Portfolio withdrawals can be a ‘sticky wicket’ in that if one is not careful, the portfolio balance can drop too early and income drop below essential spending levels. There are withdrawal schemes that ’won’t run out of money’, but the portfolio value can still drop to a point where, in reality, the portfolio is worthless.

This article will cover a variety of such schemes in a basic manner, highlighting their salient features so that one can (hopefully) visualize important metrics. I realize that these analyses do not account for market variances, but it does include an average of what will happen. If the portfolio cannot perform under ideal conditions, it only gets worse in the real world.

Perhaps the most widely withdrawal approach is the so-called 4% Rule proposed by Bill Bengen. Historically, this was of tremendous benefit in that it provided an easily understood approach to the problem in a situation where none existed. What he did was to take a standard 60/40 (stock/bond) portfolio and calculate the survivability of the portfolio using actual market returns over a 35 year period, including the 1970’s, using decreasing withdrawal rates until the portfolio ’made it’ to the end of the period. His approach included increasing the withdrawal each year by the inflation rate for that year. The highest rate that survived was the 4%. The point of failure was the early 1970s when inflation was high and market returns were low. The basic problem with this approach is that after the initial year, the year-to-year value of the portfolio is ignored. He assigned a high value on smooth withdrawals which will result because inflation is almost always positive and usually doesn’t vary much year-to-year. Bengen later published that if you add small caps to the portfolio mix, you can start withdrawals above 4%, as I recall about 4.3%.

Portfolio returns go up and down based on a variety of reasons, only one of which is inflation. And there is no year-to-year correlation between market returns and inflation. While the 4% Rule was a good starting place, it begged the question, Was the time period used the worst case? To address this point, Monte Carlo analyses have been performed. These involve calculating annual returns using random numbers in such a manner that the overall return distribution is maintained. Thousands of calculation runs are preformed. Results were disappointing. There was something like an 80% chance that the 4% Rule was valid. I believe this is caused by allowing a high number of consecutive negative market returns in the calculations. If you flip a coin 35 times, the average will be 50 heads, 50 tails. If you do this many, many times you will occasionally see a streak of heads and a streak of tails.

However, stock markets don’t go down more than 2-3 years in a row. Allowing a calculation to run with more than this is not realistic (or a cumulative loss of over maybe 60%). Market recoveries occur because there are (suddenly) more buyers than sellers. If this didn’t happen, 2 things would take place. Either the Fed would print money until there weren’t any more trees or our economy would fail and we all lose - the game is over. By the same token, a streak of up markets greater than say 10 is also of zero probability. The test of failure also needs a new definition. When the payout goes down to some level, the investor will throw in the towel and quit. Also, I think in a lengthy period of low bond yields, the investor would op out and find an alternative. I think a basic problem is that these analyses relate risk to the standard deviation, a measure of volatility. If a string of up markets (thereby volatile) is a risk, bring it on. If you made all these changes, I think the result would be that a higher stock/bond ratio is preferred. That seems to be the trend in current retirement investment advice. Bring bonds back in when they can pay their way.

An increasingly popular withdrawal scheme is the so-called “Bucket Portfolio Concept”. Generally, this approach defines how assets are segregated and doesn’t address the details of a withdrawal method. I like this concept of dividing a portfolio into segments where each has its own withdrawal rules. Several years ago I wrote an article, published here at Seeking Alpha, entitled ’Dividend Growth Investing - The End Game’ where I presented an example of this concept.

In this article, I will not discuss either the 4% Rule or the Bucket approach. Rather, I will address several other general and specific withdrawal schemes. These breakdown into the following: 1) taking a fixed percentage of the portfolio value each year; 2) 1/T - dividing the portfolio value each year by the number of remaining years the portfolio is needed; 3) IRS RMD (Required Minimum Distribution) - Joint Survivor; 4) IRS RMD - Single Survivor; 5) implied withdrawal in the Blackrock Life Path Spending Tool. Each of these approaches can use the same arithmetic, calculating the withdrawal amount by dividing the end of year portfolio value by a number, which I will call the Divisor, D, the withdrawal factor. Remember this: the year-to-year value of D will determine your yearly withdrawal. Simply divide that D into the portfolio balance at the end of the previous year to obtain the withdrawal for the current year.. Works just like RMD just using another number.

These portfolio withdrawal schemes can be characterized as follows:

1) fixed %: D is the reciprocal of the fixed % (as a decimal). Example, a 5% withdrawal (0.05), D = 1/0.05 =20. D will be this constant throughout the time period.

