Friday, February 20, 2015

Dominated Strategies and Dynamic Spending

Sharp-eyed readers will notice that I have tweaked my blog format to include some of my favorite posts from other retirement blogs. Retirement blogs may not be the best place to find sharp-eyed readers and I have three pairs of reading glasses here by my keyboard, just in case. Nevertheless, you will find these posts in the sidebar. This week, I included one from the Canadian Couch Potato blog on Spending Dividends Only and another from Wade Pfau's new website. I hope you enjoy them both.

In my last post, Dominated Strategies, I showed that for retiree's who want to keep their risk below a maximum level throughout retirement, game theory tells us that the variable sustainable withdrawal rate strategy (SWR-V) never provides worse payoffs than fixed-dollar withdrawals (SWR-F) and SWR-V provides better payoffs if the portfolio grows.

Game theory principles tell us that SWR-V weakly dominates SWR-F and that we should never play a dominated strategy, so I cross SWR-Fixed off my list of strategies to consider. (As I mentioned in my previous post, even William Bengen stated that SWR's should be revisited throughout retirement and not set in stone.)

SWR-F underperforms SWR-V, which prescribes spending a fixed percentage of an ever-changing portfolio value rather than a fixed dollar amount, because SWR-V uses new information as it develops over time, the current value of a retiree's savings. SWR-F only calculates a spending amount that was safe on the first day of retirement (an a priori expectation).

As conditions change, like our portfolio value, SWR-V takes advantage, increasing spending when it is safe to do so. By decreasing spending when it becomes riskier, SWR-V reduces sequence of returns risk. SWR-F ignores this new information.

There are other important changes besides portfolio balance to the key determinants of the probability of ruin as retirement progresses, including market return expectations, remaining life expectancy, spending needs, and risk tolerance.

As David Blanchett and Sudipto Banerjee have written (both links download PDFs), retirement spending typically declines over time, about 3% a year on average. A retiree's risk tolerance and capacity can also change over time as dependents need less support, for example, or a spouse is lost. And, of course, life expectancy constantly declines at a rate of a little less than a year per year of life. Neither the SWR-F nor the SWR-V strategies account for any of these important changes, leaving open the possibility that there is a strategy that dominates SWR-V.

If considering more data and more timely information improves retirement income spending strategies, then a strategy that considers more new information than SWR-V takes into account could be expected to dominate it. I will refer to this new strategy as "Dynamic Spending."

(David Blanchett and Larry Frank have written about this strategy previously in A Dynamic and Adaptive Approach to Distribution Planning and Monitoring, as has Ken Steiner. Larry Frank provides a nice explanation in a blog post entitled, "How income may compare between Dynamic and Safe approaches.")

Let's consider a version of the Safety First game from Dominated Strategies as a strategic game in which the retiree wishes to maximize available spending while ensuring that risk of ruin never exceeds a desired level. The SWR-Fixed strategy assumes some acceptable probability of ruin, typically 5% to 10%, at the beginning of retirement, but lets the risk drift throughout retirement in order to ensure a predictable, fixed amount of annual spending. Retirees who are happy to see steady spending even when their portfolio declines may not understand that it comes at the cost of increased probability of ruin.

SWR-Variable fixes the variable risk problem of SWR-Fixed but generates unpredictable annual spending. (A retiree spending from a volatile portfolio can have constant risk or constant income, but not both.) In fact, SWR-V "over-fixes" the risk problem because it doesn't consider a declining life expectancy. Over time, risk will decline with SWR-V and SWR-F as the retiree's remaining life expectancy declines. A retiree who thinks a 5% risk of outliving savings is acceptable, for example, might see risk decline to 3% as she ages, which means she will be spending less than she could safely spend.

A Dynamic Spending strategy will recalculate a sustainable withdrawal rate annually by considering updated portfolio balance, an updated life expectancy, changes in risk tolerance over time, changes in expected future returns and changes in spending.

Whether the retiree's portfolio balance trends downward or upward, Dynamic Spending will provide a better payoff than either SWR strategy because it considers remaining life expectancy. As remaining life expectancy declines throughout retirement, risk of ruin is reduced and the sustainable withdrawal rate increases. (The sustainable withdrawal amount will decrease if portfolio losses exceed the benefit of the life expectancy decrease.)

