*Published by Nicholas McCullum on April 8th, 2017*

Many investors purchase stocks with the intent of building wealth for retirement.

One natural question that occurs with regard to retirement planning is “how large should my portfolio be to retire?“

The easiest answer to this question comes from the 4% rule, which states that a retiree should withdraw 4% of their nest egg each year to pay for life’s expenses. 4% is deemed a safe rate, with retirement distributions ideally being composed mostly of dividends and interest payments.

Working backward, an investor can determine the necessary size of their retirement portfolio by multiplying their anticipated retirement expenses by 25x (which is the inverse of 0.04 – four percent).

Whether the 4% rule is accurate or not depends on the returns generated by an individual’s portfolio. If a retirement portfolio returns only 1% per year, then 4% annual withdrawals will inevitably reduce the portfolio’s balance to 0. On the other hand, 20% annual returns will allow the portfolio to continue to grow even with 4% annual withdrawals.

Fortunately, we can empirically test this withdrawal policy by running simulations based on the historical returns in the stock market.

This article will assess the validity of the 4% rule when it is applied to a portfolio of dividend stocks using a Monte Carlo simulation.

**Assumptions**

As with any statistical analysis, this article makes use of a few assumptions to make predictions feasible. These assumptions will be outlined in this section.

First, stock market returns are assumed to be normally distributed. What this means is that stock market returns are expected to be bell-shaped, centered around some mean with a predetermined standard deviation. The shape of a typical normal distribution can be seen below.

In practice, stock market returns are not *really* normally distributed. Stock market returns generally contain more outliers than the normal distribution accounts for, which results in the ‘tails’ of the normal distribution being smaller than the real distribution of stock market returns.

This is called the ‘fat tail’ phenomenon and is not ideal because it underestimates the probably of adverse market events like the financial crisis in 2008-2009.

The fat tail phenomenon is widespread, and has been seen in different asset classes including emerging market equities, U.S. REITs, hedge funds, and private equity. The distributions of the returns of each of these asset classes (including the fat tail phenomenon) can be seen below.

Source: JP Morgan Asset Management

With that being said, the normal distribution is still an adequate proxy for stock market returns and will be used in this analysis.

Next, I must determine a benchmark for the returns and volatility of dividend stocks. The Dividend Aristocrats is one of Sure Dividend’s first recommendations for a universe of high-quality dividend stocks because it contains only companies with 25+ years of consecutive dividend increases.

You can see the list of all 51 Dividend Aristocrats here.

To model the behavior of the Dividend Aristocrats, my first choice for a benchmark would be the ProShares S&P 500 Dividend Aristocrats ETF (NOBL).

This ETF seeks to replicate the Dividend Aristocrats exactly and is equally-weighted (rather than weighted by market cap). The ETF is rebalanced only four times per year to minimize the transaction costs associated with buying and selling stocks. Generally speaking, the NOBL ETF should mimic the Dividend Aristocrats plus or minus some small tracking error.

However, this fund’s inception date is in October of 2013. It has a relatively short track history as an investment vehicle. Assessing the validity of the 4% rule using the historical returns of NOBL would not be accurate because the fund has not gone through a serious market downturn.

Instead of NOBL, I will be using the Vanguard Dividend Appreciation ETF (VIG). This fund seeks to mimic the performance of the Dividend Achievers index, a group of stocks with 10+ years of consecutive dividend increases.

You can see the list of all 265 Dividend Achievers here.

VIG should suffice as a proxy for the behavior of dividend stocks in general. It tracks the behavior of the Dividend Achievers almost exactly.

Source: Vanguard Website

VIG was also founded in April of 2006, giving it a much longer track record than the NOBL ETF. To model the expected future behavior of dividend stocks, I will fit a normal distribution through the historical mean and standard deviation of the VIG ETF.

**Assessing the 4% Rules Using Dividend Stock Returns**

The first step in assessing the 4% rule is to download some data to base our model off of.

Downloading the VIG data from Yahoo! Finance as an Excel document is very straightforward. For this analysis, I will be using monthly data as most retirees will be withdrawing money on either a monthly or biweekly basis. You can download the monthly return history of the VIG ETF that I am using in this analysis by clicking here.

Some quick Excel math tells us that the VIG ETF has a mean monthly return of 0.72% with a standard deviation of 4.33%.

If we account for 4% annual withdrawals (which is equivalent to 0.33% spread evenly over 12 months), then the mean monthly returns after withdrawals are 0.39% with the same standard deviation of 4.33% (translating the mean left or right does not affect the standard deviation of a probability distribution). Notice that the mean monthly returns *after accounting for withdrawals* are still positive, which indicates that portfolios should still grow over time *on average*.

However, a retiree should ideally withdraw more money each year to account for the effect of inflation on consumer’s purchasing power. As such, I have increased distributions by 3% each year to account for this.

Next, I must make an assumption about the amount of time that the average person spends in retirement. The average person retires somewhere between age 62 and 65 and the mean life expectancy in the United States is 79 years. As such, this analysis will use a time sample of 17 years (the difference between 62 and 79).

I chose 62 instead of 65 (or some other number) as the starting date for the average retirement because I wanted to be conservative in my estimations. Being on the safe side when it comes to financial forecasting is always the best choice.

Using this information, I used R to run one million trials of a Monte Carlo simulation modeled after VIG for a 17-year retirement horizon. You can view the R code I used to run this simulation by clicking here.

For simplicity’s sake, I assumed an initial portfolio value of $10,000, although the results would have been the same with any initial portfolio value because the returns and withdrawals are based on percentages rather than any absolute numbers.

The results were quite positive and can be seen below.

Since the mean return of the portfolio’s return distribution is positive, it should be no surprise that there are more results north of the initial portfolio value ($10,000) then there are below the initial portfolio value.

There were also a few statistical outliers that were amusing to see – the best return generated by this simulation turned $10,000 into $588,269.80 after 17 years. The median value was more believable – $26,415.68.

Unfortunately, there are a number of negative final portfolio values, which in reality would indicate that the retiree runs out of money and would have to find ways of generating new capital to cover expenses (probably through re-entering the workforce).

All said, there were 14,817 negative portfolio values in the sample, which equates to a relatively minor ~1.5% chance of running out of retirement money if invested fully in dividend stocks.

**Final Thoughts**

A brief analysis indicates that investors have only a very minor ~1.5% probability of running out of retirement money if they apply the 4% rule to a portfolio of dividend stocks and increase their portfolio withdrawals by 3% each year.

Since this probability is so low, very conservative investors might be interested in allocating some capital to lower-risk asset classes such as fixed income. While this will reduce portfolio volatility, it might actually increase the probability of running out of money because of the lower inherent returns.

Investors concerned about volatility might be better off investing in stocks that are known to have low volatility, which deliver better returns than fixed income instruments on a risk-adjusted basis.