Information Flow Interpretation of Heteroskedasticity for Capital Asset Pricing: An Expectation-based View of Risk

Senarathne, Chamil W and Jayasinghe, Prabhath (2017): Information Flow Interpretation of Heteroskedasticity for Capital Asset Pricing: An Expectation-based View of Risk. Published in: Economic Issues , Vol. 1, No. 22 (March 2017): pp. 1-24.

Abstract

The Heteroskedastic Mixture Model (HMM) of Lamoureux, and Lastrapes (1990) is extended, relaxing the restriction imposed on the mean i.e. μt-1=0 . Instead, an exogenous variable rm, along with its vector βm, that predicts return rt is introduced to examine the hypothesis that the volume is a measure of speed of evolution in the price change process in capital asset pricing. The empirical findings are documented for the hypothesis that ARCH is a manifestation of time dependence in the rate of information arrival, in line with the observations of Lamoureux, and Lastrapes (1990). The linkage between this time dependence and the expectations of market participants is investigated and the symmetric behavioural response is documented. Accordingly, the tendency of revision of expectation in the presence of new information flow whose frequency as measured by ‘volume clock’ is observed. In the absence of new information arrival at the market, investors tend to follow the market on average. When new information is available, the expectations of investors are revised in the same direction as a symmetric response to the flow of new information arrival at the market.

• Item Type: MPRA Paper
• Language: English
• Keywords: Mixture of Distribution Hypothesis; Information Flow; Stock Volume; Systematic Risk; Capital Asset Pricing; ARCH; GARCH
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D53 - Financial Markets; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; G - Financial Economics > G1 - General Financial Markets > G14 - Information and Market Efficiency ; Event Studies ; Insider Trading; G - Financial Economics > G1 - General Financial Markets > G17 - Financial Forecasting and Simulation

References

Adrian T and Franzoni F (2009) ‘Learning about beta: Time-varying factor loadings, expected returns, and the conditional CAPM’, Journal of Empirical Finance, 16(4), 537-556.

Amatyakul P (2010) ‘The relationship between trading volume and jump processes in financial markets’, Duke Journal of Economics, XXII. Available at: https://sites.duke.edu/djepapers/files/2016/10/Amatyakul-Pat_DJE.pdf

Andersen T G (1996) ‘Return volatility and trading volume: An information flow interpretation of stochastic volatility’, Journal of Finance, 51(1), 169-204.

Andersen T. G and Bollerslev T (1998) ‘Answering the skeptics: Yes, standard volatility models do provide accurate forecasts’, International Economic Review, 39, 885-905.

Bachelier L (2011) ‘Louis Bachelier’s theory of speculation: the origins of modern finance’, Princeton U P.

Bauer R and Nieuwland F (1995) ‘A multiplicative model for volume and volatility’, Applied Mathematical Finance, 2(3), 135-154.

Bollerslev T (1986) ‘Generalized autoregressive conditional heteroskedasticity’, Journal of Econometrics, 31(3), 307-327.

Bollerslev T, Engle R F and Nelson D B (1994) ‘ARCH models’, Handbook of Econometrics’, 4, 2959-3038.

Clark P K (1973) ‘A subordinated stochastic process model with finite variance for speculative prices’, Econometrica, 41, 135-155.

Engle R F (1982) ‘Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation’, Econometrica, 50(4), 987-1007.

Engle R F, Hendry D F and Richard J F (1983) ‘Exogeneity’, Econometrica, 51, 277-304.

Engle R F, Lilien D M and Robins R P (1987) ‘Estimating time varying risk premia in the term structure: The ARCH-M model’, Econometrica, 55, 391-407.

Epps T W and Epps M L (1976) ‘The stochastic dependence of security price changes and transaction volumes: Implications for the mixture-of-distributions hypothesis’, Econometrica, 44, 305-321.

Fama E F (1965) ‘The behavior of stock-market prices’, The Journal of Business, 38(1), 34-105.

Fama E F (1970) ‘Efficient capital markets: A review of theory and empirical work’, Journal of Finance, 25(2), 383-417.

