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

Transcription

1 R E S E A R C H includes research articles that focus on the analysis and resolution of managerial and academic issues based on analytical and empirical or case research Instability and Time Scale Dependence of Beta in an Emerging Market Economy: Evidence from India Amlendu Kumar Dubey Executive Summary 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 different 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, economic 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 sixfold 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 consideration. KEY WORDS Beta CAPM Time Scale Dependence Wavelets Indian Equity Market Time-scale dependent estimates of systematic risk embedded in different stocks will provide considerable information to practitioners in terms of benefits of diversification 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 diversification. 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. VIKALPA VOLUME 39 NO 1 JANUARY - MARCH

2 Time scales of measurement are closely related with the investment horizon of different classes of investors. Most of the financial markets are characterized by heterogeneous investors, with different investment 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 investment. Consistent with their trading horizons, the behaviour of different trading class varies and may have different risk perceptions. Secondly, in such a heterogeneous market, a low frequency 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 response to the different disturbances and the heterogeneous 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 follower 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 different products. Therefore, assuming that the risk in holding 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 markets 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 major 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 participation. Market capitalization in the Indian markets was around `61,704,205 million (US $1,366,952 million) at the end of March Market capitalization ratio 1 increased to percent in 2009, substantially recovering from the drop of percent in 2008 (NSE, 2010). Table 1: Comparison of Global Stock Markets Country Market No. of Capitalization Ratio Listed Companies Australia ,913 1,924 1,882 France Germany Japan ,844 3,299 3,208 Singapore UK ,588 2,415 2,179 USA ,130 5,603 4,401 China ,530 1,604 1,700 India ,887 4,921 4,955 Russia Brazil Indonesia Korea ,767 1,798 1,778 Malaysia , Mexico Sources: S&P Global Stock Market Fact Book, 2009; World Development Indicators; 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 Pricing 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 r f be the expected returns to the risk-free asset and r m be the expected excess return to a portfolio of risky assets over r f. Now, suppose r i is the expected excess return to the asset i over r f, then CAPM may be written in a form that is known as the single index market model: r i = a i + β i r m (1.1) Here, a i represents that component of the return to asset i that is independent of the return r m to the market portfolio. Part of it is determined by the risk-free rate of return r f, but the other part may be thought of as a purely random 1 Market capitalization ratio is defined as total market capitalization of stocks divided by the GDP. It is used as a measure to denote the importance of equity markets relative to the GDP and indicates the ability to mobilize capital and diversify risk. 42 INSTABILITY AND TIME SCALE DEPENDENCE OF BETA IN AN EMERGING MARKET ECONOMY...

3 phenomenon. It is thus helpful to rewrite (1.1) as r i = a i + β i r m + ε (1.2) β i cannot be observed but may be estimated using ordinary 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 r f. 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, r im is the return on a zero-beta portfolio, which is defined as the minimum variance portfolio among all portfolios uncorrelated with m. TIME SCALE DEPENDENCE OF BETA There are several plausible reasons (Shah & Moonis, 2003), apart from the ones listed earlier (different investment horizon of investors, varied response to different shocks, and inherent nature of emerging market economies) 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. Financial risk is a function of the leverage of the firm (Hamada, 1972; Mandelker & Rhee, 1984). Since leverage can change with changes in stock prices, stock price movement can generate changes in beta. Any news that does not affect market and stock returns 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-variation in beta. Beta is found to be correlated positively with growth, leverage, and earning variability of the firm and negatively 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 - theoretical 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 correlation in the residuals would result in unstable estimates. Another reason for beta instability could be that market 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, random coefficient or random walk beta (Schaefer, 1975; Wells, 1996; Shah & Moonis (2003). But these specifications 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 estimation 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 VIKALPA VOLUME 39 NO 1 JANUARY - MARCH

