[*T**his is a letter we sent to clients on September 9. It discusses a retirement issue important enough that it should be shared with the investing public.*]

In our September 8th post, we discussed the outlook for lower portfolio returns over the next 10-20 years due to reversion to the mean from the above mean returns of recent years - a factor that has particular importance to those near or in retirement.

We promised to discuss withdrawal strategies in follow-up communications. We begin that discussion here.

Most people will be surprised to learn how much money they will need in their portfolio at retirement to provide a retirement lifetime of financial support for their lifestyle in a rising cost environment. That will become clear as you read this letter.

This letter is Part One of three letters on retirement portfolio withdrawal strategies.

- This letter examines the "4% Rule," probably the most widely known rule-of-thumb for safe maximum retirement withdrawal, and an X% derivative of the rule.
- Part Two will examine other withdrawal strategies, including variations of the 4% Rule; and examine a portfolio of mixed taxable and tax deferred accounts and tax-exempt income.
- Part Three will discuss retirement asset allocation strategies during the withdrawal stage of financial life.

Key Factors in Success or Failure of a Retirement Withdrawal Strategy:

- Life expectancy (number of years of needed withdrawals)
- Changes in cost of living
- Withdrawal rate
- Expected portfolio mean return
- Expected portfolio volatility
- Portfolio asset allocation
- Taxable status of portfolio and withdrawals.

All of these will come under consideration over the three letters.

**Life Expectancy**

Typically an uncomfortable subject, but life expectancy is an integral part of retirement withdrawal strategy selection and design. So let's quickly put some broad parameters on that and move on to the next factor.

There are differences in life expectancy based on age, gender, lifestyle, family history, and current health/disease profile as examples. However, for the purposes of this discussion, let's start with the Social Security Administration national tables that merely consider attained age and gender. An extract from that table with round numbers for attained ages in 5-year increments from 50-75 as the starting ages for retirement is as follows:

Figure 1:

From this, it appears that strategies that last from roughly 10 to 35 years may be needed in retirement.

The problem is those life expectancies are means, and you may not be average. Not everybody dies in their 80s. There is a distribution of shorter lives and longer lives around those means. Some people live into their 90s. It may well be appropriate to plan on living to 95, just in case - so you do not live longer than your portfolio.

Just imagine setting up a plan that is expected to work until age 85 - and it does work until 85 with $1 left in the portfolio - then you live 10 more years (on family or state assistance).

When thinking about "safe maximum withdrawal," death at age 95 is a better choice than a population level life expectancy table.

The IRS is more practical that way, because for their Required Minimum Distributions (RMDs), which begin at age 70, they start the distribution of your IRA assets with withdrawals at a 27-year rate (to age 97).

As a rule-of-thumb, assuming life to age 95 is probably a good idea. So, based on your age at retirement, these are good starting points for modeling a portfolio and withdrawal strategy:

Figure 2:

Let's be square about it. The longer you assume you may live, the less you can withdraw per year to avoid the "risk of ruin" (outliving your assets), but part of a "safe maximum" withdrawal rate is assuming a maximum life expectancy.

**The 4% Rule**

The 4% Rule is probably the most widely suggested withdrawal strategy. It was popularized after a 1994 article by William Bengen in the Journal of Financial Planning.

The Rule:The retiree in the first year of retirement would withdraw a fixed amount equal to 4% of the portfolio assets (e.g. $40,000 from a $1 million portfolio). Each subsequent year, the retiree would increase the fixed amount withdrawal by the rate of inflation of the preceding year; and never take less than the prior year withdrawal amount.

Bengen based the rule on this set of assumptions:

- age 65 retirement
- 30 year withdrawal period to age 95
- withdrawals from a tax deferred retirement (non-taxable rebalancing; and ordinary tax on distributions)
- no transaction or management fees
- assets allocated 50/50 between US stocks (S&P 500) and bonds (US 10-year Treasury bonds)
- the 10-year bonds were purchased at the beginning of each year, sold at the end, followed by the purchase of new bonds for the next year.

Example: with a $1 million portfolio, withdraw $40,000 (4%) in the first year, and then if inflation were 3%, withdraw $40,000 X 1.03 ($41,200) in the second year; and so on with inflation adjustments throughout retirement. In the 30th year, the withdrawal would be $94,263 (inflation raises needed income to 2.36 times original withdrawal amount). So the portfolio has to perform to support the growth in withdrawals.

The portfolio must have growth components to maintain spending power. For various life expectancies with the long-term average 3% inflation (the approximate long-term average), the terminal withdrawals would be these multiples of the initial withdrawal amount:

- 10-years: 1.30 X
- 15-years: 1.51 X
- 20-years: 1.75 X
- 25-years: 2.03 X
- 30-years: 2.36 X
- 35-years: 2.73 X
- 40-years: 3.67 X

With the 4% Rule, there is an approximate 93% chance of success, meaning the portfolio lasting throughout the 30 years (7% chance of failure, portfolio being exhausted before 30 years).

