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.

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Variable Spending Strategies: Variations on a Theme

We could easily name ten or twelve retirement income strategies but several of them are really just variations on a theme. When you're trying to choose one, it may help to visualize them that way.

In a recent post, Dominated Strategies and Dynamic Spending, I showed that fixed-dollar sustainable withdrawal rates (SWR-Fixed), fixed-percentage rate SWR (SWR-Variable), and Required Minimum Distribution strategies are all dominated by a dynamic updating strategy. Game theory tells us that dominated strategies should never be played and that guideline should narrow the field of choices.

In A Second Look at Time Segmentation, I argued that the benefits of time segmentation strategies may be largely behavioral. Holding large allocations of cash will reduce expected returns and Moshe Milevsky has shown (download Word doc) that the strategy cannot be counted on to bail us out of a bad sequence of returns, though it sometimes will. 

Nevertheless, many retirees appear to find comfort in time segmentation strategies, knowing that any spending problems are at least five years into the future. I'm always in favor of sacrificing a little economic efficiency if it helps the retiree sleep at night.

I’m now going to argue that these are actually the same strategy applied to different degrees.

A dynamic updating strategy, or dynamic spending strategy as I have sometimes referred to it, tells us to modify our spending periodically (typically annually), to reflect our ever-changing portfolio value, diminishing life expectancy, new expectations about market returns and risk, and any changes to our personal risk tolerance and risk capacity.

If we calculate a sustainable spending amount once at the beginning of retirement, we have an SWR-Fixed strategy. This strategy's attraction lies in its simplicity of implementation and maintenance, but it condemns the retiree to spend based on conditions that might have existed two or three decades earlier. In other words, it ignores any new information after retirement begins – a foolhardy approach.

Michael Kitces argues that no one really implements SWR-Fixed because retirees eventually realize they must spend less or can spend more and do so, and he has an excellent point. Wade Pfau argues that SWR-Fixed is a research technique and never was a retirement income strategy. I think he’s right, too. Yet, I don't completely buy the idea that no one tries to use the SWR-Fixed strategy by rote.

For a decade or more, Money magazine touted the SWR-Fixed strategy, relenting only after many retirements were trashed in the 2008 market crash. I recently received a sample Kiplinger newsletter suggesting the strategy. With so much ink in the popular press for so long, it’s hard for me to accept that no one believes it. I hope Pfau and Kitces are correct, but I have a nagging suspicion that they are not entirely. If you’re implementing a SWR strategy by rote, please stop.

In a post entitled, Sequence of Returns Risk and Payouts, I showed that an SWR-Variable strategy, in which a retiree spends a fixed percentage (like 4%) of remaining savings portfolio balance each year, eliminates the possibility of ruin inherent in an SWR-Fixed strategy. It provides variable annual spending but a more constant risk of failure than SWR-Fixed. SWR-Variable moves risk from longevity (running out of money) to payouts (perhaps needing to spend less), where it seems to do less harm.

SWR-Variable reduces sequence of returns (SOR) risk by reducing spending when portfolio value declines. If we recalculate a sustainable spending amount annually, instead of once at the beginning of retirement like SWR-Fixed, and only update portfolio balance, we have an SWR-Variable strategy. Because it uses more new information, it dominates SWR-Fixed, but because it doesn’t update life expectancy, market return expectations and risk tolerance and capacity changes, it is dominated by dynamic updating.

So, calculate spending once at the beginning of retirement and you have SWR-Fixed. Apply it annually, updating only your savings balance, and you have SWR-Variable.

Basing spending on IRA Required Minimum Distributions (RMDs) also exposes us to less SOR risk than SWR-Fixed because spending will be reduced when portfolio values decline. RMD bases spending on an annual updating of portfolio balance and remaining life expectancy (updated annual spending is roughly current portfolio balance divided by remaining life expectancy), but ignores changes to expected market returns and changes to risk tolerance and capacity. As a result, it is also dominated by dynamic updating.

Still, studies show that the RMD strategy is a reasonable approximation of dynamic updating strategies and a lot simpler. To quote David Blanchett, et. al. from a 2012 paper entitled, Optimal Withdrawal Strategy for Retirement Income Portfolios, "As a practical matter, for retirees who can’t replicate the results presented here or don’t have access to them, the RMD method emerges as a reasonable alternative to the more common constant dollar and constant percentage of assets withdrawal strategies."

Dynamic updating strategies calculate a new sustainable spending rate each year incorporating all critical factors of the probability of ruin: current savings balance, remaining life expectancy, market return expectations and current risk tolerance and risk capacity. Spending is no longer tied to your personal financial situation as it existed at the beginning of retirement, or even the previous year.

Lastly, let's look at time segmentation strategies. Time segmentation strategies hold four or five years of expenses in cash, the next five to seven years of expected spending in intermediate bonds, and the remainder in stocks to cover long term spending.

As I argued in A Second Look at Time Segmentation, this strategy is largely an SWR strategy with perhaps too large an allocation to cash for its own good. It could be an SWR-Fixed strategy if the retiree calculates spending once, an SWR-Variable strategy if the retiree recalculates spending periodically based on a current portfolio balance alone, or a dynamic updating strategy if the retiree updates all critical variables periodically. If we look at the portfolio holdings alone, it may be impossible to distinguish an SWR strategy from a time segmentation strategy. (A larger than expected cash holding tips us off that it is probably the former.)

The more critical parameters we consider in our retirement income strategy, the better the approximation of sustainable spending.

The following table summarizes the variables considered by each strategy. Time segmentation is not included because it dictates an asset allocation but can use any of these spending strategies.

How does this help a retiree? It should help by simplifying the broad array of retirement income strategies available. A retiree will always be better off updating her spending as her financial situation changes and the more critical information she updates in the process the better. 

SWR-Fixed, SWR-Variable and RMD strategies simplify sustainable spending calculations by ignoring critical new information. Time segmentation can be added to any of these strategies, but the financial justification for it is much weaker than the behavioral justification.

What is the benefit of ignoring relevant new information? Only that it simplifies the math and reduces the management process a tiny bit – spending is recalculated just once a year in any case, except for SWR-Fixed, of course.

