Friday, February 27, 2015

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, 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.

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.

Friday, February 13, 2015

Dominated Strategies

A while back, I had in mind to write a series of posts on how game theory might be useful for analyzing retirement income strategies. I wrote the first, A Tiny Bit of Game Theory, describing how game theory might be useful in deciding when to claim Social Security benefits. But, then I got sidetracked by questions from readers about bond ladders and bond funds and now, nearly two months later, I'll wander back to game theory. (This freedom to meander is a wonderful part of retirement.)

In game theory terms, strategy A is said to "dominate" strategy B if a player is always better off playing A instead of playing B, regardless of the strategies chosen by other players. This is the strong form of domination. If strategy A's payoff is never worse than B's and sometimes better, strategy A is said to weakly dominate strategy B.

Say we have two bets, A and B. A always pays $200 and B always $100, no matter what other players do. Strategy A is said to strongly dominate strategy B because the payoff is always better when playing A.

If, on the other hand, strategy B always pays $100 and strategy A always pays at least $100 but sometimes more, then strategy A weakly dominates strategy B. The difference is that with weak dominance, the strategies can sometimes have equal payoffs. With strong dominance, the dominant strategy must always have a better payoff.

Here's where identifying dominant and dominated strategies pays off: game theory tell us that a rational player should never play a dominated strategy. In fact, there are game theory operations that simply remove dominated strategies from the game and out of consideration to simplify the game's analysis.

Are there dominated retirement income strategies? If there are, we can simplify the planning process by eliminating them from consideration.

Let's consider two forms of the sustainable withdrawal rate (SWR) strategy and refer to them as SWR-Fixed (or SWR-F) and SWR-Variable (or SWR-V).

The SWR-Fixed strategy tells us to calculate some percentage of our initial wealth and to spend that fixed amount throughout retirement. Let's use 4% as a sustainable withdrawal rate and $100,000 as our portfolio value on the day we retire. The SWR-Fixed strategy tells us we can spend 4% of $100,000, or $4,000, every year for thirty years with about a 95% chance of not outliving our savings. This is the SWR strategy you read about in the popular trade press.

That 95% is the probability that you will not outlive your savings calculated on the day you retire. If your portfolio declines in value after you retire and you keep spending the same dollar amount, your probability of failure will grow beyond 95%. Possibly well beyond.

The SWR-Variable strategy is similar, except that the spending amount is recalculated at the beginning of each year as a percentage of our new portfolio value. In this example, we would also spend $4,000 the first year, but the next year's spending would be 4% of the value of our portfolio at the beginning of the second year of retirement. That portfolio value, of course, is unpredictable and could be more or less than $4,000, depending on market returns for the first year.

This raises a key issue. What do we mean by a "better payoff?" Is SWR-F better because its income is predictable? Is it better because it's simpler to implement?

Or, is SWR-Variable a better strategy because it has less SOR Risk, as I explained in Sequence of Returns Risk and Payouts and provides more income when the portfolio prospers?

Using game theory, we get to decide individually which payoffs are "better" by defining the game precisely. We might, for example, use game theory to explore strategies that provide the best payoff in terms of simplicity of implementation, though given that either strategy requires minimal work once a year, that might be a somewhat trivial objective.

We could also create a game that values predictable annual income more highly than maintaining a maximum allowable level of risk throughout retirement. While some might consider any of these objectives reasonable, I propose that the most rational game for retirees would be one that maximizes annual spending while maintaining a ceiling on the risk of outliving our savings, say, never exceeding a 90% probability of ruin throughout retirement. Let's call this the Safety First game.

To identify potential dominated strategies in the Safety First game from our set of available strategies at this point, SWR-Fixed and SWR-Variable, we would need to show that one strategy always provides higher payoffs than the other, or in the weak form, that one strategy never does worse than the other.

First, let's consider the scenario in which the retiree enjoys excellent market returns throughout retirement. His portfolio value increases every year, at least on average. In this scenario, SWR-V will always outperform SWR-F, because 4% of an ever-increasing portfolio value beginning at $100,000 will always be greater than 4% of the initial portfolio value of $100,000.

For example, let's say portfolio returns for year one are 8%. At the end of year one, the portfolio value would be $100,000 less $4,000 plus 8% of $96,000, or $103,680. SWR would still pay out $4,000 at the beginning of the second year, but SWR-V would pay out 4% of $103,680, or $4,147.

