Abstract
This paper evaluates the appropriateness of a Linear Market Model (LMM) which allows for systematic covariance (beta) risk. The performance of LMM will be compared against two extensions, a comparison having yet to be undertaken in the literature. The first extension is the Time-varying Linear Market Model (Tv-LMM) which allows for time-varying systematic covariance risk in the form of a mean reverting state space model via the Kalman filter. The second extension is the multivariate Time-varying Linear Market Model (MTv-LMM) which allows for the time-varying systematic covariance risk of country stock market correlation structure via the multivariate KFMR. The comparison between LMM, Tv-LMM and MTv-LMM, is implemented utilising weekly data collected from several developed and emerging markets for the periods; before and after financial crisis in October 2008, and forecasting 2 years forwards. The empirical findings of that process overwhelmingly support the use of the Multivariate Time-varying Linear Market Model (MTv-LMM) when modelling and forecasting stock market returns, especially for developed stock markets.
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References
Algieri B (2012) Price volatility, speculation and excessive speculation in commodity markets: sheep or shepherd behaviour? ZEF-Discuss Pap Dev Policy No 166:1–40
Barnett A, Mumtaz H, Theodoridis K (2014) Forecasting UK GDP growth and inflation under structural change: a comparison of models with time-varying parameters. Int J Forecast 30(1):129–143
Bekaert G, Harvey CR (1997) Emerging equity market volatility. NBER working papers 5307, National Bureau of Economic Research, Inc
Bos T, Newbold P (1984) An empirical investigation of the possibility of stochastic systematic risk in the market model. J Bus 57(1):35–41
Brooks RD, Faff RW, Lee JHH (1992) The form of time variation of systematic risk: some Australian evidence. Appl Financ Econ 2(4):191–198
Brooks RD, Faff RW, McKenzie MD (1998) Time-varying beta risk of Australian industry portfolios: a comparison of modelling techniques. Aust J Manag 23(1):1–22
Brooks RD, Faff RW, McKenzie MD (2002) Time varying country risk: an assessment of alternative modelling techniques. Eur J Finance 8(3):249–274
Campbell J, Lo A, MacKinlay A (1997) The econometrics of financial markets. Princeton University Press, Princeton
Chiang TC, Jeon BN, Li H (2007) Dynamic correlation analysis of financial contagion: evidence from Asian markets. J Int Money Finance 26(7):1206–1228
Choudhry T, Wu H (2009) Forecasting ability of GARCH vs Kalman Filter method: evidence from daily UK time-varying beta. Eur J Finance 15(4):437–444
Diebold F, Mariano R (1995) Comparing predictive accuracy. J Bus Econ Stat 13(3):253–263
Doeswijk R, Lam T, Swinkels L (2019) Historical returns of the market portfolio. Rev Asset Pricing Stud https://doi.org/10.1093/rapstu/raz010
Duffie D, Skeie DR, Vickery J (2013) A sampling-window approach to transactions-based Libor fixing. Tech. Rep. 596, Federal Reserve Bank of New York
Faff RW, Lee JH, Fry TRL (1992) Time stationarity of systematic risk: some Australian evidence. J Bus Finance Acc 19(2):253–270
Faff RW, Hillier D, Hillier J (2000) Time varying beta risk: an analysis of alternative modelling techniques. J Bus Finance Acc 27(5–6):523–554
Gibbons MR, Ross SA, Shanken J (1989) A test of the efficiency of a given portfolio. Econometrica 57(5):1121–1152
Hansen LP, Jagannathan R (1997) Assessing specification errors in stochastic discount factor models. J Finance 52(2):557–590
Harvey CR (1995) Predictable risk and returns in emerging markets. Working paper 4621, National Bureau of Economic Research
Jayasuriya SA (2011) Stock market correlations between China and its emerging market neighbors. Emerg Mark Rev 12(4):418–431
Kalman RE (1960) A new approach to linear filtering and prediction problems. Trans ASME J Basic Eng 82(Series D):35–45
Kim D (1993) The extent of nonstationarity of beta. Revi Quant Finance Acc 3(2):241–254
Lintner J (1965) The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Rev Econ Stat 47(1):13–37
Mackinlay AC, Richardson MP (1991) Using generalized method of moments to test mean-variance efficiency. J Finance 46(2):511–527
Malliaris M (2012) Comparison of currency movement before and after October 2008. J Econ Asymmetries 9(2):45–57
Markowitz H (1952) Portfolio selection. J Finance 7(1):77–91
Mergner S (2009) Applications of State Space Model in Finance. Universitätsverlag Gőttingen
Mergner S, Bulla J (2008) Time-varying beta risk of pan-European industry portfolios: a comparison of alternative modeling techniques. Eur J Finance 14(8):771–802
Mossin J (1966) Equilibrium in a capital asset market. Econometrica 34(4):768–783
Neslihanoglu S (2014) Validating and extending the two-moment capital asset pricing model for financial time series. Ph.D. thesis, The School of Mathematics and Statistics, The University of Glasgow, Glasgow, UK
Neslihanoglu S, Sogiakas V, McColl JH, Lee D (2016) Nonlinearities in the capm: evidence from developed and emerging markets. J Forecast 36(8):867–897
Odabasi A (2003) Some estimation issues on betas: a preliminary investigation in the Istanbul Stock Exchange. Bogazici J Rev Soc Econ Admin Stud 17(2):1–11
Saleem K (2009) International linkage of the Russian market and the Russian financial crisis: a multivariate GARCH analysis. Res Int Bus Finance 23(3):243–256
Santos AA, Moura GV (2014) Dynamic factor multivariate GARCH model. Comput Stat Data Anal 76:606–617
Sharpe WF (1964) Capital asset prices: a theory of market equilibrium under conditions of risk. J Finance 19(3):425–442
Takatoshi I, Wen-Ling L (1993) Price volatility and volume spillovers between the Tokyo and New York stock markets. Working Paper 4592, National Bureau of Economic Research
Wang P, Moore T (2008) Stock market integration for the transition economics: time-varying conditional correlation approach. Manch Sch 76:116–133
Yavas BF (2007) Benefits of international portfolio diversification. Graziadio Bus Rev 10(2)
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Neslihanoglu, S., Bekiros, S., McColl, J. et al. Multivariate time-varying parameter modelling for stock markets. Empir Econ 61, 947–972 (2021). https://doi.org/10.1007/s00181-020-01896-2
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DOI: https://doi.org/10.1007/s00181-020-01896-2
Keywords
- CAPM
- Multivariate model
- State space model
- Stock market returns
- Systematic covariance (beta) risk
- Time-varying beta