This is a matter where Monte Carlo simulations are able to shine, by allowing simulations to begin from today’s starting point rather than incorporating historical outcomes generated from completely different market environments.

Let’s consider outcomes for sustainable spending rates using the Monte Carlo simulations with the low-interest-rate world of today as a starting point for the simulations. We will not make any additional adjustments to reflect the high stock market valuation level, but we will preserve the historical equity premium that stocks have earned above bonds.

So when bond yields are low, stock returns must be less as well, as there is no particular reason to believe that stocks would offer even higher premiums above bonds than they have done in the past. On average, these simulations allow bond yields (and therefore stock and bond returns) to wander upward toward historical averages over time to reflect the unlikelihood that interest rates would remain low for the next thirty years or longer.

But interest rates could remain low and some simulations account for this.

Exhibit 1 provides a way to compare the success rates for the 4% rule using Monte Carlo simulations that reduce bond yields at the start of retirement. This is compared with simulations calibrated to historical averages, as well as to the results of rolling period historical simulations.

This exhibit makes clear that the low interest rate environment creates additional stresses for the 4% rule that were not apparent in Monte Carlo simulations calibrated to historical data with higher bond-yield assumptions than are available today. For a 50/50 asset allocation to stocks and bonds, these simulations indicate that the 4% rule has a 69% chance of success instead of a 94% chance. The 4% rule may work for today’s retirees, but it is far from a sure bet or a “safe” spending strategy.

With lower stock allocations, the 4% rule is less likely to work because it is placing demands on spending above what today’s interest rate environment can easily support. It is magical thinking to believe that bonds can earn higher rates of return than implied by today’s low-interest-rate environment.

Returning to the issue of sequence of returns risk for retirees, the early returns matter disproportionately in determining sustainable spending outcomes. Success is also less for higher stock allocations because of the assumption that the historical equity premium is maintained on top of a lower bond yield for the early part of retirement.

Exhibit 1

Portfolio Success Rates for a 4% Withdrawal Rate

Rolling vs. Monte Carlo Simulations

For a 30-Year Retirement, Inflations Adjustments

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Exhibit 2 provides further details by plotting failure rates (instead of success rates) for different withdrawal rates and asset allocations, using the same Monte Carlo simulations that reflect the lower interest rate environment of today. Failure for a 3% withdrawal rate hovers at about 10% for stock allocations between 40% and 100%.

This suggests that in a lower interest rate world, a 3% withdrawal rate reflects something closer to a chance of success than a 4% withdrawal rate historically provided over the broad range of historical market environments. With higher withdrawal rates, failure rates increase accordingly.

In addition, when spending rises above what the bond yield curve is able to support, bond allocations will tend to lock in failure. This explains why the 100% stock allocations support the lowest failure rates when spending rates are 4% or more.

Exhibit 2

Failure Probabilities for Inflation-Adjusted Withdrawal Strategies

Over a 30-Year Retirement Horizon

Monte Carlo Simulations Calibrated to Current Market Conditions

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