ABSTRACT
 Top of page
 ABSTRACT
 INTRODUCTION
 LITERATURE AND HYPOTHESES DEVELOPMENT
 DATA AND METHODOLOGY
 RESULTS
 RESIDUAL DIAGNOSTICS OF THE MARKOV SWITCHING MODEL
 CONCLUSIONS
 APPENDIX
 ACKNOWLEDGEMENTS
 REFERENCES
 Biographies
The equity premium of the S&P 500 index is explained in this paper by several variables that can be grouped into fundamental, behavioral, and macroeconomic factors. We hypothesize that the statistical significance of these variables changes across economic regimes. The three regimes we consider are the lowvolatility, mediumvolatility, and highvolatility regimes in contrast to previous studies that do not differentiate across economic regimes. By using the threestate Markov switching regime econometric methodology, we confirm that the statistical significance of the independent variables representing fundamentals, macroeconomic conditions, and a behavioral variable changes across economic regimes. Our findings offer an improved understanding of what moves the equity premium across economic regimes than what we can learn from singleequation estimation. Our results also confirm the significance of momentum as a behavioral variable across all economic regimes. Copyright © 2011 John Wiley & Sons, Ltd.
INTRODUCTION
 Top of page
 ABSTRACT
 INTRODUCTION
 LITERATURE AND HYPOTHESES DEVELOPMENT
 DATA AND METHODOLOGY
 RESULTS
 RESIDUAL DIAGNOSTICS OF THE MARKOV SWITCHING MODEL
 CONCLUSIONS
 APPENDIX
 ACKNOWLEDGEMENTS
 REFERENCES
 Biographies
In this paper, we argue analytically and test empirically certain hypotheses that relate excess US equity returns to certain important groups of variables across economic regimes. The review of the literature in the next section identifies three sets of variables. The three groups include fundamental factors, macroeconomic determinants, and behavioral variables. We define excess returns, also called the equity premium, in the standard way, as the difference between the index returns and the riskfree interest rate. A proxy for the riskfree interest rate is the Fed funds rate determined by the Federal Reserve Bank's monetary policy.
Excess US equity returns are used in capital asset pricing models, but when the research focus, is on excess returns for an aggregate market index, the concept of equity premium is more relevant. Fama and French (2002) defined the equity premium as the difference between the expected return on the market portfolio of common stocks and the riskfree interest rate. The historical equity premium is usually defined as the differential return of a stock market index over the riskfree rate. Associated with the equity premium, there is an academic puzzle, firstly articulated in Mehra and Prescott (1985) and recently surveyed in Mehra and Prescott (2003).
This puzzle describes the fact that the equity premium is too large to be explained by traditional asset pricing models with timeseparable preferences at reasonable values of risk aversion. Using postWWII data, economists often claim that a longrun average real growth of gross domestic product (GDP) of about 3% is related to a longrun average growth of about 7% for dividends, an average rate of inflation of about 2.5% to 3%, unemployment of about 5%, a riskfree interest rate of about 5%, and a longrun average increase of about 10% for the S&P 500 index. Using these averages, the historical equity premium is calculated to be 5%, as the difference between the 10% longrun average return of the S&P 500 index and the 5% riskfree interest rate. Obviously, all these averages are sample dependent. Heaton and Lucas (1999) cited several similar stylized facts. The challenge, both theoretical and empirical, is to explain this risk premium of about 5%.
Connected with the puzzle of the size of the equity premium is its year by year variability. Often, the equity premium variability is very large. For example, during the recent global financial crisis of 2007–2009, the S&P 500 volatility increased quite dramatically. In particular, during September and October 2008, market volatility as measure by VIX climbed to about 80%. Shiller (1989) was the first scholar to address this problem of excess volatility. In a series of papers reproduced in Shiller (1989), he and his coauthors studied the sources of such volatility and argued that these include both economic fundamentals and also changes in social psychology or changes in behavioral variables.
Campbell and Cochrane (1999), using annual data from 1871–1993, revisited the equity premium and its volatility and proposed a consumptionbased explanation. Shiller (2000) reexamined this theme with a greater emphasis on behavioral aspects by introducing the concept of irrational exuberance during the period 1996–2000. Very recently, Akerlof and Shiller (2009) introduced the Keynesian concept of “animal spirits” to illustrate the importance of human psychology as an explanatory variable of excess volatility in asset returns.
