8 days” stands for long periodicity seriescorresponding to the time scale of 8 days. Similarly, for other plots corresponding to other time scales.

Figure2: Scale-wise Decomposition of Excess Returns on NIFTY Index Series


NIFTY raw series SP series 8 days LP series 8 days







Table 3: Test of Stability of βββββ for different stocks at Different Time Horizons

Time Horizon ABB ACC Ambuja Axis BHEL BPCL Cipla GAIL HCL HDFCCement Bank

≤ 8 Days 40.909 8.5575 7.4003 0.094142 1.2121 7.0762 27.861 0.010943 1.8718 1.9031[0.0000]** [0.0035]** [0.0066]** [0.7590] [0.2710] [0.0079]** [0.0000]** [0.9167] [0.1714] [0.1679]

≤ 16 Days 37.813 13.256 21.817 0.087454 1.0766 7.8255 37.357 0.16607 0.35877 0.99718[0.0000]** [0.0003]** [0.0000]** [0.7675] [0.2996] [0.0052]** [0.0000]** [0.6837] [0.5493] [0.3181]

≤ 32 Days 32.958 12.136 19.294 0.27919 0.38585 5.0123 32.370 0.090593 0.49514 0.67483[0.0000]** [0.0005]** [0.0000]** [0.5973] [0.5346] [0.0253]* [0.0000]** [0.7635] [0.4817] [0.4115]

≤ 64 Days 29.944 12.185 17.637 0.0093069 0.068995 2.9512 34.177 0.10703 0.55370 1.1379[0.0000]** [0.0005]** [0.0000]** [0.9232] [0.7928] [0.0860] [0.0000]** [0.7436] [0.4569] [0.2862]

≤ 128 Days 24.898 12.009 15.660 0.083612 0.059741 2.3757 30.467 0.042168 0.18225 0.79542[0.0000]** [0.0005]** [0.0001]** [0.7725] [0.8069] [0.1234] [0.0000]** [0.8373] [0.6695] [0.3726]

≤ 256 Days 19.473 5.7224 8.8875 0.0093512 0.032362 3.9711 24.048 0.23338 0.038389 0.41835[0.0000]** [0.0168]* [0.0029]** [0.9230] [0.8573] [0.0464]* [0.0000]** [0.6291] [0.8447] [0.5178]

Note: ** denotes 5% level of significance.

Time Horizon HDFC HUL Hero Hindalco ICICI ITC Infosys Jindal Kotak L & TBank Honda Bank Steel Mahindra

Bank

≤ 8 Days 11.310 12.568 27.924 5.5703 0.037198 19.801 0.64195 0.045491 0.012866 0.058076[0.0008]** [0.0004]** [0.0000]** [0.0184]* [0.8471] [0.0000]** [0.4231] [0.8311] [0.9097] [0.8096]

≤ 16 Days 9.4041 16.482 33.559 5.4775 2.4199 33.816 4.6831 1.3516 1.6451 0.11544[0.0022]** [0.0001]** [0.0000]** [0.0194]* [0.1200] [0.0000]** [0.0306]* [0.2451] [0.1998] [0.7341]

≤ 32 Days 7.4950 12.445 30.497 4.8006 3.9795 36.398 3.9261 1.0296 1.4193 0.052805[0.0062]** [0.0004]** [0.0000]** [0.0286]* [0.0462]* [0.0000]** [0.0477]* [0.3104] [0.2337] [0.8183]

≤ 64 Days 7.9837 13.096 23.189 4.2706 2.4933 28.912 3.7943 1.2678 1.1777 0.012169[0.0048]** [0.0003]** [0.0000]** [0.0389]* [0.1145] [0.0000]** [0.0516] [0.2603] [0.2780] [0.9122]

≤ 128 Days 6.3253 12.811 20.927 4.3394 3.5264 28.639 3.7296 1.3688 2.4827 0.27979[0.0120]* [0.0004]** [0.0000]** [0.0374]* [0.0605] [0.0000]** [0.0536] [0.2422] [0.1153] [0.5969]

≤ 256 days 6.3245 8.2433 13.305 4.9413 1.3229 24.013 1.0399 0.28596 1.3596 0.079565[0.0120]* [0.0041]** [0.0003]** [0.0263]* [0.2500] [0.0000]** [0.3080] [0.5929] [0.2437] [0.7779]


Time Horizon M & M ONGC RIL Ranbaxy Reliance Reliance SAIL SBI Siemens SterliteCapital Infra