Fama E F, Fisher L, Jensen M C and Roll R (1969) ‘The adjustment of stock prices to new information’, International Economic Review, 10(1), 1-21.

Fama E F and French K R (1992) ‘The cross-section of expected stock returns’, Journal of Finance, 47(2), 427-465.

Fama E F and French K R (1996) ‘Multifactor explanations of asset pricing anomalies’, Journal of Finance, 51(1), 55-84.

Fang Y and Koreisha S G (2004) ‘Forecasting with serially correlated regression models’, Journal of Statistical Computation and Simulation, 74(9), 625-649.

Fleming J, Kirby C and Ostdiek B (2005) ‘ARCH effects and trading volume’, Available at SSRN 803838.

Foster F D and Viswanathan S (1990) ‘A theory of the interday variations in volume, variance, and trading costs in securities markets’, Review of Financial Studies, 3(4), 593-624.

Gallant A R, Rossi P E and Tauchen G (1992) ‘Stock prices and volume’, Review of Financial Studies, 5(2), 199-242.

Gervais S, Kaniel R and Mingelgrin D H (2001) ‘The high?volume return premium’, Journal of Finance, 56(3), 877-919.

Giot P, Laurent S and Petitjean M (2010) ‘Trading activity, realized volatility and jumps’, Journal of Empirical Finance, 17(1), 168-175.

Harris L (1987) ‘Transaction data tests of the mixture of distributions hypothesis’, Journal of Financial and Quantitative Analysis, 22(02), 127-141.

Hiemstra C and Jones J D (1994) ‘Testing for linear and nonlinear Granger causality in the stock price-volume relation’, Journal of Finance, 49(5), 1639-1664.

Karpoff J M (1986) ‘A theory of trading volume’, Journal of Finance, 41(5), 1069-1087.

Lakonishok J and Vermaelen T (1986) ‘Tax-induced trading around ex-dividend days’, Journal of Financial Economics, 16(3), 287-319.

Lambert R and Verrecchia R (2010) ‘Cost of capital in imperfect competition settings’, Working Paper, University of Pennsylvania. Available at: http://faculty.chicagobooth.edu/workshops/accounting/past/pdf/lv.01.12.10.pdf

Lamoureux C G and Lastrapes W D (1990) ‘Heteroskedasticity in stock return data: volume versus GARCH effects’, Journal of Finance, 45(1), 221-229.

Lamoureux C G and Lastrapes W D (1994) ‘Endogenous trading volume and momentum in stock-return volatility’, Journal of Business and Economic Statistics, 12(2), 253-260.

Mandelbrot B (1963) ‘The Variation of Certain Speculative Prices’, Journal of Business, 36(4), 394-419.

Mandelbrot B and Taylor H M (1967) ‘On the distribution of stock price differences’, Operations Research, 15(6), 1057-1062.

McNees S K (1980) ‘The forecasting record for the 1970s’, Federal Reserve Bank of Boston.

Pfleiderer P (1984) ‘The volume of trade and the variability of prices: A framework for analysis in noisy rational expectations equilibria’, Graduate School of Business, Stanford University.

Ross S A (1987) ‘The interrelations of finance and economics: Theoretical perspectives’, American Economic Review, 77(2), 29-34.

Shalen C T (1993) ‘Volume, volatility, and the dispersion of beliefs’, Review of Financial Studies, 6(2), 405-434.

Sharpe W F (1964) ‘Capital asset prices: A theory of market equilibrium under conditions of risk’, Journal of Finance, 19(3), 425-442.

Tauchen G E and Pitts M (1983) ‘The price variability-volume relationship on speculative markets’, Econometrica, 51(2), 485-505.

Wang T and Huang Z (2012) ‘The relationship between volatility and trading volume in the Chinese stock market: a volatility decomposition perspective’, Annals of Economics and Finance, 13(1), 217-242.

Westerfield R (1977) ‘The distribution of common stock price changes: An application of transactions time and subordinated stochastic models’, Journal of Financial and Quantitative Analysis, 12(05), 743-765.

Ying C C (1966) ‘Stock market prices and volumes of sales’, Econometrica, 43, 676-685.