This thesis is made of four self-contained papers aiming at contributing to the better understanding of asset prices formation and dynamics in a Consumption-based Capital Asset Pricing Model (CCAPM). Chapter 1 looks at the term structure of equity return in leading CCAPM models and show that allowing the cash flows to be negatively affected by volatility shocks, as observed in the data (“leverage effect”), could make the short-term assets riskier than long-term assets as recently found in some empirical papers. This modification gives more flexibility to those models in capturing various shapes of the term structure of equity returns while still matching the observed level of the equity premium and the risk free rate. Chapter 2 proposes a regimes switching model to accommodate for the changing behavior of the term structure of equity returns as observed in the data. We show that such a model allows to combine the properties of the one regime models and it gives more flexibility in the shape of the average term structure of equity returns. Chapter 3 studies the Expectation Hypothesis on equity markets. This test has mainly been done for the bonds market. We find that the EH is not rejected but the future returns are also predictable. Chapter 4 examines the estimation and the inference in the LRR model using the Generalized Method of Moments.