Importance sampling for tail risk in discretely rebalanced portfolios

Authors:
Paul Glasserman;Xingbo Xu
Affiliations:
Columbia University, New York, NY;Columbia University, New York, NY
Venue:
Proceedings of the Winter Simulation Conference
Year:
2010

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Abstract

We develop an importance sampling (IS) algorithm to estimate the lower tail of the distribution of returns for a discretely rebalanced portfolio --- one in which portfolio weights are reset at regular intervals. We use a more tractable continuously rebalanced portfolio to design the IS estimator. We analyze a limiting regime based on estimating probabilities farther in the tail while letting the rebalancing frequency increase. We show that the estimator is asymptotically efficient for this sequence of problems; its relative error grows in proportion to the fourth root of the number of rebalancing dates.