Tuesday, December 30, 2014

Happy New Year 2015

A few thoughts to wrap up 2014 and then on to what I hope is a happy and prosperous New Year for us all.

My last post on Game Theory and Social Security Benefits, in which I showed that there is no dominant strategy across the board for claiming benefits, ironically grew into a discussion of which strategies people feel certain are dominant. It was a fun discussion, nonetheless, and your participation is greatly appreciated. I'm happy to keep the discussion of that post open as long as you have questions or opinions. I will tie up the topic (Social Security, not game theory) for now with a couple of thoughts.

First, since most Americans have under-saved for retirement, most will need to claim benefits right away. If you have the luxury of choice, consider yourself very fortunate and then be advised that the rules are quite complex. Unless you’re willing to spend a lot of time studying the subject, buy some software like Maximize My Social Security or find a professional adviser you can trust. I’d do both. This is one of the most important financial decisions you will make and it is, for all practical purposes, a permanent decision. You need to get it right.

Second, be cautious of analyses you read that are based on life expectancy. About half of the population of any age will live longer than their life expectancy and our goal in retirement is to be able to pay for even a very long retirement, not just until our life expectancy.

It is correct to say that if you don’t live beyond your life expectancy there is little to be gained by delaying your benefits in terms of total lifetime payments. You will receive about the same total payments if you claim at 62 and live to your life expectancy that you would receive if you claimed at 66 and lived to the life expectancy of a 66-year old. As retirees, however, we need to protect against the risk that we will live well beyond our life expectancy and that’s when delaying benefits pays off.

Planning on living to your life expectancy is like forgoing homeowner’s insurance because your house probably won’t burn down.

But there are implications of early claiming beyond total lifetime payments. If you claim retirement benefits before your full retirement age (66 for most of us Boomers), you cannot take advantage of a higher retirement benefit that might become available later, for instance. Your benefit is locked in. If you are the higher earner of a married couple and claim early, your spouse’s survivor benefit is also locked in.

If you claim at 62 and live to 70 but your widow lives to 95, your legacy might also be at risk. Imagine her picking up a smallish benefit check at 90, shaking her head and saying, “My poor departed Harry was such a sweet man, but he royally screwed my benefits.”

If any of this is news to you, get some help before claiming.

Next topic, for those of you who showed interest in Moshe Milevsky’s probability of ruin formula, remember to use real (after inflation) returns when running the model. Long term historical real stock returns, for example, should be in the 6%-ish range. Also, the results are not directly comparable to other studies, such as those by William Bengen, that use the SWR model. Those studies assume different fixed life expectancies, like 15, 20 or 30 years. Milevsky uses a life expectancy probability. While Bengen assume a life expectancy of exactly 30 years, for example, Milevsky assumes that the length of retirement is a random variable with a mean of 30 years. They’re not the same thing.

I thank everyone for reading this past year. I especially thank the reader who sent a surprise Christmas gift – it made my holiday season. I hope to see all of you in 2015 when we can continue to try to figure this thing out together.

Our goal is to make sure we can feel secure and be happy in retirement. Make sure you don't forget the “happy” part.

Happy New Year!

Friday, December 19, 2014

Game Theory and Social Security Benefits

In A Tiny Bit of Game Theory, I explained a few basics of this study of decision theory. The Social Security claiming decision provides a good example of how to analyze a financial decision with game theory.

Our Social Security game will be a stochastic game against nature in which nature decides your life expectancy, which is, when you think about it, pretty realistic. Unrealistically, we are going to assume that you will live to age 64, to age 70, or to age 95 to simplify the game.

Your choices as the player are to claim benefits at age 62, full retirement age of 66, or at the maximum age of 70. We will assume that you are a single retiree with a typical lifetime record of FICA payments. Having a spouse makes this a very different game, of course, and a lot more complex. So would adding all the claiming age options.

For payoffs, I’ll use the total estimated lifetime benefits for each claiming option according to the Social Security website at SSA.gov for a single person born in 1955 and currently earning $75,000 annually. In this first game example, we will further assume that the retiree has adequate retirement savings to support her lifestyle between retirement at age 62 and the age at which she will claim benefits.

This simplified game in matrix form with lifetime Social Security benefits payoffs in 2014 dollars will look like this:

The retiree will need to also make a decision about her overall objectives. Many game theory analyses select strategies that will avoid the worst-case loss. Prisoner’s Dilemma, for example, encourages each perpetrator to confess first and avoid the longest prison sentence. Mutually-Assured Destruction was also an attempt to minimize the worst-case scenario, a nuclear war. These are referred to as “maximin” strategies because they seek to maximize the minimum outcomes. In other words, they seek the strategy that has the best payoff from among worst-case scenarios.

Some retirees want to minimize the chances of “leaving benefits money on the table.” They decide to claim as early as possible in case they don’t live long enough to “break even”. This strategy seems wrong to me on so many levels, but to each his own. Game theory allows us to analyze the problem with a wide range of potential objectives.

