Friday, July 19, 2013

Retirement Lengths, Withdrawal Rates, and Failure Probabilities

The Bogleheads Forum is a great resource for investors, and in a recent discussion thread, user umfundi proposed/requested a new way to illustrate the results about sustainable withdrawal rates in retirement. I thought it seemed like an interesting way to express things, and since I have the resources to perform the necessary calculations, it seems like a pretty good topic for a post.

This is based on the idea behind the 4% rule. What percentage of your retirement date assets can you withdraw, and then adjust the amount of income provided by this initial withdrawal rate for inflation in subsequent years, and sustainably maintain these withdrawals throughout your entire retirement? The 4% rule is based on a 30-year retirement duration. But umfundi is essentially asking to see the results for all the different possible retirement durations in order to help coordinate one's planning for different retirement lengths.

When we do this analysis, we naturally need to make some assumptions. I will use Monte Carlo simulations, which use computer power to extrapolate out hypothetical scenarios for future stock and bond returns. These simulated returns need to be tethered around some assumptions. Often the assumptions used to guide Monte Carlo simulations are historical averages, which include an inflation-adjusted average stock return of 8.6% for the S&P 500, and with intermediate-term government bonds, an inflation-adjusted return of 2.6%. In the second figure, I will provide results for these assumptions, but I really think they are too optimistic when looking forward from today as interest rates are so low at the present. So the baseline assumptions I will use in the first figure below are assumptions which I think are more realistic and come from a very popular financial planning software program called MoneyGuidePro. With their assumptions, average inflation-adjusted stock returns are 5.5%, with 1.75% for bonds.

Two more assumptions we need are at the asset allocation to be used by the retiree, and the probability of failure that a retiree accepts for their strategy. For these figures, I will simply use a 40% stock allocation, which I think is within a reasonable ballpark for what many retirees will use (though of course everyone's situation is different and 40% may not be a good idea for any particular reader). About the probability of failure, the whole purpose of these figures is to show what the sustainable withdrawal rates are for different probabilities of failure over different retirement lengths. So this is what is illustrated.

It is worth suggesting one more note about how these results can be used. Mainly, they are initial planning numbers about what might be a reasonable withdrawal rate in retirement. Real people, when using volatile assets like stock and bond mutual funds, will need to make adjustments to their spending over their retirement. They will not play a game of chicken in which they keep withdrawing the same amount as the portfolio plummets toward zero. And so what the different probabilities of failure really mean is that someone using a higher probability of failure (which lets them use a higher withdrawal rate) is much more likely to have to make cuts to their spending throughout retirement. There is a trade-off here. Spending more today allows for more enjoyment in the early part of retirement, but a larger chance of having to make cutbacks in the future. People have to make their own decisions about how they feel regarding these trade-offs.

And so this brings us to our figures. This first figure is the one I would suggest spending the most time with, since I believe it has a more reasonable underlying assumptions about future market returns. We can look at this figure in different ways. For instance, moving horizontally, let's consider a 4% withdrawal rate. The figure shows that 4% should work for 22 years with a 5% chance of failure, 24 years with a 10% chance of failure, 28 years with a 20% chance of failure, 32 years with a 30% chance of failure, and so on.

Another way to look at the figure is to follow one particular curve, such as the curve associated with a 10% chance of failure. With a 10 year retirement, a withdrawal rate of over 9% could be used, while for a 20 retirement the withdrawal rate is about 4.8%, for a 30 year retirement the withdrawal rate is about 3.2%, and for a 40 year retirement the withdrawal rate is about 2.8%. For an early retiree planning a 60 year retirement, the withdrawal rate they can be expected to work with a 10% chance of failure is just above 2%.

A final way to look at the figure is to move vertically and to note how small increases in withdrawal rates can quickly result in higher failure rates. For instance, consider a 30 year retirement. With a 5% chance of failure, the withdrawal rate is just above 3%. If someone increases their withdrawal rate to 4%, the failure rate will be somewhere between 20% and 30%. With a 5% withdrawal rate, the failure rate is already 60%.