2) 1/T: Determine the number of years the portfolio is required. For the first year, D = T, 2 ^{nd} year, D = 39 and so on. Portfolio balance is driven to zero at the end of the period.

3) IRS RMD Joint: D is found for various ages from Table 3 in the Appendix of IRS Pub 590-B. A linear extension was used for ages below 70.

4) IRS RMD Single: D is found in Table 1 of the IRS Pub. Note that for non-spousal beneficiaries of IRAs, Table 1 is used by entering the table, in the year after you inherit, with your age. The table provides an initial D for that year. Reduce initial D by 1 each year for subsequent withdrawals as in 2) above.

5) Blackrock: In the website you input your age and the portfolio amount and it calculates the withdrawal amount. I have reduced this to a formula and extended the range for use in years less than 65 and more than 95 in a linear fashion. The website can be found by Googling ‘Blackrock Life Path Spending Tool’.

In this article, I use a new metric, Portfolio Average Gain [PAG]. It is the running average of all previous annual portfolio gains before distributions or contributions.

For the last 3 withdrawal schemes, the annual withdrawal growth rate decreases over time and goes to zero when the withdrawal amount peaks out. The initial growth rate starts at a level below Portfolio Average Gain [PAG] of (Joint, Single, Blackrock) (0.02%,0.05%, 2%). This depends on the slope of the curve, higher slopes have a higher growth rate. For the 1/T case, the initial rate is about 0.2% above PAG and increases at a moderate rate, then increases in the last years to a multiple of PAG in the final year. For the fixed percentage, the withdrawal growth rate is the same over time and is the difference between PAG and fixed % rates. If PAG is higher, the growth is positive, zero when they are the same. A reasonable withdrawal growth rate is important to keep ahead of inflation.

One advantage of the Fixed % scheme is that if the PAG rate is higher than the Fixed % rate, withdrawals compound at the difference in rates and the portfolio balance increases over time (also compounding at the differences in rates), leaving money to heirs, if that is desired. So, if you think future inflation will average 3% and you want a 4% withdrawal rate, you need a PAG of 7% (0.07) - insuring that your income will keep up with inflation and leave your heirs an amount equivalent to your initial balance.

A lot of insight on how a portfolio reacts to these withdrawal concepts is provided by a chart of D vs. Age as shown in Figure 1. Here age can be interpreted as time. One other metric is needed, one I call the Portfolio Average Gain [PAG]. This is the annual portfolio gain averaged over several years, the gain taken before portfolio withdrawals (or contributions). It is calculated by adding back in withdrawals to the balance (subtracting contributions) for the current year, dividing by the previous year balance, then subtracting one. These calculations are performed for as many years as possible. PAG is the running average of each years calculation.

The blue curve is IRS RMD Joint. The green curve is IRS RMD Single. The red curve is Blackrock. Values of D for fixed % is a horizontal line. For example D=20 for 5% fixed withdrawal. For the 1/T case, the D curve is a straight line from a D equal to the portfolio lifetime (T) at the start age ending at D = 0 at age plus T. For example, for a T of 30 at age 60, the curve goes from (x,y) (60,30) to (90,0) in a straight line. Now, imagine a horizontal line at the reciprocal of PAG, let‘s call it Dp. For example, a PAG of 8% (0.08) Dp is 12.5. Now start the clock and progress alone the D curve. For D values above the Dp line portfolio balances are increasing because the portfolio gain rate is larger than the withdrawal rate. At the age (time) the D curve hits the Dp line the portfolio peaks and thereafter decreases. The age this happens is at the intersection of these lines. One needs to insure this crossover happens at an advanced age, otherwise you may reduce the portfolio until it is essentially of no value.

My IRA has a yield of about 4% (D=25). Following that line to the IRS Joint (Blue curve) shows that I was able to pay my RMD with dividend income up to age 73 - which turned out to be true. At age 85 with a D of 15 (withdrawal = 0.0667), I had to sell 2.67% in shares to make up the difference (0.0667-0.04=0.0267). This will increase over time. Actually, this is an opportunity to both ‘clean’ up the portfolio as well as harvesting capital gains. If I don’t want to sell shares, I can transfer shares to my taxable account knowing I still have to pay the tax. Hint: this implies that the best time to transfer shares out of an IRA is when the market is down, you pay tax on a lower value.