4 process. However, as is evident, the standard Kalman filter estimates the market model under the assumption of homoscedastic normally distributed errors. If the assumption 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 returns. Financial returns are known to show volatility clustering and temporal dependence in the second moments which may result in conditional or unconditional nonnormality (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 analysis, 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 timescale 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 (Maximum Overlap Discrete Wavelet Transform 2 ) wavelet filter associated with scale λ j = 2 j-1, where L j (2 j 1)(L 1)+1, is the width of the filter. Let X t be a real valued stochastic process with variance and let be the MODWT-wavelet coefficient at level j. Then wavelet variance for scale λ j =2 j-1, is defined as and follows the relationship (1.5) (1.6) 2 For a complete description of wavelet analysis of time series, see Percival and Walden (2000). Thus, the wavelet variance decomposes with respect to different time scale. The unbiased MODWT estimator of the wavelet variance for scale, is given by (1.7) where, 1 is the number of coefficients unaffected by the boundary conditions. Similarly, the unbiased MODWT estimator of the wavelet covariance for scale λ j =2 j-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 λ j =2 j-1, can be defined as EMPIRICAL ANALYSIS (1.9) The data set consists of all the constituent stocks of the NIFTY index as on March 31, 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 days dynamics, scale 5 with days dynamics, scale 6 with days dynamics, and scale 7 with days dynamics, 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 44 INSTABILITY AND TIME SCALE DEPENDENCE OF BETA IN AN EMERGING MARKET ECONOMY...

5 Table 2: List of all the NIFTY Constituent Companies as on March 31, 2010 Company Name 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. 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. Source: National Stock Exchange of India 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 r i,t and r m,t be the excess returns on the individual stock and market portfolio respectively. Then, β i is estimated by the OLS estimation 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. Now, the following model is estimated, Company Name Larsen & Toubro Ltd. Mahindra & Mahindra Ltd. Maruti Suzuki India 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. (1.11) (1.12) where, is corresponding to the series representing short periodicities and is corresponding to the series representing the long periodicities. The stability of β at the scale j can be tested by F-test of the following null hypothesis, EMPIRICAL RESULTS (1.13) Figure 1 shows the time series plots of the excess returns on the NIFTY index series as well as on its different constituent 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 Communications 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. VIKALPA VOLUME 39 NO 1 JANUARY - MARCH

6 For the third group of stocks consisting of Bharat Petroleum 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 hypothesis 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 trading stocks in the Indian equity markets show considerable instability. These results suggest that the perception of risk in holding any particular stock varies with the horizon of investment. Also, in emerging markets, conditions 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 taking into account different horizons of investment. Therefore in Table 4, the values of time-scale dependent betas are provided, which have been estimated following equation (1.9). CONCLUSIONS The results of this study show that in the Indian equity markets, different trading stocks exhibit considerable instability in their beta estimates as far as different investment horizons are concerned. It has been argued that financial markets are characterized by heterogeneous investors, with different investment 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 follower or vice-versa. Moreover, firms themselves are changing: 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 Considerable instability was found in beta estimates of different stocks across different horizons of investment during this period. Timescale dependent beta estimates for all these stocks were also provided. The results have important implications for practitioners who are planning portfolio diversification, or constructing different strategies for hedging risk in the Indian equity markets. Time-scale dependent estimates of systematic risk embedded in different stocks will provide considerable information to practitioners in terms of benefits of diversification while constructing different portfolios using different stocks traded in the Indian equity markets. As has been shown in Figure 3, the results show that conventional OLS estimates of beta underestimates the extent of systematic risk embedded in some stocks, thus overstating 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, practitioners will be able to incorporate their horizons of investment while planning for portfolio diversification. Also, the results emphasize the importance of a hedging strategy that varies for different time horizons of investments over a static strategy where the hedge ratio is invariant 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 dependence of the optimal hedge ratio on the hedging horizon even though individuals and institutions, which use futures contracts for hedging purposes, do not have the same hedging horizon (Lien & Shrestha, 2007). 46 INSTABILITY AND TIME SCALE DEPENDENCE OF BETA IN AN EMERGING MARKET ECONOMY...

7 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. VIKALPA VOLUME 39 NO 1 JANUARY - MARCH

8 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 48 INSTABILITY AND TIME SCALE DEPENDENCE OF BETA IN AN EMERGING MARKET ECONOMY...

