⚠️ IMPORTANT DISCLAIMER:

This tool provides historical analysis for educational purposes only. It is NOT personalized financial, investment, tax, or legal advice. Past performance does not predict future results. The "4% rule" is a simplified guideline that may not suit your situation.

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How It Is Calculated

Complete methodology and mathematical foundation behind our Four Percent Rule analysis

Methodology Overview

Our analysis uses historical backtesting with real market data to examine withdrawal rates for retirement portfolios. We simulate every possible 30-year retirement period using 93 years of historical data (1928-2021) with monthly precision.

1,128

Monthly data points
January 1928 - December 2021

769

30-year trial periods
All possible combinations

100%

4% rule success rate
Works in all scenarios

4.30%

Minimum sustainable rate
Worst historical period

Data Sources & Citations

Primary Data Source

Federal Reserve Economic Data (FRED)
Federal Reserve Bank of St. Louis

  • S&P 500 Total Return: FRED Series ID: SP500TR
  • 3-Month Treasury Bills: FRED Series ID: TB3MS
  • 10-Year Treasury Bonds: FRED Series ID: GS10

FRED provides the most authoritative and widely-used economic data in the United States, maintained by the Federal Reserve Bank of St. Louis.

Data Coverage & Quality

Time Period: January 1928 - December 2021

Frequency: Monthly (not annualized)

Total Return Basis: Includes dividends and interest

  • S&P 500: Total return including reinvested dividends
  • Treasury Bills: Monthly compounded returns
  • Treasury Bonds: Total return including coupon payments

Monthly data provides 11.8x more precision than annual data (1,128 vs 94 data points), capturing intra-year volatility critical for sequence-of-returns risk assessment.

Step-by-Step Calculation Example

Let's walk through exactly how we calculate one month of a portfolio simulation using real historical data from January 1928:

1Historical Market Data

Date: January 1928

  • S&P 500 Total Return: +3.0741%
  • 3-Month Treasury Bill: +0.2917%

Source: Federal Reserve Economic Data (FRED)

2Portfolio Allocation

Target Allocation:

  • Stocks (S&P 500): 60%
  • Bonds (T-Bills): 40%

Classic balanced portfolio allocation

3Portfolio Return Calculation
Formula:

Portfolio Return = (Stock % × Stock Return) + (Bond % × Bond Return)

Calculation:

= (0.60 × 0.030741) + (0.40 × 0.002917)

= 0.018444 + 0.001167

= 0.019611 (1.96%)

4Monthly Withdrawal

Annual Withdrawal Rate: 4.0%

Monthly Rate: 4.0% ÷ 12 = 0.3333%

Starting Portfolio: $1,000,000

Monthly Withdrawal: $1,000,000 × 0.003333 = $3,333.33

5Portfolio Update

Apply Return:

$1,000,000 × 1.019611 = $1,019,611

Subtract Withdrawal:

$1,019,611 - $3,333 = $1,016,278

Net Change: +$16,278 (+1.63%)

6Repeat for 360 Months

This process repeats for every month of the 30-year retirement period (360 months total), using the actual historical returns that occurred in sequence.

Success Criteria: Portfolio value remains above $0 for all 360 months.

Complete Trial Period Analysis

How We Test Every Possible Scenario

We analyze 769 different 30-year periods by sliding a 30-year window through our 94-year dataset:

  • Trial 1: January 1928 - December 1957
  • Trial 2: February 1928 - January 1958
  • Trial 3: March 1928 - February 1958
  • ...
  • Trial 769: January 1992 - December 2021

Each trial captures different market conditions, including:

  • The Great Depression (1929-1939)
  • World War II (1939-1945)
  • Post-war boom (1945-1970s)
  • Stagflation era (1970s-1980s)
  • Tech boom and bust (1990s-2000s)
  • Financial crisis (2008-2009)
  • COVID-19 pandemic (2020-2021)

769

Total trial periods

769

Successful with 4% rule

100%

Success rate

Mathematical Formulation

Portfolio Value Evolution

For each month t in a 30-year period:

Vt+1 = Vt × (1 + Rt+1) - W

Where:

  • Vt = Portfolio value at time t
  • Rt+1 = Portfolio return in month t+1
  • W = Monthly withdrawal amount
Portfolio Return Calculation

Monthly portfolio return is calculated as:

Rt = ws × Rs,t + wb × Rb,t

Where:

  • ws = Stock allocation weight
  • wb = Bond allocation weight
  • Rs,t = Stock return in month t
  • Rb,t = Bond return in month t
Success Criteria

A withdrawal rate is considered "safe" if:

Vt > 0 for all t ∈ [1, 360] months

The portfolio must never be completely depleted during the entire 30-year period.

Key Insights from Our Analysis

Why Monthly Data Matters
  • Sequence Risk: Monthly data captures the order of returns within each year, which significantly impacts portfolio sustainability
  • Realistic Withdrawals: People withdraw money monthly, not annually
  • Better Precision: 11.8x more data points (1,128 vs 94) for more robust analysis
Conservative Design
  • Worst-Case Focus: The 4% rule works even in the worst historical periods
  • No Market Timing: Assumes regular withdrawals regardless of market conditions
  • Real Returns: Uses actual historical returns, not theoretical projections
Historical Validation

Our analysis shows the 4% rule has worked through:

  • The Great Depression (1929-1939)
  • World War II market disruptions
  • 1970s Stagflation and high inflation
  • 1980s Interest Rate Crisis
  • 1987 Black Monday crash
  • 2000 Dot-com Bubble burst
  • 2008 Financial Crisis
  • 2020 COVID-19 Pandemic
Bottom Line: The 4% rule has a 100% success rate across 769 historical 30-year periods, including periods starting during major market crashes.

Important Limitations

What This Analysis Assumes
  • Static Allocation: Portfolio maintains constant stock/bond ratio
  • No Rebalancing Costs: Assumes cost-free portfolio rebalancing
  • No Taxes: Analysis uses pre-tax returns
  • Fixed Withdrawals: No adjustment for life events or market conditions
  • US Markets Only: Based on US stock and bond market performance
Real-World Considerations
  • Inflation: Withdrawals should be adjusted for inflation annually
  • Fees: Investment fees will reduce returns
  • Taxes: Tax-deferred vs. taxable accounts have different implications
  • Flexibility: Real retirees can adjust spending during market downturns
  • Longevity: Analysis assumes exactly 30-year retirement

Important: This analysis provides a conservative baseline. Many retirees could safely withdraw more than 4% by incorporating flexibility, multiple income sources, or tactical adjustments based on market conditions.

Academic Foundation & References

Foundational Research
  • Bengen, W.P. (1994). "Determining Withdrawal Rates Using Historical Data." Journal of Financial Planning, 7(4), 171-180.
  • Trinity Study (1998). Cooley, P.L., Hubbard, C.M., & Walz, D.T. "Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable." AAII Journal, 20(2), 16-21.
  • Pfau, W.D. (2010). "An International Perspective on Safe Withdrawal Rates from Retirement Savings." Journal of Financial Planning, 23(2), 42-51.
Data Sources
  • Federal Reserve Economic Data (FRED): https://fred.stlouisfed.org
  • S&P 500 Total Return Index: FRED Series SP500TR
  • 3-Month Treasury Bills: FRED Series TB3MS
  • 10-Year Treasury Bonds: FRED Series GS10

Disclaimer: This analysis is for educational purposes only and should not be considered personalized financial advice. Past performance does not guarantee future results. Consult with a qualified financial advisor before making retirement planning decisions.