Our work makes a contribution in two critical ways: first, we propose a wider list of factors with special emphasis on momentum as a behavioral variable, and second, we trace the relative significance of these factors across three economic regimes. The three economic regimes are determined by the range of volatility of the equity premium. The statistical methodology identifies what factors determine with what significance the equity premium across three regimes of low, medium, and high volatility. This contribution both generalizes and also enriches previous results.
The theoretical hypotheses that motivate the empirical testing propose certain scenarios dependent on the level of volatility. During periods of low volatility, we argue that the low level of risk may encourage risk taking and be a factor to an aboveaverage equity premium, whereas during periods of very high volatility associated with stock market turbulence and crashes, the equity premium could be negative. Studies that explain the equity premium without accounting for changes in the volatility of this premium only discover an average influence over the full sample of the independent factors.
In addition to formulating certain hypotheses that indicate the groups of variables explaining equity premia across three volatility regimes, we also propose that the significance of these groups of variables changes over economic regimes and proceed to test the suggested hypotheses.
In the next section, we first review the relevant literature to select groups of appropriate variables and then formulate our hypotheses. Afterwards, we carry out the Markov switching regime methodology and interpret our results. Finally, we perform various diagnostic tests to confirm the appropriateness of our methodology and conclude by summarizing our main findings.
DATA AND METHODOLOGY
 Top of page
 ABSTRACT
 INTRODUCTION
 LITERATURE AND HYPOTHESES DEVELOPMENT
 DATA AND METHODOLOGY
 RESULTS
 RESIDUAL DIAGNOSTICS OF THE MARKOV SWITCHING MODEL
 CONCLUSIONS
 APPENDIX
 ACKNOWLEDGEMENTS
 REFERENCES
 Biographies
We use monthly data covering the period June 1965 to December 2008. The macroeconomic variables for inflation, interest rate, and unemployment are obtained from the website of the Federal Reserve Bank at St. Louis. In particular, we calculate the inflation rate from the CPI for all urban consumers for all items (CPIAUCSL). The data item for shortterm interest rate is the constant maturity 3month Treasury bill (TB3MS) from the secondary market as a proxy for the Fed funds rate representing the riskfree shortterm interest rate. This is used to compute the historical equity premium, defined as the differential return of the S&P 500 index over the risk free. We let civilian unemployment rate (UNRATE) represent the level of unemployment rate in the model. Although some authors such as Ferrara (2003) use the inverted unemployment rate in macroeconomic analysis of business cycles, we use the direct measure of unemployment rate in our study. The aggregate equity market level is represented by the S&P 500 obtained from DataStream (S&PCOMP (PI)). DataStream also provides dividend yield (S&PCOMP (DY)) data. We use this dividend yield to compute the level of dividend and use that as a fundamental variable along with inflation and the unemployment rate as macroeconomic variables.
As the unemployment rate and the CPI are subject to revisions and corrections, we use the average of the past 2 months to coincide with the other monthly data in our analysis. We also find that the unemployment rate and the dividend data are all nonstationary. We, therefore, use the first differences of these variables in the model implementation.
Before proceeding further with our analysis, we outline the relevance of the regimebased approach that we adopt in this paper. Long economic time series are also subject to some form of structural breaks as the economy moves through different phases. The concept of regime thus depends on the problem at hand. Besides, the regimes may be unobservable to the statisticians carrying out ex post analysis. Lee and Chen (2006) showed that a Markov switching regime model for exchange rates performs very well in prediction. They justify the use of such models, and the regimes appear consistent with popular known exchange rate regimes in the world. Fong and See (2002) also demonstrated the validity of using a Markov switching regime model for volatilities in oil futures price series. Raymond and Rich (1997) used regime switching to study the role of oil prices in accounting for shifts in the mean of US GDP and to predict the transition between lowgrowth and highgrowth states. Andreopoulos (2008) estimated a Markov switching model for the interest rate, unemployment, and real oil price.
Next, we define the variables in our study before we describe the models for ease of representation. For a particular month (t), the label used for excess return is, xsr_{t}, for unemployment rate is, uem_{t}, for inflation rate is, inf_{t}, and for dividend is div_{t}. To indicate a first differenced variable, we use the common symbol Δ.