9 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. VIKALPA VOLUME 39 NO 1 JANUARY - MARCH

10 Figure2: Scale-wise Decomposition of Excess Returns on NIFTY Index Series NIFTY raw series SP series 8 days LP series 8 days NIFTY raw series SP series 16 days LP series 16 days NIFTY raw series SP series 32 days LP series 32 days NIFTY raw series SP series 64 days LP series 64 days NIFTY raw series SP series 128 days LP series 128 days NIFTY raw series SP series 256 days LP series 256 days 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 series corresponding to the time scale of 8 days. Similarly, for other plots corresponding to other time scales. 50 INSTABILITY AND TIME SCALE DEPENDENCE OF BETA IN AN EMERGING MARKET ECONOMY...

11 Table 3: Test of Stability of β for different stocks at Different Time Horizons Time Horizon ABB ACC Ambuja Axis BHEL BPCL Cipla GAIL HCL HDFC Cement Bank 8 Days [0.0000]** [0.0035]** [0.0066]** [0.7590] [0.2710] [0.0079]** [0.0000]** [0.9167] [0.1714] [0.1679] 16 Days [0.0000]** [0.0003]** [0.0000]** [0.7675] [0.2996] [0.0052]** [0.0000]** [0.6837] [0.5493] [0.3181] 32 Days [0.0000]** [0.0005]** [0.0000]** [0.5973] [0.5346] [0.0253]* [0.0000]** [0.7635] [0.4817] [0.4115] 64 Days [0.0000]** [0.0005]** [0.0000]** [0.9232] [0.7928] [0.0860] [0.0000]** [0.7436] [0.4569] [0.2862] 128 Days [0.0000]** [0.0005]** [0.0001]** [0.7725] [0.8069] [0.1234] [0.0000]** [0.8373] [0.6695] [0.3726] 256 Days [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 & T Bank Honda Bank Steel Mahindra Bank 8 Days [0.0008]** [0.0004]** [0.0000]** [0.0184]* [0.8471] [0.0000]** [0.4231] [0.8311] [0.9097] [0.8096] 16 Days [0.0022]** [0.0001]** [0.0000]** [0.0194]* [0.1200] [0.0000]** [0.0306]* [0.2451] [0.1998] [0.7341] 32 Days [0.0062]** [0.0004]** [0.0000]** [0.0286]* [0.0462]* [0.0000]** [0.0477]* [0.3104] [0.2337] [0.8183] 64 Days [0.0048]** [0.0003]** [0.0000]** [0.0389]* [0.1145] [0.0000]** [0.0516] [0.2603] [0.2780] [0.9122] 128 Days [0.0120]* [0.0004]** [0.0000]** [0.0374]* [0.0605] [0.0000]** [0.0536] [0.2422] [0.1153] [0.5969] 256 days [0.0120]* [0.0041]** [0.0003]** [0.0263]* [0.2500] [0.0000]** [0.3080] [0.5929] [0.2437] [0.7779] Note: ** denotes 5% level of significance. Time Horizon M & M ONGC RIL Ranbaxy Reliance Reliance SAIL SBI Siemens Sterlite Capital Infra 8 Days [0.0072]** [0.3146] [0.0147]* [0.0001]** [0.0000]** [0.0000]** [0.0000]** [0.8736] [0.0000]** [0.2259] 16 Days [0.1032] [0.5675] [0.0208]* [0.0000]** [0.0000]** [0.0000]** [0.0000]** [0.1420] [0.0010]** [0.0396]* 32 Days [0.0731] [0.6784] [0.0435]* [0.0000]** [0.0000]** [0.0001]** [0.0000]** [0.1030] [0.0004]** [0.0671] 64 Days [0.0208]* [0.7014] [0.0281]* [0.0000]** [0.0000]** [0.0004]** [0.0000]** [0.1011] [0.0008]** [0.0967] 128 Days [0.0085]** [0.7864] [0.0545] [0.0000]** [0.0000]** [0.0002]** [0.0002]** [0.0997] [0.0035]** [0.1047] 256 Days [0.0281]* [0.8003] [0.0586] [0.0007]** [0.0000]** [0.0022]** [0.0060]** [0.2097] [0.0012]** [0.1075] Note: ** denotes 5% level of significance. VIKALPA VOLUME 39 NO 1 JANUARY - MARCH

