This study presents theoretical and empirical models regarding the effect of unwanted excess positions on spreads. Unlike prior research, it assumes that dealers are risk-averse and that foreign exchange brokerage transactions occur continuously. Under the assumption of transaction continuity, the spread reflects the uncertainty of excess positions arising from incomplete brokerage of foreign exchange, rather than the uncertainty of inter-transaction time intervals. In this case, the relationship between uncertainty and spread transforms from a time dimension to a volume dimension. The most distinctive feature of this study is that the uncertainty in spread determination arises from the volatility of excess positions rather than from price volatility. In this study, as unwanted excess positions increase, dealers hold unwanted portfolios, thereby reducing their expected utility. The spread compensates dealers for the decrease in expected utility due to the risk of excess position fluctuations. The Maximum Likelihood estimation results of a GARCH(1,1) model using daily data from the Korean won/U.S. dollar market for the period from January 2, 2004, to June 29, 2004, strongly support the hypotheses of this study.