We compute the opportunity cost for rational risk averse agents of using technical trading rules in the foreign exchange rate market. Our purpose is to investigate whether these rules can be interpreted as near-rational investment strategies for rational investors. We analyze four different exchange rates and find that the opportunity cost of using chartist rules tends to be prohibitively high. We also present a method to decompose this opportunity cost into parts related to investor's irrationality and misallocation of wealth. The results show that irrationality of chartist beliefs is an important component of the total opportunity cost of using technical trading rules.