In addition to the above, we define a proxy for the behavioral variable to represent recent performance or momentum return. We follow the definition used in Koijen, Rodriguez, and Sbuelz (2009). In their continuous time setup, they calculate the shortterm performance of the equity market as a weighted function of the past returns. Given that S_{t} represents the index level at time t, then the momentum return mmt_{t} is given by:
where e^{− (t − u)} is the weighting scheme. Koijen et al. (2009) showed that there is no need to consider any more general weighting scheme because this simple approach is capable of matching the shortterm and longterm autocorrelations of the stock returns. Later in this section, we define a discrete version of this momentum variable for empirical investigation.
The target variable of our investigation is the equity premium (xsr_{t}) defined earlier. The explanatory macroeconomic variables are inflation (inf_{t}) and the civilian unemployment rate (uem_{t}). The fundamental explanatory variable is the dividend yield (div_{t}), and the behavioral variable is momentum (mmt_{t}).
In order to obtain a basic idea of the explanatory power of the selected variables, we investigate the ordinary linear regression model as:
 (1)
The lagged excess return helps to take care of residual serial correlation. The parameter estimates of this linear regression are given in the following table, with tstatistics below the parameters. In the first instance, we let the residual variance be constant.
c_{0}  c_{1}  c_{2}  c_{3}  c_{4} 

0.00226  −0.05491  0.38394  0.00318  0.61625 
1.90  −44.57  1.30  0.37  21.24 
In order to understand how well such a linear regression relation performs, we carried out the cumulative sum (CUSUM) of squares test with the residuals in EViews™ (IHS EViews, Irvine, CA). The details are not included here (but available on request). This test clearly shows that this linear model is incapable of addressing either the parameter instability or the variance instability over the sample period. As a further step, we estimate the same model but this time with a generalized autoregressive conditional heteroscedasticity (GARCH) specification of the residual variance. In this instance also, the CUSUM of squares test of residuals indicates parameter and/or variance instability. Although the GARCH specification addresses timevarying conditional variance, the unconditional variance is constant. If there is indeed structural change in the unconditional variance, a GARCH specification is inadequate to demonstrate it. Besides, structural change may imply different coefficients of the regression relation.
A natural alternative to the model in Equation (1) is to allow such a relationship to be dependent on the regime prevailing at a given date. Using a monthly data set, Guidolin and Ono (2006) found overwhelming evidence of regime switching in the joint process for asset prices and macroeconomic variables. They also found that modeling explicitly the presence of such regimes improves considerably the outofsample performance of a model of the linkages between asset prices and the macroeconomy.
Once the regime breakdown is achieved, then we can disentangle the relationships among the variables depending on the regime. As it is difficult to stipulate where regime changes may have occurred, we rely on the data to decide on this. In addition, if the different regimes are allowed to have different variances or volatilities, then it also caters for heteroscedasticity in the data, which is a common occurrence in financial and economic time series. In this context, the best applicable methodology is to allow an unobserved Markov chain to drive the regimes under a timehomogeneous transition probability.
The most intuitively appealing way to classify the regimes is based on the level of the residual variance or in other words the surrounding level of uncertainty. If there are indeed different levels of uncertainties, then not allowing for regime differences will lead to misspecified models and may not allow full understanding of the relationships among the variables of interest to us.
The adoption of a regimedependent strategy is not only confined to macroeconomic analysis. Alexander and Dimitriu (2005) adopted a similar regimedependent strategy to investigate complex hedge fund investment styles where the traditional approach fails to uncover the underlying dynamics. Our study thus follows a similar regimedependent strategy.
We have already pointed out that a particular regime at any given date is to be determined by an unobserved state variable whose evolution is governed by a probability law. This approach also addresses the structural breaks in the relationship in a straightforward manner. In addition, this is a different approach to address heteroscedasticity than the GARCH modeling. In a GARCH setup, the conditional variance changes but the unconditional variance is fixed, whereas with regimedependent variance specification, the unconditional variance itself is changing.
There is another advantage of the regimedependent approach to our analysis. In the table previously shown, not all of the estimated parameters of the linear regression model in Equation (1) are significant. Without any regime structure, the results may simply be indicating the average effect. With a regimedependent model, it is likely that we will find a particular parameter to be significant in one regime but not in another one. If this does occur, it then provides additional insight into the background economic dynamics. In fact, we document evidence of this occurring later in the discussion of our results.
