The authors examine how the use of extreme value theory yields collateral requirements that are robust to extreme fluctuations in the market price of the asset used as collateral. In particular, they study the risk and cost attributes of market risk measures by constructing a risk-cost frontier for the collateral pledged to cover exposures in a securities settlement system. The frontier can be used as a diagnostic tool to understand the risk-cost trade-off of different methodologies to calculate collateral value (haircuts) and select the most efficient alternative in a variety of settings.