Note well, that all of the calculations in this letter are before investment costs. It is critical that the sum of transaction costs, fund expenses and advisory fees are kept as low as possible. In effect, they are part of your cost of living and reduce the sustainable amounts you can withdraw from your portfolio in retirement.

You may retire at a different age, have a different tax status of your assets, and a different portfolio allocation; which may justify or require a different percentage than 4%.

We will examine variations in length of withdrawal, stock/bond allocation and beginning percentage withdrawal in the next section (the X% Rule).

**X% Rule - Based On Actual Historical Returns**

Let's generalize from the 4% Rule, and acknowledge that for different circumstances and investment assumptions, different percentages could be applied to the same logic structure as the 4% Rule: an inflation indexed, fixed amount withdrawal, beginning with a certain percentage of the beginning portfolio.

Figure 3 is based on applying the X% rules (from 3% to 7%) to the actual annual returns of 11 different allocations between the S&P 500 (or large-cap precursors) and US 10-year Treasury bonds from 1928 through 2015 (88 years of actual annual returns).

This period included the Great Depression, WWII, periods of high and low inflation, the period of steeply rising interest rates into the early 1980s and the declining interest rates since then, and the DotCom crash and the 2008-2009 stock market crash.

You can see that a 3% rule worked for a 40-year retirement for all allocations, except the 100% bonds allocation, and a 4% allocation worked for 30 years for all allocations except either 100% bonds or 100% stocks.

A stock/bond allocation of between 50/50 and 80/20 gave the best results.

Figure 3:

Figure 4 from 1972-2015 (44 years) was selected to ignore the Great Depression and WWII, and to specifically experience the huge run up in interest rates to the early 1980s and the long period of declining interest rates to the end of 2015.

A 3% initial withdrawal rate worked for a 40-year retirement for all of the asset allocations. A 4% initial withdrawal rate worked for a 30-year retirement for all asset allocations except 100% bonds, and 10% stocks/90% bonds.

Figure 4:

**X% Rule - Based On Monte Carlo Simulation**

Let's see how the X% rule might be expected to work using Monte Carlo simulation based on historical return and inflation data from 1972 to 2015 (44 years).

Monte Carlo will be described below, but for the moment understand that it is a method to explore thousands of plausible portfolio returns to test how withdrawal strategies might work.

We examine the general method of the 4% Rule, but with variations at 3%, 3.5%, 4%, 4.5%, 5%, 5.5%, 6.0%, 6.5% and 7.0%; and tested all of those initial withdrawal rates' ability to survive without complete portfolio exhaustion over multiple periods of 15, 20, 25, 30, 35, and 40 years - 9 different withdrawal rates tested over 6 different periods of years (54 scenarios).

What the results suggest is that if you want nearly 100% confidence (based on history) of not outliving assets over 30 years, 3% initial withdrawal is about as far as you should go. If you want to toss the dice a bit, and possibly have a 7% chance of outliving your portfolio (a 93% success rate), then 4% could be attempted. If you are totally ill-advised and chose to withdrawal 6.5%, you have less than a 50% chance of success.

The table further shows that the shorter the number of years the portfolio is expected to last, or the lower the initial withdrawal rate, the lower the "risk of ruin" (outliving the portfolio).

Some people have commented that these data are silly, because they believe they know of people who have been retired for years and taken out a lot more than 4% indexed for inflation and have done well, and their portfolios are larger than when they started. Maybe so and maybe not, but not with these or similar core assets. We would bet that if all the facts are known, few if any people beat these odds. We will discuss asset allocation in Part Three.

Figure 5:

**What Is Monte Carlo Simulation?**

Monte Carlo Simulation is a computerized method of using random selection of returns to construct huge numbers of plausible portfolio outcomes (instances), and then to see the frequency distribution of results of those portfolio instanced to understand what is most likely, and how far from the mean some results may end up.

Specifically in the case of the table above in Figure 5, the computer created 10,000 instances of the 50/50 portfolio for each of the 54 scenarios in the table above (540,000 portfolio instances).

Because there were 44 annual returns for each of stocks and bonds from 1972-2015, the computer could randomly choose between 1,936 possible stock and bond return combinations for each of the years in each instance of each scenario. And, because there were also 44 possible inflation values to choose at random each year in each instance of a scenario, there are 85,184 possibilities results per instance.

In all the computer made over 30 million random selections of individual annual returns and inflation levels for portfolio assets to assemble the probabilities in the table in Figure 5.

