A Mathematical Framework for Sequence Risk
摘要
Sequence risk refers to the dependence of terminal wealth on the order in which a fixed set of returns is realized. It is present whenever an investor contributes to or withdraws from a portfolio during the investment horizon and is absent when there are no intermediate cash flows.
This paper derives a second-order approximation for the expected value and variance of terminal wealth under uniform permutations of a fixed return multiset. Both moments reduce to closed-form expressions involving two quantities: the within-multiset variance of returns and a measure of how capital exposure is distributed across time. The ratio of the two moments gives a Sequence Sensitivity Index that summarizes path dependence in a single coefficient of variation and does not require enumerating permutations.
Monte Carlo experiments confirm the approximations in decumulation, accumulation, and zero-cash-flow regimes, and indicate the horizons and dispersion levels at which the second-order truncation loses accuracy.