Big swings in the data and perceived changes in the risk premia

Stock markets experience periods where stocks or market returns are consistently higher than their mean and other periods where the individual stocks and markets’ volatility fluctuates from high to low. Since these periods do not necessarily coincide, a related question is whether periods where individual stock markets are higher than their mean, usually identified as αs different from zero in the conditional regressions, disappear once the researcher accounts for changing states of the economy. In this spirit, we develop and estimate a state-dependent version of the CAPM pricing model that accounts for considerable swings in the data. We use U.S. financial data to assess the model’s validity and find support for a state-dependent version of the CAPM for the data under consideration. We show how important it is to consider changes in stock and market returns and changes in their variance-covariances, and that, when not accounting for changes in market conditions, may spuriously yield significant α values. We stress that to assess changes in the risk premium, we should not only focus on βs but also allow for changes in the market premium; otherwise, changes in risk premia may be over- or underestimated. In addition, the classification between investment opportunities may be mistaken for a single regime model, even when rolling regressions are used.