≤ 8 Days 7.2455 1.0118 5.9589 16.023 32.996 21.653 25.305 0.025328 18.464 1.4672[0.0072]** [0.3146] [0.0147]* [0.0001]** [0.0000]** [0.0000]** [0.0000]** [0.8736] [0.0000]** [0.2259]

≤ 16 Days 2.6575 0.32698 5.3544 23.101 47.420 24.433 30.546 2.1573 10.807 4.2387[0.1032] [0.5675] [0.0208]* [0.0000]** [0.0000]** [0.0000]** [0.0000]** [0.1420] [0.0010]** [0.0396]*

≤ 32 Days 3.2154 0.17195 4.0804 22.864 41.271 14.878 24.433 2.6610 12.451 3.3555[0.0731] [0.6784] [0.0435]* [0.0000]** [0.0000]** [0.0001]** [0.0000]** [0.1030] [0.0004]** [0.0671]

≤ 64 Days 5.3547 0.14702 4.8306 19.848 35.904 12.373 19.236 2.6901 11.308 2.7619[0.0208]* [0.7014] [0.0281]* [0.0000]** [0.0000]** [0.0004]** [0.0000]** [0.1011] [0.0008]** [0.0967]

≤ 128 Days 6.9446 0.073446 3.7029 18.185 34.468 13.589 14.307 2.7126 8.5290 2.6354[0.0085]** [0.7864] [0.0545] [0.0000]** [0.0000]** [0.0002]** [0.0002]** [0.0997] [0.0035]** [0.1047]

≤ 256 Days 4.8300 0.063993 3.5807 11.485 20.634 9.4204 7.5765 1.5746 10.495 2.5929[0.0281]* [0.8003] [0.0586] [0.0007]** [0.0000]** [0.0022]** [0.0060]** [0.2097] [0.0012]** [0.1075]


52

Time Horizon Sun Tata Tata Tata Unitech Wipro Bharti Cairn DLF IdeaPharma Motors Power Steel Airtel India Cellular

≤ 8 Days 47.113 1.6365 1.6478 1.4284 1.4472 10.206 0.012112 1.0896 15.831 1.0679[0.0000]** [0.2010] [0.1994] [0.2322] [0.2291] [0.0014]** [0.9124] [0.2969] [0.0001]** [0.3018]

≤ 16 Days 64.200 0.63504 0.82533 3.7057 0.42486 2.9332 0.41449 0.60989 27.765 0.97601[0.0000]** [0.4256] [0.3637] [0.0544] [0.5146] [0.0869] [0.5198] [0.4351] [0.0000]** [0.3235]

≤ 32 Days 47.386 0.73866 0.36728 2.3809 0.027788 1.3506 0.23375 0.45639 33.642 2.3050[0.0000]** [0.3902] [0.5446] [0.1230] [0.8676] [0.2453] [0.6288] [0.4995] [0.0000]** [0.1294]

≤ 64 Days 47.708 0.79675 0.14569 2.2718 0.0083010 0.57560 0.14367 0.53382 33.742 3.0916[0.0000]** [0.3722] [0.7027] [0.1319] [0.9274] [0.4481] [0.7047] [0.4652] [0.0000]** [0.0791]

≤ 128 Days 43.390 0.89568 0.099878 1.6783 0.015035 0.35744 0.065080 0.30651 30.961 2.8519[0.0000]** [0.3441] [0.7520] [0.1953] [0.9024] [0.5500] [0.7987] [0.5800] [0.0000]** [0.0917]

≤ 256 Days 32.559 1.2046 0.28977 0.37285 0.071268 0.34872 0.012273 0.0024019 19.857 2.0635[0.0000]** [0.2725] [0.5904] [0.5415] [0.7895] [0.5549] [0.9118] [0.9609] [0.0000]** [0.1513]

Note: ** denotes 5% level of significance

Time Horizon IDFC JP Maruti NTPC Punjab Power RComm RPower Suzlon TCSSuzuki National Grid Energy

Bank≤ 8 Days 3.0807 5.6722 2.5527 0.43362 1.5778 1.2519 6.9230 0.00050949 0.92514 1.1125

[0.0795] [0.0174]* [0.1103] [0.5103] [0.2092] [0.2636] [0.0086]** [0.9820] [0.3363] [0.2917]