Spending gains due to decreasing life expectancy increase exponentially. Even if portfolio value remained flat throughout retirement, decreasing life expectancy would more than double spending by the end of a long retirement (see chart). SWR-V and SWR-F ignore this increase.

When portfolio values trend upward, Dynamic Spending will have a larger payoff than SWR-V because it will be augmented by a declining life expectancy contribution. When portfolios trend downward, Dynamic Spending will limit increasing risk of ruin by reducing the spending percentage and by adding the declining life expectancy contribution.

As I mentioned in Dominated Strategies, SWR-Variable "over-fixes" risk reduction. Spending a percentage of remaining portfolio balance and ignoring the life expectancy contribution with a declining portfolio eventually lowers risk too much, unnecessarily lowering spending. By considering both, Dynamic Spending adjusts spending to the retiree's current risk tolerance and maximizes spending at that level.

Now, let me try to simplify this rather lengthy post. All three of these strategies use the same basic mechanism. They calculate a sustainable spending amount using Milevsky's formula, simulation or historical data and all three are based on the same information regarding the retiree's financial situation.  The difference is when we recalculate using new data.

SWR-Fixed makes a single calculation at the beginning of retirement and ignores any new information thereafter, no matter how critical that information might be. (Intuitively, this should feel like a bad idea.) The information to calculate the SWR-Fixed sustainable spending amount should include initial portfolio value, expected market returns, life expectancy, and asset allocation based on risk tolerance.

SWR-Variable uses the same information except it recalculates the sustainable spending amount every year, taking into consideration changes to the portfolio value from the previous year, but nothing more. And it assumes that the withdrawal percentage calculated at the beginning of retirement remains the best one. Doing so reduces sequence of returns risk, but it doesn't maximize sustainable spending.

Dynamic Spending recalculates sustainable spending every year, too, but it doesn't stop with updating portfolio values, as does SWR-V. It also updates a decreasing life expectancy, changes in risk tolerance and capacity, and expectations about future market returns. Dynamic Spending maximizes the sustainable spending amount given the retiree's current risk tolerance.

Dynamic Spending always provides better payoffs when risk is considered appropriately than does SWR-Fixed or SWR-Variable. SWR-Fixed and SWR-Variable are strategies that are dominated and should never be played. That's a stronger message than "some of these strategies are sometimes better than others."

One of my hobbies is shooting sporting clays, so the following analogy works for me. Hopefully, it will help you visualize the comparison of strategies, too. In sporting clays, the objective is to break a clay target with a shotgun.

Trap and skeet throw targets in predictably similar paths all the time, but sporting clays can come from anywhere and go anywhere, relatively speaking. In retirement finance, breaking the clay is symbolic of reaching the end of retirement with at least a little money to spare. That's our target.

SWR-Fixed is analogous to aiming where targets have ended up most often in the past, yelling "pull" and shooting in that direction.

SWR-Variable adds some data to the calculation: the changing value of your savings over time.

SWR-V is like deciding that you will track every target through its path and shoot a foot in front of it (lead it).  A foot will work for some shots that quarter away from you, but it won't be enough for a target that crosses directly in front of you or is farther away. Nonetheless, you are a bit more likely to hit the shot than by aiming where a lot of targets have gone in the past because you are now considering more information, that being where the target currently is and not just where targets have historically been.

Dynamic Spending is like tracking the target, knowing where it has been and where it is, and consequently where it is likely to soon be, estimating its vertical and horizontal speed and meeting the target with the correct lead. If the target is falling, you shoot below it. If it's a crossing target, you shoot farther ahead. You adjust your aim constantly. You hit a lot more targets that way.

Although all three of these strategies are proposed as viable alternatives, game theory tells us that Dynamic Spending dominates the other two and should always be our choice from among these three.

The explanation may be complex, but the advice is straightforward. If you're going to fund retirement by spending from a volatile portfolio of stocks and bonds, recalculate a sustainable withdrawal amount every year based on your revised expectations of future market returns, life expectancy, risk tolerance and capacity and estimated future spending needs.

Even if you ultimately decide to spend more, you'll at least know how much risk you're taking.

Next, I'll consider the application of game theory's Pure and Mixed Strategies.


  1. hi Dirk, i hope you can clarify if your SWR-Variable is refering to the work done by either Guyton or Zolt. in any case i am interested in your upcoming post if any to determine how we can estimate life expectancy.

    1. Kyith, I was not referring to either Guyton or Zolt, though their strategies provide for variable spending. I'm not big on decision rules that "would have worked in the past".

      By SWR-Variable, I am simply referring to spending, say, 4% of your remaining portfolio balance annually instead of 4% of whatever your balance was back on the day you retired.

      I feel pretty certain that Dynamic Spending will outperform any SWR-variable strategy.

      There are many good life expectancy calculators on the web, like this one at Vanguard.

      Thanks for your question!

    2. Hi Dirk, thanks for the clarification. 4% on current sum will impact fulfilling expenses. I was thinking for my financial independence plan for 40 years old on this and thought decision rules from guyton and zolt will work well for me. I am also exploring funding expenses by dividend cash flow rather than selling capital.

    3. Kyith, I suggest you read the sidebar of this post regarding the Spending Dividends Only strategy. The academics and practitioners I follow agree that it is not a rational strategy and the idea that you are not spending capital is an illusion.

      Good luck!

    4. Hi Mr Cotton thank you for the advice. I have heed your recommendation before i posted that comment by reading canadian couch potato's series of post. i have also heard his interview at radical personal finance.

      i agree with what canadian couch potato said but if i get his message, his view addresses the general heresay a lot have about dividend investing, which is that they confuse dividends as having no downside. also that blue chips are more stable and therefore its good to invest in them.

      dividends are paid out of free cash flow and if dividends are paid out, there is a high chance growth is going to taper. so there is no free lunch there.

      if i read his message on those that succeed is because of quality it is that the investors buy good businesses, much like a retiree owning a business that he delegate to a CEO. in that case we worry how the business stand up during recession.

      but i can't shake the idea that its the same between selling stakes in business versus taking dividend payout from the free cash flow of business.

      ultimately i believe its wrong to spend dvidends or to go for high dividend companies just for the sake that they satisfy your desired withdrawal rate.

      i would rather go for a free cash flow strategy. if its a business that generates ample cash flow but pays out something lower than my withdrawal rate, then i can rebalance by selling my stake for the cash flow shortfall required as part of my withdrawal.

      then again i am being a active investor here, which is totally different from an index strategy.

    5. Kyith, a couple of points. First, the issue is not that stocks that pay dividends will see lower future growth. The stock price will adjust the day the dividend is paid because on the day the company pays out say, a million dollars in dividends, that company is worth a million dollars less. If you own a stock worth $10 a share today and it pays out 30 cents tomorrow in dividends, the stock will be worth $9.70 tomorrow (plus or minus any price change that would have occurred had the dividend not been paid). Instead of owning $10.00 worth of stock, you will own $9.70 worth of stock and 30 cents cash. You are no better or worse off.

      Second, don't confuse dividend-paying stocks with "good companies." Some good companies pay dividends, some don't. Some bad companies pay dividends, some don't. Many companies that pay high dividends are in trouble. The dividend is high (as a percentage) because their stock price is so low.

      An index strategy would tell you to buy some growth fund indexes with less dividends and some value funds with higher dividends, because you can't predict which will outperform in any given year. (See these diagrams. LV are value stocks which probably pay out more dividends. LC contains both value and growth stocks.)

      Hope that helps.

    6. hi Mr Cotton, thanks for explaining

    7. Thank you for writing, Kyith. Its discussions like these that make the blog useful.

    8. yes. u know i been trying to find folks to talk about this wealth de-accumulation topic for so long but not many are in that mood to talk about it. to have you explaining, and at the same time forthcoming in exploring my concerns, i cannot ask for anything more.

      my situation is a bit different from majority of your readers considering i am singapore based and for us to assess to a passive indexing instrument that is low cost is challenging. we have to go for non-synthetic ETF from vanguard in Hong kong or london to create something like that. london have inheritence tax, which is like estate tax in us which is a problem. so yeah, US folks should really be glad they are so fortunate.

      thus we have to explore individual stock strat just to achieve something mediocre.

  2. Hi Dirk,

    Just some technical details about Dynamic Updating ... what you call Dynamic Spending ... a better paper than the one you cited above, that explains the entire concept as well as how portfolio allocation differences matter as well may be found summarized in this JFP Mar 2012 paper here:

    Those readers who would like to see the data and more in-depth discussion on the above paper may find that here (which more graphs and data appendices):

    The blog post you reference above includes dynamically updating the mortality data as well (just in case your readers miss your subtle transition between SWR-V and dynamic) - that is why the trend lines in the blog's graph go up with age (shorter periods remaining, i.e., older with fewer years, can spend more money compared to longer periods remaining.

    What matters? 1) Risk & return data characteristics of the ACTUAL portfolio a retiree has (not a general rule of thumb or data from a generic allocation); 2) difference between present age and expected longevity from a period life table (which sets this year's time frame for spending; 3) how sensitive to success (percentage of simulations that fail) one is (the more you constrain success to a higher rate - the less you are able to spend). These represent the 3D aspects we've researched.

    #3 above is important to understand in that under the Dynamic Updating (you call it Spending) as long as one keeps setting the future expected longevity age using tables, one should also always have a portfolio balance from which to spend – you’re constraining spending to continue to last into future years. The impression one gets from SWR-F work, is that money ends when the fixed time period does, which is not true (but SWR-F fails to say how to transition into older ages or use of the money once the time period has been survived).

    This said, as the time frame shortens, there is an exponential growth to spending – which endangers the portfolio money lasting into future older ages obviously. Our research continued to look at how to adjust spending to mitigate the exponential nature of shortening time frames when spending – that JFP December 2012 paper may be found here:

    How it is done is to adjust the raw calculated withdrawal rate by (1 - 1/n) where n is the present time frame from the mortality tables.

    Please don’t take it wrong citing our own papers – I simply would like your readers to be aware that more advanced work on the subject has and still is taking place, and what that work looks like that should be applied to retirees.

    All this sounds complicated – it is no more complicated than modern medicine procedures as compared to those in the early 1900’s. I think the retirement income profession for managing income from one’s portfolios should advance from the rules of thumb approach into measuring and monitoring prudent income using more advanced insights and procedures.

    We're on the same page as usual. Great job advancing the discussion and understanding with others!

    1. Thanks for passing along the links and additional information, Larry. I'm sure many readers will want to go into greater detail on the subject of dynamic updating/spending and I don't plan to. I'm primarily investigating ways that game theory can be used to look at retirement planning from a slightly different perspective and I think these three are great examples of dominated strategies.

      There are many retirement income strategies out there and dominated strategies is one way to winnow the list.

      Having said that, the important point I wanted to make aside from the dominated strategies issue is that retirement spending needs to be reconsidered periodically and especially after any of the key variables change significantly, which I believe is your major contention. I highly recommend the papers Larry mentions to anyone who wants to gain a deeper understanding of dynamic updating, or as I referred to it, dynamic spending.

      Dynamic updating doesn't have to be more complicated than SWR-Fixed to be beneficial. You just have to do the calculation every year instead of once. I agree that its more complicated with life expectancies less than about a decade because spending increases exponentially, but maybe at that age spending from a stock and bond portfolio isn't the best approach.

      Thanks for the contribution. Larry's links follow.

      An Age-Based, Three-Dimensional Distribution Model Incorporating Sequence and Longevity Risks

      An Age-Based, Three Dimensional, Universal Distribution Model Incorporating Sequence Risk

  3. For some reason Dirk, the March 2012 paper link got duplicated above so the December 2012 link didn't make it ... this is the "Transition Through Old Age in a Dynamic Retirement Distribution Model"

    Sorry about that ...

    1. Thanks, Larry. Here's a clickable link for readers: Transition Through Old Age in a Dynamic Retirement Distribution Model.

      If you're interested in the research behind dynamically updating your spending in retirement, I highly recommend you read Larry Frank and David Blanchett.