For those cases where D decreases over time, withdrawal amounts continue to increase even as the portfolio is decreasing. For example, for the IRS RMD Joint case, values for (PAG, portfolio peak, withdrawal peak) are (0.05,78,93), (0.07,85,98), (0.10,92,101). This gives us (15,13,9) years of withdrawal increases after the portfolio peaks. Actually, if your intent is to spend the portfolio down you need to program the crossover at the ‘correct’ age. For the Blackrock case, the corresponding values are (0.05,72,91), (0.07,83,99), (0.10,93,103) for differences between portfolio peak and withdrawal peak of (19,16,10).

Note that for the Blackrock and IRS Single curves at age 65 show a D between 20 and 25. This corresponds to a withdrawal rate between 5 and 4% with Blackrock being the more conservative.

As a practical matter, designing a withdrawal strategy for ages over 100 is not a prime concern. It should suffice to design one that has an increasing payout to that time while keeping up with a presumed inflation rate, noting the portfolio balance at that time. Life expectancy for a female age 65 is 86.7 where half are surviving. The life expectancy of those is 93.1 (1/4 surviving); of those, expectancy is 96.8 (1.8 left) and on to 99.9 (1/16 = 6.25%). Not to ignore those remaining, but how many of them have portfolios and if they do, it might be better to look at the remaining balance and design a more appropriate strategy for one of that advanced age.

Figure 2 shows cumulative total returns [PAG] for the IRA and S&P500, 30 years worth of data.

The red curve is for the S&P500 and the green my IRA. The first few years are choppy because that are only a few years to average. The 3 ^{rd} low point is the dotcom crash in 2003 and the next the financial bust in 2008. The IRA is more stable and appears to recover more quickly than the S&P500 after these major crashes. This is probably due to the fact that the IRA is actively managed. Using the year-to-year data, the (standard deviation, average) for the S&P500 is (16.9,11.6) and for the IRA (13.6,9.2). A question is: Would I have been better off with just the S&P500 in my IRA? I’ll never know. The difference from a Dp point of view doesn’t appear to be significant, but the power of compounding cannot be ignored. On the other hand, would I join a club where the sole membership requirement was that you were big? And a group that participated in every fad that came along (as long as you were big)? I think not.

The IRA can be characterized as follows: 49 holdings (20 of which are ETFs); 76% domestic equities, 21% foreign equities, 0.7% bonds, 0.6% other; 73% large cap, 20% mid cap, 7% small cap; Current yield 3.2%; Sector distribution: 3.44% Energy, 3.19% Material, 15.61% Industrial, 14.62% Consumer cyclical, 3.01% Consumer defensive, 3.74% Healthcare, 12.32% Financial, 7.43% Tech, 11.32% Telecom, 12.3% Utilities, 13.02% Real Estate. Note the heavy weighting in the Telecom, Utility, Real Estate sectors.

I would recommend measuring your portfolios and determining where you stand. For IRAs and 401 type accounts this should be fairly easy. For each year, subtract out your contributions from the current balance, divide that by the previous end of year balance and subtract 1. That is your total return for the that year. Average out as many years as you can to estimate PAG. For other accounts where there are multiple money inputs and expenditures, the calculation is more complicated. As seen in Figure 2, PAG values for the S&P500 is 11.6 and IRA 9.2 with 30 years of date. In one of my daughters IRA, PAG is 10.1 (5 data years). In my other account, PAG is 10.7 with 8 years of data. This last account has a variety of income inputs and output expenditures which essentially cancel out except for a net withdrawal, it is the dividends/interest income that is not re-invested. This net withdrawal is the one used to calculate PAG.

Figure 3 shows the IRA end of year balance vs. my age in retirement. The data has been re-scaled to make it more useful in general. It starts with a balance of $100,000. The smooth portion at the end is the projected balances based on my PAG. The curve peaks when I am 90, which could also be gleaned from Figure 1 with my Dp of 10.9.

The red curve is the IRA Balance. The green curve is the initial balance compounded at 9.2%. I am on the blue curve (IRA RMD Joint) of Figure 1. Does the projection look reasonable? I think yes, even a little conservative. I have been following a spreadsheet with these data for 20 years or so and the projections seem to pan out. The peak year varies in the low 90s.

Figure 4 is a curve of the withdrawal amounts, again re-scaled.