Based upon the above analysis and as we have hypothesized earlier, we would expect to detect varying degrees of influence of these explanatory variables across different regimes in the market. We, therefore, propose the following model representation. The lagged value of (xsr_{t}) is not used here as we do not find this important when regimes are allowed.
 (2)
The main task now is to decide how many different regimes might be there. In order to explore this issue, we examine certain influential papers relevant to our topic that also employ multistate regime switching models.
First, Bansal, Tauchen, and Zhou (2004) found a tworegime description of the US economy adequate in the context of a varying risk premium in the term structure of interest rates. They also assume the transition probability of the Markov chain to be time homogeneous. Second, Guidolin and Timmermann (2006) found that a threeregime description fits well for the US bond and equity returns when modeled separately. But, they needed a fourregime description to fit the joint distribution of bond and stock returns. The transition probability in this case is also time homogeneous. It is also apparent from their paper that the numerical difficulty of estimation increases as the dimension of the model increases.
Thus, approaching the issue of the number of regimes purely on statistical grounds is not the best course as efficiency of estimation becomes a problem with each increase in the number of states as the number of parameters rapidly increases. As we are modeling univariate time series, we follow Ferrara (2003) to capture such regimes with a Markov switching framework with prespecified number of states. Similar to Ferrara (2003), we also allow a threestate unobserved Markov chain to drive the parameters of the model in Equation (2). Our dataset covers the period analyzed in Ferrara (2003). In our analysis, the regimes are classified by the level of variance of the model residual. The Markov switching model is a dynamic model of the equity premium that allows for endogenous structural breaks and thus allows the data to formalize the beginning and the ending of each regime. A similar approach is adopted by Boyer, Kumagai, and Yuan (2006). They find an increased level of comovement among emerging market stock index returns during highvolatility periods.
Regarding the parameter estimation issue from the threestate unobserved sample paths, we use maximum likelihood method as in Kim and Nelson (1999), together with the expectation maximization (EM) algorithm. The EM algorithm has proven to be robust with respect to initial parameter values. The number of parameters for a threeregime model is 21 and may be considered large for most econometric analyses.
In the second stage of our analysis, we include the behavioral variable, momentum return, as an additional explanatory variable in Equation (2) and estimate the threestate Markov switching model. The behavioral element, in addition to the other macroeconomic and fundamental variables, may have incremental explanatory power. In fact, we demonstrate this incremental explanatory power later in the Results section. Connolly and Stivers (2003) reported the existence of momentum in weekly equity returns in a number of markets, and this appears to be related to the turnover. They also pointed out that any theoretical reasoning of this behavior is still an open question. Nevertheless, such observations have taken hold in behavioral finance. Although a workable definition of momentum return is being used by various market participants, such as technical traders, we need a proxy for our aggregate equity market based upon the index itself. Chordia and Shivakumar (2002) utilized past 6 months' return to define this concept. Barberis and Thaler (2005) used the notion of shortterm persistence as a proxy for the momentum return. Earlier in this section, we have already defined the performance variable (momentum return) in a continuous time setting. In Equation (4), we use the equivalent discrete time version of the same notion.
The modified model, with the inclusion of the proxy for the behavioral variable, now looks like:
 (3)
The discrete version of the new explanatory performance variable mmt_{t} captures the momentum return defined as,
 (4)
where r_{t} is S&P 500 price levelbased return for the month t. The estimation methodology is still based on the EM approach, and the number of parameters in this case is 24.
RESULTS
 Top of page
 ABSTRACT
 INTRODUCTION
 LITERATURE AND HYPOTHESES DEVELOPMENT
 DATA AND METHODOLOGY
 RESULTS
 RESIDUAL DIAGNOSTICS OF THE MARKOV SWITCHING MODEL
 CONCLUSIONS
 APPENDIX
 ACKNOWLEDGEMENTS
 REFERENCES
 Biographies
This section interprets the results in Tables 1 and 2. As we interpret the results, it is important to point out that the models with regimes clearly dominate the nonregime model in increasing the explanatory power of the variables.
