به اشتراک گذاری ریسک و تنوع ضد ادواری در همبستگی های بازار

I present a consumption-based dynamic asset pricing model in which international market correlations vary counter-cyclically over time. The driving force in the model is the time-varying effective risk aversion induced by external habit formation. Market returns are driven by fundamental outputs and discount rates. When risk aversion is high, the effect of discount rates on market returns rises with the market price of risk. To the extent that countries share risk, the cross-country correlation of discount rates exceeds the cross-country correlation of fundamental outputs. In bad times, market correlations rise as returns are mostly driven by discount rates. Thus, consistent with the empirical evidence, periods of high risk aversion are associated with high market correlations and high market volatility. After calibration, my model is consistent with the observed variation in market correlations, as well as other features of asset prices including the equity premium and market volatility.

International stock market correlations vary substantially over time. Market correlations depend on the phase of the business cycle: they are high when countries are simultaneously in recession. Market correlations also increase in periods of high stock market volatility. The dynamic behavior of market correlations is an important input to international investment decisions. Investors may diversify their portfolios more efficiently if they know the economic forces driving the market correlations up during recessions. Policymakers need to know how the dynamics of market correlations are related to economic fundamentals and international risk sharing to evaluate the welfare gains from financial liberalization. What economic forces drive the dynamics of market correlations and lead to high market correlations during recessions, however, remains an open question. I explore the dynamics of market correlations in an international dynamic asset pricing model with time-varying risk aversion. In my model, counter-cyclical variation in risk aversion leads to counter-cyclical variation in both market volatility and market correlations when there is international risk sharing. When the model is calibrated to international production data and to several moments of observed asset prices, the amount of variation in market correlations is consistent with the observed variation in the data. The level of market correlations significantly increases with the level of international risk sharing. While increased correlations could imply low benefits to risk sharing in a partial equilibrium setting due to decreased diversification benefits, my calibrated general equilibrium model implies that significant welfare gains can be achieved through risk sharing. In my model, the key elements driving the counter-cyclical variation in market correlations are risk sharing and time-varying risk aversion. Using the Clark–Ocone Theorem from Malliavin calculus, I characterize the individual impacts of fundamental output shocks and discount rate volatility on market returns. To the extent that countries share risk, the cross-country correlation of discount rates exceed the cross-country correlation of fundamental outputs. In bad times, the conditional volatility of discount rates rises with the increasing market price of risk. As discount rates become more volatile and dominate outputs in driving market returns, market correlations increase due to the high correlation of discount rates across countries induced by international risk sharing. Through risk sharing, time-varying risk aversion becomes a global economic force driving both market volatility and market correlations counter-cyclically over time. The amount of variation in market correlations is related to the endogenous level of risk sharing between countries. In the benchmark case with frictionless markets, perfect risk sharing obtains and discount rates are perfectly correlated across countries. With perfect risk sharing, market correlations are close to 1.00 in all states of the world and show significant counter-cyclical variation.1 With segmented financial markets, there is no international risk sharing. Such a lack of risk sharing equates the market correlations to the correlation of outputs. Since the correlation of outputs is constant over time, market correlations show no counter-cyclical variation when there is no risk sharing. The amount of variation in market correlations is non-monotonically related to the level of risk sharing. To give role for partial risk sharing in my model, I impose restrictions on foreign investment. In particular, agents are allowed to invest in a fixed and limited share of foreign markets at the beginning of the economy, as in a foreign direct investment (FDI). In equilibrium, the average level of market correlations attains a value between the correlation of fundamental outputs and the correlation of discount rates, which increases in the amount of foreign investment. When the amount of foreign investment is set such that the average level of market correlations matches the data for developed countries, the variation in market correlations is larger than the variation in market correlations associated with perfect risk sharing. With near-perfect risk sharing, market correlations are close to 1.0 in all states of the world, leaving little room for large increases in correlations in bad states. Consequently, the amount of variation in market correlations increases with the level of risk sharing, except when risk sharing is near-perfect. These results suggest that as risk sharing between developed countries improve, the amount of variation in market correlations may slightly decrease. However, there will be a significant amount of counter-cyclical variation in market correlations even when risk sharing becomes perfect. I measure the welfare gains from international risk sharing in my calibrated general equilibrium model. Partial equilibrium models with exogenous stock returns imply that benefits to international diversification for a small investor are large. Consumption-based general equilibrium models usually predict very small welfare gains from international risk sharing. Lewis (1996) argues that the difference between the predictions of the consumption-based and stock-return-based models can be explained by the inability of the consumption-based models to account for the observed features of asset prices. My model bridges the gap between the two approaches to computing the welfare gains from international risk sharing