12 Time Horizon Sun Tata Tata Tata Unitech Wipro Bharti Cairn DLF Idea Pharma Motors Power Steel Airtel India Cellular 8 Days [0.0000]** [0.2010] [0.1994] [0.2322] [0.2291] [0.0014]** [0.9124] [0.2969] [0.0001]** [0.3018] 16 Days [0.0000]** [0.4256] [0.3637] [0.0544] [0.5146] [0.0869] [0.5198] [0.4351] [0.0000]** [0.3235] 32 Days [0.0000]** [0.3902] [0.5446] [0.1230] [0.8676] [0.2453] [0.6288] [0.4995] [0.0000]** [0.1294] 64 Days [0.0000]** [0.3722] [0.7027] [0.1319] [0.9274] [0.4481] [0.7047] [0.4652] [0.0000]** [0.0791] 128 Days [0.0000]** [0.3441] [0.7520] [0.1953] [0.9024] [0.5500] [0.7987] [0.5800] [0.0000]** [0.0917] 256 Days [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 TCS Suzuki National Grid Energy Bank 8 Days [0.0795] [0.0174]* [0.1103] [0.5103] [0.2092] [0.2636] [0.0086]** [0.9820] [0.3363] [0.2917] 16 Days [0.0087]** [0.0015]** [0.1397] [0.2799] [0.0903] [0.3179] [0.0009]** [0.3127] [0.1215] [0.0152]* 32 Days [0.0046]** [0.0024]** [0.0771] [0.2577] [0.0766] [0.1252] [0.0019]** [0.2955] [0.1013] ]** 64 Days [0.0263]* [0.0085]** [0.0967] [0.3956] [0.1193] [0.1292] [0.0011]** [0.0970] [0.1112] [0.0114]* 128 Days [0.0286]* [0.0113]* [0.0236]* [0.4152] [0.1601] [0.1655] [0.0016]** [0.0437]* [0.0611] [0.0167]* 256 Days [0.2565] [0.0326]* [0.0403]* [0.5233] [0.8012] [0.3467] [0.0010]** [0.1203] [0.0923] [0.0346]* Note: ** denotes 5% level of significance. Table 4: Time Scale Dependent β Estimates ABB ACC Ambuja Axis Bank BHEL BPCL Cipla GAIL HCL HDFC OLS β β at Scale β at Scale β at Scale β at Scale β at Scale β at Scale β at Scale HDFC HUL Hero Hindalco ICICI ITC Infosys Jindal Kotak L & T Bank Honda Bank Steel Mahindra Bank OLS β β at Scale β at Scale β at Scale INSTABILITY AND TIME SCALE DEPENDENCE OF BETA IN AN EMERGING MARKET ECONOMY...

13 HDFC HUL Hero Hindalco ICICI ITC Infosys Jindal Kotak L & T Bank Honda Bank Steel Mahindra Bank β at Scale β at Scale β at Scale β at Scale Note: Scale 1: 2-4 days; Scale 2: 4-8 days; Scale 3: 8-16 days; Scale 4: days; Scale 5: days; Scale 6: days; Scale 7: days. M & M ONGC RIL Ranbaxy Reliance Reliance SAIL SBI Siemens Sterlite Capital Infra OLS β β at Scale β at Scale β at Scale β at Scale β at Scale β at Scale β at Scale Sun Tata Tata Tata Unitech Wipro Bharti Cairn DLF Idea Pharma Motors Power Steel Airtel India Cellular OLS β β at Scale β at Scale β at Scale β at Scale β at Scale β at Scale β at Scale Note: Scale 1: 2-4 days; Scale 2: 4-8 days; Scale 3: 8-16 days; Scale 4: days; Scale 5: days; Scale 6: days; Scale 7: days. IDFC JP Maruti NTPC Punjab Power RComm RPower Suzlon Energy TCS Suzuki National Grid Bank OLS β β at Scale β at Scale β at Scale β at Scale β at Scale β at Scale β at Scale Note: Scale 1: 2-4 days; Scale 2: 4-8 days; Scale 3: 8-16 days; Scale 4: days; Scale 5: days; Scale 6: days; Scale 7: days. VIKALPA VOLUME 39 NO 1 JANUARY - MARCH