Retirees unwilling to do that little bit of extra work will likely be better off with a set-and-forget strategy like TIPS bond ladders and life annuities.

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The sidebar shows a link to a recent post by Wade Pfau at Advisor Perspectives entitled, The Hidden Peril of Sequence of Returns Risk. SOR risk is complicated and nuanced. In several ways, it is unlike any other form of retirement financial risk, and certainly different than investment risk. No retirement income strategy is perfect, but the risks of SWR strategies are more difficult to understand than the rest. A great read.

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Unraveling Retirement Strategies: Variable Spending from a Volatile Portfolio

 In Unraveling Retirement Strategies: Constant-Dollar Spending (4% Rule), I described retirement funding strategies like the “4% Rule” that base portfolio spending on a calculation made at the beginning of retirement that remains unchanged in real dollars regardless of how the household’s finances unfold over time.

Constant-dollar spending is like the Stephen Colbert joke about a man whose beliefs are constant. He believes the same thing on Thursday that he believed on Tuesday ... no matter what happened on Wednesday.

That doesn't work well for retirement planning, either.

Variable-spending strategies are similar to constant-dollar strategies in that they spend periodically from an investment portfolio but differ in that they spend a periodically updated amount based on portfolio performance – they spend more in good markets and less in bad markets.

This is a huge difference. We have two basic choices in portfolio-drawdown strategies: spend a predictable amount annually and risk depleting our portfolio or spend an unpredictable, possibly painful, amount annually to avoid portfolio depletion.

Spending strategies, including these two, explore ways to draw down a portfolio without outliving it but they do so without considering the expense side of the equation.

Regardless of which of these strategies you choose, you will spend the amount you need to spend after retiring. If you need a kidney operation or a new roof or a check for the IRS, you will pay for those things regardless of what your spending strategy recommends. That will increase your chances of outliving your savings but that risk isn't considered by these "income-side" strategies.

There are many variable spending strategies. I recently attended a webinar in which Wade Pfau identified a half dozen of the better known and in Making Sense Out of Variable Spending Strategies for Retirees[1] he compares several more.

Joe Tomlinson, Steve Vernon and Wade Pfau recently recommended using the spending percentage for Required Minimum Distributions (RMDs) from qualified retirement accounts[2]. Vernon provides a summary of the study in "How to Pensionize Any IRA or 401(k)."[6]

RMD is based on the assumption of a retiree and a spouse 10 years younger. Retirees closer in age to their spouse can perhaps use the Modified RMD strategy and spend 10% more. Your investment company will calculate RMDs for your qualified retirement accounts when the time comes or you can find a calculator online.[3] You are required by tax law to use these calculations on tax-deferred retirement accounts but you can, of course, use them on all types accounts if you choose.

Another strategy is to spend a fixed percentage, say the same 4%, of the new portfolio balance each year, though the safe spending rate actually increases as life expectancy decreases. It makes more sense to spend that gradually-increasing percentage of one’s current portfolio balance each year than to always spend a fixed percentage of a changing portfolio balance. It approaches 10% late in retirement but grows slowly at first.

Most Americans are eligible for Social Security benefits so most have a floor. It may not be an adequate floor in the event that your portfolio is depleted, but it is a floor. The variable spending strategies and the constant-dollar strategies, therefore, technically manage the upside portfolio of a floor-and-upside strategy and will rarely be a standalone strategy.

I recommend, once again, reviewing this strategy in Pfau and Jeremy Cooper’s The Yin and Yang of Retirement Income Philosophies[4]. I particularly recommend the introduction to the work of Blanchett, Mitchell and Frank[6] on dynamic spending at the end of the variable spending strategies review. Their strategy periodically updates the critical assumptions of a retirement plan. (Frankly, I don’t see a rational alternative.)

It effectively says, “When the road in front of you turns or ends, modify your car’s behavior accordingly.”

A light pole oddly stood in the middle of the Sears gravel parking lot in my hometown. Some wise person had painted two arrows on the pole curving away in opposite directions. Below the arrows were the words, “Turn. Go left or right.”

Sounds like sage advice.

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Variable-spending strategies make a lot more sense.

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The challenge with the dynamic spending strategy is that it is mathematically complex and will be difficult for most retirees or even planners to implement. I suspect, however, that you would achieve similar results with any variable spending strategy if you updated your spending percentage annually to reflect decreasing life expectancy (strategies like RMD do this for you) and based the spending amount on your current portfolio balance. Blanchett, Frank and Mitchell point out that asset allocation plays a smaller role.

The Blanchett-Frank-Mitchell study shows that life expectancy plays a critical role in determining a safe spending amount. Life expectancy declines as we age. Some variable-spending strategies, like RMD and actuarial approaches, consider decreasing life expectancy in their calculations while others, like spending 4% of remaining portfolio balance, don't. I recommend you choose one that does — it's a key factor.

To implement a variable spending strategy, choose a variable spending rule that suits your fancy[1]. Which you choose probably has less impact on portfolio depletion risk than the act of recalculating it annually, so long as it incorporates changing life expectancy.

I personally prefer the dynamic strategy, Modified RMD for simplicity, Milevsky’s formula[4], and actuarial strategies[5].

I’ve written several posts on asset allocation and it has been thoroughly discussed in several threads, including Unraveling Retirement Strategies: Constant-Dollar Spending (4% Rule). You won’t go terribly wrong with an equity allocation between 40% and 60% and it’s difficult to prove that another will work better across a broad range of outcomes. The same rules apply to variable spending portfolios.

I recommend a floor to go along with an upside variable spending portfolio to make sure you can survive if the improbable happens.

Constant-dollar strategies tell you to spend the same amount every year and that you probably won't run out of savings over a fixed thirty-year retirement. They don't consider what happens if you do.

Variable spending strategies tell you to spend more when you have more money and spend less when you have less money. The better variable spending strategies also consider remaining life expectancy and tell you that you can spend a higher percentage of your remaining savings as you age. Annual spending isn't predictable but you are unlikely to outlive your savings.

Again, seems like sage advice. Variable-spending strategies are so much more rational that I personally dismiss constant-dollar spending strategies entirely.