Now, let's consider the other extreme, an ever-declining portfolio value. Playing SWR-V in this situation will always provide less income than playing SWR-F, but recall that we also have an objective in the Safety First game to manage risk of ruin throughout retirement.

A retiree with a $100,000 portfolio at the beginning of 2007 planning for a 30-year life expectancy and planning to spend 4% annually had a 9.8% probability of outliving her savings, according to Moshe Milvesky's formula for probability of ruin. Had her portfolio fallen 25% by 2009 to $75,000, she had two choices. She could lower her spending to about 4% of $75,000 ($3,000), and still have a probability of ruin of about 9.8%. Alternatively, she could continue to spend $4,000, which would be a 5.33% spending rate and and would raise her probability of ruin from 9.8% to 21%.

That is an example of what could happen over two or three years. Most simulated SWR-Fixed strategies end with the retiree's portfolio holding about half its initial value in real dollars at the end of retirement. What happens to the 9.8% probability of ruin if a retiree's portfolio declines in value to $50,000 and she still has a 15-year life expectancy? According to Milevsky, she can continue to spend $4,000 and have a 28% probability of going broke, or lower spending to $2,600 and hold the risk steady at her original 9.8% probability of ruin. A portfolio's value can decline very quickly, or over many years.

If she played the game I mentioned above that values consistent income over maintaining acceptable risk, then SWR-F would have a higher payoff than SWR-V, but not so in the Safety First game that maximizes spending while maintaining an acceptable level of risk.

In plain English, this shows that when our portfolio declines in value and we continue to spend the same dollar amount, as with SWR-Fixed, we expose ourselves to greater risk of outliving our savings. When our portfolio value declines, we can spend less and maintain a constant probability of ruin (the SWR-V strategy), or we can spend the same amount and take on more risk of ruin (the SWR-F strategy).

The fixed-spending sustainable withdrawal strategy is mostly an invention of the financial press. Even William Bengen noted in Conserving Client Portfolios During Retirement that "the adviser should examine the projected current withdrawal rate through the entire time horizon of the clients, not just the first year of retirement."

Noted retirement experts like Michael Kitces have long suggested that SWR-Fixed is a research technique and that no one actually implements it. I hope that is true, but I have reason to doubt it. I talk to readers and clients frequently who plan to implement fixed-withdrawal SWR strategies, Money magazine recommended it for perhaps 20 years (but backed off after the huge losses of the Great Recession), and I recently received a sample Kiplinger newsletter that suggested it, so I have to think someone is doing it.

In the rising-portfolio value scenario, SWR-V always pays off more.  Risk of ruin is not a concern when portfolio values increase. In the declining-portfolio scenario, SWR-V has a better payoff (though not higher) because, although it provides less and unpredictable income, it shows the maximum amount we can spend without taking on more risk. In this game, SWR-V dominates SWR-F and, according to game theory, SWR-F should never be played.

The only retiree who should play SWR-Fixed is one who cares about the probabilities of outliving his savings the day he retires, but is unconcerned with that risk for the rest of his retirement. Sounds a bit irrational, no?

There is an important, though often overlooked point I should add. Retirees tend to spend what they need to spend. Strategies like SWR tell us how much we can safely spend, but we aren't required to spend that amount. This issue is also sometimes raised by retirees regarding Required Minimum Distributions from IRA accounts. If the withdrawal from either of these is more than you need to spend, no one is telling you that you have to spend it. We're just telling you the maximum amount of spending we think should be safe.

Is there a strategy that dominates SWR-Variable? I'll look at a candidate next time in Dominated Strategies and Dynamic Spending.

Monday, February 9, 2015

The Sustainable Withdrawal Range

I had an interesting discussion this past week at Adviser Perspectives with two financial advisers who are frustrated by the fact that there are a wide range of recommendations for sustainable withdrawal rates. I sympathize with their frustration, but their suggestion of getting the industry to agree on one specific model of the future that would provide a single, agreed sustainable withdrawal rate isn’t a reasonable solution.

We could get every meteorologist in America to agree that the high temperature in Chapel Hill next Friday will be 42 degrees, but that wouldn’t make it any more likely that the prediction would be correct. In fact, it would be less likely. Different models with different predictions give us a range of possible outcomes to consider. When you can’t accurately predict something, like future market returns or future temperatures, providing upper and lower bounds for the most likely range is the next best information to have.

