It is commonly felt that a financial market achieves informational efficiency as traders with the best information and the most skill make profits at the expense of those with inferior information or ability and come to dominate the market. This paper develops a model of a speculative market in which this redistribution of wealth among traders with different information and ability can be studied. In the short run the market tends toward increased efficiency, but in neither the short nor the long run is full efficiency likely. The average deviation from efficiency is shown to depend on traders' characteristics such as the quality and diversity of their information and their risk aversion.