Retirees who have a pension, Social Security benefits or have purchased an annuity, which covers practically all American retirees, will actually be building a floor-and-upside strategy and managing the upside portfolio with a variable-spending strategy. Floor-and-upside strategies, however, will focus more on the floor and will likely recommend one higher than Social Security benefits alone are likely to provide.

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REFERENCES

[1] Making Sense Out of Variable Spending Strategies for Retirees, Pfau.



[2] Optimizing-Retirement-Income-Solutions-November-2017-SCL-Version.pdf, Pfau, Tomlinson, Vernon. (Very lengthy, consider [6], instead.)



[3] Estimate your required minimum distributions in retirement, Vanguard.



[4] The Yin and Yang of Retirement Income Philosophies, by Wade D. Pfau, Jeremy Cooper.



[5] How Much Can I Afford to Spend in Retirement?: Spreadsheets, Ken Steiner.



[6] How-to-pensionize-any-IRA-401k-final.pdf, Steve Vernon.



[7] An Age-Based, Three-Dimensional Distribution Model Incorporating Sequence and Longevity Risks, David Blanchett, Larry Frank, John Mitchell.

Retirement Expenditures and Costs of Retirement

Some great questions and comments about my previous posts on spending in retirement, beginning with Spending Typically Declines as We Age, suggest that I should add a bit more to my explanation. Or as Ricky Ricardo might have said, "I got some 'splainin to do."

Will the cost of retirement decline as you age?

The fact is I don't have any idea how much you will spend late in retirement, nor does anyone else. I can't predict what a household's finances will look like in two or three decades (which is why glide path discussions don't much interest me). My arguments about declining expenses as we age and dynamic updating are about how much you can spend now based on what you now know, not about how much you will spend later in life.

(Reminder to readers: Hover your mouse pointer over yellow text for further explanation. Double-click any chart to see a larger version. Orange text is a hyperlink. "PDF" denotes that clicking will download a PDF of the referenced document.)

The Banerjee and Blanchett studies show that retirement expenditures typically decline with age. Expenditures, however, are not the same as the generally accepted definition of “cost". Think of expenditures as consisting of non-discretionary spending (“basic costs") and discretionary expenses (“lifestyle costs”). In fact, Blanchett showed that the group of retirees with high net worth and low spending are the ones most likely to experience an increase in expenditures, not because their costs go up in many cases, but because at some point they realize they can safely spend more money on their lifestyle than they have been.

No one knows if your spending or your costs will decline as you age, but these studies (and many others) show they are very likely to. Banerjee shows that expenditures decline for two out of three retired households. That is the best initial assumption until experience with your actual retirement results indicates that you are on a different track. (You can refine that initial assumption, as I explained in Retirement Spending Assumptions and Net Worth.)

Is it dangerous to assume that costs will decline?

Not really, and for two reasons. Theoretically, using this approach, if we assume costs will decline and they don’t, we will spend money early in retirement that we might come to need late in retirement. That’s a risk.

It's important to note that the risk of overspending early in retirement isn't exclusive to a plan that assumes decreasing spending. 

But, Banerjee showed that spending declines for about 66% of retirees and increases for about 16% in real dollars. If many of the 16% of retirees who eventually spend more do so because they realize they can afford to, then the danger zone is the 18% chance that spending will remain flat.

However, assuming declining costs in order to provide the most accurate assessment of how much money a retiree can spend today isn’t a one-time calculation, at least it shouldn't be. These calculations should be made annually (see Dominated Strategies and Dynamic Spending). A retiree who initially assumes declining expenditures but ends up in the 18% or so of retirees who don’t see declines in spending should quickly notice the divergence from plan and correct spending within a few years. Annually adjusting spending and assumptions about future spending should should provide for a quick and relatively smooth correction. This is the first way we hedge the risk of assuming declining expenditures.

The second hedge is control of our discretionary spending. We can budget discretionary spending to target a planned decline in spending as we age to increase the probability that our spending does, in fact, decline as we assumed it would. In other words, we have some control over those spending declines. As Blanchett shows, the larger the portion of our budget that consists of discretionary expenses, the more our spending is likely to decline with age. If your spending is largely non-discretionary, then your expectations for spending declines should be modest from the beginning.

There are other arguments for assuming flat spending, including building in a margin of error and having the excess available to pass to heirs. Perhaps the first argument is a matter of personal choice, but I prefer to make the best prediction that I can of future expenses and allow for a margin of error separately. I like to understand both the expected costs and the risk, and not have risk tossed in as an afterthought.

Assuming flat spending as a safety margin is, after all, quite arbitrary. Why not assume a half-percent annual increase in spending, instead of flat spending? Without studies like Banerjee and Blanchett, most retirees and planners couldn’t identify the magnitude of that margin, let alone determine if that is the correct safety margin. Regardless, in my opinion, the risk of running out of savings should be addressed in the floor portfolio, not as additional margin in the risky portfolio.

I have a similar concern with planning legacies as an afterthought of spending, first because I believe that any serious concern about a legacy deserves its own plan and, second, because Scott, Sharpe and Watson (PDF) have shown that planning with “reserves” (hedging sequence of returns risk with over-saving) can be very costly.

In my next post, Retirement Expectations: A Reality Check, I'll write about what we should hold as reasonable expectations of retirement. Hope to see you there.

The Chain of Longevity Risk

I've spent the last several weeks working on some interesting portfolio survival research with my son and daughter, so my posts have been a bit few and far between. My apologies. Cary and I realized one day this summer, over a local craft beer after a round of sporting clays, that retirement portfolio survival and the medical research he does are largely the same research problem. I hope to have something here on my blog about our findings in a few weeks. In the meantime, here are some thoughts about portfolio survival in general.

Longevity risk is the risk that a retiree will outlive his or her retirement savings. It develops in four stages as we make decisions about funding retirement.

Let’s consider those risks by imagining a retiree who splits his retirement savings portfolio in half on the day he retires. The first "legacy" portfolio is intended for his heirs and the second “funding” portfolio is intended to fund his retirement expenses.

