Retirement Withdrawal Rate Simulation Study (Monthly Data)

Authors

Lucas Young

Van Godbold

Published

15 February 2024

Modified

22 February 2024

Disclaimer

  • This analysis is for informational and educational purposes only.

  • There could be bugs in our programmatic analysis. We are not liable for any actions you take as a result of anything you read below. Please conduct your own due diligence before making investment decisions.

  • Any decisions influenced by the information in this analysis are made at your own risk.

Overview

This analysis revisits the ideas presented in the withdrawal Retirement Withdrawal Rate Simulation Study linked below:

Retirement Withdrawal Rate Simulation Study

The Retirement Withdrawal Rate Simulation Study was conducted using annual data. We have since found monthly data and in this analysis will use it to quantify the effects of different withdrawal rates using an optimal cash buffer as well as no cash buffer.

Note: Cash is assumed to be held inside a tax advantaged account (401k, 403b, IRA, etc.) to avoid tax implications. All references to “stocks” should be interpreted to mean index funds of stocks rather than individual stocks (e.g. Google (GOOGL), Amazon (AMZN), Apple (AAPL), Deere and Co. (DE)).

Data

Four data sources were pieced together for this analysis:

  • https://datahub.io/core/s-and-p-500
  • https://www.gurufocus.com/economic_indicators/63/sp-500-index
  • https://www.gurufocus.com/economic_indicators/59/sp-500-dividends-per-share
  • https://fred.stlouisfed.org/series/CPIAUCSL

The combined data set contains the following information:

  • S&P 500 Total Return (price changes plus dividends, used to represent the stock portion of asset allocations)

  • Consumer Price Index (CPI) (used to make inflation adjustments to dollar values)

Below are month-over-month summary plots of the data sources.


S&P 500 Data







CPI Data







No Cash Buffer Withdrawal Rate Results

The following assumptions were used for the no cash buffer simulation:

  • Retirement length of 30 years

  • Starting retirement savings of $2.5M

  • Withdrawal rate is fixed based on initial account value

    • With a starting retirement savings of $2.5M, a 4% withdrawal rate would equate to a withdrawal of $100,000 during every year of the simulation (before inflation adjustment)

  • One 30-year simulation will be run starting each year from 1921 to 1993

  • All investment returns are reinvested

  • All invested dollars will have a 100% stock / 0% bond asset allocation

  • All plot and table values will be inflation adjusted to 2023 dollars

In the plots below, each gray line represents the simulation for a single start year. The red line is the mean value across all the simulated start years; the blue line is the median value across all the simulated start years.





No Cash Buffer Final Values



4% Withdrawal Rate, Descending


6% Withdrawal Rate, Descending


8% Withdrawal Rate, Descending


No Cash Buffer Comparison Plots

Next, we will compare the mean and median performance between the different withdrawal rates.



No Cash Buffer Failure Rate

Now that we’ve compared the range of outcomes and average performance for each withdrawal rate, let’s look at how the failure rates compare. A failure is defined as any start year where the account value hit zero at any point. Failure rate is calculated by dividing the number of failures by the total number of start years simulated (73 in this case).



Optimal Cash Buffer Withdrawal Rate Results

The following assumptions were used for the optimal cash buffer simulation:

  • Retirement length of 30 years

  • Starting retirement savings of $2.5M

  • Withdrawal rate is fixed based on initial account value

    • With a starting retirement savings of $2.5M, a 4% withdrawal rate would equate to a withdrawal of $100,000 during every year of the simulation (before inflation adjustment)

  • One 30-year simulation will be run starting each year from 1921 to 1993

  • All investment returns are reinvested

  • All invested dollars will have a 100% stock / 0% bond asset allocation

  • Optimal cash buffer parameters from Retirement Cash Buffer Simulation Study

    • 1 year of spending cash target

    • 3% minimum investment return threshold for deciding when to take withdrawals from cash vs investments and when to replenish cash

    • 1 year of spending maximum single year investment liquidation

  • All plot and table values will be inflation adjusted to 2023 dollars

In the plots below, each gray line represents the simulation for a single start year. The red line is the mean value across all the simulated start years; the blue line is the median value across all the simulated start years.










Optimal Cash Buffer Final Values



4% Withdrawal Rate, Descending


6% Withdrawal Rate, Descending


8% Withdrawal Rate, Descending


10% Withdrawal Rate, Descending


12% Withdrawal Rate, Descending


14% Withdrawal Rate, Descending


16% Withdrawal Rate, Descending


18% Withdrawal Rate, Descending


Optimal Cash Buffer Comparison Plots

Next, we will compare the mean and median performance between the different withdrawal rates.




Optimal Cash Buffer Failure Rate

Now that we’ve compared the range of outcomes and average performance for each withdrawal rate, let’s look at how the failure rates compare. A failure is defined as any start year where the account value hit zero at any point. Failure rate is calculated by dividing the number of failures by the total number of start years simulated (67 in this case).



Conclusions

The following conclusions should be interpreted within the confines of the simulation assumptions described in the sections above.

  • An optimal cash buffer will allow a considerably higher withdrawal rate with a similar probability of failure compared to an aggressive asset allocation (100% stock / 0% bond).

    • Without a cash buffer and a 100% stock / 0% bond asset allocation, we saw a 5.48% failure rate with a 6% withdrawal.

    • With an optimal cash buffer and a 100% stock / 0% bond asset allocation, we saw a 4.11% failure rate with a 16% withdrawal.

  • Each 2% increase in withdrawal rate substantially decreased average account value.

    • Without a cash buffer and a 100% stock / 0% bond asset allocation, we saw an average decrease of $4.3M after a 30-year retirement.

    • With an optimal cash buffer and a 100% stock / 0% bond asset allocation, we saw an average decrease of $1.7M after a 30-year retirement.