The 10,000 portfolio simulations of each scenario were compiled in a statistical distribution to determine success probabilities. From practical experience with the software, repeating simulations over and over seldom resulted in a different success rate, and when it did a few times, the variance was only 1 percentage point.

Suffice is to say for now, that Monte Carlo simulation is a well-established method of attempting to examine risk and opportunity.

Here are the annual returns data used in the random selection of stock and bond returns for the portfolio simulation:

Figure 6:

And here are the inflation data points in the random selection for the annual increase in the withdrawal:

Figure 7:

If you care to look more into Monte Carlo simulation, a good place to start is Wikipedia.

Before moving on to see how the X% Rule might work in the lower expected return world of the next couple of decades, let's look at more of the data that came out of the simulation of the 4% Rule over 30 years with a 50/50 portfolio.

**What Do The 10,000 Outcomes Per Instance Look Like?**

First, for the 4% Rule, although 7% (700 of 10,000 iterations) of the portfolio failed to work (portfolio did not last 30 years with a positive balance), 93% did last.

Specifically, 75% of instances began with $1 million, took out an inflation indexed $40,000 (initial 4%) and ended up with at least $2.3 million after 30 years; and 25% ended up with more than $8.8 million; and 50% ended up with more than about $5 million.

So why not take out a lot more than 4%. You could, but let me quote Clint Eastwood in the 1971 movie "Dirty Harry" pointing his Smith & Wesson 0.44 magnum revolver at a bad guy (that is the metaphor for betting that you will not be in the 7% who outlived their assets): "Do you feel lucky? Well Do ya?" That is the question.

By the way, if you are old enough to remember the movie, you are probably old enough to retire. If not, you probably have years to go before this is a big issue for you, but this data can give you good clues to how much you need to accumulate to have the retirement you desire.

Figure 8:

**When Does the 4% Rule Begin To Fail in a 50/50 Portfolio Based on Historical Data?**

This chart of failure points shows the 4% Rules in a 50/50 portfolio working well through about 20 years, but then more and more instances failing until it reaches 700 failures (7% failure, or 93% success).

Figure 9:

**What Is The Distribution of Return Outcomes In This Instance?**

While the median outcome is around a $5 million ending portfolio, the range is $0 to $21 million; but there are very many more zero outcomes than very high ones (7% at zero)

Figure 10:

**What is the Distribution of Maximum Drawdowns in this Instance?**

Definition: A maximum drawdown is the maximum portfolio value change from a peak to a trough of a portfolio, before a new peak is attained.

It looks like a good 5% or so of the outcomes could have maximum drawdowns in the negative mid-30%, with the average maximum drawdown of about 26% and the median drawdown about 17%. However, note that around 5% also drawdown to zero (presumably, those near the end of the portfolio life for those 7% that do not last as long at 30 years).

Figure 11:

**Comparison Of 20-Year Required Portfolio Life Using Different Historical Data Sets, And Forward View Of Asset Performance**

Now let's look at a 20-year time horizon. That is the longest period for which we can find future return expectations from a recognized institutional source. This will create some informational value for those with a 20-year horizon - those 75 years old, or perhaps those with illnesses that make a 30-year horizon unrealistic. Primarily, however, a 20-year horizon allows us to compare a future view of lower returns with actual historical periods when using the X% rule.

The tables in Figure 12 examine the success rate of inflation-indexed fixed dollar amount withdrawals over 20 years representing the 5 generic allocations. Those 5 allocations circumscribe the mostly likely range of most retirement portfolios (30% stock/70% bonds, 40/60, 50/50, 60/40 and 70/30). They are generic because they involve only two US assets; S&P 500 and 10-year US Treasury bonds. Other asset selections may be more appropriate for specific retirees, but these generic portfolios are useful to study the withdrawal strategy. Part Three of this letter series will discuss asset allocation choices.

The rows of each table present Monte Carlo simulations based on different historical periods of time ranging from 94 years from 1928-2015 to 10 years from 2006-2015; and simulations based on the 20-year forward view of returns published by McKinsey Global Institute, "Why Investors May Need to Lower Their Sights" (April 2016). We presented information about the McKinsey 20-year forward view (along with other essentially corroborating institutional view) in our September 5th letter.

The conclusion we draw is that lower expected returns, also means lower safe withdrawal rates in retirement.

The columns of each table present the success rate (not outliving assets) for each withdrawal rate (from initial 3% to 7%) for simulations based on different historical asset performance periods, and one future 20-year period of expected asset returns (the McKinsey view). The bottom row of each table is based on the McKinsey forward view of lower return from 2016-2036.

