The purpose of this paper is to study the implications of model uncertainty for the cross sectional properties of asset prices in a simple equilibrium setting.
The recent focus on model uncertainty in the literature is driven by the difficulty of reconciling traditional asset pricing theories with the empirical data. Limited success of the standard theories could be in part due to the commonly made assumption that economic agents possess perfect knowledge of the data generating process. For instance, the classical theories of Sharpe (1964), Lucas (1978), Breeden (1979) and Cox, Ingersoll and Ross (1985), assume that, while the payoffs of financial assets are random, agents know the underlying probability law exactly. In reality this is often not the case. Then the natural question is: how are the prices of financial assets affected by investors’ lack of knowledge about the probability law, or their uncertainty about what the true model is.
The importance of model uncertainty has long been recognized in finance. While the literature appears under different names, such as parameter uncertainty, Knightian uncertainty, the defining characteristic of that literature is the recognition of the fact that the agents of the economy do not have a perfect knowledge of the probability law that governs the realization of the states of the world. Various issues have been studied. Dow and Werlang (1992) use the uncertainty averse preference model developed by Schmeidler (1989) to study a single period portfolio choice problem. Maenhout (1999) examines a similar problem in a continuous-time economy, but from the point of view of robust portfolio rules.
Kandel and Stambaugh (1996), Brennan (1998), Barberis (2000), and Xia (2001) show that parameter uncertainty can affect significantly investors’ portfolio choice. Frost and Savarino (1986), Gennotte (1986), Balduzzi and Liu (1999), Pastor (2000) and Uppal and Wang (2001) examine the implication of model uncertainty for portfolio choices when there are multiple risky assets. Detemple (1986), Epstein and Wang (1994), Chen and Epstein (2001), Epstein and Miao (2001), and Brennan and Xia (2001) study the implications for equilibrium asset prices in the representative agent and heterogenous agent economies respectively. Routledge and Zin (2002) examine the connection between model uncertainty and liquidity. There is also a significant literature, for example Lewellen and Shanken (2001) and Brav and Heaton (2002), on the effect of learning about an unknown parameter on the equilibrium asset prices.
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A Simple Theory of Asset Pricing under Model Uncertainty
