An optimal schedule for dollar cost averaging under different transaction costs

Dollar cost averaging is a popular habit adopted by investors who recognize the difficulty in consistently timing the market. Recent technological innovations allow for the direct deposit of a predetermined portion of each paycheck into a brokerage account for the purchase of equities. Since most payperiods are biweekly or monthly, the automatic and frequent purchase of small amounts of equity produces substantial transaction costs. If funds were allowed to accumulate for a time in a money market account prior to equity purchase, then transaction costs may be lowered. However, since equity returns are generally more than that earned in the money market, delayed purchases would forfeit higher returns. In this study, we determine the optimal transaction size to maximize returns. We use the classical economic order quantity framework of inventory management and extend that framework to deal with the special discounting structures commonly offered by brokerage firms. Numerical examples and sensitivity analysis of fixed and variable transaction cost structure models are presented.