Saturday, January 18, 2014

Analyzing Multiple Scenarios

Multiple Scenarios 

While it is very useful to see possible scenarios for future income and savings one at a time, there is merit in getting a view of the range of possible outcomes over many possible scenarios. Starting with RIS-20120120, my software on the Scratch site allows for the analyses of multiple scenarios. This post will describe the required procedures and show some examples, but will be short on analysis. Future posts will discuss the relevant economics and analyze alternative retirement income strategies.

In a previous post I discussed the scenario settings. There is now one additional setting that indicates the number of scenarios that you wish to create for multiple scenario analyses. It is the last one shown in the figure below. To obtain meaningful results you will need to analyze a great many scenarios so the setting is stated in thousands. The default is 5 thousand. I allow as few as one thousand but strongly recommend at least five thousand and more if you are willing to take the time.

 The Main Page

The main page now contains the ten buttons shown below. The new ones provide for  Analysis Settings, Multiple Scenarios and Analyses


The Multiple Scenarios Button

To create multiple scenarios, you need only click on the Multiple Scenarios button. After a short while you will be given an estimate of the time required to complete the process and asked whether you wish to proceed. If you say no, you will return to the main page but there will be no scenario statistics available to be used for any subsequent analyses. If you say yes, the desired number of scenarios will be generated and statistics gathered. You will see the progress on the screen  and it is very important that you do not interrupt the process. After it is completed, you may click the Analyses button at any time to see various properties of the scenarios.

Analysis Settings

The Analysis Settings button allows you to change the default settings for various analyses. At present there are only two settings, although more will be added. They are shown below.

The first setting indicates whether you want to see the actual probabilities of receiving income (A) or the contingent probabilities (C). As shown, the default is actual. I'll describe the two alternatives below.

The second setting indicates the time that the software should wait between years when plotting multiple yearly outcomes. The default is 0.25 seconds, which makes the plots come rather fast. You may want to use a larger value to slow down the display, although you can always stop temporarily by pressing and holding the 's' key (then resuming by pressing the space bar).

The Analysis Page

When you press the Analysis button on the main page, you will be transferred to the Analysis Page. The figure below shows its current state.

At present, only the first button is operative. The other two will be programmed in the future, and more may be added as well. Note that all analyses will use the multiple scenarios that you generated most recently. As usual, you may return to the main page by pressing the left arrow key.

Yearly Income Analyses

Now to the good part --what happens when you press the Yearly Income button.

I strongly suggest that you start by doing this using the software initial defaults settings (which include 5,000 multiple scenarios previously produced) to see the results in their full animated glory.

I'll start with graphs produced using all the default settings (based on an RMD account). In this case the  Analysis Setting calls for Actual probabilities. The figure below shows the graph after 18 years.

To produce this figure, I froze the display by pressing and holding the 's' key after the 18th year was shown. To produce the next figure, I simply pressed the space bar. (As usual, you can find context-sensitive help instructions by pressing the up arrow key to get a help message).

Let's look at the results. As shown at the top of the graph, the red curve is for year 18 (18 years in the future since the current year is year 0). The chance that you, your partner or both will be alive in that year is 89.7%. The horizontal axis shows levels of income from 0 to 80 $ thousand (the upper limit, taken from your scenario settings). There are twenty vertical grid lines, so in this case, each covers 4 ($thousand). Here the values shown on the horizontal axis are for real income, also taken from your scenario settings. You may change any of the Scenario Settings to produce different graphs, then producing a new set of multiple scenarios by pressing the Multiple Scenario button.

 As indicated, the vertical axis shows the chance that (1) income will exceed the value shown on the horizontal axis and (2) that one or both of you will be alive. Values range from 0% to 100% (or, for those of you who think in probability terms, from 0 to 1.0). Each horizontal grid line covers 5%, and the 50% (median) line is indicated as well. 

You can read this graph in either of two ways. 

You could pick a real income goal, say $40,000, find it on the horizontal axis, then go up to the curve and look over to the vertical axis to see your chances of doing that well or better -- in other words, beating that goal. Clearly, the better your chances, the happier you will be. Thus higher curves are better than lower ones.

Or you could pick a chance, say 50%, find it on the vertical axis, then go to the curve and look down to the horizontal axis to see the goal that you have a 50% chance of beating. The higher that goal, the happier you will be. Thus curves farther to the right are better than ones to the left.

If you have a statistical background, you may recognize this graph as similar to a cumulative probability distribution, but with one key difference. The typical statistical graph shows the probability of falling below the value on the horizontal axis, not the probability of exceeding it. I think this is not the way most human beings think about attaining goals and strongly prefer the approach I've employed in my prior research and incorporated in the RIS software. I'll probably have more to say about this "goal/chance" approach in future blogs.