≤ 16 Days 6.9044 10.063 2.1835 1.1688 2.8714 0.99938 11.137 1.0214 2.4020 5.9104[0.0087]** [0.0015]** [0.1397] [0.2799] [0.0903] [0.3179] [0.0009]** [0.3127] [0.1215] [0.0152]*

≤ 32 Days 8.0752 9.2427 3.1299 1.2823 3.1397 2.3581 9.7375 1.0969 2.6891 7.4698[0.0046]** [0.0024]** [0.0771] [0.2577] [0.0766] [0.1252] [0.0019]** [0.2955] [0.1013] 0.0064]**

≤ 64 Days 4.9511 6.9529 2.7619 0.72222 2.4283 2.3080 10.768 2.7639 2.5412 6.4246[0.0263]* [0.0085]** [0.0967] [0.3956] [0.1193] [0.1292] [0.0011]** [0.0970] [0.1112] [0.0114]*

≤ 128 Days 4.8054 6.4366 5.1365 0.66437 1.9747 1.9282 9.9769 4.0887 3.5138 5.7466[0.0286]* [0.0113]* [0.0236]* [0.4152] [0.1601] [0.1655] [0.0016]** [0.0437]* [0.0611] [0.0167]*

≤ 256 Days 1.2890 4.5762 4.2132 0.40768 0.063442 0.88678 10.870 2.4216 2.8397 4.4762[0.2565] [0.0326]* [0.0403]* [0.5233] [0.8012] [0.3467] [0.0010]** [0.1203] [0.0923] [0.0346]*


Table 4: Time Scale Dependent βββββ Estimates

ABB ACC Ambuja Axis Bank BHEL BPCL Cipla GAIL HCL HDFC

OLS β 0.937909 0.951738 0.942602 1.02729 1.00776 0.894300 0.869832 0.982473 1.05483 0.979742

β at Scale 1 0.58211 0.57323 0.57740 0.41267 0.57635 0.42027 0.59316 0.50934 0.39996 0.52628

β at Scale 2 0.60847 0.60951 0.59528 0.43431 0.57971 0.46161 0.61558 0.55845 0.40508 0.54946

β at Scale 3 0.61113 0.64985 0.62461 0.46516 0.59537 0.48021 0.58126 0.60825 0.44983 0.57019

β at Scale 4 0.74282 0.82990 0.81143 0.68079 0.82279 0.64042 0.81279 0.77105 0.65720 0.79339

β at Scale 5 0.81820 0.87802 0.89357 0.72408 0.88905 0.76577 0.92154 0.84790 0.77554 0.92721

β at Scale 6 0.90289 0.92817 0.92254 0.83260 0.92972 0.94966 0.96209 0.93090 0.89438 0.95711

β at Scale 7 0.96374 0.92407 0.93887 0.96412 0.97923 1.09890 1.03180 1.02410 0.98501 0.98436

HDFC HUL Hero Hindalco ICICI ITC Infosys Jindal Kotak L & TBank Honda Bank Steel Mahindra

Bank

OLS β 0.938092 0.866183 0.865360 1.03056 1.07109 0.886676 0.973179 1.08979 1.03969 1.03820

β at Scale 1 0.60088 0.63471 0.52236 0.53708 0.52823 0.64278 0.58324 0.42385 0.38433 0.59035

β at Scale 2 0.62129 0.65095 0.50791 0.54216 0.50201 0.66357 0.56937 0.41384 0.37357 0.59714

β at Scale 3 0.67449 0.61661 0.58778 0.55729 0.52048 0.67445 0.60172 0.43272 0.3951 0.60918



HDFC HUL Hero Hindalco ICICI ITC Infosys Jindal Kotak L & TBank Honda Bank Steel Mahindra

Bank

β at Scale 4 0.86546 0.86885 0.81779 0.69501 0.67564 0.88259 0.78109 0.58186 0.60107 0.8075

β at Scale 5 0.94511 0.96698 0.84786 0.78447 0.80554 0.89948 0.8477 0.73295 0.72657 0.86614

β at Scale 6 0.96344 0.99796 1.0002 0.89252 0.84822 0.99876 0.93943 0.78527 0.78198 0.88156

β at Scale 7 1.0249 1.0292 1.011 0.94821 0.98442 1.024 0.9331 0.91412 0.9874 0.96242

Note: Scale 1: 2-4 days; Scale 2: 4-8 days; Scale 3: 8-16 days; Scale 4: 16-32 days; Scale 5: 32-64 days; Scale 6: 64-128 days; Scale 7: 128-256 days.

