CAPM with View Bias Adjustment Under Imperfect Information

Abstract

In this paper, we extend the traditional CAPM theory by introducing a new concept of risk-reward measurement based on view bias adjustment under imperfect information. Within that general framework, people might only know the possible results of an uncertainty, they do not know the exact probabilities of each state, but just have a vague assessment. Consequently they are not view neutral anymore, but have either pessimistic or optimistic view bias. The main conclusion is that the generalized expectation of the excess rate of return can still be described in a single beta representation, except that the systematic risk is now the weighted average of exposed risk and potential risk. Meanwhile imperfect information can induce instantaneous profit by repackaging portfolios, and we name it information premium. Empirical study indicates that this new concept can help to explain the equity premium puzzle in a way that people have pessimistic view bias, when there is no perfect information in the postwar US, and it explains the momentum by the fact that view bias reciprocates from pessimism to optimism, and it might be a mean reversion process. Further more, since there is no existing econometrics method to test VCAPM (view bias based CAPM), we develop VOLS (we make this name in accordance with the mathematical model VCAPM), including resetting the assumptions, looking for new estimators, developing the appropriate asymptotic tools to do hypothesis test. At last, we try to use GMM integrated with VOLS method to do VCAPM empirical analysis. That would be another contribution of this research.