14 Figure 3: Plots of Betas of Different Stocks at Different Time Scales with their OLS Betas REFERENCES Alexander, G., & Chervany, N. L. (1980). On the estimation and stability of beta. Journal of Financial and Quantitative Analysis, 15(1), Beaver, W., Kettler, P., & Scholes, M. (1970). The association between market determined and accounting determined risk measures. The Accounting Review, 45(4), Black, F. (1972). Capital market equilibrium with restricted borrowing. Journal of Business, 45(3), Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics. 31(3), Bollerslev, T., Chou, R. F., & Kroner, K. F. (1992). ARCH modeling in finance: A review of the theory and empirical evidence. Journal of Econometrics, 52(1), Bos, T., & Newbold, P. (1984). An empirical investigation of the possibility of systematic stochastic risk in the market model. Journal of Business, 57(1), Brooks, R. D., Faff, R. W., & McKenzie, M. D. (1998). Time varying beta risk of Australian industry portfolios: A comparison of modeling techniques. Australian Journal of Management, 23(1), Buckland, R., & Fraser, P. (2001). Political and regulatory risk: Beta sensitivity in UK electricity distribution. Journal of Regulatory Economics,19(1), Cheng, J. W. (1997). A switching regression approach to the stationarity of systematic and nonsystematic risks: The Hong Kong experience. Applied Financial Economics. 7(1), Collins, D. W., Ledolter J., & Rayburn J. D. (1987). Some further evidence on the stochastic properties of systematic risk. Journal of Business, 60(3), Fabozzi, F., & Francis, J. (1978). Beta as a random coefficient. Journal of Financial and Quantitative Analysis,13(1), Fernandez, V. (2006). The international CAPM and a waveletbased decomposition of value at risk. NBER working paper No Fisher, L. (1971). On the estimation of systematic risk. Proceedings of the Wells Fargo Symposium, July, Fisher, L., & Kamin, J. (1985). Forecasting systematic risk: Estimates of raw beta that take into account the tendency of beta to change and the heteroscedasticity of residual returns. Journal of Financial and Quantitative Analysis, 20(2), INSTABILITY AND TIME SCALE DEPENDENCE OF BETA IN AN EMERGING MARKET ECONOMY...

15 Garbade, K., & Rentzler, J. (1981). Testing the hypothesis of beta stationarity. International Economic Review, 22(3), Gencay, R., Selcuk, F., & Whitcher, B. (2002). An introduction to wavelets and other filtering methods in finance and economics. San Diego: Academic Press. Gencay, R., Selcuk, F., & Whitcher, B. (2005). Multiscale systematic risk. Journal of International Money and Finance. 24(1), Groenewold, N., & Fraser, P. (1999). Time varying estimates of CAPM betas. Mathematics and Computers in Simulation. 48(4-6), Hamada, R. S. (1972). The effect of the firm s capital structure of the systematic risk of the common stock. Journal of Finance, 27(2), Jagannathan, R., & Wang, Z. (1996). The conditional CAPM and the cross-section of expected returns. Journal of Finance, 51(1), Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, ASME Transactions, Series D, 82, Kantor, M. (1971). Market senstivities. Financial Analysts Journal, 27(1), Kon, S. J., & Jen, F. C. (1978). Estimation of time-varying systematic risk and performance for mutual fund portfolios: An application of switching regression. Journal of Finance, 33(2), Kon, S. J., & Jen, F. C. (1979). The investment performance of mutual funds: An empirical investigation of timing, selectivity, and market efficiency. Journal of Business, 52(2), Lien, D., & Shrestha, K. (2007). An empirical analysis of the relationship between hedge ratio and hedging horizon using wavelet analysis. The Journal of Futures Markets, 27(2), Mandelker, G., & Rhee, S. G. (1984). The impact of degrees of operating and financial leverage on systematic risk of a common stock. Journal of Financial and Quantitative Analysis, 19(1), NSE (2010). Indian securities market: A review. Mumbai, India: National Stock Exchange of India Ltd. Ohlson, J., & Rosenberg, B. (1982). Systematic risk of the CRSP equal-weighted common stock index: A history estimated by stochastic parameter regression. Journal of Business, 55(1), Percival, D. B., & Walden, A. T. (2000). Wavelet methods for timeseries analysis. Cambridge: Cambridge University Press. Rosenberg, B., & Guy, J. (1976). Prediction of beta from investment fundamentals. Financial Analysis Journal, 32(3), Rosenberg, B. (1973). Random coefficient models: The analysis of a cross-section of time series by stochastically convergent parameter regression. Annals of Social and Economic Measurement, 2(4), Sahaefer, S.M., Brealey, R.A., Hodges, S.D., & Thomas, H.A. (1975). Alternative models of systematic risk. In E. Elton & M. Gruber (Eds.), International Capital Markets, North Holland, Amsterdam, Scott, E., & Brown, S. (1980). Biased estimators and unstable betas. Journal of Finance, 35(1), Shah, A., & Moonis, S. A. (2003). Testing for time variation in beta in India. Journal of Emerging Markets Finance, 2(2), Szeto, M. W. (1973). Estimation of the volatility of securities in the stock market by Kalman filter techniques. Fourteenth Joint Automatic Control Conference of the American Automatic Control Council, Preprints of technical papers, Columbus, Ohio, Wells, C. (1996). The Kalman filter in finance. Dordrecht: Kluwer Academic Publishers. Yamada, H. (2005). Wavelet based beta estimation and Japanese industrial stock prices. Applied Economic Letters, 12(2), Amlendu Kumar Dubey is an Assistant Professor in the Economics Area of the Indian Institute of Management Indore. He has a Ph.D from IGIDR, Mumbai. His current research interests include broader areas of empirical macroeconomics. Some of his recent papers have appeared in Applied Economics and Economic Modelling. amlendu@iimidr.ac.in VIKALPA VOLUME 39 NO 1 JANUARY - MARCH