To simplify the example, let’s assume he invests both identically in the same 40%-equity index fund on the same day. The only difference between the funding portfolio and the legacy portfolio is that he will spend annually from the funding portfolio and then re-balance it to 40% equities. The legacy portfolio will remain untouched to be left to his estate.

A retiree can pretty much avoid longevity risk altogether by purchasing life annuities or TIPS bonds. There are plenty of good reasons to invest at least some of our savings in stocks and bonds, though, and that decision leads to the first risk, known as market risk. Market risk refers to the volatility of stock prices over time. Once we invest in risky assets like stocks, outliving our savings becomes a possibility.

We can mitigate market risk by reducing our equity exposure or we can completely eliminate it, by purchasing life annuities or TIPS bonds. Our imaginary retiree has decided to mitigate market risk in both portfolios by investing only 40% in equities, but he has not avoided market risk altogether.

If this retiree never spends from or saves to either portfolio, those portfolios will have equal values at the end of retirement. We don't know what that value will be, however, because both are exposed to unpredictable market risk. We only know that they will be exposed to identical market risk and that their "terminal value", or value at the end of life, will be the same.

When a retiree begins to spend from her funding portfolio, the outcomes of those two portfolios go their separate ways. No matter how little our retiree spends each year, so long as there is net spending, there is no future in which the terminal value of the legacy portfolio will not be larger than the terminal value of the funding portfolio at the end of retirement for two reasons.

The first cause is obvious – her funding portfolio will be smaller  because she is spending some of it – but the second cause, path-dependent risk, can make her legacy portfolio's terminal value larger or smaller. The funding portfolio will always, however, have less value than her legacy portfolio, again because she is spending some wealth and never saving, but path-dependent risk can leave the funding portfolio fatter or thinner than it would have been with no path-dependent risk.

Path dependence refers to the fact that, once we begin spending from a volatile portfolio, the order of market returns can change the portfolio’s value. A buy-and-hold portfolio has no path dependence (“Path dependence” means the outcome depends on the path we take to get there, which in this discussion refers to the order of annual portfolio returns.)

Let me provide a quick example to explain path dependence. Assume that over the next five years, the stock market will provide the following returns in the following order: 5%, -7%, 9%, 3% and 4%. If we invest $1,000 in this market at the beginning and neither buy nor sell additional shares, we will end up with $1,140 five years later, no matter which order those returns occur.

If we spend $30 at the beginning of each of the five years, however, the order of returns does matter. There are 120 different ways (5 factorial) those five returns can be ordered and each will provide a different outcome. The outcomes will range from $966 to $988, but always less than $1,140. Once we spend from or save to a volatile portfolio, the outcome is path-dependent.

Note that in none of these 120 permutations is our account balance depleted. Path dependence isn't the same as risk of ruin and if we are only spending 3% annually ($30), it is very unlikely that we will exhaust our savings.

Some refer to path dependence as “sequence of returns risk” but the term isn’t always used in that way, so I prefer to avoid it whenever possible. If returns are experienced with the highest gains early in retirement and the lowest gains toward the end, this path dependence helps our portfolios over time and if returns are experienced with the worst returns early in retirement, path dependence hurts our portfolio.

The best possible outcome is achieved when our market returns are ordered from best to worst. The worst possible outcome is the reverse. With 30 years of annual market returns over a long retirement, the odds of experiencing the best or worst outcome are literally astronomical (1 in 30 factorial, each – there are fewer than 30 factorial stars in the visible universe).

The source of path-dependent risk is selling in the spending phase of retirement finance and buying in the accumulation phase. We have no idea what price we will receive for the securities we will sell (or buy) in the future and that price risk is path-dependent. TIPS bond ladders held to maturity and life annuities have no path dependence risk because we know their future values relatively accurately.

(As an aside, savings portfolios during the accumulation phase also have path-dependence risk because we don’t know the future price at which we will buy equities. A lot less attention is paid to path-dependence in the saving phase because it doesn't lead to portfolio ruin. It does, however, greatly impact wealth accumulation.)

So far, our retiree’s legacy and funding portfolios are both exposed to market risk, and the funding portfolio is exposed to additional risk (path-dependent risk) once she starts spending from it. Note that this risk is introduced by the retiree’s decision to sell shares. Path dependent risk is not market risk, cannot be diversified away like market risk, and therefore we can’t be compensated for it. In general, more risk means a greater expected return, but the market doesn’t compensate us for taking path-dependence risk.

Our retiree will make another decision that affects path-dependence risk, how much to spend annually. The more she spends each year, the more she exposes her portfolio to that selling-price risk each year and the more path dependence risk and risk of ruin she accepts. Simply said, a 4% “sustainable withdrawal rate” is riskier than a 3% rate.

The term “sequence of returns risk” is also sometimes used to refer to the probability that a retiree will outlive his savings, which I refer to as "risk of ruin." Path dependence doesn’t cause a retiree’s portfolio to fail, at least it is not the proximate cause. Refusing to reduce spending when our portfolio declines in value causes portfolios to fail is the proximate cause of portfolio failure. This is not a market risk or path-dependence risk, but a poor decision on the part of the retiree. If your portfolio declines significantly in value and you don't start spending less, you risk ruin.

Most spending strategies, like ARVA, constant-percentage spending and "RMD" rarely or never deplete a portfolio because they reduce spending as a portfolio declines in value, lowering the risk of ruin. Constant-dollar spending is the exception.

I wrote a post some time ago entitled, "When You Have Less Money, You Probably Ought to Spend Less", showing that portfolio failure occurs under the (absurd) assumption that a retiree will continue to spend the same amount from his portfolio every year, even when it becomes obvious that the portfolio will soon be depleted. This is an interesting technique to use in research, but it is not a realistic retirement spending strategy. We sometimes refer to this as “constant dollar spending.”

That post also shows that retirees who spend a reasonable constant percentage of remaining portfolio balance each year will not deplete their savings. Their portfolio will eventually recover and spending can increase.