The table below shows how much Social Security benefits a retiree might “leave on the table” by waiting to claim but dying before the break-even age, which in this example ranges from ages 75 to 78 depending on the claiming ages.

As you can see from the payoffs, if you won’t live very long, you will maximize your total lifetime benefits by claiming as early as possible (Table 1) and if your objective is to wring every available dollar out of the U.S. Treasury (Table 2), claiming early would be the way to go. Of course, if you’re wrong about your checkout date, you might have done significantly better by claiming at a later age.

If you live to be very old, then you will receive the greatest lifetime benefit by claiming at age 70, when benefits top out. If you plan to live a long time but don’t, you will have missed years of benefits by not claiming early.

For retirees with the “maximin” objective of protecting against the worst-case scenario, claiming at 70 is the best choice, because minimizing your benefits by claiming them at age 62 and then living well into your 90's will be very painful for a very long time. The formal name for Social Security retirement benefits is Old Age and Survivors Insurance (OASI) and claiming as late as possible is the best use of benefits if you view them as insurance. Delaying the claim date for your benefits is the cheapest way to purchase longevity insurance.

I mentioned earlier that for this example game we would assume that the retiree has adequate resources to retire at age 62 and pay for her standard of living until she claims benefits. Another way to implement this strategy is to work longer, if you have the option.

Retirees who don’t have the option to work longer and don’t have substantial retirement savings can’t play this game. They will need to claim early because they will need the income immediately. So, you have more options with Social Security if you also have a lot of money.

I’m sure you’re shocked.

There is one other game theory concept we can introduce with this example, that of dominant strategies.

If you were offered two bets and the first bet always paid at least as much as the second bet and sometimes more, you would always choose the first bet, right? Game theory refers to the first bet as a dominant strategy and the second as a dominated strategy. Game theory tells us never to play a dominated strategy. (And, it tells us that there usually isn’t a dominant one.)

In the Social Security benefits game I have described, there is no dominant strategy that always provides the best results under all circumstances. Sometimes claiming at age 62 pays more lifetime benefits and sometimes claiming at age 70 does, depending on how long you live.

However, claiming at age 62 is a dominant strategy if the objective is merely to leave the minimum amount of benefits on the table and claiming at age 70 is a dominant strategy if the objective is to minimize longevity risk.

Note that I’m not trying to use game theory to explain the best Social Security benefits-claiming strategy. That will depend on your individual resources and goals. I’m suggesting that it provides a good framework for laying out all the options and outcomes and for clearly identifying our objectives so we don’t focus only on the most likely outcomes.

Hopefully, that supports a better decision.

Monday, December 15, 2014

A Tiny Bit of Game Theory

I’m fascinated by game theory and I’ve lately been thinking about retirement finances through that lens.

You may be familiar with three products of game theory, whether you realize it or not. The first is the strategy of Mutually-Assured Destruction, with the appropriate acronym MAD, that was developed from game theory in the 1960's as a response to the threat of nuclear war. The second is "Nash equilibrium", suggested in the book and movie, "A Beautiful Mind". (John Nash won a Nobel Prize for his work on game theory.) The other is called "Prisoner's Dilemma", a game that pits two "perps" against one another to obtain a confession that seems to part of every TV crime drama ever created.

Game theory is the study of strategic decision-making or, according to expert Roger Myerson, "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers.”

I keep his book, Game Theory: Analysis of Conflict, on my desk. On days when I want to humble myself, I try to understand the math. But, there is a lot to learn from game theory even if you wouldn’t touch linear algebra with a ten-foot pole.

Game theory can model strategic decisions in a number of ways, but the simplest is by using a matrix of Player A’s strategies versus those of Player B’s. The cells of the matrix contain the payoffs for each player when each chooses a particular strategy. A pair of numbers describes the payoffs. The first of the pair (boldface) is Player A’s payoff and the second is Player B’s.

Here’s an example. In this “game”, if Player A chooses Strategy 1 and Player B chooses Strategy 2, then Player A will receive a payoff of 3 “points” and Player B will receive 0 points. Each player will look at the potential payoffs for each strategy available to her, guess what Player B might do, and choose a strategy accordingly. The outcome of the game will be determined by the contents of the cell at the intersection of the two strategies.

(In case you're interested, the game above is “Prisoner’s Dilemma”, where each player’s Strategy 2 is to confess and rat out his partner in crime. Strategy 1 is to keep silent. The payoffs are the number of years in prison, so I suppose they should be negative numbers.)

In financial planning, we rarely are interested in a game between two individuals, but a game, instead, of an individual against a system of markets with random outcomes. Game theory refers to these as “stochastic games against nature”, a phrase you may never need to hear again. On the other hand, when someone asks what you're doing about retirement, you could impress them by answering, "I'm playing a stochastic game against nature."

In these games, there will be only one payoff in each cell, since “nature” doesn’t need payoffs.

Here’s an example. Let’s say that nature has two possible strategies in a game: it can rain or not rain where you are. You, in turn have two strategies. You can carry an umbrella, or leave it at home.

If you leave your umbrella at home, there are two possible outcomes. It may rain, in which case you will get wet, or it may not rain, and you will have a good outcome. You stay dry and don’t have to lug an umbrella around for no reason.

If you choose the umbrella strategy instead of leaving it at home, you also have two possible outcomes. If it rains, you stay dry. If it doesn’t rain, you will have to carry an umbrella around all day, looking stupid and encumbered for no good reason.

A matrix to describe this game might look like this:

The correct strategy choice in this game, of course, depends on the weather forecast’s probability of rain and its accuracy. It is called a stochastic game because the outcome depends on chance. It is called a “game against nature”, not because we’re talking about rain, but because we are playing against a complex system and not against an individual. The stock market, for example, would also be included in this definition of nature.

If these were the payoffs (I made them up), at what probability of rain would you switch strategies?

I think we can gain some insight into some retirement financial decisions if we look at them from a game theory perspective. In particular, I think game theory can make us focus on all possible results of our financial decisions and not just the most likely outcomes. In my next few blogs, I’ll provide some examples from retirement finance and we’ll find out if you agree, starting with Game Theory and Social Security Benefits.


Friday, December 5, 2014

Think Like a Bayesian Pig

OK, one more barnyard animal theme and I promise to move on.

I spoke at the RIIA Fall Conference of retirement planners a few weeks back on the topic, "Think Like a Pig". I suggested that they view retirement from the perspective of a retiree who would actually feel pain if their retirement plan failed as opposed to the perspective of a somewhat-interested third-party. I suggest you do the same with your own retirement planning because being retired isn't quite the same as thinking about retiring one day.

It's for real.

Now, I would like to recommend a further adjustment to your view of retirement planning.

Academics often treat retirement as if it is one integrated whole that begins around age 65 and could last thirty years (spherical cow alert!). This often makes sense in an academic environment when we are trying to understand the financial process involved.

Systematic withdrawals of constant dollar amounts are a good example. We can use the strategy to study the probability of failure over 30-year periods and learn about sequence of returns risk, but implementing that strategy doesn't make sense in real life. Calculating that you can spend 4% of a million dollar nest egg, or $40,000 a year for the next 30 years with little chance of outliving your savings and then actually doing that requires that you ignore any new information along the way.

When was ignoring new data ever a good idea?

At the beginning of World War I, horse-mounted cavalry ignored new data and charged machine guns.

That $40,000 spending estimate is based on what statisticians call "prior probabilities," meaning it's the best guess from the starting gate. After retirement begins, things happen that change your probability of success. The updated probability is called the "conditional probability."

Here's an example I used in a post some time ago. Let's say that you leave Los Angeles on a flight to Honolulu and you learn from the airlines that they have attempted this flight 1,000 times and only 10 of those flights didn't reach Honolulu because mechanical problems, weather or something else forced them to return. Your prior probability of reaching Honolulu would be 99%. That looks pretty darned good.

During the flight, your crew will constantly update their forecasts based on new information, running into headwinds, perhaps, or needing to fly around storms (a good model for your retirement plan). They will continuously create a conditional probability of reaching Honolulu and if that probability drops below a certain threshold, they will return to Los Angeles.

At least, you hope they will.

Should you find yourself halfway to Honolulu and discover that a wing has fallen off your plane, the conditional probability of reaching your planned destination has just declined considerably. (That's why I hate when flight attendants announce, "We'll be on the ground shortly." I need more details than that.) Once the wing is gone, you should take little comfort from the fact that your prior probability of reaching Honolulu was actually quite high.

Retirement works the same way. You might start retirement with a million bucks and a safe spending amount of $40,000, but if your portfolio declines 50% in a bear market you need to start spending less. That original $40,000 safe spending amount flew out the window with your bear market losses. To continue spending the same $40,000 after a large decline in your savings balance is simply ignoring new information, to wit, that you have less money.

In the 1700's, Thomas Bayes thought about how new information should be used to adjust our previous expectations. Bayes Theorem essentially says that we should begin with a prior probability, like a sustainable withdrawal rate or the percent of successful flights to Honolulu in the past, and modify that original expectation in light of any relevant new data that comes along.

Relevant new data for an airplane would be like, remaining fuel, unexpected headwinds and structural integrity of the wings.

This Bayesian approach is the way we retirees should view a retirement plan. Rather than view it as one integrated whole, we should think of it as planning for a 30-year retirement based on some set of prior assumptions. After a year, we should take stock of our new life expectancy, new portfolio balance, and any changes in expected spending along with several other variables and use that new information to plan a 29-year retirement.

Rinse and repeat.

That isn't what we do when we plan on a constant-dollar spending SWR strategy. Instead, it is what Larry Frank refers to when he describes Dynamic Updating and what Ken Steiner is getting at when he explains how to re-budget your spending every year with actuarial techniques.

And, it's what Moshe Milevski's equation for the probability of ruin (also an actuarial approach, by the way) tells us: it is a function of current retirement savings balance, expected spending, expected market returns and volatility (asset allocation) and remaining life expectancy. It doesn't matter what those were back on the day you retired.

What matters is what they are today.