Merton dynamic withdrawal calculator

Merton (1969) solved the risky share and consumption together. This page uses the teaching form: myopic share from risk aversion, then a remaining-horizon annuity at the implied return.

The calculator

Risky share78%(premium) / (γ × variance), clamped to 0–100%
Implied return4.1%
First-year spending$54,490
Ending portfolio$0
Success rate100%1000 seeded paths of this rule — last-year spend-down is not ruin
10th percentile last-year spend$11,215
Median last-year spend$38,849
90th percentile last-year spend$123,436

The two pieces

The risky share is (μ − r) / (γ σ²). A 4% premium, γ of 2 and 16% volatility is 78% equities. The implied portfolio return is then r + share × premium, and spending is the same remaining-horizon annuity VPW uses. Completing the nine-rule set; not a continuous-time solver.

Assumptions

No labour income, no fees, no taxes, share clamped to 100%. See the withdrawal hub for the rest of the set.

Frequently asked questions

What is a Merton withdrawal?
Merton (1969) solved optimal consumption and the risky share for a CRRA investor. This calculator uses the myopic share (equity premium) / (risk aversion × variance) and spends the remaining-horizon annuity at the implied return.
Is this the full continuous-time solution?
No. It is the finite-horizon teaching form: one risky share, one implied return, VPW-style spending. Enough to complete the withdrawal-rule set; not a research solver.
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