**What do we see?**

- 3% works well (100% to 99% - dark green shaded) for all historical allocations; and for the McKinsey lower return future for the 30/70/ 40/60 and 50/50 allocations, but slightly less than well (97% to 98% - light green shaded) for the 60/40 and 70/30 allocations for the McKinsey lower future returns
- 3.5% works well for almost all of the historical allocations, but slightly less than well for all of the McKinsey lower return future allocations.
- 4% mostly works mostly well for the 30/70, 40/60 and 50/50 historical allocations, but slightly less than well for the 60/40 and 70/30 historical allocations; and works slightly less than well for all of the allocations for the McKinsey lower future returns
- 4.5% works mostly slightly less than well for all of the historical allocations, except for the 70/30 where it works only moderately in great part (lower 90s, shaded yellow); and it works poorly (less than 90%, shaded in degrees of pink to red) for all of the allocations for the McKinsey lower return futures
- 5% works mostly moderately for historical allocations, except for the 70/30 which tends toward poorly; and poorly for McKinsey lower return futures.
- 5.5% and greater allocations, run into success rate problems pretty much across the spectrum of history and allocations

The 4% Rule essentially holds up under Monte Carlo simulation with historical data, but the comfortable success probabilities drop back to 3.5% if the McKinsey lower return futures discussed in our September 8th materialize.

Figure 12:

**Data Parameters For Figure 12**

For 1972-2015, the actual annual returns were the possible random choices (see Figures 6 and 7).

For the other historical periods and the McKinsey forward view, only the return and standard deviation parameters were provided; and the computer randomly generate returns with a mean equal to the specified mean and with a standard deviation equal to the specified standard deviation as shown in Figure 13 below. The inflation rate was constant as listed in Figure 13.

FIGURE 13:

**Conclusion**

Best to bet your survival on the workable withdrawal rates from a tested strategy (such as in this letter), and hope that the markets are generous, leaving a large estate to your beneficiaries. Also, just as we are told these days to think of multiple jobs or careers, maybe we should think of multiple retirements.

Joyously, if the markets are so generous that our portfolios are growing substantially, perhaps "re-retiring" every 5 years or so, could rationally allow for an upward adjustment. And sadly, it the markets are punishing, we may have to consider "re-retiring" at a lower withdrawal rate than our initial retirement rate; or foregoing some of the inflation increases to our withdrawals.

So, how much money do you need to retire?

In really rough terms, if all of your money was in tax deferred accounts, and you expected to need a 20 to 30 year retirement, you would need portfolio assets in the neighborhood of 25 to 33 times the annual pre-tax income you require from the portfolio. That multiple will vary based on different facts, including the mix of taxable and tax deferred assets and tax exempt income; and the specific assets you hold, But as a yardstick, first cut, back of the envelope form of retirement readiness testing - ask yourself how much pre-tax equivalent income you need from the portfolio and multiply that by 25 to 33 to get a rough idea of needed investment assets. You either have to save and invest until you reach a good multiple, or scale back spending expectations.

For the young investor, keep the 25 to 33 multiple in front of you as you lay out your plans and execute your savings and investment.

In Part Two, we will look at other withdrawal strategies, and discuss the significance of taxable and tax deferred accounts (and RMDs), and tax exempt income in the withdrawal strategies; and in Part Three, we will look at retirement asset allocation strategies for retirement.

**Securities Relating To This Post **

The models in this post are based on portfolios consisting exclusively of the S&P 500 and 10-year Treasury bonds - not a recommendation, just the basis of most safe retirement withdrawal models.

The bonds can be purchased directly from the Treasury or from a broker, but are sold through a broker.

The three leading ETFs for the S&P 500 along with their expense ratios are: IVV, expense ratio 4 basis points; VOO, expense ratio 5 basis points; and SPY, expense ratio 9.5 basis points.

There are, almost unbelievably, load mutual funds out there charging a 5% front sales commission load with annual expenses of 150 basis points (typically with a 25 basis point annual payment to the sales person). First, you would have to be nuts to purchase one of those when you could purchase IVV, VOO or SPY with costs approaching zero. If anyone ever proposes you buy a load S&P 500 fund or one with a large expense ratio, run do not walk from that, and assume that the balance of their ideas are equally not good for you (but great for them). Second, you could not come even close to the withdrawal rates in this post if you owned such funds.

Remember the sum of fund expenses and advisor fees are effectively part of the cost of living in retirement. Those are a direct take-away from the amount you can withdraw reasonably safely.

**Disclosure:** QVM has positions in SPY as of the creation date of this article (September 13, 2016). We certify that except as cited herein, this is our work product. We received no compensation or other inducement from any party to produce this article, and are not compensated by Seeking Alpha in any way relating to this article.

**General Disclaimer:** This article provides opinions and information, but does not contain recommendations or personal investment advice to any specific person for any particular purpose. Do your own research or obtain suitable personal advice. You are responsible for your own investment decisions. This article is presented subject to our full disclaimer found on the QVM site available here.