## Paul Glasserman

### “Importance Sampling for Tail Risk in Discretely Rebalanced Portfolios”

Coauthor(s): Xingbo Xu.

**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.

**Source:** *Proceedings of the 2010 Winter Simulation Conference*

**Exact Citation:**

Glasserman, Paul, and Xingbo Xu. "Importance Sampling for Tail Risk in Discretely Rebalanced Portfolios." In *Proceedings of the 2010 Winter Simulation Conference*, 2655-2665. Baltimore, MD: IEEE, 2010.

**Pages:** 2655-2665

**Place:** Baltimore, MD

**Date:**
2010