Table 1. Parameter estimates that determine the equity premium (Equation (2)) threestate Markov switching model  S_{t} = 1  S_{t} = 2  S_{t} = 3 


c_{0} (Intercept)  −0.036830*  0.017667*  0.007656*** 
(−2.93)  (7.89)  (1.94) 
c_{1} (Δ Dividend)  −0.247037*  −0.414413*  −1.654876* 
(−3.63)  (−15.03)  (−12.37) 
c_{2} (Inflation)  5.015457*  −1.454474**  −2.771233* 
(2.74)  (−2.48)  (−3.72) 
c_{3} (Δ Unemp. rate)  −0.028334  0.045672*  −0.085522* 
(−0.59)  (2.92)  (−4.79) 
σ^{2} × 10^{− 3}  4.037*  0.556*  0.539* 
(4.90)  (10.13)  (7.72) 
Transition probability matrix p_{i, j} : j i 
 j = 1  j = 2  j = 3 
i = 1  0.783918*  0.036780**  0.019468 
(9.75)  (2.49)  (1.56) 
i = 2  0.216082*  0.950202*  0.005075 
(2.69)  (60.06)  (0.71) 
i = 3  1.00E−08  0.013018  0.975456 
Average duration in a particular state (months) 
 4.63  20.08  40.74 
Table 2. Parameter estimates that determine the equity premium (Equation (3)) threestate Markov switching model  S_{t} = 1  S_{t} = 2  S_{t} = 3 


c_{0} (Intercept)  0.002602  −0.001939  −0.000400 
(0.51)  (−1.77)  (−0.60) 
c_{1} (Δ Dividend)  −0.575593*  −7.897492*  −2.042740* 
(−3.64)  (−22.25)  (−27.63) 
c_{2} (Inflation)  0.572984  0.709286*  0.136024 
(1.23)  (3.13)  (0.87) 
c_{3} (Δ Unemp. Rate)  0.132181*  −0.002867  0.007629** 
(6.27)  (−0.81)  (2.07) 
c_{4} (Momentum)  2.597215*  2.004013*  2.087992* 
(24.95)  (59.73)  (73.32) 
σ^{2} × 10^{− 3}  0.092**  0.051*  0.047* 
(2.27)  (9.05)  (9.64) 
Transition probability matrix p_{i, j} : j i 
 j = 1  j = 2  j = 3 
i = 1  0.519984*  0.027659  0.008635 
(83.66)  (1.34)  (1.43) 
i = 2  0.338973  0.964489*  0.016363 
(1.48)  (51.52)  (1.79) 
i = 3  0.141044  0.007852  0.975002 
Average duration in a particular state (months) 
 2.08  28.16  40.00 
Table 1 summarizes the parameter estimates, the transition probability matrix, and average duration in months for the regimes identified for model Equation (2). Regimes are classified based on residual variances, and there is an order of magnitude difference between the lowest and highest estimated variances. As would be expected, the diagonal elements of the transition probability matrix show that the highest variance state is least likely to persist. The expected duration of the highest variance state is only 4.6 months, whereas the lowest one has an expected duration of 40.7 months. Economists such as Mishkin (2007) have argued that high volatility periods are often related to turning points in business cycles. Such periods are often brief, and it is hard to find consistent economic factors explaining these turning points. Worth pointing out is the magnitude of the variance in the highest state: 4.037 vs 0.556 and 0.539 in the medium and low variance states. In other words, when markets correct during turning points, the volatility of the equity premium is very large compared with the volatility during normal times.
Although we find that the average realized equity premium is negative in the highest variance state, it is positive in the low and medium variance states. All these average returns are statistically significant. Similarly, all the coefficients of the change in dividend are negative and statistically significant. We are using price levelbased returns, and increases in dividends are likely to lead to price reductions. This result is intuitive.
Focusing on the inflation variable, the impact of increased inflation on the equity premium is negative in both the low and medium variance states. This is what we would normally expect, possibly because higher inflation leads to higher prices and lowers demands for goods and services. This is likely to reflect in lower earnings by firms and ultimately lower stock prices. Higher inflation may also lead to higher costs for firms as well, whereas they may not be able to raise prices soon because of price stickiness. Furthermore, higher inflation also increases the riskfree interest rate and reduces the equity risk premium. The behavior in the high variance state is quite different, and the coefficient of inflation is positive and significant. This suggests that in the highvolatility regime, stocks are a good hedge for inflation. However, this may be a shortlived phenomenon and is reflected by the shortest expected duration of this state.
