In this project, we develop an equilibrium model of asset returns for the cross section with endogenous exposure to the priced risk(s) that is consistent with both the equity premium and the stock return volatility. Essentially, we use time-series properties of aggregate stock returns, the risk-free rate and potentially returns on other large asset classes to construct a stochastic discount factor and then focus on the cash-ﬂows of individual stocks and stock portfolios. The strategy of this investigation is inspired by the work of Menzly, Santos and Veronesi (2004), Cochrane, Longstaﬀ and Santa-Clara (2007) and Santos and Veronesi (2010) and is based on a novel approach in modelling cash-ﬂows for the cross-section. Speciﬁcally, we model the cash-ﬂows of diﬀerent assets or portfolios of assets, e.g. industries, as fractions of the aggregate stock market dividend. Our choice of the portfolios is crucial because of the necessary assumption that the dividend shares are jointly stationary. In the same spirit, we also model the aggregate stock market dividend as a fraction of the aggregate consumption and take consumption as exogenous. The aggregate consumption is modelled as conditionally normal with time-varying moments.
In this project, we propose a novel methodology to measure dynamic optimal portfolio allocations. Our key insight is to model portfolio weights using a mean-reverting dynamic in which the time-variations are driven by the gradient of the investor’s realized certainty equivalent. The long-run average portfolio weights capture the strategic asset allocation. The estimated parameters of the dynamic indicate to what extent it is beneficial to deviate from the long-run asset allocation, and hence to engage in tactical asset allocation. The gradient of the realized certainty equivalent is the optimal instrument to change portfolio weights over time, is a non-linear function of past returns, complements firm characteristics used in other studies, and can be used when the cross-section of assets is small or other instruments are not easily identifiable. We show using different sets of assets the superior empirical performance of our methodology compared to other benchmark portfolio allocations.