Search for contacts, projects,
courses and publications

Trading Asset Pricing Models



Schneider P.


Trojani F.


Tedeschini D.



Asset pricing models investigate the relation between a set of relevant risk factors and the prices of financial instruments, in the time series and/or the cross-section, using either a reduced-form or a more structural approach. Key quantities of interest that asset pricing models try to explain are the market prices of risk of the relevant risk factors, which determine the risk premia of financial assets, i.e., their conditional expected excess returns.

In practice, quantifying the risk premia of financial assets using asset pricing models is a challenging task. The procedure involves solutions that depend on model-implied pricing kernels, which are often not available in closed form, in order to estimate, or at least calibrate, the model to market data. In the majority of the cases, the last step is performed by optimizing a statistical criterium, based on market price information implied, for instance, by a panel of derivative prices. The estimated model is then used to analyze the properties of fitted model-implied quantities, such as risk premia. The quality of these risk premium estimates depends on several dimensions, including the degree of model misspecification and the amount of estimation risk implied by the estimation procedure.

A coherent application of asset pricing models requires that model-implied risk premia should explain the conditional excess returns of trading strategies by creating exposure to the relevant risk factors. However, estimated model-implied risk premia and average realized excess returns of corresponding trading strategies may be alarmingly different to the point that the risk premia of apparently similar models can imply very different gain and loss profiles of trading strategies generating optimal exposures to the relevant risk factors. In fact this is almost always the case.

This project proposes a new framework for the study of asset pricing models, which directly and efficiently incorporates in the analysis the risk premia of model-dependent risk factors, by means of appropriate traded instruments. The main goal of our approach is twofold.

- First, given a pricing kernel specification, we introduce a general approach for designing traded instruments that reflect direct exposure to the relevant state variables in the pricing kernel, in order to provide a more consistent and efficient tool for the estimation and specification analysis of asset pricing models.

- Second, given a specification of the appropriate traded instruments, we propose different objective functions for estimating and testing asset pricing models, which are designed to incorporate more exhaustively the properties of risk premia and optimal traded portfolios in the data.

Our approach will allow us to re-assess with a new perspective the main implications of asset pricing models, e.g., in terms of the out-of-sample properties of model-implied risk premia and the excess returns of corresponding trading strategies. Clearly, these aspects are relevant for a successful application of these models in practice.

Additional information

Start date
End date
36 Months
Funding sources
Swiss National Science Foundation / Project Funding / Humanities and social sciences (Division I)