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Constantine Asaturov 

The paper examines dynamic systematic risk nature of the Indian companies in the frame of the market model. The closing weekly prices of 89 Indian stocks and BSE 100 index as the market index during the period from January 2000 to December 2013 are analyzed with rolling OLS, multivariate GARCH models, semiparametric regression and a Kalman Filter. According to the results for the analyzed period, in 44 out of 89 cases Kalman Filter is the best model, while semiparametric regressions – in the other 45 cases. As for the forecasted period, for 41 out of 89 stocks multivariate GARCH-models surprisingly outperform both semiparametric models (33 out of 89) and a Kalman Filter technique (15 out of 89). Moreover, analysis of the betas dynamic shows that for 5% signifi cance level 59 and 62 out of 89 time-varying betas processes are non-stationary according to ADF and Philips–Perron tests respectively and the only one of the processes is stationary according to KPSS test.

time-varying beta, Indian stock market, DCC–GARCH-model, Kalman Filter, semiparametric regression
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Asaturov K.G., Teplova T.V. (2014). Postroenie koehffitsientov khedzhirovaniya dlya vysokolikvidnykh aktsij rossijskogo rynka na osnove modelej klassa GARCH // Ehkonomika i matematicheskie metody. T. 50. № 1. S. 37–54.

Ang A., Kristensen D. (2012). Testing Conditional Factor Models // Journal of Financial Economics. Vol. 106. P. 132–156.

Bodurtha J., Mark N. (1991). Testing the CAPM with Time-Varying Risk and Returns // Journal of Finance. Vol. 46. P. 1485–1505.

Bollerslev T. (1986). Generalized Autoregressive Conditional Heteroscedasticity // Journal of Econometrics. Vol. 31. P. 307–327.

Bollerslev T., Engle R.F., Wooldridge J.M. (1988). A Capital Asset Pricing Model with Time-Varying Covariances // Journal of Political Economy. Vol. 96. P. 116–131.

Bollerslev T., Engle R.F., Woolbridge J.M. (1992). ARCH Modeling in Finance: A Review of the Theory and Empirical Evidence // Journal of Econometrics. Vol. 52 (1–2). P. 5–60.

Bos T., Newbold P. (1984). An Empirical Investigation of the Possibility of Stochastic Systematic Risk in the Market Model // Journal of Business. Vol. 57. P. 35–41.

Bos T., Fetherston T.A. (1992). Market Model Nonstationarity in the Korean Stock Market // Pacifi c Basin Capital Market Research. Vol. 3. P. 287–301.

Bos T., Fetherston T.A., Martikainen T., Perttunen J. (1995). The International Comovements of Finnish Stocks // The European Journal of Finance. Vol. 1. P. 95–111.

Brooks R.D., Faff R.W., McKenzie M.D. (1998). Time-Varying Beta Risk of Australian Industry Portfolios: A Comparison of Modelling Techniques // Australian Journal of Management. Vol. 23. P. 1–22.

Brooks R.D., Faff R.W., McKenzie M.D. (2002). Time-Varying Country Risk: An Assessment of Different Modelling Techniques // European Journal of Finance. Vol. 8. P. 249–274.

Cappiello L., Engle R.F., Sheppard K. (2006). Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns // Journal of Financial Econometrics. Vol. 4. P. 537–572.

Choudhry T., Wu H. (2008). Forecasting Ability of GARCH vs Kalman Filter Method: Evidence from Daily UK Time-Varying Beta // Journal of Forecasting. Vol. 27. P. 670–689.

Collins D.W., Ledolter J., Rayburn J. (1987). Some Further Evidence on the Stochastic Properties of Systematic Risk // Journal of Business. Vol. 60(3). P. 425–448.

DeJong D., Nankervis J., Savin N., Whiteman C. (1992). The Power Problems of Unit Root Tests in Time Series with Autoregressive Errors // Journal of Econometrics. Vol. 53. P. 323–344.

Eisenbeiss M., Kauermann G., Semmler W. (2007). Estimating Beta-Coeffi cients of German Stock Data: A Non-Parametric Approach // The European Journal of Finance. Vol. 13(6). P. 503–522.

Engle C., Rodrigues A. (1989). Tests of International CAPM with Time-Varying Covariances // Journal of Applied Econometrics. Vol. 4. P. 119–138.

Engle R.F. (2002). Dynamic Sonditional Sorrelation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroscedasticity Models // Journal of Business and Economic Statistics. Vol. 20. P. 339–350.

