Retirement Withdrawal Rate Simulation Study

Authors

Lucas Young

Van Godbold

Published

14 November 2023

Modified

23 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 is an extension of the Retirement Asset Allocation and Retirement Cash Buffer Simulation Studies linked below:

Retirement Asset Allocation Simulation Study

Retirement Cash Buffer Simulation Study

In the Retirement Asset Allocation Simulation Study, we quantified the trade-offs between various stock and bond asset allocations during both working / saving and retirement / spending years. We observed that high stock allocations resulted in the best average returns, the most volatility, and poor worst-case performance (through the Great Depression, for example).

In the Retirement Cash Buffer Simulation Study, we quantified the benefits of keeping a portion of retirement assets in cash and taking withdrawals from that cash during poor investment return years. We found that the optimal way to manage the cash buffer (with non-cash assets invested in 100% stock index funds / 0% bond index funds) was to target 4 years of spending in cash, spend cash in years with total investment returns below 20%, replenish any depleted cash in years with total investment returns above 20%, and cap single year cash liquidations to 2 years of spending.

In both of the aforementioned simulation studies, we used a 4% investment withdrawal rate. In this analysis, we’ll 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

Two data sources were used in this analysis:

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

    • https://www.slickcharts.com/sp500/returns

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

    • https://data.bls.gov/timeseries/CUUR0000SA0?years_option=all_years

Below are annualized summary plots of the data sources.




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 1926 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. These plots can be confusing at first glance. If this type of plot is unfamiliar to you, it might help to just look at the best case at the end, the worst-case at the end, and the average; be sure to pay close attention to the vertical axis scale which changes from one plot to the next.





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 (67 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 1926 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

    • 4 years of spending cash target

    • 20% minimum investment return threshold for deciding when to take withdrawals from cash vs investments and when to replenish cash

    • 2 years 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


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 5.97% failure rate with a 6% withdrawal.

    • With an optimal cash buffer and a 100% stock / 0% bond asset allocation, we saw a 4.48% failure rate with a 10% 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 $4.1M after a 30-year retirement.

    • With an optimal cash buffer and a 100% stock / 0% bond asset allocation, we saw an average decrease of $3.3M after a 30-year retirement.