Accesso libero

Revisiting the 4% Withdrawal Rule Using Monte Carlo Simulations with Random Market Declines

Nabil Tamimi

Nabil Tamimi

Professor, Operations & Analytics Department, University of Scranton
Cerca questo autore su
Sciendo|Google Scholar
Tamimi, Nabil
, 
Rose Sebastianelli

Rose Sebastianelli

Professor, Operations & Analytics Department, University of Scranton
Cerca questo autore su
Sciendo|Google Scholar
Sebastianelli, Rose
, 
Murli Rajan

Murli Rajan

Economics and Finance Department, University of Scranton
Cerca questo autore su
Sciendo|Google Scholar
Rajan, Murli
 e 
Vincent Rocco

Vincent Rocco

Faculty Specialist, Operations & Analytics Department, University of Scranton
Cerca questo autore su
Sciendo|Google Scholar
Rocco, Vincent
  
17 dic 2024
Revisiting the 4% Withdrawal Rule Using Monte Carlo Simulations with Random Market Declines's Cover Image
INFORMAZIONI SU QUESTO ARTICOLO
Articolo precedente
Articolo Successivo
Cita
Scarica la copertina
Pubblicato online: 17 dic 2024
DOI: https://doi.org/10.2478/fprj-2024-0001
Parole chiave
© 2024 Nabil Tamimi et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1:

Weibull Distribution of S&P 500 Historic Returns.Note: the Weibull distribution (mean = 11.60%, standard deviation = 18.77%) is used to simulate yearly equity growth rates. This distribution is skewed to the left, which allows for the simulation of large negative values, thereby mimicking historical returns.
Weibull Distribution of S&P 500 Historic Returns.Note: the Weibull distribution (mean = 11.60%, standard deviation = 18.77%) is used to simulate yearly equity growth rates. This distribution is skewed to the left, which allows for the simulation of large negative values, thereby mimicking historical returns.

Figure 2:

Logistic Distribution of US T-Bonds Historic Returns.Note: the Logistic distribution (mean = 4.40%, standard deviation = 7.39%) is used to simulate US T-Bonds returns. The shape of the logistic distribution is similar to that of the normal distribution but with relatively longer tails.
Logistic Distribution of US T-Bonds Historic Returns.Note: the Logistic distribution (mean = 4.40%, standard deviation = 7.39%) is used to simulate US T-Bonds returns. The shape of the logistic distribution is similar to that of the normal distribution but with relatively longer tails.

Figure 3:

Logistic Distribution of Baa Bonds Historic Returns.Note: Like the distribution of US T-bonds, the Logistic distribution (mean = 6.75%, standard deviation = 7.33%) is used to simulate Baa bonds returns.
Logistic Distribution of Baa Bonds Historic Returns.Note: Like the distribution of US T-bonds, the Logistic distribution (mean = 6.75%, standard deviation = 7.33%) is used to simulate Baa bonds returns.

Figure 4:

Lognormal Distribution of Historic Inflation Rates.Note: The lognormal distribution is used to simulate inflation rates. The distribution is positively skewed, with a mean inflation rate of 3.70% and a standard deviation of 2.66%. Simulated inflation rates allow for an adaptive withdrawal strategy that responds to the prevailing inflation environment.
Lognormal Distribution of Historic Inflation Rates.Note: The lognormal distribution is used to simulate inflation rates. The distribution is positively skewed, with a mean inflation rate of 3.70% and a standard deviation of 2.66%. Simulated inflation rates allow for an adaptive withdrawal strategy that responds to the prevailing inflation environment.

Figure 5:

Single Simulation Run with Two Market Crashes and 15% Portfolio Decline in Each Instance.Note: This figure illustrates a single trial example for a 70% equities – 30% bonds allocation where two simulated market crashes (i.e., portfolio declines) occur, one at age 67 and the other at age 89. Each decline results in a 15% decrease in portfolio value. The simulated returns on assets and inflation rates are generated from their respective distributions, as indicated by their mean values. The ending balance is calculated by deducting the withdrawal amount from the beginning balance and then adjusting it with the simulated returns. The adjusted ending balance checks whether the ending balance column is negative. If the value is negative, then the adjusted ending column corrects the value to zero. Otherwise, a negative ending balance will be carried over to the next period’s beginning balance.
Single Simulation Run with Two Market Crashes and 15% Portfolio Decline in Each Instance.Note: This figure illustrates a single trial example for a 70% equities – 30% bonds allocation where two simulated market crashes (i.e., portfolio declines) occur, one at age 67 and the other at age 89. Each decline results in a 15% decrease in portfolio value. The simulated returns on assets and inflation rates are generated from their respective distributions, as indicated by their mean values. The ending balance is calculated by deducting the withdrawal amount from the beginning balance and then adjusting it with the simulated returns. The adjusted ending balance checks whether the ending balance column is negative. If the value is negative, then the adjusted ending column corrects the value to zero. Otherwise, a negative ending balance will be carried over to the next period’s beginning balance.