Esteban M.V., Orbe-Manadaluniz S. (2010). A Nonparametric Approach for Estimating Betas: the Smoothed Rolling Estimator // Applied Economics. Vol. 42. P. 1269–1279.

Fabozzi F., Francis J. (1978). Beta as a Random Coeffi cient // Journal of Financial and Quantitative Analysis. Vol. 13. P. 101–116.

Faff R.W., Hillier D., Hillier J. (2000). Time-varying beta risk: An analysis of alternative modeling techniques // Journal of Business Finance and Accounting. Vol. 27. P. 523–554.

Faff R.W., Lee J.H.H., Fry T.R.L., (1992). Time Stationarity of Systematic Risk: Some Australian Evidence // Journal of Business and Accounting. Vol. 19. P. 253–270.

Fama E.F., French K.R. (1993). Common Risk Factors in the Returns on Stocks and Bonds // Journal of Financial Economics. Vol. 33(1). P. 3–56.

Glosten L. R., Jaganathan R., Runkle R. (1993). On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks // Journal of Finance. Vol. 48(5). P. 1779–1801.

Groenewold N., Fraser P. (1999). Time-Varying Estimates of CAPM Betas // Mathematics and Computers in Simulations. Vol. 48. P. 531–539.

Hastie T., Tibshirani R. (1993). Varying-Soeffi cient Models // Journal of the Royal Statistic Society, Series B (Methodology). Vol. 55(4). P. 757–796.

He Z., Kryzanowski L. (2008). Dynamic Betas for Canadian Sector Portfolios // International Review of Financial Analysis. Vol. 17. P. 1110–1122.

Johansson A.C. (2009). Stochastic Volatility and Time-Varying Country Risk in Emerging markets // The European Journal of Finance. Vol. 15(3). P. 337–363.

Jostova G., Philipov A. (2005). Bayesian Analysis of Stochastic Betas // Journal of Financial and Quantitative Analysis. Vol. 40(4). P. 747–778.

Kalman R.E. (1960). A New Approach to Linear Filtering and Prediction Problems // Journal of Basic Engineering. Vol. 82 (1). P. 35–45.

Kim D. (1993). The Extent of Non-Stationarity of Beta // Review of Quantitative Finance and Accounting. Vol. 3. P. 241–254.

Kok K.L. (1992). Stability and Predictability of Betas of Malaysian Securities // Securities Industry Review. Vol. 18. P. 65–74.

Li Q., Racine J.S. (2010). Smooth Varying-Coeffi cient Estimation and Inference for Qualitative and Quantitative Data // Econometric Theory. Vol. 26. P. 1607–1637.

Li X. (2003). On Unstable Beta Risk and Its Modelling Techniques for New Zealand Industry Portfolios. Massey University Commerce. Working Paper 03.01.

Li Y., Yang L. (2011). Testing Conditional Factor Models: A Nonparametric Approach // Journal of Empirical Finance. Vol. 18. P. 972–992.

Lie F., Brooks R., Fama R. (2000). Modelling the Equity Beta Risk of Australian Financial Sector Companies // Australian Economic Papers. Vol. 39. P. 301–311.

Lintner J. (1965). The Valuation of Risky Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets // Review of Economics and Statistics. Vol. 47. P. 13–37.

Markowitz H.M. (1952). Portfolio Selection // Journal of Finance. Vol. 12. P. 77–91.

Mergner S., Bulla J. (2008). Time-Varying Beta Risk of Pan-European Industry Portfolios: A Comparison of Alternative Modeling Techniques // European Journal of Finance. Vol. 14(8). P. 771–802.

Schwert G.W., Seguin P. (1990). Heteroskedasticity in Stock Returns // Journal of Finance. Vol. 45. P. 1129–1155.

Shah A., Moonis S.A. (2003). Testing for Time Variation in Beta in India // Journal of Emerging Markets Finance.Vol. 2(2). P. 163–180.

Sharpe W.F. (1964). Capital Asset Prices: a Theory of Market Equilibrium under Conditions of Risk // Journal of Finance. Vol. 45. P. 425–442.

Sunder S. (1980). Stationarity of Market Risk: Random Coeffi cients Tests for Individual Stocks // Journal of Finance. Vol. 4. P. 1129–1155.

Wells C. (1994). Variable Betas on the Stockholm Exchange 1971–1989 // Applied Economics. Vol. 4. P. 75–92.

Yun J. (2002). Forecasting Volatility in the New Zealand Stock Market // Applied Financial Econometrics. Vol. 12. P. 193–220.