نوسانات بازار سهام و حقوق صاحبان سهام بازده : شواهدی از دو حالت مدل مارکوف سوئیچینگ با قهقرایی

This paper proposes a two-state Markov-switching model for stock market returns in which the state-dependent expected returns, their variance and associated regime-switching dynamics are allowed to respond to market information. More specifically, we apply this model to examine the explanatory and predictive power of price range and trading volume for return volatility. Our findings indicate that a negative relation between equity market returns and volatility prevails even after having controlled for the time-varying determinants of conditional volatility within each regime. We also find an asymmetry in the effect of price range on intra- and inter-regime return volatility. While price range has a stronger effect in the high volatility state, it appears to significantly affect only the transition probabilities when the stock market is in the low volatility state but not in the high volatility state. Finally, we provide evidence consistent with the ‘rebound’ model of asset returns proposed by Samuelson (1991), suggesting that long-horizon investors are expected to invest more in risky assets than short-horizon investors.

Markov switching models have been extensively used in studies involving stock market returns, interest rates, foreign exchange rates, and return volatility forecasts. Researchers employ these regime switching techniques to account for specific features of macro-economic and financial time series such as the asymmetry of economic activity over the business cycle (Hamilton, 1989) or the fat tails, volatility clustering and mean reversion in stock prices (e.g., Cecchetti et al., 1990, Schaller and van Norden, 1997 and Turner et al., 1989), interest rates (e.g., Ang and Bekaert, 2002, Gray, 1996 and Hamilton, 1988), foreign exchange rates (e.g., Bollen et al., 2000, Dueker and Neely, 2007, Engel, 1994 and Engel and Hamilton, 1990), and for improving volatility forecasts (e.g., Haas et al., 2004 and Klaassen, 2002). The appeal of Markov switching models is that they give rise to parsimonious representations of state space models by letting the mean, variance as well as the dynamics of the series depend on the realization of a finite number of discrete states. They are particularly suited in situations where there are large changes in market volatility.1 In this paper we propose a two-state Markov switching model for stock market returns in which the state-dependent mean and return volatility as well as the transition probabilities of regime-switching are allowed to respond to changes in market information. We use this model to investigate the relationship between expected returns and market volatility accounting for shifts in investment opportunities linked to state-dependent changes in market volatility. In particular, we examine the explanatory and predictive power of price range and trading volume for return volatility. Our findings indicate that equity market returns are negatively correlated with volatility and that the effect of price range is asymmetric across the two regimes. However, we find no evidence that trading volume innovations are a significant determinant of state-dependent volatilities. Furthermore, although either the low expected return and high volatility state or the high expected return and low volatility state are persistent over short periods, our findings indicate a higher incidence of regime shifts between the two states over longer horizons. These results are consistent with the rebound model of mean-reverting asset returns proposed by Samuelson (1991), implying that long-horizon investors are expected to invest more in risky assets than short-horizon investors. The time series of stock returns typically demonstrates several stylized facts characterizing the distributional and temporal properties of financial returns series; namely, leptokurtosis and asymmetry in the distribution, volatility clustering, structural breaks, and long memory. Markov switching models where the distribution of stock returns for a given period is a mixture of normals are capable of describing these stylized facts (Bulla and Bulla, 2006 and Ryden et al., 1998). Turner et al. (1989) were the first to apply a Markov mixture of normal distributions to study the relation between the market risk premium and variance of stock returns using monthly excess returns on the S&P 500 index. They used a two-state Markov model characterized by two constant state-dependent expected returns and variances where the state dynamics are governed by a two-state first-order Markov chain with constant transition probabilities. Extending the Turner et al. (1989) model, Schaller and van Norden (1997) include the price–dividend ratio as a determinant of both state-dependent expected returns and associated transition probabilities. Using monthly excess returns on the S&P 500 index, they provide robust evidence of Markov switching behavior for stock market returns. In particular, they report strong asymmetry in the effect of the price–dividend ratio on future expected returns; in the low-return state this effect is about four times larger than in the high-return state. On the other hand, they find that the price–dividend ratio has no significant effect on transition probabilities. Our model for stock market returns is closest to the models considered by Schaller and van Norden (1997) and Turner et al. (1989), but with some important differences. We extend these models by incorporating regressors in the state-dependent volatilities through a link function, which allows us to directly assess sources of persistence on state-dependent volatilities. We use this model to produce new evidence on the relationship between market volatility and expected returns. In particular, we study the effect of two important volatility determinants; namely, price range and trading volume assessing their importance in terms of both explanatory power and predictability for return volatility. The paper is organized as follows. Section 2 presents the proposed two-sate Markov switching model for stock market returns. Section 3 discusses the estimation method and volatility forecast performance measures. Section 4 describes the data, while Section 5 reports the empirical results. Finally, Section 6 presents conclusions.

In this paper we have proposed a two-state Markov-switching model for stock market returns where the state-dependent expected returns and volatilities depend on regressors and the dynamics of the state for stock market returns are governed by a two-state first-order Markov chain with regressor-dependent transition probabilities. We have used different specifications of this model to investigate the explanatory and predictive power of two volatility determinants, namely price range and trading volume. We find that price range has significant explanatory and predictive power for return volatility. However, we find no evidence that trading volume shocks have a significant effect on intra- and inter-regime volatility. Our findings indicate that even if we account for shifts in investment opportunities (state-dependent changes in volatility) via price range, the level of risk measured by state-dependent return volatility remains negatively correlated with the state-dependent expected return. We also find state-dependent differences in the effect of price range on volatility; the intra-regime effect is stronger in the high volatility state whereas the inter-regime effect appears to be stronger in the low volatility state. These findings provide new evidence of asymmetry in the relationship between time-varying conditional volatility and equity market returns. In addition, our analysis indicates that by using information on price range, market agents may be able to obtain better volatility forecasts. An increase (decrease) in price range over a week indicates an increase (decrease) in the market volatility, whereas an increase (decrease) in the average price range over the last six months signals an increase decrease) in the likelihood that the stock market is in the high volatility regime. Overall, our findings demonstrate strong evidence of switching behavior in the US stock market with equities switching between two states: a low expected return and high volatility state, and a high expected return and low volatility state, respectively. While either of the two states is persistent over short periods, the average probability of remaining in the current state over the whole sample period is 0.483 for the high expected return state and 0.335 for the low expected return state, respectively. This suggests a higher incidence of regime shifts over longer horizons, which is broadly consistent with the rebound process for asset returns proposed by Samuelson (1991). Samuelson shows that in the presence of rebound or mean-reverting process for security returns risk-averse investors with strictly concave long-term utility functions will tolerate a higher fraction of risky assets in their portfolio than they would with serially independent returns; and they are more likely to increase their exposure to the risky asset as the investment horizon increases. Thus our findings have potentially important implications for financial practice. With mean-reverting security returns, long-horizon investors are expected to invest more in risky assets than short-horizon investors if there is a higher probability to switch between regimes rather than stay in the current state. These findings contrast earlier results suggesting that investors with longer horizons would favor fewer risky assets when there are recurrent but infrequent regime shifts.