Now, I am also including the figure below based on historical averages without further comment, except to note that you can see outcomes are much more optimistic across the board, as this figure can be interpreted in the same way. I know some people really want to hold onto the belief that it is okay to use these historical average assumptions but I suggest that readers beware when making their retirement plans based on this second figure. I think the first figure is much more applicable.


  1. Thank you for your very helpful research and sharing.

    Since it is likely that retirees will adjust their asset allocations during their retirement, would it be possible to do these calculations with a variable asset allocation? For instance: 1st 10 yrs, 50% stock; 2nd 10 yrs, 45% stock; 3rd ten years, 40% stock; etc.


    1. Helium,

      Yes, I could re-create these figures will a declining stock glidepath like that.

      But please watch for my next blog post on Wednesday which will be introducing a new article that suggests it is not helpful to continue decreasing a stock allocation during retirement.

  2. Excellent post Wade. What you find replicates our (Frank, Mitchell and Blanchett (FMB)) findings in the Journal of Financial Planning (Nov 2011 - link to paper series by clicking my name above). That work also addresses helium's post above by looking at both asset allocations and time frames (later papers added longevity tables so it is clearer for retirees what time frame to use based on their present age).

    Thus, there are three dimensions to this: withdrawal rate (which is sensitive to the failure rate as you illustrate above), asset allocation, and age (which determines the appropriate time period to use for the simulation).

    Reason for my comment: the FMB paper suggests that a way to use failure rates as a decision signal is what you hint at in your paragraph just above your Figure 1. Why would a failure rate increase? Because the portfolio value has declined due to poor market returns (or retiree removing/spending more from the portfolio than planned).

    Therefore, a rising failure rate is a useful signal to the retiree that they should evaluate the level of their spending given the current facts about their situation.

    About variable allocations for a simulation ... that could be done, but I would caution interpreting the results as predictive. The purpose of any simulation is to get a sense of feasibility and prudence given the present circumstances. It remains to be seen which of the thousands of simulated paths, if any, one may actually follow. Such an approach also addresses the rates of returns one might use ... that data too would slowly change and be updated as time passes and the future becomes the past. Thus, annual reviews are needed to continually update prudence and feasibility. We've discussed this before elsewhere Wade, so I suspect you'd agree.

    Another great post Wade!


    1. Thanks Larry,

      I see that indeed this is leading in the direction of your FMB articles.

      I think what Helium is asking is just rather than using a fixed asset allocation, could we see how things turn out under and implicit assumption that the stock allocation will decline over time. Just to see about feasibility. The answer is that this would cause all of the withdrawal rates to be slightly lower.

      In terms of asset allocation... does your annual portfolio review adjust the asset allocation in the direction of what provides the lowest failure rate for the planned remaining time horizon? Do you put constraints on how much the asset allocation is allowed to adjust from year to year?

    2. Hi Wade,

      Your first question: the paper I referenced above looked at adjusting allocation during retirement and not surprisingly trying to change allocation didn't materially improve success rates (i.e.,market timing doesn't work). (Figure 5 in referenced paper)

      Your second question: yes, in that paper we changed the allocation up or down by 10% when the switching rule triggered a change. However, we also compared the data from a switching regime to benchmark data without switching demonstrated very little differences between success/failure rates (hence conclusion I mentioned in above paragraph).

      The significant differences in data resulted when we compared data for changing spending rates (withdrawal rates) against the same benchmark data. How much a retiree spends or doesn't spend is the strongest factor that determines whether they outlive their money or not. (Figure 4 in referenced paper).

      We did notice a tendency, because of shorter time frames associated with older ages, and the effect of portfolio volatility on withdrawal rates, that as you age, moving slightly more into bonds with less volatility bumped up the withdrawal rates slightly (a hump in Figure 2 in the paper ... which is easier to see in the SSNR working paper data). However, the probability of failure "membranes" are almost horizontal so the effect of allocation is low at any given age.

