This study uses stochastic dominance with and without risk-free assets to examine whether trading days can affect patterns of the day-of-the-week effect in the Taiwan foreign exchange market. Our results generally indicate that higher returns appear on the first three days of the week across different trading-day regimes in the Taiwan foreign exchange market, confirming day-of-the-week effect. Allocating part of investors’ assets in risk-free assets is useful in distinguishing returns among weekdays for all currencies.