How Much Do I Need to Retire? When It’s Safe Enough to Start Spending..

Most retirement advice suggests you can safely withdraw 4% of your savings annually, but what if that number isn’t as foolproof as it seems? Whether you're aiming for FIRE (Financial Independence, Retire Early) or planning a traditional retirement, you’re probably wondering: Will my savings actually last? What if there were a more flexible, evidence-based formula for deciding how much you can afford to spend each year?

This is where Merton’s "1/e" rule comes in. This simple rule, derived from complex economic modeling, offers a surprisingly practical way to calculate sustainable withdrawals. All you need to know is how much you’ve saved ("W" - your wealth) and how long you expect to live ("e" - remaining life expectancy). Simple.

1. The Spending Rule: W/e

The "1/e" rule simplifies complex retirement planning by providing a straightforward approach to sustainable annual spending. In this formula, "W" represents your total wealth or retirement savings, and "e" denotes your remaining life expectancy, often based on actuarial data or personal health factors. This approach stems from Merton’s portfolio model, which goes beyond the single-period focus of Modern Portfolio Theory (MPT). Unlike MPT, Merton’s model adapts both spending and asset allocation over time, adjusting in response to market performance and changing personal needs -

The rule annual retirement portfolio consumption = W / e proposes that retirees should divide their wealth by their remaining life expectancy to determine a sustainable annual withdrawal. Here’s how this model works in practice:

• If you’re 60 and life expectancy is about 25 more years (e ≈ 25), then you would withdraw 4% of your portfolio each year.
• As you age, "e" decreases, meaning the withdrawal amount grows relative to remaining assets, creating a gradual increase in income with age.

The simplicity of the W/e formula laid in intuitive financial guidance while factoring in diminishing life expectancy. It balances the two opposing risks of spending too quickly (risking depletion) and spending too slowly (risking underconsumption). While this rule might need slight adjustments depending on market conditions, growth assumptions, or personal financial circumstances, it provides a solid baseline.

2. Merton’s Model: Adding Asset Allocation to the Equation

The W/e rule is even more effective when combined with a tailored asset allocation approach. In Merton’s model, the proportion of stocks in your portfolio adjusts based on your future income (e.g., pensions or Social Security). This future income is treated as a stabilizing “bond-like” component, offsetting the volatility of stocks. The model suggests:

Why It works:

• Future Income as a Stabilizer: When future income (like a pension) is significant, more risk can be taken with stocks. This bond-like income acts as a buffer against market downturns.
• Conservative Adjustment: When future income is minimal, a more conservative bond-heavy allocation is preferred to protect against market risk.

For example, if a retiree has a pension equal to half their wealth, this approach would suggest around a 75% allocation to stocks. Conversely, if future income is minimal, the model leans more conservatively.

3. Why Choose W/e Over Complex Models?

Despite being based on sophisticated models, the W/e rule is remarkably effective without the need for complex inputs. Here’s why it holds up so well:

• Minimal Assumptions: W/e and the adaptive allocation rule don’t rely on precise inputs like discount rates or risk preferences, making them broadly applicable and easy to implement.
• Near-Optimal Performance: In empirical tests, the simple W/e rule performs similarly to more complex methods for moderate portfolios. More advanced techniques like Stochastic Dynamic Programming (SDP) may theoretically improve performance, but only by marginal amounts and often at the cost of practicality.
• Natural Adjustments to Longevity and Portfolio Growth: The interplay between longevity risk and portfolio growth tends to offset each other, making the simple rule resilient to changing circumstances without the need for precise adjustments.

4. Alternatives and Limitations of the W/e Rule

While W/e is a strong general rule, there are alternative approaches that may slightly outperform it in specific scenarios:

• Variable Percentage Withdrawal (VPW): This method performed about 1% better in certain tests, though W/e is still competitive.
• W / max(e, 8): This modification prevents overly high spending at advanced ages by assuming a minimum life expectancy of 8 years, providing a safety net for longevity risk.

Potential Limitations: The W/e rule may be less effective when:

• Interest rates rise significantly, requiring more nuanced discounting of future income.
• Consumption preferences change (e.g., aiming to leave a bequest), which may not align with the straightforward withdrawal model.
• Risk tolerance fluctuates: Adjustments may be needed if consumption satisfaction changes or if longevity expectations shift unexpectedly.

5. Practical Application W/e to Life Expectancy Tables

For practical use, you can determine "e" based on actuarial life tables or adjust it according to personal health and lifestyle. Sites like aacalc.com , founded by Gordon Irlam, provide life expectancy tables and tools to help visualize "1/e" over time, helping individuals make informed decisions based on their specific situations.