A Study on stock returns and volatility
Global Asset Allocation
Finance 656
(Please return to Fang Song’s locker #552)
Michelle Bien
Yushao Karen Chiu
Srinivas Mudireddy
Fang (Derek) Song,
12/08/2013
A Study on stock returns and volatility
Abstract
This paper applies two models to examine the intertemporal relationship between expected returns and market risk. By using ARIMA models, two findings can be found: 1) A positive correlation exists between the expected market risk premium and the predictable volatility. 2) There is no correlation between the expected market risk premium and the unpredictable volatility. The 2nd finding is different from [French 1987], which states a substantial negative relationship between market risk premium and the unpredictable volatility. Employing GARCH-in-mean models, we find there is a “positive” relationship between expected risk premiums and volatility. Our analysis are inconsistent with French, Schwert and Stambaugh, (1987), which presents no relationship between expected risk premiums and volatility.
1. Introduction
Many studies have demonstrated that there exists a relationship between expected returns and risk on stocks. Most of these examine different betas which are defined as risks relative to other variables. For example, the capital asset pricing model (CAPM) examines the risk relative to the market portfolio, (Treynor (1962), Sharpe (1964), Lintner (1965) and Mossin (1966)). An important alternative, the consumption-based CAPM (CCAPM) proposed by Breeden (1979) examined the covariance between returns and consumption. Later, Fama-French Three Factor Model (Fama and French (1992)) added two more risks relative to size and book-to-market ratio. One extension of this model is the Carhart four-factor model which includes a momentum factor. In this paper, we focus on the intertemporal relationship between expected returns and market risk. There was no conclusive answer to the question whether this relationship
Finance 656
(Please return to Fang Song’s locker #552)
Michelle Bien
Yushao Karen Chiu
Srinivas Mudireddy
Fang (Derek) Song,
12/08/2013
A Study on stock returns and volatility
Abstract
This paper applies two models to examine the intertemporal relationship between expected returns and market risk. By using ARIMA models, two findings can be found: 1) A positive correlation exists between the expected market risk premium and the predictable volatility. 2) There is no correlation between the expected market risk premium and the unpredictable volatility. The 2nd finding is different from [French 1987], which states a substantial negative relationship between market risk premium and the unpredictable volatility. Employing GARCH-in-mean models, we find there is a “positive” relationship between expected risk premiums and volatility. Our analysis are inconsistent with French, Schwert and Stambaugh, (1987), which presents no relationship between expected risk premiums and volatility.
1. Introduction
Many studies have demonstrated that there exists a relationship between expected returns and risk on stocks. Most of these examine different betas which are defined as risks relative to other variables. For example, the capital asset pricing model (CAPM) examines the risk relative to the market portfolio, (Treynor (1962), Sharpe (1964), Lintner (1965) and Mossin (1966)). An important alternative, the consumption-based CAPM (CCAPM) proposed by Breeden (1979) examined the covariance between returns and consumption. Later, Fama-French Three Factor Model (Fama and French (1992)) added two more risks relative to size and book-to-market ratio. One extension of this model is the Carhart four-factor model which includes a momentum factor. In this paper, we focus on the intertemporal relationship between expected returns and market risk. There was no conclusive answer to the question whether this relationship
References: [Breeden 1979] Breeden, Douglas T. (1979). An intertemporal asset pricing model with stochastic consumption and investment opportunities. Journal of Financial Economics 7, 265-296. [Carhart 1997] Carhart, Mark M. (1997). On Persistence in Mutual Fund Performance. Journal of Finance 52 (1): 57–82. [Fama 1992] Fama, Eugene F. and French, Kenneth R. (1992). The Cross-Section of Expected Stock Returns. Journal of Finance 47 (2): 427–465. [French 1987] French, K., G.W. Schwert, and R. Stambaugh, (1987). Expected stock returns and volatility, Journal of Financial Economics 19, 3-29. [Mossin 1966] Mossin, Jan. (1966). Equilibrium in a Capital Asset Market, Econometrica, Vol. 34, No. 4, pp. 768–783. [Lintner 1965] Lintner, John (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, Review of Economics and Statistics, 47 (1), 13–37. [Merton 1973] Merton, R.C., (1973), An Intertemporal Capital Asset Pricing Model. Econometrica 41, Vol. 41, No. 5. (Sep., 1973), pp. 867–887 [Sharpe 1964] Sharpe, William F Figure 1a. Monthly percent standard deviations of the returns to the Standard & Poor’s composite portfolio, , estimated from returns for days i within the month t, , 1963-84.