Beyond the 4% Rule: Flexible Withdrawal Strategies Using Certainty-Equivalent Spending

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Bill Bengen’s original "4% rule" (subsequently updated) says that you can invest 50/50 in stocks and bonds, withdraw 4% of your starting portfolio each year of retirement, adjust that number for inflation every year, and in a 30-year retirement, you would never have exhausted your money in any retirement cohort since 1928.

Bengen’s approach finds the highest withdrawal rate subject to a hard no-shortfall constraint.

Then I started thinking, what would happen if, instead of a hard no-shortfall constraint and a fixed withdrawal rate, we asked what flexible rule would maximize spending for different levels of risk aversion?

Using Python (a programming language with excellent data science, simulation, and optimization modules), I maximized certainty-equivalent spending, i.e. actual spending discounted by volatility, at different levels of risk aversion, using modern optimization frameworks.

This leads to us to a generalized set of rules, where:

  • The Bengen 4% rule is the infinite-risk-aversion solution that requires a fixed constant withdrawal level and never experiences any shortfall or reduction in withdrawals.
  • A risk-neutral rule finds the withdrawal amount that historically maximized spending irrespective of volatility, tolerating reductions in spending or shortfalls in some years, as long as they are offset by gains in other years (not recommended for most people).
  • In between, different levels of risk aversion lead to different rules that trade off higher mean withdrawals against the risk of lower worst-case withdrawals.

Here are a couple of example results first, and then I’ll explain in more detail what it means, and how it was computed: