Tuesday, October 15, 2013

A New Formula for Retirement Withdrawals

This post is the fourth is a new weekly tradition of a video blog post made in cooperation with The Wealth Channel at the American College. The first three were about articles I had been a part of, but as David Blanchett is the only person I know who could indefinitely sustain writing new weekly research articles, it is time to move on to discussing the research of others.

In this case, the aforementioned David Blanchett, who is head
of retirement research at Morningstar Investment Management, published a very interesting article in the September 2013 Journal of Financial Planning. It is called, "Simple Formulas to Implement Complex Withdrawal Strategies."

I do not have a transcript for these video presentations (though I would welcome any volunteer to prepare one). The first five I recorded were based on handwritten notes made on an airplane. For the next round I will record in a couple of weeks, I will try to prepare notes on a computer, which will allow for me to more easily prepare a transcript. I bring this up, because in this case, I think there are some interesting issues discussed in the video which haven't been written about much before. Please have a look:

You can also find David's spreadsheet for implementing the formula at his personal website.

For email readers, the videos never show up in the email, but you can see the video by clicking here.


  1. Wade,

    I have been using a similar approach for a while now, recalculating the withdrawal rate each year based on current portfolio, new return projections, etc. Since we plan for a fluctuating yearly "income" a floor is established to meet basic needs.

    I do it the long way, using a detailed cash flow analysis with Monte Carlo simulations. Two things I always struggled with is how far out to plan and what a proper success rate should be. Would you agree that the actuary age plus 2 with an 80% probability is appropriate for a long hand approach as well? I can appreciate these short cuts, especially if they work well, but if someone is paying me 1% they should get a more customized analysis in my opinion.


    1. Chris,

      While I did replicate the analysis to confirm that the equation is correct, I did not personally replicate the part to confirm that 80% success and life expectancy +2 are the optimal parameters. Though I do approve of the methodology used to find that, which is to plug all the spending paths into a utility function seeking to find the best balance between spending more and protecting from spending drops.

      One thing to note, however, is that this article is written under the assumption that someone has no other assets outside their financial portfolio. For someone who has Social Security and other income sources, the optimal parameters will be different. So this article does not provide a complete solution to the retirement income problem. But it's a useful contribution, nonetheless.

  2. Hi Wade--

    This is interesting! And it is fun to download Blanchett's spreadsheet and then backsolve the target prob(success) for various withdrawal rates.

    I'm still a bit puzzed by the 2.5% inflation rate parameter embedded in the "simple calculator " spreadsheet (in the hidden CMAs sheet). Was the inflation rate varied in the Monte Carlo analysis? Or was it held constant at this parameter value?

    For your video, a couple of tweaks would help: (1) the W% formula is listed in the video as changing based on 10 years, not the 15 that you talk about or Blanchett refers to, and (2) the spelling of "withdrawel" in the video needs fixing. To make the videos easier to watch, I also suggest that you look at the camera throughout; the angled views of your looking away while talking are distracting and un-natural looking.

    I also want to point out that although Blanchett's R-squared value for his w% formula is certainly impressive, it capitalizes on characteristics unique to the historical data. This is especially true with the empirically-derived selection of variables and weights in his w% formula. Applying the same formula to decades of stock/bond market performance going forward (i.e., an independent sample) would undoubtedly produce a good deal of shrinkage in the R-squared value and less robust research findings. Blanchett may be showing too much confidence in his formula as a predictive tool.

    1. Thanks for the video feedback. Hopefully that camera switching can be improved if I'm reading a script. That had to be done when I stumbled on words and had to restart what I was saying.

      About your inflation question, he is assuming a fixed 2.5% inflation rate. It is held constant. I can indicate from my own past experience that while I do usually allow inflation to fluctuate as a random variable, it doesn't make much difference to the results, perhaps suprisingly.