M & M ONGC RIL Ranbaxy Reliance Reliance SAIL SBI Siemens SterliteCapital Infra

OLS β 0.990916 0.963252 1.03218 0.905132 1.17454 1.11834 1.12033 1.01159 0.985790 0.988045

β at Scale 1 0.53813 0.61495 0.69366 0.50203 0.44542 0.48413 0.41202 0.64224 0.52388 0.1596

β at Scale 2 0.53758 0.58805 0.68139 0.51417 0.45377 0.48775 0.4024 0.65963 0.53002 0.17246

β at Scale 3 0.54582 0.59014 0.67792 0.53122 0.44886 0.52365 0.44382 0.65075 0.5368 0.15186

β at Scale 4 0.74279 0.81518 0.8655 0.70286 0.60781 0.71182 0.63229 0.79922 0.73098 0.33759

β at Scale 5 0.85386 0.86797 0.87892 0.78761 0.69628 0.7914 0.6626 0.8536 0.76851 0.42303

β at Scale 6 0.94714 0.94391 0.96821 0.89152 0.73728 0.77762 0.81852 0.93075 0.85423 0.54937

β at Scale 7 0.93602 1.0241 0.96672 0.94037 0.90815 0.92473 0.96111 0.98066 0.95906 0.77224

Sun Tata Tata Tata Unitech Wipro Bharti Cairn DLF IdeaPharma Motors Power Steel Airtel India Cellular

OLS β 0.824321 1.04840 1.00544 1.10642 1.07290 1.04499 0.959623 0.982436 1.23069 1.00742

β at Scale 1 0.49545 0.49969 0.53105 0.5313 0.27807 0.49638 0.48452 0.61042 0.36961 0.62426

β at Scale 2 0.51949 0.51773 0.54062 0.53901 0.30743 0.53467 0.51058 0.62967 0.36149 0.59849

β at Scale 3 0.50895 0.52445 0.59652 0.52886 0.33414 0.55343 0.5397 0.65583 0.41554 0.549

β at Scale 4 0.77407 0.75799 0.77396 0.71215 0.47079 0.75031 0.78407 0.74358 0.37517 0.57728

β at Scale 5 0.94258 0.7697 0.82957 0.75574 0.55894 0.88741 0.80935 0.82596 0.4543 0.72801

β at Scale 6 1.0013 0.83751 0.9269 0.84059 0.65643 0.92597 0.92879 0.88454 0.63359 0.83951

β at Scale 7 1.0388 0.93625 0.98396 0.9151 0.84859 0.94721 0.99302 0.94834 0.59338 0.77659


IDFC JP Maruti NTPC Punjab Power RComm RPower Suzlon Energy TCSSuzuki National Grid

Bank

OLS β 1.09726 1.17249 0.965186 0.939636 0.996597 0.912004 1.08174 1.03070 1.13733 0.990453

β at Scale 1 0.521 0.41395 0.61727 0.73856 0.47243 0.56227 0.5549 0.54605 0.44322 0.70692

β at Scale 2 0.51811 0.43346 0.63676 0.7125 0.50807 0.55766 0.60684 0.47846 0.46456 0.67573

β at Scale 3 0.56739 0.47111 0.62909 0.78059 0.53148 0.60262 0.58147 0.51962 0.41954 0.6802

β at Scale 4 0.75224 0.60566 0.82126 0.92698 0.73221 0.53749 0.81268 0.54641 0.60404 0.85027

β at Scale 5 0.87815 0.77007 0.87951 0.95648 0.76128 0.88424 0.82903 0.76181 0.75541 0.86532

β at Scale 6 0.87326 0.79431 1.0024 1.02 0.90978 1.0452 0.88647 0.61413 0.73309 0.95531

β at Scale 7 1.0182 0.87872 0.98329 1.0314 1.0491 0.6194 0.85997 1.3009 0.76332 0.96496


54

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Figure 3: Plots of Betas of Different Stocks at Different Time Scales with their OLS Betas

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Amlendu Kumar Dubey is an Assistant Professor in the Eco-nomics Area of the Indian Institute of Management Indore.He has a Ph.D from IGIDR, Mumbai. His current researchinterests include broader areas of empirical macroeconom-

ics. Some of his recent papers have appeared in Applied Eco-nomics and Economic Modelling.

e-mail: [email protected]

56

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