Applying Recent Developments in Computational Statistics to Behavioral Asset Pricing and Portfolio Selection

In the classical finance literature, the pricing kernel (or stochastic discount factor) represents the unified framework for asset pricing (see Cochrane 2001). Two results from finance theory imply the centrality of the pricing kernel. First, in the absence of risk-free arbitrage, prices can always be written as expected payoffs weighted by the pricing kernel (see Duffie 1988). Second, in many representative agent models the pricing kernel can be easily linked to investor's preferences when these satisfy the expected utility theory of von Neumann and Morgenstern (1944). Behavioural finance identifies several pricing anomalies or puzzles, i.e., empirical observations that cannot be understood using classical models for asset pricing. However, pricing anomalies generally do not imply risk-free arbitrage investment opportunities, thus the pricing kernel remains the unified framework for asset pricing also in the context of behavioral asset pricing. The question of how the investor sentiment, i.e., the way people form beliefs in practice (thus also their biases), impacts the pricing kernel has recently attracted the attention of researchers; see, for example, De Bondt and Thaler (1985), Lee, Shleifer, and Thaler (1991), Swaminathan (1996), Neal and Wheatley (1998), Shefrin (1999), Han (2004) and Baker and Wurgler (2006). Shefrin (2001) and De Giorgi and Post (2008) propose behavioral asset pricing models where the link between the pricing kernel and the investor sentiment is formalized. In De Giorgi and Post (2008) the pricing kernel corresponds to a distortion of markets' returns which implies a pessimistic view on the market, i.e., investors attach higher probabilities to negative returns compared to the true distribution. The aim of this project is to contribute to this growing literature on behavioral asset pricing. More specifically, we want to (1) Extend the asset pricing model of De Giorgi and Post (2008) along several directions, in order to derive a formal link between the pricing kernel and the investor sentiment under more general assumptions on the market and on investors' preferences, compared to De Giorgi and Post (2008). (2) Use advanced techniques from computational statistics to calibrate the model from point (1) on market data, in particular the dynamics of the pricing kernel and the link to a set of behavioral risk factors. (3) Derive directly from market data a model-independent estimation of the pricing kernel and link it to a set of behavioral risk factors. (4) Develop a time-series model for the pricing kernel. (5) Apply the results from the previous points to price options and to derive behavioral investment strategies.