Rebels, Conformists, Contrarians and Momentum Traders

We develop a model of optimal investment with two types of agents with different beliefs about the market dynamics. Market conformists agree with the true log-normal price distribution and rebels believe in price predictability. Depending on their exact beliefs, the rebels may follow either a momentum or a contrarian strategy. It is difficult to detect rebels' beliefs that are not far-fetched from the market perspective. The long-run investment portfolios of both conformist and rebels need not be biased towards equities.