      PS. Figure 1 in that paper shows the 3-D nature of what you're discussing here.

      PPS. The JFP March 2012 paper introduces use of longevity tables to determine the length of distribution periods and how to use table longevity percentiles to measure "consumption," "inheritance/bequest", or normal spending goals. JFP Dec 2012 paper showed how to measure and manage prudent spending into very old, superannuated ages so the retiree doesn't outlive their money.

    3. PPPS. I should clarify the allocation effect, being almost horizontal, applying to 50% or less to equity. Above that mark, volatility drag appears to reduce the withdrawal rates a little in order to have more simulations survive the target success/failure rate (e.g., 10% failure rate ... Higher volatility would logically require a lower withdrawal rate in order to have 90% simulations survive; as compared to a lower volatility portfolio. I'll be interested in reading your post next week.

    4. Larry,

      Thanks for the detailed comments about your article.

      Regarding market timing, naturally there is no role for that in a Monte Carlo with independent and identically distributed asset return assumptions. There is no role in the real world as well, but even less of a nonexistent role with those assumptions. What I meant was... if you are on a good market trajectory, your current withdrawal rate is getting pushed down, which will generally lead to a minimum probability of failure at a lower stock allocation. That was what I was thinking about with regard to changing the asset allocation.

      When I get to my work computer tomorrow, I am thinking to make a similar figure as above but with different stock allocations for a given probability of failure. Actually, I remember making something like that on my blog before, and as I recall, high bond allocation minimize failure for short horizons, and then there is a cross-over point where stocks start minimizing failure for longer time horizons. This would seem imply a declining equity glidepath... however, actually, rising equity glidepaths tend to support higher withdrawal rates. I'll be talking about that again on Wednesday.

  3. Wade--

    Thanks for your analysis extending beyond the 30-year window assumed for the 4% rule! I'm personally working with a 42 year planning window (i.e., to age 95 for myself and my spouse).

    For an additional set of analyses, what would be really useful would be for you to present the failure rates in terms of the assumed annualized real return on the portfolio (perhaps going from -1 or -2% to +5 or +6%), rather than working with a fixed proportion of the portfolio that is invested in stocks (40% in your example above), with the rest presumably in bond funds. This might take several tables or graphs to depict as you also incorporate the assumed length of retirement.

    1. Hi,

      This is an interesting idea, thanks! I'll be thinking about how I might be able to illustrate this.

      I think, you are essentially talking about what sort of fixed return would support different withdrawal rates over different time horizons. Is it right? The thing about retirement though, is the sequence of returns risk, which can cause withdrawal rates to be lower than implied by the average return obtained over the retirement period.

    2. Yes, your first question is right, thinking primarily in terms of real rather than nominal return rates. It might be helpful to think of a hypothetical laddered all-TIPS portfolio, with bonds held to maturity (similar to Zvi Bodie's approach). This largely neutralizes the sequence of returns issue. The question then becomes: What real average return rate on the TIPS is associated with different failure rates over different planning horizons?


    3. If you are building a TIPS ladder over a specific time horizon, you don't really have to worry about failure over that time horizon. You've locked in the spending backed by the US government.

      Perhaps what you are asking is: what withdrawal rate could be supported from a TIPS ladder over different time horizons?

      This is an old blog post which begins to address this question, as it answers: what percent of assets are needed to build a 30-year TIPS ladder with a 4% withdrawal rate.

  4. What would be helpful to me would be to take the data in these graphs and overlay assumptions consistent with reduced spending in later years of retirement, consistent with research. So, for example, one would use 4% SWR assumption from 65-75 with annual inflation adjustment, then reset withdrawals at 10 or 15% lower level beginning at age 75 for ages 75-85, and begin adjusting for inflation again, and then reset withdrawals at another 10 or 15% lower level at age 85 for the final ten years. What would the probablility of failure be under this set of assumptions? It seems to me that simply inflating the 4% throughout 30 years of retirement is not realistic and provides overly pessimistic results. Thoughts?

