Modelling Alpha-Opportunities Within the CAPM

We consider a simple CAPM with heterogenous expectations on assets mean returns while keeping the assumption of homogenous expectations on the covariance of returns. Our first result derives the security market line as an aggregation result without using the two-fund-separation property. In particular every investor can hold optimal portfolios that are underdiversified.In our model alpha-opportunities can be explained as a feature of financial market equilibria and we can show that alpha-opportunities erode with the assets under management and that the hunt for alphaopportunities is a zero-sum game. Then we endogenize the agents information by allowing them to be either passive, in which case they invest according to the average expectation embodied in the market returns, or to be active, in which case they can acquire superior information at some cost. It is shown that expecting a positive alpha is not necessarily a good criterion for becoming active. Moreover, the less risk averse investors are more inclined to be active and delegating active investment to portfolio managers only makes sense if the performance fee increases with the skill of the portfolio manager. Finally, in our model it turns out that only a market in which all investors are passive and share the same correct belief is stable with respect to information acquisition. Hence the standard CAPM with homogenous beliefs can be seen as the long run outcome of our model.