The  “RMD” spending strategy avoids ruin, as well, by dividing the remaining portfolio balance by your remaining life expectancy to calculate a safe withdrawal amount, similar to the manner in which the IRS calculates required minimum distributions for IRA's. Waring and Siegel's ARVA strategy (download PDF) does something similar. Both strategies reduce spending when a portfolio is faltering. In fact, constant-dollar spending is the only widely acknowledged spending strategy that results in portfolio ruin under reasonable spending assumptions.

The third layer of risk in the chain of longevity risk is that of portfolio ruin. It is introduced when a retiree decides to keep spending the same amount after significant portfolio losses. Rational, knowledgeable retirees will reduce spending when their portfolio wealth dwindles dangerously low, but they expose themselves to the risk of a permanent reduction of spending if they wait too long to adjust. (This is a key reason I recommend dynamic spending and annual adjustments. Small, annual adjustments are easier to tolerate and help avoid larger, permanent adjustments by limiting damage.)

To summarize, our decisions can lead us down a chain of retirement wealth risk. It begins when we decide to invest some of our savings in equities. We increase risk by allocating more of our portfolio to equities and decrease it by allocating less.

The next step is our decision to spend from our savings portfolio. Spending more raises the risk and spending less lowers it.

The final step in the chain of risk depends on the decisions we make when our portfolio dwindles in value.  Path-dependence can lead to portfolio ruin, but it probably won't if we lower spending when our portfolio is stressed.

Each step we take, we add more risk. Except for the final, "overspending" step, these can all be reasonable risks to assume. Understanding them can help retirees understand how much of each risk they should accept.

Positive Feedback Loops: The Other Roads to Ruin

Positive feedback like, “Nice post!” is always welcome, but positive feedback that gets stuck in a loop can have catastrophic results.

The most memorable experience of positive feedback is the head-splitting screech that fills an auditorium when the PA system experiences feedback. Someone speaks into the microphone and the sound is amplified. Amplified sound from the speakers is picked up by the microphone and amplified again through the speakers and back to the microphone and . . . well, by about the fifth cycle through the amp everyone in the room is holding their hands over their ears and mouthing silent profanities.

The most common experience of a negative feedback loop is your home thermostat that reduces heat when the temperature gets higher. You’d think that a screeching PA system would be negative and a thermostat controlling your home heating and cooling would be positive, but that isn’t how feedback loops are named.

According to one website, a more formal explanation of the difference is this:

“Positive feedback loops enhance or amplify changes; this tends to move a system away from its equilibrium state and make it more unstable. Negative feedback loops tend to dampen or buffer changes; this tends to hold a system to some equilibrium state, making it more stable."

So, when does a retirement income system “tend to move away from its equilibrium state and become unstable”?

To answer that, I'll tell a story about a retired couple in 2007, because I was raised in the South where every question is answered with a story. My story is not strictly true (a long-standing tradition of Southern stories). I will build a composite retired household from personal observations of multiple actual households from that time, some of whom weren't really even retired but, as my grandfather would’ve said with a grin if he were telling this story, “they might'a been.”

Jim and Linda retired in Omaha in 2005. The family seemed well-to-do, but they lived in a large, heavily mortgaged home. Jim had built a small fortune over his working career investing in rental homes, also heavily mortgaged, and most of their retirement income came from those properties. They both had retirement accounts invested in index funds worth about $200,000 and significant income from several CD’s and a money market fund.

Life went pretty much as planned until late 2007 when the stock market began a 50%, 18-month drop, interest paid on safe investments dropped to zero and, worse for Jim and Linda, the real estate market tanked, all simultaneously. Though most people would eventually recover from these crises, Jim and Linda wouldn't – a financial crisis can be a very personal thing.

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Market losses aren't the only road to ruin in retirement.

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With the rental income gone and the CD's and money market funds now paying a pitiful fraction of one percent, Jim could no longer afford the mortgage on his home plus the mortgages on fifty or so rental properties so he let the unprofitable rentals go. There were no buyers, so “letting go” meant skipping mortgage payments until the banks foreclosed.

The family’s rental business had drifted into a positive feedback loop wherein foreclosed properties reduced income, which reduced their ability to pay other mortgages, which resulted in more foreclosures, which resulted in even less income. It didn't stop until all the properties, including their home, were foreclosed. In less than a year, Jim and Linda's once-shiny finances looked like PA system feedback sounds.

The couple’s plan had assumed that their portfolio of rental properties was well diversified. Sure, a few of the fifty properties might fail from time to time, but what were the odds that a catastrophic number of them would fail in short order? Incidentally, this is the same assumption that led to the Wall Street collateralized mortgage obligations crisis on a much grander scale and as Jim, Linda and several Wall Street giants soon learned, the correlations had been much higher than they had believed.

Jim needed to sell their stocks, intended to fund decades of retirement, at lower and lower prices as the stock market continued its collapse. The stock market would recover years later, as stock brokers promise it always will, but Jim and Linda wouldn't participate in that recovery. Their stocks had long been sold. The stock market had also entered a positive feedback loop with selling encouraging more selling for a year and a half.

Their retirement planner had told them that they could safely spend 4% of their portfolio value each year, or about $8,000. There was a small chance, around 5%, that a series of poor returns early in retirement would result in their outliving their savings, but an even smaller chance if they spent less when their portfolio declined in value. Unfortunately, they did realize that unlikely poor performance right after they retired.

Jim, Linda and their planner had assumed that spending might need to be reduced during a bad market spell. (We say “spell” in this context a lot in Southern stories. It’s a very versatile word. We can sit for a spell, Uncle Howard can have one of his spells, or in Louisiana we might even cast one.) What they hadn’t considered is that forces other than market volatility – like expense surprises and lost income, for example – might preclude their ability to make those needed spending cuts.

Each year that Jim and Linda spent more than planned from their portfolio increased their probability of ruin. The continual shrinking of their portfolio value as the market fell increased it even more. Soon that probability of ruin was a lot more than the original 5%. An example is provided in the table below.

Their portfolio spending strategy had drifted into a positive feedback loop (that's three if you're keeping score), wherein every year that they overspent from their savings they increased the risk of portfolio ruin, reduced their capacity to recover when the market did, and decreased the amount of spending that would be considered safe the following year, increasing the probability that they would need to overspend yet again. The way to escape this loop would have been to reduce spending from their portfolio. Without the rental income and fixed income interest, they couldn’t.

The good (and coincidentally true) ending to this story is that today, eight years later, all of the households in this composite have recovered to some degree, though one middle-aged couple divorced under the strain. The investment portfolio is gone, as is the real estate wealth, but they have a "spell" to recover because, as I said, none of them were actually retired. The outcome would have been worse had they been. Younger people have more risk capacity and remaining human capital.

Most people survived and completely recovered from these simultaneous stock, interest rate and real estate crashes, but Jim and Linda did not. Had their investment properties not simultaneously tanked, they would have easily survived the bear market and kept their home.

What types of spending shocks can initiate a positive feedback loop? There are several candidates. A late-life divorce can be financially devastating and, though you may imagine them rare, they are not. I am aware of three among my circle of acquaintances over the past five years. (One gentleman was 80 and he married again within a year.)

Unexpected medical expenses, particularly onerous with dementia (see Costs for Dementia Care Far Exceeding Other Diseases), aren't uncommon. Two families within my circle of acquaintances are retired and financially stressed by the high support costs of their grown children who have medical problems. A combination of small underestimates of spending, expected market returns, and longevity could also do the trick in an otherwise survivable economic downturn. (As I showed in 100% Certain That We're Not Sure, there is no certainty that you picked the correct portfolio spending rate to begin with. You may already be overspending.)

Research shows that well-diversified retirement portfolios are unlikely to completely fail as a result of market volatility. (See, for example, Larry Frank.) The portion of the portfolio that is unlikely to disappear is sometimes referred to as a “soft floor.” Stout and Mitchell (download PDF) showed that retirees who reduce spending when their portfolio is stressed can reduce the risk of ruin by 30% to 40%.

These studies don't address spending volatility, however, so they don't predict what happens if retirees, like Jim and Linda, are unable to make the needed spending reductions. Mean reversion and diversification won't save those who can't due to divorce, dementia, debt or dependents.

The positive feedback loops are present in these studies if you look for them carefully. Observe what happens to a portfolio in a constant-dollar spending model and you will see that when a portfolio declines in value and the retiree keeps spending a constant-dollar amount, she increases the risk of portfolio ruin going forward. When this happens several years in a row, the probability of ruin grows quite quickly. In the following table, a 65-year old couple in 1974 with a 50% equity portfolio wishing to spend $52,000 from a $1M portfolio each year would see their probability of ruin nearly triple in five years. (Probability of ruin calculated using Milevsky formula.)

Year	Return on 50% Equity Portfolio	Portfolio Balance	Withdrawal Rate for $52k Spending	Probability of Ruin
Initial		1,000,000		5.0%
1974	-8%	872,160	6.0%	5.2%
1975	-11%	729,942	7.1%	8.5%
1976	18.5%	803,362	6.5%	14.4%
1977	6.5%	800,200	6.5%	10.6%
1978	-4%	718,272	7.2%	14.4%

The table above demonstrates a positive feedback loop that would have developed had the retiree felt it was safe to continue the same amount of spending yearly as the market declined (it isn't), but it would also have developed if the retiree hadn't been able to reduce spending.

Positive feedback loops disappear in dynamic-updating models that assume that the retiree will be able to cut spending when necessary. Since there are no unmet liabilities (overspending) in these models, there are no positive feedback loops. The difference between probabilities of ruin between the two types of models offers an estimate of the risk of not being able to reduce spending.

Stout and Mitchell found that adjusting spending reduces risk of ruin 30% to 40% compared to constant-dollar spending, so we can infer that not adjusting spending is about 43% to 67% riskier than adjusting it. The risk that we will deplete our portfolio because we can't adjust our spending is that 43% to 67% probability times the probability that we won't be able to reduce spending. The probability that we can't is far more difficult to estimate.

We can, however, ballpark that probability by considering our financial risk capacity. If we have lots of money saved relative to our spending needs, we have lots of risk capacity and the odds are better that we won't find ourselves unable to reduce spending from our portfolio when needed. The less savings we have relative to our spending, the greater the likelihood that we may be unable to reduce spending when necessary and the greater the chances that we will trigger a positive feedback loop that ends in ruin.

(Another way to look at risk capacity is your portfolio spending rate. If you only need to spend 1% to 2% annually, you're far safer from spending crises than if you need to spend 4% or more annually.)

Most Southern stories have a moral and this one is no exception. Market volatility isn't the only road to portfolio depletion. Studies that ignore spending risk understate the probability that a retiree will outlive savings.

Here's my intuition: retirees are more likely to outlive their savings as the result of a spending crisis that triggers a downward, self-feeding spiral than they are to outlive their savings as a result of slowly overspending 4% a year instead of 3.5%, especially if they dynamically update their plans. I readily admit I don't have data to back that up, so take it for what it is. I also suspect that long-term persistent overspending and sequence risk are far more likely to result in a permanent loss of standard of living than outright ruin.

Retirement income systems are vulnerable to positive feedback loops that can preclude the option to reduce spending in times of portfolio stress. Nor is retirement uniquely the domain of positive feedback loops. My personal experience with pre-retirement households that ended in personal bankruptcy displayed evidence of loops. Long bouts of unemployment or disability trigger them; consumer debt, divorce and foreclosure combine to finish them, in good stock markets and bad.

Another impression I have is that most of us have far more confidence in retirement models than our understanding of them merits, and "us" includes financial planners. I appreciate models as research and learning tools and as tools that can support a good retirement plan, but I've been building and studying them for perhaps 20 years and the list of their weaknesses is long. They can't predict an individual household's future and they are not by themselves a retirement plan (see Michael Kitces' recent post.)

Positive feedback loops are a characteristic of chaos theory. Is our retirement income system a chaotic system that is normally in equilibrium but can unpredictably be drawn into the influence of a point attractor like ruin? I'm not certain, but I have been doing some research and having some interesting discussions. Check out Retirement Income and Chaos Theory.

