The Conditional CAPM, Cross-Section Returns and Stochastic Volatility

Fung, Ka Wai Terence and Lau, Chi Keung Marco and Chan, Kwok Ho (2013): The Conditional CAPM, Cross-Section Returns and Stochastic Volatility.

Abstract

Bansal and Yaron (2004) demonstrate, by calibration, that the Consumption-Based Capital Asset Pricing Model (CCAPM) can be rescued by assuming that consumption growth rate follows a stochastic volatility model. They show that the conditional equity premium is a linear function of conditional consumption and market return volatilities, which can be estimated handily by various Generalized Autoregressive Conditonal Heterskedasticity (GARCH) and Stochastic Volatility (SV) models.We find that conditional consumption and market volatilities are capable of explaining cross-sectional return differences. The Exponential GARCH (EGARCH) volatility can explain up to 55% variation of return and the EGARCH model augmented with (cay) ̂ -a cointegrating factor of consumption, labor income and asset wealth growth- greatly enhance model performance. We proceed to test another hypothesis: if Bansal and Yaron estimator is an unbiased estimator of true conditional equity premium, then the instrumental variables for estimating conditional equity premium should no longer be significant.We demonstrate that once the theoretical conditional risk premium is added to the model, it renders all instrumental variables redundant. Also, the model prediction is consistent with observed declining equity premium.

• Item Type: MPRA Paper
• Language: English
• Keywords: Financial Economics, Macroeconomics and Monetary Economics, Equity Premium Puzzle, Fama-French Model
• Subjects: E - Macroeconomics and Monetary Economics > E0 - General > E00 - General; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E32 - Business Fluctuations ; Cycles; G - Financial Economics > G0 - General > G01 - Financial Crises

References

Bansal, R., Yaron, A., 2004. Risks for Long-Run: A Potential Resolution of Asset Pricing Puzzles. Journal of Finance. 59, 1481-1509.

Bansal, R., Kiku, D., Yaron, A., 2012. An Empirical Evaluation of the Long-Run risks Model for Asset Prices. Critical Finance Review. 1, 183-221.

Bansal, R., Kiku, D., Shaliastovich, I., Yaron, A, 2012. Volatility, the Macroeconomy and Asset Prices. National Bureau of Economic Research Working Paper: 18104.

Banz, R., 1981. The Relation between Return and Market Value of Common Stocks. Journal of Financial Economics. 9, 3-18.

Black, F., Jensen, M, C., Scholes, M., 1972. The capital asset pricing modeL Some empirical tests, in: Jensen, M. (Eds.), Studies in the Theory of Capital Markets. Pareger, New York, pp. 79-121.

Bollerslev, T., Chou, R., Kroner, K., 1992. ARCH Modeling in Finance: A Review of the Theory and Empirical Evidence. Journal of Econometrics. 52, 5-59.

Bollerslev, T., Engle, R., Nelson, D., 1994. Arch Models, in Engle, R., McFadden, D. (Eds.), Handbook of Econometrics, Volume 4. Elsevier Science, Amsterdam, pp. 2959-3038.

Campbell, J.Y., 1991. A Variance Decomposition for Stock Returns. Economic Journal. 101, 157-79.

Campbell, J., Shiller, R., 1988. The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors. Review of Financial Studies. 1, 195-227.

Chen, N., Roll, R., Ross, S., 1986. Economic Forces and the Stock Market. The Journal of Business. 59, 383-404.

Cochrane, J., 1996. A Cross-Sectional Test of Investment-Based Asset Pricing Model. Journal of Political Economy. 104, 572-621.

Colacito, R., Croce, M., 2011. Risks for the Long Run and the Real Exchange Rate. Journal of Political Economy. 119, 153-181.

Constantinides, G., Ghosh, A., 2011. Asset Pricing Tests with Long Run Risks in Consumption Growth. Review of Asset Pricing Studies. 1, 96-136.

Durbin, J., Koopman, S., 1997. Monte Carlo Maximum Likelihood Estimation of Non-Gaussian State Space Model. Biometrika. 84, 669-84.

Fama, E., French K., 1993. Common Risk Factors in the Returns on Stocks and Bonds. Journal of Financial Economics. 33, 3-56.

Fama, E., MacBeth, J., 1973. Risk, Return and Equilibrium: Empirical Tests. Journal of Political Economy. 81, 607-36.

Fleming, J., Kirby, C., 2003. A Closer look at the Relation between GARCH and Stochastic Autoregressive Volatility. Journal of Financial Econometrics. 1, 356-419.

Ghysels, E., Harvey, A., Renault, E, 1996. Stochastic Volatility, in: Maddala, G., Rao, C. (Eds.), Handbook of Statistics, Volume 14, Statistical Methods in Finance. North-Holland, Amsterdam, pp: 119-191.

Hansen, L., Heaton, K., Li, N., 2008. Consumption Strikes Back? Measuring Long Run Risk. Journal of Political Economy. 116, 260-302.

Hansen, L., Singleton, K., 1982. Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models. Econometrica. 50, 1269-86.

Harvey, A., Ruiz, E., Shephard, N., 1994. Multivariate Stochastic Variance Models. Review of Economic Studies. 61, 247-64.

Heynen, R., Kat, H., 1994. Volatility Prediction: A Comparison of the Stochastic Volatility, GARCH (1,1) and EGARCH (1,1) Models. Journal of Derivative. 2, 50-65.

Hull, J., White, A., 1987. The Pricing of Option on Assets with Stochastic Volatilities. Journal of Finance. 42, 281-300.

Jagannathan, R., Wang Z., 1996. The Conditional CAPM and the Cross-Section of Expected Returns. The Journal of Finance. 51, 3-53.

Lamont O., 1998. Earnings and Expected Returns. Journal of Finance. 53, 1563-87.

Lettau, M. Ludvigson, S., 2001. Resurrecting (C)CAPM: A Cross-Sectional Test When Risk Premia are Time-Varying. Journal of Political Economy. 109, 1238-1287.

Marakani, S., 2009. A long-Run Consumption Risks: Are They There? City University of Hong Kong Working Paper.

Preminger, A., Haftner, C., 2006. Deciding between GARCH and Stocastic Volatility Via Strong Decision Rules. Monaster Center of Economic Research, Ben Gurion University of the Negev, working paper no. 06-03.

Roll, R., 1977. A Critique of the Asset Pricing Theory’s Test: Part 1: On Past and Potential Testability of the Theory. Journal of Financial Economics. 4, 129-76.

Shanken, J., 1992. On the Estimation of Beta-Pricing Models. Review of Financial Studies. 5, 1-34.

Taylor, S., 1999. Modeling Stochastic Volatility: A Review and Comparative Study. Mathematical Finance. 4, 183-204.