The red curve is the withdrawals and the green curve is initial payout compounded at a 3.5% inflation rate. From age 70 on I was using the RMD Joint rules, but in some years took out more. Withdrawals are projected to peak out at age 100, 10 years after the portfolio balance peaked at age 90. I can live with that. Note that there were no withdrawals during the first 5 years of retirement. The reason was that I had a company pension that I took out in 5 years to supplement other dividend income for living expenses . Meanwhile, the IRA was compounding at 9% (and change). The first withdrawal is about 5% of the original start point and peaks out at 9 times that, should I be there to enjoy.

In fact, I do not think of this portfolio as my IRA. I am really managing my heirs beneficiary IRA, which (to me) justifies a more aggressive investment style. They are now in their early 60s. In 5.7 years, my life expectancy, they will be 70ish. This portfolio will then be under a 1/T withdrawal plan. From Figure 1, at age 68, D is 18. This means their portfolio will be depleted in 18 years - in their 86 ^{th} year. It may be in time for them to delay withdrawals from their personal IRAs before the 70 year RMD, and should provide a good cash flow at a good time in their lives. Since they don’t have children, it should be money well spent.

As an example, let’s look at the Blackrock case - it is interesting. Using their Tool and inputting age 65 and portfolio balance 100,000, the payout is 4285. Repeating for age 85 (same balance) results in a 7341 payout. We can calculate the D values of Figure 1 by dividing 100,000 by these payouts, yielding (age, D) of (65, 23.34) and (85, 13.62), reflected in Figure 1. The D values are linear (which I discovered by repeating this procedure for other ages). So we can calculate the slope by noting that D drops 23.34-13.62 = 9.72 in 20 years for a slope of 9.72/20 = 0.486. So to generate the D curve we start with the 23.34 value and subtract 0.486 every year. Suppose now, at age 85, we want the portfolio to peak (PAG = 1/13.62 = 0.0734). This is the average gain the portfolio needs to generate. Getting into how to compile, or improve, a portfolio to do just that is beyond the scope of this article. Note that higher PAGs will move the peak age out, lower PAGs in. The design PAG is the minimum needed to keep up with inflation.

Now, with a spreadsheet to do the heavy lifting, inputting these metrics: start age, initial D, slope, PAG, we can generate a portfolio balance vs. age and a withdrawal amount vs. age as shown in Figures 5 and 6.

The red curve is the withdrawal amount and the green curve is the initial payout compounded by an average 3.5% inflation. The portfolio balance at the withdrawal peak, age 99, is 92900 or 28850 in current value. This, 29% of the start amount, should be sufficient to fund a new withdrawal plan for any survivors.

To check our work, we can input age and portfolio balance from Figures 5 back into the Blackrock Tool and compare results with withdrawal amounts from Figure 6. From ages 65 to 90, the Spreadsheet data is 3.7% low at age 65 and 2.0% high at age 90, with age 85 about spot on. The reason for this difference is that their curve is varying from a straight line to a smaller slope meaning more output at lower ages (look closely at age 95 in the red line of Figure 1). A linear regression of the D calculations from the Blackrock website from ages 65 to 90 in 5 year steps shows a slope of -0.4846 with a correlation coefficient, r, of -0.99994; D = 0 at age 113.

These results show that if you want to achieve performance as shown in Figures 5 and 6, you need a PAG of 7.34% as used in this example. Higher is better because it lifts the portfolio balance and withdrawal amounts above the inflation curve as shown in Figure 4. It keeps you above the rocks (no matter their color). This is important because in the real world with market volatility, you need the space (also seen in Figures 3 and 4). The equivalent of these results can also be achieved by a combination equity/bond ratio as was used by Blackstone in developing the Tool. The website has a summary of the methodology and metrics used. The equity/ bond ratio was 40/60 with assumed annual returns of 5.9/3.1. This would give a weighted average of (40*5.9 + 60*3.1)/100 = 4.22%. Some boost in performance can be achieved by re-balancing. They do not mention re-balancing, but it is a common practice. It is hard to imagine that much improvement because the improvement needed is (7.34 - 4.22 = 3.12). But in this example the same results were generated by the spreadsheet and illustrated in Figures 5 and 6. Besides, if we had chosen another balance peak age, it would imply a different PAG and that cannot happen unless the equity/bond ratio is changed. Something else is going on.

Actually, I am not surprised at this. I am an Electrical Engineer and doing circuit analyses, it is common to express an output of a 2 terminal ‘black box’ in a variety of ‘equivalent circuits’. Again, their way of analyzing a ‘system’ versus the way I would do it also has a counterpart in engineering. Sometimes electronic systems are analyzed in the time domain using Fourier Series and sometimes in the frequency domain using Laplace Transforms, the link between the two. I am comfortable will these approaches. It just needs to be understood better in this situation. I have more to learn. Maybe Blackstone is operating in one domain and I in another, and the link between the two is the withdrawal strategy reflected in Figure 1. Since this article is about withdrawal strategy, I will take their ‘gift’, work with it and not worry where it came from.

