Coskewness Risk Decomposition, Covariation Risk, and Intertemporal Asset Pricing

We develop an intertemporal asset pricing model where cash-flow news, discount-rate news, and their second moments are priced by the market. This model generalizes the market-return decomposition framework, showing that intertemporal considerations imply a decomposition of squared market returns (coskewness risk). Our model accounts for 68% of the return variation across portfolios sorted by size, book-to-market ratio, momentum, investment, and profitability for a modern U.S. sample period. Further, our findings highlight the importance of covariation risk, that is, the risk of simultaneous unfavorable shocks to cash flows and discount rates, in understanding equity risk premia.

Intertemporal Asset Pricing: Preliminary Evidence from an Emerging Economy

In this paper, we test a simple Merton-style (1973) intertemporal capital asset pricing model (ICAPM) by allowing for time variations in certain key state variables for a sample of firms listed on the Karachi Stock Exchange. We evaluate the model’s ability to account for returns on portfolios sorted by size, book-to-market ratio, and momentum. Our findings provide evidence of an intertemporal asset pricing setting with significant coefficients for innovations in state variables. Innovations in dividend yield, term, and risk-free rates are systematically priced in time series of returns and should be considered when evaluating the risk premium for investments. We do not find the market premium to be a significant variable, which suggests that a traditional capital asset pricing model is unable to capture variations in stock returns for our sample period. These results favor the use of an ICAPM framework for optimal decision-making.