Most of those who analyze retirement income strategies pick one, two or three probabilities (chances), then show the incomes associated with each of them in each future year. I feel that it is far better to show the entire ranges, as does the RIS software. I'll undoubtedly have more to say about this as well in the future.

To return to the figure, note that when income exceeds the maximum shown on the horizontal axis, the plot is just to the right of the vertical right edge of the graph box. Here, the actual income values are greater than 80 $thousand maximum plotted, but there is no way to tell how much greater they may be. If this is of concern you may want to change the Scenario Settings to provide higher maximum incomes, then run a new set of multiple scenarios, and analyze the results using the appropriate Analysis tools.

Now, back to the case at hand. The figure below shows the graph after all the years specified in the Scenario Settings have been shown. Not surprisingly, as time goes on, the chance of any income diminishes as mortality takes its toll. Moreover, there is a wide range of possible incomes in all but the initial year, and the range tends to be larger for later years. In future posts I'll discuss such matters at length when analyzing specific retirement income strategies.

I'll finish this post with graphs produced using the Contingent Probability setting in the Analysis Settings. (Happily, you do not have to run a new set of Multiple Scenarios to  change between Actual and Contingent probabilities).

The figure below shows years 0 through 14 in yellow and year 15 in red. For the first few years the graphs are virtually the same is in the previous case, since the probability that one or both of you will be alive in the near future close to or equal to 100%. The only difference is the heading for the vertical axis, which shows that the results indicate the chance that income will exceed the amount on the horizontal axis if one or both is alive. (In that sense, it is contingent). Note that this shows that for at least the next 15 years the median (50%) real income is larger in future years, the low-probability worst cases (90% and above) are somewhat worse, and the rosier low-probability cases (say, 25% and below) are considerably better.

The figure below completes the picture, including all the future years through year 49. As can be seen, the prospects for the very distant years become quite dismal. But of course the chances that anyone will be alive at the time are small.

Note also that in this case the curves for distant years are far from smooth. This reflects the fact that while the results were based on 5,000 scenarios, there are very few scenarios in later years in which anyone is alive, so the sample sizes are insufficient to provide good indications of the overall range of possible future outcomes. For example, in year 49 (shown in red), there were only 5 scenarios (0.1% of 5,000) -- far from sufficient to make well-informed estimates of the whole range of possibilities. Unfortunately, the only way to improve the reliability of distant forecasts is to take the (considerable) time required to run many more scenarios. But with at least 5,000 you should be able to get a rough idea of possible prospects.

There are profound differences between viewing future retirement income prospects using actual probabilities and conditional probabilities, as these figures show. Indeed, there is considerable debate about the extent to which people should weigh each of these two views when choosing among alternative retirement income strategies. I'll have more to say about this anon. Meanwhile, please do use the software to experiment with these new features.

Thursday, January 2, 2014

RMD Accounts

As indicated in previous posts, an analysis using the RIS software can employ one or more accounts, each of which provides retirement income. Earlier I described the X% Rule account. This post covers another type, based on the Required Minimum Distribution requirements specified by the U.S. Internal Revenue Service for those older than 70 ½ holding investments in tax-deferred accounts such as Individual Retirement Accounts and 401(k)s.

The IRS rules are provided in IRS Publication 590. Required distributions each year are determined by dividing the value of an account by a life expectancy. Equivalently, the required distribution is equal to a percentage of the value of the account, with the percentage equal to the reciprocal of the life expectancy. For example, if the life expectancy is 20 years, the required withdrawal percentage is 1/20, or 5%. The required distribution amount each year must be moved from tax-deferred accounts and declared as income subject to regular income tax rates; otherwise a prohibitive tax is levied.

Life expectancies are given in three tables, each of which is applicable for taxpayers in a particular category. The simplest and most widely applicable is Table III, which is required for use by: “Unmarried Owners, Married Owners whose Spouses are Not More than 10 Years Younger, and Married Owners Whose Spouses are Not the Sole Beneficiaries of their IRAs” (IRS Publication 590, p. 109).

The first two columns of the table below are taken directly from publication 590. “Dist Period” is the Distribution Period (Life Expectancy). I have added the final column, which shows the percentage of an account that must be distributed at each age.