Let’s look at the current predictions for future sustainable withdrawal rates. The original SWR studies by William Bengen predict a 95%-safe SWR of about 4.4% for a 30-year retirement with a 50% equity portfolio. Wade Pfau et al recently produced a study suggesting that, based on today’s low-return environment, 3.5% might be a better guess. Even Bengen commented that Pfau might be onto something. (If you follow Wade Pfau's blog, by the way, he has a new website at, where you will need to re-subscribe to his email posts.)

Bengens’s approach uses historical market returns, assuming that the future will look like the past. Pfau et al use Monte Carlo simulation based on lower expected returns in the future than we have seen historically. Moshe Milevsky’s formula for probability of ruin using stochastic calculus calculates a 95% safe withdrawal rate of about 3.25%. In his paper, Milevsky notes that his formula often produces withdrawal rates significantly lower than many advisers recommend. Depending on the spending level, Milevsky’s calculation can differ from simulation results dramatically.

There are other studies that predict safe rates both higher and lower than these. The discussion at Adviser Perspectives was about why we can’t just all decide on one approach using the same assumptions and settle on one sustainable withdrawal rate. In other words, which model is right? The reason we can't is that these are all completely justifiable opinions about the future and we can’t know which model will work best. Any of them might turn out to be right.

The safest bet would be that the future 30-year SWR will not be 3.25%, 3.5% or 4.4% precisely. I would bet, however, that the correct answer will turn out to be not much lower than 3.25% and not much higher than 4.5% because that is the range several models suggest. I would plan for the possibility that it will be significantly lower.

If that sounds like a hedge instead of a commitment, that’s exactly what it is. Financial advisers hoping to hear “3.4%" or even “3.3% to 3.5%” would be disappointed.

These are not insignificant differences. If the actual SWR turns out to be 3.25%, a retiree will need to have saved 31 times his retirement income shortfall after Social Security benefits and pensions. If it is 4.5%, he will “only" need to have saved about 22 times that shortfall. If the shortfall is $10,000 a year, those savings requirements would be $307,692 and $222,222.

The wide discrepancy of recommended sustainable withdrawal rates is not a problem with the models that predict them, it is a result of our inability to predict the future of market returns. It is impossible to prove that any of the models are incorrect. . . well, not for 30 years, anyway.

Human beings have a poor record of predicting the future for even a few years, let alone for thirty. A little more than five years ago, there were widespread predictions that by not taking a path of austerity out of the Great Recession we would soon see rampant inflation. The inflation rate last year was 0.8% and deflation seems possible today. The EU took the austerity path and is trying to avoid an existential deflationary spiral. Both predicted their way would be best.

Studies show that “experts” are no better at predicting the future than us non-experts. Investment manager, Ken Fisher, used to project the coming year’s market return by looking at the projections of the same handful of “market experts” every year. He noticed that actual returns usually fell in the gap that no expert had predicted and that there was always such a gap. In other words, he simply chose the return that no one else had chosen. This worked eerily well for several years until others caught on. (Once everyone is playing the same game, no one can win.)

The wide range of projections is a result of our inability to predict market returns and the length of retirement, and thereby SWR’s, not an ability to agree on a model.

Financial risk is defined as the uncertainty of outcomes. Future sustainable withdrawal rates cannot be identified with a great deal of precision, so different models and different assumptions, all reasonable, produce widely disparate estimates of sustainable rates. This is just proof of what we already knew – sustainable withdrawal rates is a risky strategy.

Some advisers at Adviser Perspectives asked how they should communicate this complicated information when a client asks, “How much can I spend each year for the next 30 years and be 95% certain that I won't outlive my savings?" Here is what I would say to a client (or reader):

That amount is impossible to identify with any accuracy because we can’t predict future market returns or know how long you and your spouse will live. The current estimates from a wide range of models and assumptions range from about 3.25% to about 4.5% of your initial portfolio value for the first year, assuming your life expectancy is about 30 years. That percentage, by the way, increases as you age. It could approach 10% of your remaining portfolio balance near the end of your retirement. I would recommend a guess near the low end of the range because that will be safest, but that will also significantly reduce the amount you can spend. I would also recommend that you have a backup plan in case the sustainable rate turns out to be even lower than we expect, because it certainly could. I realize this is a broad estimate, but that’s because SWR is unpredictable, which is the financial definition of “risky.” If that’s more uncertainty than you are comfortable with, there are safer, more predictable spending strategies we can discuss.