Blackrock has a nice Tool, results in a good withdrawal strategy. The problem is: 1) that site may not be there when you are my age, 2) it is only good to age 95, 3)it has no memory of you year-to-year. Let’s address these issues:

1) From Figure 1 you can pick the start age and corresponding D. This will establish the initial withdrawal. For subsequent years, subtract 0.486 from the previous year D (which will be using the implied Blackstone withdrawal strategy). Develop and maintain a portfolio PAG no less than (say) 7%.

2) Note from Figure 1 that the Blackrock curve melds into the IRS Joint curve in the later years. Just switch to the Joint curve for ages above 95. D Values are in Appendix Table 3 in the IRS IRA Pub.

[Note: tweaking the Blackrock metrics slightly - start balance $100,000; initial withdrawal 4.5% (D=22.22); start age 65; slope -0.455; transfer to Joint at age 95; design balance peak age 85 (Dp=13.1, PAG=7.6% round up to 8%) Results: balance peak age 86; withdrawal peak age 98; current value of balance at age 98 is $36,860; 3.5% inflation crossover with withdrawal at age 102.]

3) This one is more complicated. In my IRA spreadsheet that I have been using for the past 20 years (or so), at the start of every year I overlay the previous year’s actual withdrawal amount and portfolio balance. That freezes in the past. At the top, where the portfolio average gain [PAG] is, I use the current year’s actual PAG so the projected data reflects the performance of my portfolio. I monitor that for stability and note when portfolio balance and withdrawal amounts peak. If these drift away from acceptable years, I know I have to improve the portfolio. Year to year, the projected amounts vary up and down with market returns. In up years, the ages for these events move out, moving in for down years.

With the Tool, if the user’s portfolio closely relates to the design performance implicit in the Blackrock model, the payout suggested will be close to the proper amount, with yearly updates and corrections. If the user’s portfolio is better, every year will reflect higher and higher payouts (but understate the potential). The reverse is true for portfolios that are worse. I don’t know when the user would recognize that he has an underachieving portfolio. Maybe it is not a problem, I don’t know.

This type of analysis in engineering is called a steady state analysis. There are too many variables in designing a retirement portfolio withdrawal strategy. Not including the ‘noise’ of market volatility allows the designer a chance to see interaction of the salient metrics to better understand the system.

Another common complaint is using a strategy with a non-smooth payout. Requiring a smooth payout puts such a constraint on the system, as in the 4% rule approach, that it results in a non-optimum solution. All of these withdrawal plans will have a non-smooth payout with market volatility. You have to learn to live with it. One solution, which I have adapted, is to transfer the IRA RMD funds into another account that has other income streams, some smooth such as Social Security and some not, such as dividends and interest from another portfolio. Expenses are paid from this account and the cash from the IRA can be used if needed. However the total income exceeds expenditures (in my case), so there are re-investment monies available. Re-investment takes place only when excess funds are available or waiting and ‘buy the dip‘. In reality, this is putting income volatility to my advantage. As the market goes up, I harvest the extra profit from a high PAG portfolio; spend the cash if needed; save some for re-investing at market lows. Just another way to re-balance.

What links this all together?: the standard 65 year retirement, pioneering work by Bengen and the popular 4+% initial withdrawal, the government’s guidelines on single and joint survivability and a linking path between these discovered by Blackrock in a very intense technical analysis. Cobbling all these together into one withdrawal strategy makes sense. It is the first thing I noticed (by shear coincidence) when putting Figure 1 together . Look at it, a Blackrock type withdrawal strategy provides a reasonably high initial withdrawal at low (relative) ages, in line with the Bengen (now traditional) 4%ish amount and a government regulation for singles on one end. This satisfies a retiree wish to get as much up front because he may not live forever. At the other end, where another regulation confronts the case where the retiree has lived this long, she might live to the end, the Blackrock withdrawal strategy bridges these two points with an almost perfect straight line with a top drawer detailed technical analysis as a measure of proof, it has to be right.

In writing this article, I learned (and now understand) more about portfolio withdrawal schemes and investment strategy. I hope you do as well. Good Hunting (for a good portfolio and safe withdrawal plan in retirement, one that fits your needs).

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.