We explore how to manage a portfolio of passwords. We review why mandating exclusively strong passwords with no re-use gives users an impossible task as portfolio size grows. We find that approaches justified by loss-minimization alone, and those that ignore important attack vectors (e.g., vectors exploiting re-use), are amenable to analysis but unrealistic. In contrast, we propose, model and analyze portfolio management under a realistic attack suite, with an objective function costing both

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... s and user effort. Our findings directly challenge accepted wisdom and conventional advice. We find, for example, that a portfolio strategy ruling out weak passwords or password re-use is sub-optimal. We give an optimal solution for how to group accounts for re-use, and model-based principles for portfolio management.