The other macroeconomic variable, unemployment, has differing impact on the equity premium in the medium and low variance regimes. Unemployment has no significant effect during the shortlived high variance state. In the most stable state, that is, the low variance one, a rise in unemployment leads to a fall in the equity premium, probably indicating an expected drop in overall consumption demand. However, in the medium variance state, unemployment affects the equity premium positively, although at about half the magnitude of that of the low variance state. One explanation of this finding is that during periods of increasing unemployment, the Fed adopts an easier monetary policy that lowers the riskfree interest rate. Such an easy monetary policy is usually favorable to equity returns. Thus, higher equity returns and a lower riskfree interest rate result in a higher equity premium. The average duration of the medium variance state is nearly half of that of the most stable state.
Figure 1 depicts the probability of the respective states occurring. The second half of the sample period (from mid1980s onward) is dominated by the medium variance level with occasional emergence of the high variance state. The intercept term representing the average excess return for the medium variance regime is positive and significant. From the data, we could easily verify that the sample average excess return for the period of March 1991 to March 1998 is 0.010 and for the period August 2003 to August 2007 is 0.006. This is an indirect verification of the success of the regime separation by the model we employed in this study.
The parameter estimates of the model, including the performance variable, momentum return, are given in Table 2. The average duration of the most stable state in this scenario is almost the same as that of the previous case given in Table 1. The most volatile state, however, is reduced to about half the duration of that of the previous case. This is possibly due to the momentum factor changing the persistence of a highvolatility regime. Figure 2 captures the probability of different regimes occurring in the case when momentum return is included. The sharper nature of the most volatile state (regime 1) supports the observation of reduced average duration in a regime. However, the probability of the highest volatility state occurring spans the similar duration as in Figure 1. Thus, it appears that the inclusion of the behavioral variable in the model reduces the “stay” in the highvolatility regime.
The introduction of momentum, as an additional explanatory variable, does not impact the significance of dividends. Observe that Table 2 indicates that dividends are significant in all three states. In fact, their significance increases when compared with the corresponding numbers in Table 1. However, the significance of the two macroeconomic variables, inflation and unemployment, is reduced with the introduction of momentum. Specifically, inflation is now only significant in the medium variance state, with a positive coefficient and with lower strength. The effect of the unemployment rate is very small but significant in the most stable state. In the least stable state, the unemployment rate affects excess returns positively. Most importantly, the coefficients of momentum are statistically significant in all states. In the least stable state, momentum has the maximum positive impact on the equity premium. Thus, it is possible that this behavioral variable subsumes many of the effects of other explanatory variables in the model. It makes it difficult to comment on the magnitudes of the other coefficients.
The results of Tables 1 and 2 confirm the importance of macroeconomic factors such as unemployment and inflation in addition to the fundamental factor, dividend yield, in explaining the equity premium. Also, when momentum is introduced as an explanatory variable of the equity premium, it is found to be significant across all three regimes.
The results of Tables 1 and 2 and the preceding analysis allow us to draw the following conclusions about the hypotheses proposed.
First, the time duration of the lowvolatility regime is indeed longer than that of the medium regime, and both are longer than the highvolatility regime. From Table 1, we read durations of an average 40.63, 20.08, and 4.63 months, respectively. From Table 2, the corresponding average monthly durations are 40, 28.16, and 2.08.
Second, dividends emerge as a significant explanatory variable in both models presented in Tables 1 and 2 and in all regimes; they also have the expected negative sign. This confirms our second hypothesis and the numerous findings of previously published research cited in the bibliographical review.
Third, the two macroeconomic variables we selected, inflation and unemployment, give us conflicting results. In Table 1, both variables are significant in all three regimes, but the signs alternate. In Table 2, the significance declines. We conclude that Table 1 gives partial support to our hypothesis that during periods of low volatility, inflation and unemployment are significant, but Table 2 indicates that only unemployment is significant when momentum also enters as an explanatory variable. Thus, our third hypothesis receives only partial confirmation.
Fourth, momentum is significant and has the correct sign, indicating that high momentum increases net returns. Tables 1 and 2 clearly support this hypothesis and confirm the importance of momentum in explaining the equity premium in all regimes. These results support our fourth hypothesis.
Finally, dividends and momentum emerge as the two most significant variables in Table 2 for all three regimes. In the lowvolatility regime, returns are driven by dividends, but momentum adds to net returns. When volatility is the highest, dividends are still significant, but momentum becomes the most significant variable. This confirms the fifth hypothesis.