Dominated Strategies, Illogical Strategies, Problematic Strategies and Strategies That Just Make Me Queasy

In Pure and Mixed Strategies, I noted that we can make life simpler for retirees by winnowing out dominated strategies and strategies that are logically unsound. I showed in Dominated Strategies and Dynamic Spending that dynamic updating of sustainable spending amounts dominates the SWR-Fixed and SWR-Variable strategies, so I cross those off my personal list of reasonable alternatives for retirement income plans.

I believe that there are strategies that are flawed, some logically sound strategies with problems, and others that just give me a queasy feeling. So, in this post, I will share my feelings on those three categories of retirement income strategies.

Dominated Strategies: There are strategies that appear to be dominated by better strategies and, according to game theory at least, should not be played. In previous posts, I noted that SWR-Fixed and SWR-Variable strategies are dominated by a dynamic updating strategy. Are there other dominated strategies that are often proposed? 

The RMD Strategy, in which the retiree bases her spending on the required minimum distribution amounts the IRS mandates for IRA’s is also a dominated strategy. (You can read about RMDs here.) Dynamically updating all important variables of sustainable spending will always perform better than a strategy of updating only the retiree’s age and new portfolio balance, as the RMD strategy does.

Logically Unsound Strategies: There are also retirement income strategies that simply aren't logically sound, like the "Spend Dividends Only" strategy. This strategy seems to be based on a misunderstanding of how dividends work.

I won’t devote a lot of explanation here, because the topic has been thoroughly vetted by others. I recently recommended this explanation by Canadian Couch Potato.  But, in short, when a company pays you a dividend on a stock worth $10.00, they pay you perhaps 30 cents in cash and the market immediately reduces your stock’s value to $9.70. You are no better off and no worse off. (You may actually be a tad worse off if you hold the stock in a taxable account because dividend payments can be a taxable event.) Furthermore, investing primarily in dividend-paying stocks will limit your portfolio’s diversification.

I cross Spend Dividends Only off the list because it is illogical and, as Wade Pfau recently put it, simply isn’t a valuable strategy. 

SWR is another logically unsound strategy when applied literally. It ignores conditional probabilities of failure. A common counter-argument is that no one implements SWR literally. I hope that is correct, but I doubt it.

Problematic Strategies: Now, let’s look at an example of a strategy that has not been shown to be dominated and that is logically sound, yet still problematic. The Bond Ladder and Longevity Insurance (BLLI) strategy proposed by Professor S. Gowri Shankar, for example, is logically sound but suffers from two problems.

(If the BLLI strategy is unfamiliar, there is a nice summary of it and several other strategies in this paper by Wade Pfau and Jeremy Cooper.)

The BLLI strategy proposes building a 20-year TIPS Bond Ladder and funding later years (beginning age 85 for someone retiring at 65) with Deferred Life Annuities (DLAs). The idea is that the retiree won’t have to give up control of his capital for the first 20 years – a common complaint with annuities – and that deferred life annuities are cheaper than immediate life annuities. (See Wade Pfau's Why Retirees Should Choose DIAs Over SPIAs.)

The BLLI strategy, however, has an inflation problem. Because DIAs will provide income well into the future, insurance companies typically won’t offer them with inflation protection and, of course, "well into the future" is when inflation takes its biggest toll. When inflation protection is offered, it does not cover the period from purchase to the first payout, in this example 20 years.

This is different than funding half of your retirement income with a TIPS bond ladder and the other half of the income with annuities. BLLI suggests exclusively funding the first half (or so) of retirement with a TIPS bond ladder and the second half exclusively with annuities.

The idea of maintaining control of capital and liquidity is also somewhat problematic, since the retiree will need the money in her bond ladder for living expenses to age 85 and can’t really spend it in an emergency. Funding the entire 30 years with a TIPS bond ladder and prematurely spending the most distant rungs is problematic enough, but it is possible that she won't live the full 30 years and may not need to spend that money ever. Diverting funds meant to meet living expenses during the first 20 years of retirement is significantly riskier.

Nonetheless, it is neither flawed nor dominated and stays on the list.

Strategies that Make Me Queasy: Some strategies can be logical and not dominated and perhaps not problematic to some, but still make me feel uncomfortable. To wit, the Floor-leverage Rule and Zvi Bodie's floor-and-upside strategy of 90% TIPS bonds and call options (LEAPS). Both are known as "barbell strategies" because they invest in extremely safe and extremely risky assets with nothing in between.

As I suggested in Hope and Your Retirement Portfolio, most retirees won't be comfortable with the possibility of losing all or most of their upside "hope" even with a comfortable floor in place. Retirees who purchase call options will often see those options expire "out of the money", in other words, worthless. The financial argument will be that the options served their intended purpose, even the ones that expired worthless, and that is correct. Most of the retirees I know, however, will find that cold comfort when they see a few ten thousand-dollar call positions disappear in a poof of smoke. Actually, it isn't even that dramatic. It's just not there, anymore.

Zvi Bodie's friend, Jeremy Siegel, seems to agree (download PDF). On multiple occasions Siegel has said, "You know, I find it a little strange — Zvi says he’s giving conservative investment advice, and then advising all your clients to buy call options."

The Floor-leverage Rule makes the LEAPS approach look tame in comparison. The idea for its upside portfolio is to employ triple leverage at the equity end of the barbell. The typical investor can't purchase a stock portfolio with triple leverage. It's illegal. But, as Sharp and Watson point out, they can purchase shares of a 3x leveraged ETF like UPRO.

I'm crossing Floor-leverage off the list of reasonable strategies not because it makes me queasy to apply huge leverage to my entire upside portfolio (it does), but because the upside strategy doesn't work. The problem is that these ETFs are not the same as a triple-leveraged stock index fund. In fact, they aren't portfolios of stocks, at all. They're portfolios of derivatives that only track stock indexes for short periods of time. They're best suited to short term investments, which shouldn't be part of a retirement income plan.

Bodie's options strategy stays on the list. It's riskier than I can accept and I don't think it will fit the temperament of most retirees, but it isn't flawed. It will outperform other strategies in some scenarios, so it isn't dominated.

Some of the strategies I've crossed off the "sound" list may fit your individual financial situation and may be bets you're willing to take. Some of them will even be recommended by advisers. I would pare down the list of reasonable retirement income strategies by at least a third, as shown in the following table. This is my personal perspective and not everyone would agree.

