The Cost of Resilience

A median U.S. service worker earns $2,500.08 a month. Of that, $2,385.69 is allocated to essential spending, leaving $114.39 of free cash flow. The standard financial advice is to build an emergency fund of three months of expenses before doing anything else. It would take the median service worker 62.07 months to reach this target. This paper asks where that $114.39 should go. It formulates the choice among liquid savings, debt repayment, and risky investment as a two-stage stochastic mixed-integer program with a Conditional Value-at-Risk penalty on the worst five percent of outcomes over a 24-month horizon. Monthly income is determined through a five-state Markov chain fitted to Current Population Survey microdata. Each state's level is drawn non-parametrically. Balance sheets and credit access are taken from the Survey of Consumer Finances. Based on the data three archetypes are calibrated: a salaried professional, a gig worker, and a service worker.

Precautionary cash saving is optimal in a single-period version of the model, activating at risk-aversion weights of 3.25 to 6.50, and never optimal over 24 months at any weight tested up to 30. When given an extended time horizon, the household draws its credit line once and invests the proceeds in the higher-returning account. Regardless of the risk level, the gig worker and service worker archetypes draw that line to 100% of capacity. Emergency-fund-first requires an income above the median of both groups before it clears their debt within the horizon.