Figure 6:

Projected Retirement Portfolio Value at Age 93: Median and Standard Deviation Across Different Asset Allocations and Market Crashes.Note: The figure displays the median and standard deviation performance metrics for each asset within a hypothetical portfolio subject to both a decline and an increased frequency of market crashes.
Projected Retirement Portfolio Value at Age 93: Median and Standard Deviation Across Different Asset Allocations and Market Crashes.Note: The figure displays the median and standard deviation performance metrics for each asset within a hypothetical portfolio subject to both a decline and an increased frequency of market crashes.

Figure 7:

Autocorrelation Functions for SP 500.Note: The figure displays the autocorrelation function for various market assets using lag periods ranging from 1 to 12 years.
Autocorrelation Functions for SP 500.Note: The figure displays the autocorrelation function for various market assets using lag periods ranging from 1 to 12 years.

Projected Retirement Portfolio Value at Age 93: Average Balance and Probability of Fund Running Out of Across Different Asset Allocations and Market Crashes

Two Market Crashes
Allocation: 50% Stocks - 50% Bonds Allocation: 60% Stocks - 40% Bonds Allocation: 70% Stocks - 30% Bonds
Portfolio Decline Average Ending Balance Probability of Fund Running Out of Money at Age 93 Portfolio Decline Average Ending Balance Probability of Fund Running Out of Money at Age 93 Portfolio Decline Average Ending Balance Probability of Fund Running Out of Money at Age 93
5% $2,572,924 22% 5% $3,440,807 21% 5% $4,448,100 20%
10% $2,098,119 27% 10% $2,866,918 25% 10% $2,773,931 24%
15% $1,684,465 33% 15% $2,341,817 30% 15% $3,110,075 28%
Three Market Crashes
Allocation: 50% Stocks - 50% Bonds Allocation: 60% Stocks - 40% Bonds Allocation: 70% Stocks - 30% Bonds
Portfolio Decline Average Ending Balance Probability of Fund Running Out of Money at Age 93 Portfolio Decline Average Ending Balance Probability of Fund Running Out of Money at Age 93 Portfolio Decline Average Ending Balance Probability of Fund Running Out of Money at Age 93
5% $1,998,895 27% 5% $2,691,420 25% 5% $3,537,160 24%
10% $1,427,056 37% 10% $2,009,766 32% 10% $2,685,524 30%
15% $968,235 46% 15% $1,445,437 41% 15% $1,976,380 38%
Four Market Crashes
Allocation: 50% Stocks - 50% Bonds Allocation: 60% Stocks - 40% Bonds Allocation: 70% Stocks - 30% Bonds
Portfolio Decline Average Ending Balance Probability of Fund Running Out of Money at Age 93 Portfolio Decline Average Ending Balance Probability of Fund Running Out of Money at Age 93 Portfolio Decline Average Ending Balance Probability of Fund Running Out of Money at Age 93
5% $1,526,137 33% 5% $2,133,393 30% 5% $2,777,253 29%
10% $953,182 46% 10% $1,380,912 41% 10% $1,903,689 38%
15% $569,125 59% 15% $850,908 53% 15% $1,233,732 48%

Pairwise Pearson Correlation Coefficients

Sample 1 Sample 2 Correlation (r) P-Value
UST. Bond S&P500 0.02 0.87
Baa Bonds S&P500 0.40 0**
Inflation S&P500 −0.16 0.12
Baa Bonds US T. Bond 0.60 0**
Inflation US T. Bond −0.09 0.42
Inflation Baa Bonds −0.20 0.05*
Lingua:
Inglese
Frequenza di pubblicazione:
2 volte all'anno
Argomenti della rivista:
Economia e business, Economia politica, Teoria economica, sistemi e strutture, Business management, Business Management, altro, Settori, Banche, servizi finanziari, assicurazioni
Feed RSS della rivista