Conditioning the Capital Asset Pricing Model with Volatility

Financial economists are always interested in improving models to predict expected returns. Previous research indicates that variations in time of expected returns are connected with business cycles. Particularly, investors are less likely to hold risky assets during economic recessions, so expected returns during those times are higher than expected returns in times of economic expansions. Thus, it is implied that variables of the business cycles affect time variations in equity premiums. Supporting this assumption and expanding on previous research, we develop a conditional macroeconomic variable by the Johansen cointegration method, a method used to determine a stationary relationship between multiple non-stationary time series, to measure time variations in risk premiums and incorporate it into the Capital Asset Pricing Model and the Fama and French Three Factor Model. The conditional term includes the following macroeconomic variables: dividend yield, default spread, term spread, short-term interest rate, and implied volatility. Using linear regression our analysis of the models show that the multi-factor models generally predict better than CAPM, but there is room to improve upon the accuracy of all of the models. This paper is heavily based on and will continue the work of Maria Jansen and Maria Casandra Rusti’s “Cointegrating the Capital Asset Pricing Model to Incorporate Macro-Economic Based Variables” from the 2010 WPI REU Program in Industrial Mathematics and Statistics.

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