CONCLUSIONS
 Top of page
 ABSTRACT
 INTRODUCTION
 LITERATURE AND HYPOTHESES DEVELOPMENT
 DATA AND METHODOLOGY
 RESULTS
 RESIDUAL DIAGNOSTICS OF THE MARKOV SWITCHING MODEL
 CONCLUSIONS
 APPENDIX
 ACKNOWLEDGEMENTS
 REFERENCES
 Biographies
The behavior of the stock market across various economic regimes has been a central topic of research. In this paper, we augment the list of important fundamental and macroeconomic variables by adding trading momentum as a behavioral variable. Our goal is to use fundamental, macroeconomic, and behavioral variables to explain US equity returns during the 1965–2008 period, across three economic regimes.
We do an extensive literature review to identify three broad categories of factors that can influence the US equity premium. The first fundamental variable is dividends. Next, we identify certain macroeconomic variables such as inflation and unemployment. Finally, we also introduce a behavioral variable called momentum to explore its influence on the equity premium. We also review the role of monetary policy that is charged to maintain economic and financial stability by promoting economic growth and controlling for inflation. The main tool of monetary policy is the Fed funds rate. We use this Fed funds rate to define the riskfree interest rate that is subtracted from the index returns to define the equity premium.
The theoretical hypotheses propose three regimes of economic conditions. The everchanging dynamic pattern of the equity premium is explained by placing different weights and significance between fundamental, macroeconomic, and behavioral variables across the various phases of an economic cycle. To capture the most important phases, we propose three regimes of market volatility: low volatility, average volatility, and aboveaverage volatility. We formulate and test six hypotheses about the equity premium: first, we hypothesize that when economic regimes are divided according to the level of volatility of the equity premium, the time duration of low volatility will be longer than the duration of the mediumvolatility regime, and both will be longer than the duration of the highestvolatility regime. Empirical evidence supports this hypothesis. In Table 1, the average durations for highvolatility, mediumvolatility, and lowvolatility regimes are 4.63, 20.08, and 40.74 months, respectively, and in Table 2, the durations are 2.08, 28.16, and 40, respectively.
Second, we hypothesize that dividends are very important as an explanatory variable and are expected to be significant across all regimes with a negative coefficient as high dividends reduce net returns. Evidence in Tables 1 and 2 supports this hypothesis.
Third, during periods of economic stability with low volatility, we expect macroeconomic variables such as inflation and unemployment to play a significant role in explaining the equity premium. This hypothesis is partially confirmed because the significance of macroeconomic variables changes across the three volatility regimes for both models as reported in Tables 1 and 2.
Fourth, we hypothesize that momentum is present across the three regimes and higher momentum contributes to higher returns. This is confirmed with very high significance in Table 2. Next, we hypothesize that during periods of high volatility, momentum becomes the most significant variable among the ones considered in this model. This is partially confirmed. Table 2 presents evidence that momentum along with dividends and unemployment determines the equity premium in the highvolatility regime.
Finally, during periods of very low volatility for the equity premium, dividends initially drive returns, but momentum also becomes important. Similarly in periods of very high volatility, both dividends and momentum explain returns but the significance of momentum increases. This hypothesis is also partially confirmed. Momentum, dividends, and unemployment are significant explanatory variables for the equity premium both in the lowvolatility and highvolatility regimes, but the significance of momentum does not increase during the highvolatility regime as hypothesized.
In conclusion, we empirically test two models that differ in the number of independent variables that explain the equity premium. The first model includes dividends, inflation, and unemployment whereas the second considers these three independent variables and also momentum. Empirical evidence demonstrates that fundamental variables represented by dividends are significant across all three regimes and in both models. Momentum also is highly significant across all three regimes. Inflation and unemployment fluctuate in their significance across the three regimes and the two models. In particular, during the long periods of low volatility that last on average of about 40 months each, the equity premium is influenced by dividends and momentum that each offset the other. Dividends have a coefficient of −2.0427 whereas momentum has a coefficient of 2.088. During the very short periods of aboveaverage volatility that last on average of only 2 months, momentum dominates as an explanatory variable. Finally, during periods of average volatility that last about 28 months, both dividends and momentum are significant along with inflation. These results support our hypotheses that both fundamentals and behavioral variables explain the equity premium with different significance across volatility regimes.