Optimal investing with perceived mispricing

We derive optimal portfolio weights for an investor who has a strong belief on the distribution of the stock price at a future time. That distribution may be in disagreement with standard equilibrium pricing models, and the investor wants to take advantage of the perceived mispricing and attractive risk premium. We compute numerically optimal weights for models in which the investor believes that there is a range in which the price is likely to remain. As practiced by active managers, the optimal strategy is to take significant long/short positions as the price nears its lower/upper boundary. The risk, expected stock return and the optimal investments strategy are thus dependent on the stock price relative to the boundaries.