  4. Kyith asked above how to find life expectancy and I provided a link to a calculator at I recently referred to a formula for calculating probability of ruin that was developed by Moshe Milevsky. I placed a shared Excel file here that incorporates his formula.

    This formula uses a single life expectancy. Couples should use joint-life probability, instead. It will be longer. The calculator at Vanguard provides this option, but Milevsky's formula does not easily accommodate it.

    Milevsky's formula can incorporate joint-life probabilities by simply using the joint life expectancy of the two spouses, but only if you are willing to accept the assumption that expenses won't decrease after the death of the first spouse. That isn't realistic, of course, so the spending rate calculated will be somewhat conservative.

    This could be accomplished by using a calculator such as the one provided by Vanguard and using the joint-life probability it calculates for the couple instead of a single life expectancy. And again, consider the results somewhat conservative.

  5. can you rerun the chart with lower real returns, say 3%? to get the withdrawal rates

    1. That would obviously translate the curve straight down. I can't easily redo the chart, but would you settle for three points, one at each end and one in the middle, and sketch your own curve?

      5 years = 8.6%
      15 years = 3.6%
      30 years = 2.3%

      Of course, if you thought real returns were only going to be 3%, you probably wouldn't choose SWR, at all.

      Thanks for writing!

  6. Just wondering if you are familiar with the Waring and Siegel paper titled "The Only Spending Rule Article You'll Ever Need".

    1. I wasn't until you mentioned it. Did you have a question about it?

  7. It is paper about another approach to dynamic spending in retirement. Just hoping you might share your thoughts about it.

    1. I've only had a chance to skim it, but it looks like the same approach to me. The title is hyperbole (there is more than one decision) but publishers frequently change titles after they get the paper. From my initial read, it looks like good stuff. I'll get back to you after I've had a better look and give you some comments. Thanks for forwarding.

    2. I finished the paper and find it completely consistent with the approach I recommend on this blog. It references most of the work I have built my philosophies on. I haven't read their book, but I suspect it could be quite helpful for retirees. Thanks for passing it along, Garth.

    3. Thanks for sharing your thoughts. Really enjoy your blog!

  8. Such an impressive article, author has nailed the topic. Thanks for sharing.

  9. I'm definitely on board with your dynamic spending ideas and with the Waring and Siegel (ARVA) approach. I think that any strategy that does not periodically adjust for changes in the portfolio, risk aversion, return and inflation expectations, changes in longevity expectations, etc. is probably looking for trouble, at least in extreme situations. The inconvenience of changing withdrawals/spending is the cost of not blowing up a retirement I guess. Now, a question on game theory. This is a good addition to the thinking on this stuff and takes us in a good direction. I'm a little confused though. If you are player 1 -- if I am getting this right -- choosing amongst the strategies, who is player 2? I'm having a hard time seeing the 'matrix' of the game. Also, is this dominance (dynamic spending) a strict, pure dominance or is there some kind of mixed strategy of two strategies vs a third going on here or maybe a mixed against a pure game? Fwiw, agree on Polak and Spaniel; I think you had that in another post.

  10. "I think that any strategy that does not periodically adjust for changes in the portfolio, risk aversion, return and inflation expectations, changes in longevity expectations, etc. is probably looking for trouble, at least in extreme situations."

    Exactly, Will. There is no "trouble" until a retiree's portfolio declines in value and he/she tries to keep spending as much as before. In fact, adjustments aren't necessary when the portfolio value increases, but they are possible (and safe). The downside of not adjusting is introduction of the the risk of ruin. I'll be writing about that in my next post.

    Re: game theory and considering "a version of the Safety First game from Dominated Strategies as a strategic game in which the retiree wishes to maximize available spending while ensuring that risk of ruin never exceeds a desired level", I assume this is the game to which you refer.

    This is a class of games referred to as "stochastic games against nature", so Player 2 is "nature", also referred to as "the odds." There are many pure strategies to maximize spending while controlling risk of ruin. Life annuities are one, a TIPS bond ladder is another. These can be combined into many mixed strategies such as floor-and-upside, dynamic updating (adjusting the strategy mix over time), dynamic asset allocation, etc.

    Thanks for writing!

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