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Pure and Mixed Strategies

In a few recent posts, I suggested how game theory might be used to gain a different perspective on the Social Security claiming decision (Game Theory and Social Security Benefits) and why updating your sustainable spending amount periodically (Dominated Strategies and Dynamic Spending) will always perform better than spending a fixed amount based on your initial portfolio balance in retirement (SWR-Fixed), or by spending a fixed percentage of remaining portfolio balance each year but ignoring other determinants of portfolio survival like decreasing life expectancy (SWR-Variable).

The benefit of the spending strategy analysis it that is allows us to winnow out inferior strategies when we choose our retirement income plan. SWR-Fixed and SWR-Variable are dominated strategies. Game theory tells us never to play a dominated strategy, which only makes common sense.

I admit two motives for these posts. The first is that I am fascinated by game theory and believe it provides valuable perspective on the retirement planning problem and the second is that I'm convinced we can simplify retirement planning. 

How does this simplify the retirement income strategy choice? By eliminating dominated strategies as game theory recommends, and eliminating other strategies that aren't logically sound, we can winnow a dozen or more proposed strategies to a significantly smaller number of truly valuable strategy choices. 

In this post, I'll consider another concept of game theory, pure and mixed strategies, and how they might be useful for analyzing retirement income strategies.

According to GameTheory.net, a pure strategy defines a specific move or action that a player will follow in every possible attainable situation in a game. A mixed strategy is created by playing members of a set of available pure strategies at some proportion of each.

Assume a tennis player has two pure strategies available: serve to her opponent's forehand or to her opponent's backhand. She might also attempt to keep her opponent guessing with a mixed strategy by randomly serving to her opponent's backhand or to her opponent's forehand.

Game theory will use the server's success rate serving and the opponent's success rate returning serve from both sides to calculate the optimum proportion of serves to each. Based on probabilities of success for both pure strategies and responses, game theory might tell her, for instance, that the optimum strategy is to randomly serve to a particular opponent's forehand 30% of the time. This is a mixed strategy.

Let's consider some pure retirement income strategies including sustainable withdrawal rates (the dynamic kind, since game theory tells us that SWR-Fixed and SWR-Variable are dominated), a Social Security benefits strategy, an annuity strategy, a time-segmentation strategy and a TIPS bond ladder strategy. Other strategies have been proposed, but let's go with this shorter set of pure strategies for now.

Why isn't the floor-and-upside strategy on the list? Glad you asked. Because floor-and-upside is a mixed strategy consisting of some mixture of pure floor strategies and pure upside strategies.

The floor strategy could consist of life annuities, TIPS bonds held to maturity, Social Security benefits or some combination of these.

The upside strategy contains risky assets like stocks and bonds. SWR portfolios typically recommend something like 50% stocks and 50% bonds. Jason Scott's and John Watson's floor-leverage rule (download a PDF) recommends 15% of assets be invested in a triple-leveraged ETF of derivatives. Zvi Bodie and Nassim Taleb have recommended an upside portfolio of 10% of assets invested in long term index options (LEAPS).

Note that a mixed strategy can allocate zero percent to some available pure strategies, so for instance, an SWR strategy can be considered a floor-and-upside strategy allocated 100% to the upside portfolio and 0% to the floor strategy. More importantly, because nearly all Americans have some Social Security income or public pension income, it will be very rare that a retiree plays a pure upside strategy.

An exception to this observation is retirees who postpone claiming Social Security benefits and spend from a stock and bond portfolio until those benefits start, but by age 70 at the latest, they will likely have a floor-and-upside strategy, though they may not think of it that way.

While it will be rare for a retiree to implement a pure upside strategy with no floor, it is easy enough to implement a pure floor strategy with no upside portfolio. A retirement income plan based solely on pension or Social Security income would qualify as a 0% upside/100% floor portfolio, as would any strategy comprised solely of Social Security benefits, TIPS bond ladders and life annuities.

In other words, nearly all of us will have a floor. Those of us with adequate retirement savings can choose to add more floor, add an upside strategy, or implement some combination of the two. This is the first decision in choosing a retirement income strategy. It answers the question, "how much of your retirement savings are you willing to risk in the stock market in hopes of being able to spend more?"

For those who answer that they wish to take no risk with their standard of living, the next step will be to determine how to most effectively build a floor of income. For the rest, the next step will be to determine how much of their desired standard of living should be locked in with a floor portfolio, with the remainder put at risk in the market.

Viewed from this perspective, sustainable withdrawal rates is a floor-and-upside mixed strategy with a floor consisting of Social Security or pension benefits. A TIPS Bond Ladder strategy is a floor-and-upside mixed strategy of Social Security or pension benefits and a TIPS Bond Ladder with zero percent upside portfolio strategy. Floor-leverage rule is a floor-and-upside mixed strategy with a floor consisting of 85% of our portfolio plus Social Security or pension benefits and an upside portfolio strategy consisting of investing 15% of assets in a triple-leveraged derivatives portfolio.

Most strategies can be viewed as a form of a mixed floor-and-upside strategy and understanding this may simplify your decision of which strategy to implement.

Pure upside strategies will be rare, because most Americans will have Social Security benefits or public pension income at some point. That leaves a floor strategy or a mixed floor-and-upside strategy as the options available to most retirees.

This, of course, is the root of the "safety first" versus "probabilities" divide, but I don't see the divide so much as a disagreement on whether or not to put standard of living at risk as one of how much of our standard of living we should bet in the market. Because most of us are going to have a floor and probably a mixed strategy, the big question is, "how much floor?"

I think this is a far more reasonable approach than having retirees read about a dozen or so strategies to pick the one with which they feel most comfortable.

If you're interested in game theory, William Spaniel has an outstanding series of tutorials on YouTube entitled Game Theory 101.  If the academics of the subject interest you, Yale filmed Professor Ben Polak teaching Econ 159 Game Theory. He is an amazing professor and, although it doesn't use modern on-line teaching technology, it is probably the best on-line class I have ever taken.

Made me wish I'd gone to Yale. Go figure.

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