Abstract. For an investor with constant absolute risk aversion, we informally derive the leading-order asymptotics of the optimal investment strategy in the presence of small proportional transaction costs. For general Itô processes, the optimal strategy corresponds to the minimal amount of trading necessary to remain in a state-dependent no-trade region around the frictionless optimizer. Its width is determined explicitly in terms the local quadratic variation of the latter. The corresponding certainty equivalent loss compared to the frictionless case is found to be a suitable average of the squared width of the no-trade region. These results also apply in the presence of random endowment, thereby leading to utility-indifference prices and hedging strategies. This is joint work with Jan Kallsen.