by generating realistic asset prices in a consumption-based general equilibrium model, driven by a realistic pricing kernel induced by the habit-formation preference specification. The welfare gains from international risk sharing in my model are significantly larger than the welfare gains implied by earlier consumption-based models. Large welfare gains are driven by both the high level of risk aversion and the variance of risk aversion. The welfare gains in my model, however, are still lower than those implied by stock-return-based models. I argue that this result is driven by two reasons. First, models with exogenous stock returns do not capture the endogenous relationship between the level of risk sharing and the level of market correlations. Second, models with exogenous stock returns mostly ignore the counter-cyclical behavior of market correlations.2 My results suggest that benefits to international risk sharing may be overstated by stock-return-based models. The empirical evidence on the counter-cyclical behavior of stock correlations and the lack of such dynamics in economic fundamentals have been presented in several studies. Bollerslev et al. (1988) and Moskowitz (2003) show that stock return correlations significantly change over time in domestic markets, and correlations move with the business cycle. Riberio and Veronesi (2003) show that international market correlations have counter-cyclical dynamics while output correlations are stable over the cycle. Ang and Bekaert (2002) and Karolyi and Stulz (1996) show that market volatility and market correlations move simultaneously in the data.3Forbes and Rigobon (2002) argue that the increased market correlations during periods of crisis can be explained by the increased volatility of a common factor. My model is consistent with the empirical evidence, and points to time-varying risk aversion as the common economic force driving the market volatility and market correlations. I present empirical evidence for the counter-cyclical dynamics of market correlations using up-to-date data in Table 1.4My model generates counter-cyclical variation in risk aversion by assuming habit formation in preferences. Each country is inhabited by a representative agent whose preferences are of the form in Campbell and Cochrane (1999). Each agent has a habit level defined as a non-linear function of past consumption in his country. My model is a two-country version of a standard pure-exchange asset pricing economy in the spirit of Lucas (1978), where each country consists of a representative agent and a Lucas tree. Therefore, my model also can be seen as a more general version of the two-tree asset pricing economy studied in Cochrane et al. (forthcoming) – identical when the level of habits are zero, risk aversion is equal to one, and financial markets are frictionless. Menzly et al. (2004) also analyze a general equilibrium economy with external habit formation and multiple dividend processes, where each process is a stochastic fraction of a Lucas tree representing the aggregate consumption, with no one process dominating the economy. The main distinction of my paper is the objective to explore the dynamics of counter-cyclical market correlations. Despite the large volume of empirical literature, economic models are rarely used to study the time-variation in market correlations. Riberio and Veronesi (2003) provide us a rational expectations equilibrium model, and conclude that market correlations show counter-cyclical variation because of the increased uncertainty in bad times. Dumas et al. (2003) provide an equilibrium model linking stock market correlations to countries’ output correlations in order to demonstrate the strong link between market integration and the level of market correlations. The focus of their paper is the level of market correlations. Through its construction, their model yields constant market correlations over time. To determine the endogenous dynamics of asset returns, I use a volatility decomposition that requires the use of the Clark–Ocone formula from Malliavin calculus.5 The volatility decomposition – first used by Gallmeyer (2002) – is analogous to the volatility decomposition used by Campbell and Shiller (1988). In particular, the volatility decomposition is based on the standard asset pricing formula, and identifies the impact of cash flows and discount rates on the volatility of stock returns separately. Overall, this method provides a very tractable way for characterizing the stock return dynamics in a continuous-time general equilibrium model. The paper is organized into six sections. Section 2 introduces the details of my model as well as the calibration. Section 3 studies the dynamics of market correlations when markets are fully integrated. Section 4 documents how the dynamics of market correlations respond to changes in the level of market integration. Section 5 computes the welfare gains from international risk sharing. Section 6 briefly concludes the paper.

I have shown that the observed counter-cyclical variation in market correlations is consistent with the predictions of a general equilibrium model in which markets are, at least, partially integrated and agents’ levels of risk aversion move counter-cyclically over time. In a frictionless world with integrated markets, market correlations are high in all states of the world because of perfect international risk sharing. Depending on the phase of the cycle, correlations vary between 0.90 and 1.00. When markets are partially integrated, there is less risk sharing and market correlations are lower on average. When the average level of market correlations matches the data, market correlations exhibit strong counter- cyclical variation and attain values from 0.65 to 0.81. When markets are segmented, risk sharing diminishes and market correlations are as smooth as economic fundamentals, which show no counter-cyclical variation. My model has implications on assessing the benefits of international risk sharing. Earlier consumption-based models predict several times lower welfare gains from risk sharing than the predictions of stock-return-based models. My consumption-based model predictssignificant welfare gains from risk sharing. I show that a similar model based on power utility preferences predicts several times lower welfare gains, even with higher levels of risk aversion. These results support the view that earlier consumption-based models predict low welfare gains because they lack consistency with the observed features of asset prices, such as the equity premium and stock return volatility.