      About your point on the R^2, that is based on Monte Carlo simulations with alpha parameters ranging from -2% to +2%. So you are right with your suggestion to the extent that future market returns might imply a need for an alpha even less than -2%. It would be worthwhile to replicate this analysis with a different set of underlying market returns. Good idea. But I'd be willing to guess that this is not one of the variables that will have a big impact on R^2. I think the time horizon is the biggest one.

      Thank you.

    2. How well would Blanchett's formula work with historical stock/bond market returns in other countries, e.g., Japan?

    3. The formula is based around the US historical situation, but at least allows the possibility to assume lower future returns by up to 2%. If the underlying return distributions start moving too far away from that, then the formula is trying to estimate a line outside of the range in which it was calculated and could be off to the extent that these underlying relationships are nonlinear.

      So it may or may not work all that well, it's a bit hard to guess about this. It's worth further investigation. In fact, I'll suggest this to him, as I bet he could modify his program pretty quickly to get a formula based on the historical experience of each country, and then we could see how different each of these formulas are.

  3. I wouldn't really focus on the country (e.g., US versus Japan), just on what you expect the return of a portfolio to be going forward. Just make the adjustment as the alpha value, as noted above, in the spreadsheet you can find here: http://www.davidmblanchett.com/tools!

    1. Thanks David. That's the idea. The alpha term provides the user a way to move away from the historical averages. Negative alpha can just be interpreted as lower future market returns.

  4. Long time reader, first time poster.

    We’re a 45-year-old couple trying to estimate our safe withdrawal rate for our current age. It’s been difficult to come up with a reasonable projection given that most of the research focuses on 30-year durations, and of course the added complications of the low interest rate environment.

    I find David’s new dynamic framework to be a helpful and logical approach. That said, I’m having trouble when I attempt to give the historical data a haircut in the above-described manner; or at least getting the results to sync with analysis from one of your earlier blog postings concerning reduced return assumptions in the context of longer retirement periods:


    My understanding from Table 1 of your blog post is that the SWR for a 50 year period with 90% certainty (under the reduce return assumptions) was about 2.2%. In using David’s spreadsheet with the same 40% equity allocation the results were 2.19% with 80% certainty. But after adding an additional 2% of negative Alpha, which seemed roughly consistent with the lower return assumptions referenced in Table 1, the SWR dropped to 1.18%. This is a much lower result than anything else I’ve seen, even after adjusting for the lower return assumption.

    Perhaps I’m making a mistake by adding too much negative Alpha. You commented above that the Monte Carlo analysis already incorporated the possibility of -2 Alpha, so adding an additional -2 Alpha may be creating the distortion.

    I’d really appreciate any feedback you might have on the discrepancy, and more directly what might constitute a reasonable SWR for such a longer duration. 2.2% vs. 1.18% is the difference between being a happy camper and being a corporate cog for another decade, or two.

    Keep up the great research; I've really enjoyed reading your blog over the last few years.

    1. Good question, thanks for writing.

      I thought I had a quick answer for you. But when I look at David's Figure 1, it seems that his equation never estimated something less than 1.8% for all the scenarios he considered. So your choice of 80%, 40 years, -2% alpha, and 40% stocks should be covered in this universe. I will need to play around with this more when I can get into my office next week and then get back to you.

      Do note that you shouldn't try to plug years higher than 40 into this, because as you can see from the other blog post, decreases in the withdrawal rate start leveling off as the number of years increases. But this equation would fit a line and would underpredict for beyond 40 years.

      I'll be in touch.

    2. Hi, I hope your Thanksgiving went well. I'm following up with you now from your questions before regarding the spreadsheet. I confirm that I get that same 1.18% number when plugging in 40% stocks, -2% alpha, 0.2% fees, 49 year life expectancy, and 80% success rate.

