Transaction costs and efficiency of portfolio strategies

Some recent results for frictionless economies show that popular dynamic portfolio strategies such as stop-loss and lock-in are inefficient, i.e. for each of these strategies there exists an alternative portfolio strategy that gives the same final payoff distribution at lower initial costs. However, the alternative strategies require considerably more active trading than the simple strategies. The results rely heavily on the assumption of no transaction costs. Under this assumption the initial investment required is a linear function of the prices of the contingent claims that build the final payoff distribution. In this paper we demonstrate that, even for modest levels of transaction costs, the efficient strategies are more costly than the simple strategies, i.e. a strategy that replicates the final payoff distribution of an efficient strategy is excessively costly due to the transaction costs and the heavy trading involved. Since the initial investment is no longer a linear function of the contingent claims, the optimization problems to find the most efficient strategy are complicated combinatorial optimization problems which can only be solved for trees with a small number of steps. In a world without transaction costs, options are redundant instruments, since all payoff distributions can be replicated by trading in stocks and bonds. In the second half of this paper we show that the use of options in a world with transaction costs enables investors to realize final value distributions at lower initial costs than would be possible with trades in stocks and bonds only. Hence, although in theory options do not give rise to other portfolio strategies, they do in a more restrictive setting with transaction costs.