    1. Hi, I've written about this topic before. My views about it haven't changed since then. Please see:

  5. Great article -- Great charts. A very helpful and informative chart would to have an animated chart that has many input choices. For example, regarding the two charts you provided, the input choice would be a sliding bar to let the viewer choose between historical averages (8.6% S&P and 2.6% Bonds) and more realistic averages (MoneyGuidePro’s recommended 5.5% Stocks and 1.75% Bonds). These averages could even be broken out into two sliding bars for both equities and bonds. Maybe even other alternative investment types could be offered, such REITs, Precious Metals, Options Sell/Buy Contracts, etc. with their associated historical averages on individual sliding bars. There would be a multitude of other charts for all the various return rate assumptions.

    There could also be a starting option that defaults to a best case ‘ideal’ scenario chart and the user could choose to toggle to what a worst case scenario chart would look like so as to give the user an image of what good charts and bard charts look like.

    I see three main variables in the charts provided: (1) Length of Retirement, (2) Sustainable Withdrawal Rate, and (3) Acceptable Failure Probability. Some users already know two of these inputs and could select two of three radio buttons under the animated chart to highlight an intersection of the two chosen options, thus illustrating where the third option would move to as they slide the input bars around. For example, if a user knows she has a 45 year LOR and wants/needs a 4% SWR, then a highlighted vertical line at the 45 along the LOR axis would intersect with another highlighted horizontal line at the 4 along the SWR axis would illustrate the intersection along the nearest Failure Probability. Likewise, someone could choose to select the FP and LOR fixed options to find the intersection of the SWR. This is important because as they play around with the sliding input options, the animated chart would illustrate where the intersection would move to.

    Other input options on a sliding bar would be to allow the user to adjust:
    --the mix of equities and bonds over time**; I like your recent article on the Rising Equity Glidepath.
    --the withdrawal rate over time**; i.e. constant expected withdrawal rate, graduated decreasing withdrawal rate (party now - sleep later ideology), increasing withdrawal rate (other financial incomes such as the sale of property at the start of retirement that disappear after a fixed amount of time means less initial withdrawal from the retirement nest egg), curved up, curved down, etc. People have complicated retirement dreams/plans.
    --the desired probability of failure over time**; i.e. someone might have more risk aversion the closer they get to their expected LOR.
    --other options could be made available upon users’ suggestions/complaints.

    **to illustrate changes over time, the user would need to input their age. The sliding bars could then have a left input limit of ‘Retirement Year #1’ and a right input limit of ‘Retirement Year #Last’ where #Last is calculated as 121 minus their inputted age. For example, if someone inputs their age as 55, then the right input limit would be ‘Retirement Year #66. Age 121 is an accepted mortality age for 99.99% of all people born today.

    Now who would build this animated chart? No one expects you to have the free time to run 1000+ Monte Carlo Simulations and compile those charts into an animated website with sliding inputs and radio buttons for options, but maybe MoneyGuidePro could. I have received their simulations in the past and I was really impressed with their products. They are located near us in Virginia. Maybe with your credentials and charm, you could convince them to build it and offer it free on their website (with a link from your blog for your readers). I don’t know if it would be a good use of their resources to provide a free product for the public, but it might let CFP’s sway their clients to use MoneyGuidePro.

    Anyway, great article.

    1. Paul,

      Thanks for the thoughts. I've been wanting to do something along these lines for some time, and I'm now working with inStream Solutions as they are working to incorporate a distribution management system into their software. They will be including "safe savings rates" among other things.

      I always thought it would be neat if the contents of this article could be incorporated into interactive software as well:

      You've offered lots of other good suggestions and I will keep readers posted about developments with new blog entries.

  6. Thank you very much for your excellent analysis. I would like to know if the data you used to plot your two figures are available somewhere. I tried to extract them from the graphs but it was not very accurate.