                  Age         Dist Period             Percent
70 27.4 3.65%
71 26.5 3.77%
72 25.6 3.91%
73 24.7 4.05%
74 23.8 4.20%
75 22.9 4.37%
76 22.0 4.55%
77 21.2 4.72%
78 20.3 4.93%
79 19.5 5.13%
80 18.7 5.35%
81 17.9 5.59%
82 17.1 5.85%
83 16.3 6.13%
84 15.5 6.45%
85 14.8 6.76%
86 14.1 7.09%
87 13.4 7.46%
88 12.7 7.87%
89 12.0 8.33%
90 11.4 8.77%
91 10.8 9.26%
92 10.2 9.80%
93 9.6 10.42%
94 9.1 10.99%
95 8.6 11.63%
96 8.1 12.35%
97 7.6 13.16%
98 7.1 14.08%
99 6.7 14.93%
100 6.3 15.87%
101 5.9 16.95%
102 5.5 18.18%
103 5.2 19.23%
104 4.9 20.41%
105 4.5 22.22%
106 4.2 23.81%
107 3.9 25.64%
108 3.7 27.03%
109 3.4 29.41%
110 3.1 32.26%
111 2.9 34.48%
112 2.6 38.46%
113 2.4 41.67%
114 2.1 47.62%
115 and over 1.9 52.63%

The calculations made by the IRS to generate this table are not specified. Presumably, mortality tables were utilized, with some sort of averaging across possible combinations of unmarried investors of both sexes and those married with spouses of both sexes and with differing ages.

There is no presumption that the owner of a tax-deferred account must spend the amount on which taxes must be paid. And many investors have additional sources of retirement income. This said, it has occurred to some investors and analysts that it might be desirable to adopt a retirement income strategy with a policy of spending the percentages of overall savings given in the final column above. Prominent studies of the efficacy of such an approach include:

Sun, Wei and Anthony Webb, 2012, “Should Households base Asset Decumulation Strategies onRequired Minimum Distribution Tables?” Center for Retirement Research at Boston College Working Paper (available here).
Blanchett, David, Maciej Kowara and Peng Chen, 2012, “Optimal Withdrawal Strategy for Retirement-Income Portfolios,” Retirement Management Journal, 2(3): 7-20

Blanchett, David M. 2013. “Simple Formulas to Implement Complex Withdrawal Strategies.” Journal of Financial Planning 26 (9): 40–48, available here .

In their 2012 paper, Sun and Webb concluded that the RMD approach was preferable to the 4% rule. In his 2013 paper, Blanchett found that “the RMD approach works well for periods less than 15 years...” and advocated the use of a more complex approach for subsequent years. I remain agnostic on the issue but feel that the approach is worthy of investigation.

Now, to the details of the RMD account.

To cover ages not shown in the IRS table, I have made the assumption that the life expectancy for any age younger than 70 will be (70 – age) years longer than that for age 70. Thus for a 65-year old the assumed life expectancy is 27.4 + 5, or 32.5 years. Moreover, when there are two participants (you and your partner), I base the withdrawal percentage each year on the age of the older participant in that year.

The settings for an RMD account are shown below.

The initial setting (line 2) is the usual one that determines whether or not the account is active. The second (line 4) indicates the initial balance – here, a million dollars (1,000 $ thousand). The next setting allows for a variation of the strategy in which the RMD longevity numbers are altered by adding or subtracting a constant number of years. For example, if the adjustment is 2, the life expectancy at age 70 will be 29.4 (27.4 + 2) years, and every other life expectancy will be adjusted by adding 2 years to the amount shown in the table. Lengthening the life expectancies in this manner will reduce the percentages of savings paid, lowering retirement income payments and increasing possible estate values. If desired, you may enter a negative number for this setting. This will reduce the life expectancies and increase the percentage payments. (Not to worry -- if this would result in any expectancies less than one, they are replaced with 1.0).

The remaining settings are the same as those for the X% Rule settings. The fee indicates the annual percentage of the account value charged as fees to third parties. The three settings for the investment strategy are, as for the X% Rule, the initial proportion of the account invested in the market portfolio, the number of years for any glide path, and the proportion of the account invested in the market portfolio at and after the end of the glide path period. As with the X% Rule, the default settings provide for a constant investment solely in the market portfolio in each year.

The RMD approach is a special case of a more general class that I have called Proportional Payout (PPO) strategies, in which a pre-specified proportion of an investment account is paid out to provide retirement income in each year. In previous research, I have used a set of proportions specified for the Fidelity Income Replacement 2042 Fund, which is designed to pay out all the assets in the portfolio by the end of 2042. For a detailed analysis, see my paper in the European Financial Management Journal, a version of which is here. While the Fidelity Funds are designed specifically for producing retirement income, they will pay out all assets by a target date no more than 30 years in the future. In contrast, the RMD approach as implemented in the RIS software will provide some income until the both participants are gone, leaving at least some funds for an estate. For this reason, and because it uses non-proprietary data, I chose to include the RMD method in the software. However, it would be a simple matter for a user to alter the longevity table used for the calculations to produce different results.

Do try the RMD account. Unlike the X% Rule, it conforms with two sensible criteria in each year:

      The amount you spend should depend on
              1. How much money you have, and
              2. How long you are likely to need it

This doesn't mean it is the best approach for you. But, combined with a sensible investment policy, it might provide a desirable component for your overall retirement income strategy.