16 Vikalpa: The Journal for Decision Makers Call for Papers Vikalpa: The Journal for Decision Makers, a quarterly publication of the Indian Institute of Management, Ahmedabad, India, primarily addresses people engaged in the practice of management. It seeks to communicate management knowledge generated by academic thinking and reflection to practitioners and policy makers in the private, public, governmental and civil society sectors. We invite contributions that serve this purpose by presenting new concepts, fresh conclusions from research, lessons from practice, and insights into management excellence. Vikalpa s scope extends to all areas of management such as general management, marketing, finance, organizational behaviour, and human resources, operations, etc. Vikalpa features articles on various sectors like industry, agriculture, banking, international trade, urban and rural development, public systems, and information systems. Please refer to the Guidelines for Authors, presented elsewhere in this issue, for details of the features under which articles can be submitted: PERSPECTIVES, RESEARCH, INTERFACES, NOTES AND COMMENTARIES. Vikalpa also invites contributions to its MANAGEMENT CASE feature Every issue of Vikalpa carries a management case, and its analyses. A case is a description of a reallife situation, that may (a) include problems, solutions attempted, results and conclusions (research cases) or (b) conclude with a decision-point or dilemma faced by the organization or some of its members. Management cases that are based on information directly collected by the writer from the organization are preferred; however, cases based largely on secondary data that is publicly available, may also be considered. In the latter kind of cases, particular attention must be paid to adequate and appropriate citing of sources, and the norms of correct academic writing must be followed. A case submitted to Vikalpa must be well-researched and documented and must present a faithful view of the organization s problems, actions and decisions. Its quality will be evaluated on the basis of the following: Identification of significant problems/situations/issues/processes Adequacy and quality of information and data Realism and effectiveness Completeness, complexity, and focus Potential to illustrate ideas, concepts or processes Citation of secondary sources Organization, readability, and style of presentation A management case submitted to Vikalpa must be accompanied by a Teaching Note, which is in the nature of an instructor s manual that facilitates the use of the case in a classroom situation. The length of the case, excluding any exhibits or appendices, should be about 3,000 words. Please send your submissions to: Editor, Vikalpa Indian Institute of Management, Vastrapur, Ahmedabad , India You may also send your submissions at: vikalpa@iimahd.ernet.in 56 VIKALPA VOLUME 39 NO 1 JANUARY - MARCH 2014