Yes, its complicated and probably not what a client wants to hear. But, it is honest and that’s what clients need to hear.

Friday, February 6, 2015

Long Ladders

Long TIPS bond ladders demonstrate the challenge of matching liabilities in the more distant future, say, funding the last half of a 30-year retirement.

This is one of the toughest pieces of retirement funding to figure out for several reasons. First, we don't know if we will still be alive when it begins, which is a major reason people don't like annuities. Retirees who don't live beyond their life expectancy won't get much benefit from an annuity.

Or, we might live that 15 years and then some, possibly outliving a bond ladder and wishing we had purchased the annuity. Inflation has a much greater impact on more distant years of spending, and even when inflation protection can be purchased it is quite expensive.

In short, the further into the future we plan, the more uncertainty we must deal with. Life annuities remove the uncertainty of living a very long time (longevity risk). Long TIPS bond ladders provide an alternative, but come with a different set of risks, including some degree of longevity risk.

I'm a big advocate of floor-and-upside strategies that secure an acceptable level of income before investing in a risky portfolio. A lot of really bright people, like Zvi Bodie (Risk Less and Prosper), Nassim Taleb (The Black Swan), William Bernstein (too many to list) and Wade Pfau (How Do I Build a TIPS Bond Ladder for Retirement Income?) like TIPS bonds in the safe "floor" portfolio.

TIPS bonds held to maturity are considered risk-free assets – they have no default risk, no interest rate risk, no inflation risk and no correlation to market returns – but no asset is absolutely risk-free. With a TIPS bond ladder, there is the aforementioned risk that you might live longer than the ladder you buy and there is also a risk that you won't be able to hold all of your TIPS bonds to maturity, despite your intentions, in which case you will have interest rate risk.

The risk that you will not be able to hold all the bonds to maturity is obviously greater for a 30-year ladder than for a 5-year ladder and that is one reason I separate this discussion of long ladders from the previous post addressing short ladders. Short ladders are about as risk-free as investments assets can be, but risk grows with the length of the ladder.

Here is the scenario that makes me waiver just a bit. Let's say I buy a 30-year TIPS bond ladder today. Since yields are at record lows currently, I will likely lock in low interest rates for the next thirty years and when interest rates begin to rise in a few years, which seems more likely than not, I will regret not having waited.

I shouldn't regret the purchase because I will ultimately get what I want, a near-certain match of those future liabilities. It's just that the price for this income will decline in this scenario and I'll feel like the guy whose neighbor gets a better deal on a car identical to his. It shouldn't make me feel any worse about my own car, but it does.

If I buy a TIPS bond ladder, my goal isn't to invest to optimize my return or to get the best deal (risk-free assets never achieve that over time), it's to provide certainty of future income.

A second concern I have is that I would need to buy several long bonds.

I hate long bonds.

They're almost as risky as stocks and their return doesn't adequately compensate for that risk. As I mentioned in my last post, Funds and Ladders: What Matters?, in 2013, a bad year for bonds, iShares intermediate ETF TIP lost 8.65%, while long duration (27) bond ETF PIMCO ZROZ lost 22% of its value.

Long bonds fall much faster in value when yields increase than short or intermediate bonds do. To build a long ladder, I'll need to purchase 15 to 20 years of expenses in long bonds. And speaking of the stock-like risk of long bonds, after losing 21% of its value in 2013, ZROZ gained 49% in 2014. PIMCO LTPZ, not limited to zero coupon bonds, fell 20% in 2013 and gained 20% in 2014, still a wild ride. Don't try to match long-duration liabilities with long-duration bond funds. Long bond funds have no place in a safe floor portfolio.

Many advisers make what I call the "mark-to-market" argument that funds and ladders are identical. This argument says that a ladder has the same volatility as the fund but that the ladder-holder simply ignores daily price volatility. That is correct, but the ladder offers the possibility of ignoring volatility by holding bonds to maturity while the fund does not, and if the investor is able to hold the bonds to maturity, that volatility is irrelevant.

While I am generally not swayed by this argument, its advocates do have a point. Even if I plan to hold all those bonds to maturity, there is a risk that I won't be able to, and this risk should be considered.

Retirees who are building a 4- or 5-year ladder to fund a gap or pay for college, for instance, are far less likely to be forced to sell bonds they intended to hold to maturity than are retirees who hold a 30-year ladder simply because there is less time for something to go wrong.