      Now, what to make of that number? With the years higher than 40 and combined alpha at -2.2%, this is getting to be outside the range that the equation was meant to handle. I would suggest that 1.18% is too conservative, especially if you do have flexibility with your budget. His equation fits a straight line in an area where some curve shape would be more appropriate. And you are also right that the blog post I did which you mentioned using the "MoneyGuide Pro" assumptions gives about 2.2% for 50 years and 10% failure. I would be comfortable using that number. I don't think you'd really need to seriously think about a withdrawal rate less than 2%. Of course, there are no guarantees and the sustainable withdrawal rate could be less than 2%, but this would represent a real economic catastrophe and you would not be alone in your misery.

      I'm working on developing my own variable withdrawal rate system now as well, and hopefully I will be able to add more to the discussion soon.

    3. I appreciated your feedback.

      I was hoping to clarify the SWR percentage using the 80% success threshold recommended in David's article, when using the MoneyGuide Pro discounted expectations for 50 years. Your earlier chart seems to suggest about 2.6-2.7%, but I wasn't sure.

      I tend to be conservative about SWR assumptions, particularly given the longer timeframe involved, so my natural inclination is to use the lower 2.2% withdrawal rate with the 10% failure probability. But I don't want to play it too safe either, and forgo flexibility early on in life. And though I would never be comfortable with a fixed 80% success rate (i.e. a 20% chance of failure), given the ability to make annual adjustments, we could likely steer the portfolio away from danger with only moderate spending reductions along the way. Furthermore, the MoneyGuide Pro assumptions already discount the historical data by more than 35%, so there is a degree of buffer built back into the modeling. Finally, though we are resistant to reducing spending during retirement, if times were truly difficult, we could sustain a 25% reduction and still be fine. As you say, there would be a lot of shared misery.

      So, with all that said, I guess I'm asking whether you would you feel reasonably safe going with the more aggressive SWR, or do you feel it might be more prudent to save a few more shillings and maintain the added buffer.

      Thank you for your help. There are not many people with your expertise, and it's comforting for us to get your feedback. To tell you the truth, it can be a little disconcerting how a few tenths of one percent in either direction can make such a difference to ones planning options.


  5. Terrific, thanks for your help.

    David's spreadsheet predicts the life expectancy of a 45-year-old couple to be 47 years; so we plugged 49 years into the equation. Also, we used an alpha of - 2.2%, to reflect 0.2% for investment costs in addition to the -2 alpha. These assumptions resulted in the 1.18%.

    When we used 40 years for the duration with the same assumptions, the resulting withdrawal rate was 1.93% which continues to be lower than Table 1 from your earlier blob post. But it's moving in the right direction.

    Enjoy the Boggleheads forum.

  6. Hello, Wade. Thank you for your extremely important work in the area of safe withdrawals. I am excited what the next few years will bring to this critical area of retirement planning and implementation. I will readily admit much of this level of material exceeds my ability to comprehend as my educational background is limited.

    As most of us have SS and other outside incomes (and many are do-it-yourself types), would you explain further your comment in the response above...."One thing to note, however, is that this article is written under the assumption that someone has no other assets outside their financial portfolio. For someone who has Social Security and other income sources, the optimal parameters will be different. So this article does not provide a complete solution to the retirement income problem. But it's a useful contribution, nonetheless."

    Many thanks.

    1. Hi,

      The basic argument is:

      Retirees who have additional streams of income from Social Security, pensions, and annuities actually have a greater capacity to endure the depletion of their financial assets and so can be justified to spend and invest more aggressively earlier in retirement.

      So, by assuming there are no other assets outside the financial portfolio, the mathematical formulas to calculate the optimal withdrawal rate will end up being overly conservative.

  7. Why can't everyone have a Monte Carlo? See Flexible Retirement Planner. You could then input you specific income stream and desired expense stream and any one time expenditures. You would get a number specific for you. I agree the 'help' section could be horrific explaining and making recommendations. But as a year or two goal. I think the short equations sometimes are too short and too assumptive to really be an overall success.