Waiting to Borrow From a 457(b) Plan

This paper formulates and solves the optimal stopping problem for a loan made to one's self from a tax-advantaged retirement account such as a 401(k), 403(b), or 457(b) plan. If the plan participant has access to an external asset with a higher expected rate of return than the investment funds and indices that are available within the retirement account, then he must decide how long to wait before exercising the loan option. On the one hand, taking the loan quickly will result in many years of exponential capital growth at the higher (external) rate; on the other hand, if we wait to accumulate more funds in the 457(b), then we can make a larger deposit into the external asset (albeit for a shorter period of time). I derive a variety of cutoff rules for optimal loan control; in general, the investor must wait until he accumulates a certain amount of money (measured in contribution-years) that depends on the disparate yields, the loan parameters, and the date certain at which he will liquidate the retirement account. Letting the horizon tend to infinity, the optimal (horizon-free) policy gains in elegance, simplicity, and practical robustness to different life outcomes. When asset prices and returns are stochastic, the (continuous time) cutoff rule turns into a "wait region," whereby the mean of terminal wealth is rising and the variance of terminal wealth is falling. After his sojourn through the wait region is over, the participant finds himself on the mean-variance frontier, at which point his subsequent behavior is a matter of personal risk preference.