A retiree might be forced to sell bonds sooner than planned due to a financial crisis, such as a medical emergency, but there is also a significant risk that the bonds will be sold, not by the retiree, but by her estate or her heirs. I suppose this could be called "reverse longevity risk."

Longevity risk is the risk of outliving our savings. Buying a 30-year TIPS ladders and living 35 years would be an example of longevity risk. But, there is also a risk that a retiree might buy a 30-year ladder and live only 15 years. The bonds could then be sold at a loss by her estate if yields have risen, or by her young heirs who don't have a lot of need for a portfolio of long TIPS bonds at the age of 25.

Of course, should interest rates fall over time, the bonds might be sold before maturity at a profit, but I can live with that risk.

Put these three factors together and you see my concern: I buy a 30-year TIPS bond ladder today and lock in historically low interest rates. Rates rise for the next ten years, lowering the market value of my bonds, especially the long ones, and I die soon after that. The remaining bonds are inherited by my children, whose financial needs aren't well met by holding long TIPS bonds to maturity, so they sell them at a loss. Since the basis of these bonds is stepped up, they won't even get a tax break.

(I would suffer the same fate in this scenario if I funded those liabilities with a long TIPS bond fund instead of a ladder. So, this is also a concern with funding distant future liabilities with a bond fund.)

I have to weigh this risk of unplanned sales against the certainty, offered by a TIPS ladder held to maturity, of meeting future liabilities. Many factors would exacerbate or mitigate this risk. A married couple is much more likely to have at least one spouse who will survive long enough to use most of the ladder. The longer at least one spouse survives, the less likely the ladder will contain bonds with a large loss, because a bond's price will approach its face value as time passes.

Retirees with no bequest motive may care less about these risks than those who wish to leave an inheritance. (With no bequest motive, however, they might find a life annuity a better fit.) Retirees who have lots of other retirement income (over-savers) are less likely to need to sell bonds from their ladder in an emergency. Retirees who fund a lot of annual income with a ladder will have greater risk exposure than those that need only fund a small annual shortfall. The risk of needing to sell bonds before maturity varies significantly based on the household's individual situation.

Is there a way to fix this problem? Not a good one. We could use an annuity, but it will have even less liquidity than a ladder. A retiree who insists on following the daily market value of a TIPS fund should also want to follow the resale value of an annuity, and it will be even worse. The heirs of the TIPS bond ladder may see a loss, but the heirs of the retiree with an annuity will receive nothing at all.

Ultimately, I believe that Bernstein, Bodie, et al have it right. The safest way to provide certain future income is to purchase TIPS bonds and hold them to maturity. Yes, you may lock in low rates for a long time if you're unlucky, the strategy has opportunity cost and you might need to sell some bonds at a loss before they mature, but if your goal is strictly to provide income with certainty, this strategy is the best bet.

It is only when you add additional requirements, like a goal of maximizing yield or one of maximizing a bequest, or a concern about the market value of your assets should you have to sell them in a fire sale tomorrow, that the strategy shows some weaknesses. None of these are great objectives for a floor portfolio, by the way.

Still, on an individual basis, those additional requirements might be important to you and should be given consideration, especially for long ladders. They shouldn't be an issue for short ladders.

For most do-it-yourself retirees, I would summarize the last few posts on bond ladders and funds as follows. Retirees who aren't using bonds to match future liabilities will probably realize little advantage from buying a ladder instead of a fund. I believe TIPS ladders are the way to go for funding a few years, but using a short-duration fund for this purpose, instead, probably isn't a deal-breaker.

Long ladders and long bond funds are a different story. For the safest approach to providing certain income, ladders are the solution, especially if there is little risk that you will need to sell the bonds before maturity or if the residual value of the ladder isn't a concern. As I mentioned, long bond funds can be extremely volatile and do not belong in a safe floor portfolio.


P.S. Several readers asked after my recent discussion of bond funds versus ladders why I focussed on TIPS bond ladders. Wouldn't duration- and convexity-matching arguments also hold for funds and ladders of say, corporate bonds or munis?

They would, but Treasury bonds have no default risk so there is no need to diversify among issues. Other bonds, including corporates, do have default risk and we need to diversify among many issues for an acceptable level of safety. It would be difficult for most retirees to buy enough individual corporate bonds to adequately diversify, so mutual funds win over ladders in non-Treasury bond asset classes right off the bat based on their diversification advantage.