Friday, April 29, 2016

A Random Walk, A Sequential Game, Part 3

In A Model of Retirement Planning, Part 1, I wrote that the challenge of retirement income planning is to best position ourselves to maintain our desired standard of living throughout an unpredictable length of retirement with somewhat-predictable future income but largely unpredictable future expenses. A mighty challenge.

In Adding Risk to the Model, Part 2, I added to the model tolerance toward the risk of losing standard of living, because within a fairly small range of expected income and expenses, some households will choose to spend more early in retirement at the risk of having less to spend late in retirement, and some households will choose the opposite. Some can live with more risk than others.

We need to add one last important characteristic to the top-level model of retirement finance, its “chained state” nature. Retirement finance is not a “set-and-forget” decision that we implement and never revisit. It's a series of moves in a sequential game.

Retirement finance is not a “set-and-forget” decision that we implement and never revisit. It's a series of moves in a sequential game.
[Tweet this]

I often use the sailing metaphor. At the end of a day of sailing – or a year of retirement – we will find that we have drifted off course and we need to correct our heading. We can't just continue using the heading we set at the start.

Game theorists refer to this as a sequential game against nature, meaning that the game is a series of alternating moves in which Player 1 (your household) makes a move and nature (defined in game theory as "a fictitious player having no known objective and no known strategy") responds.

Although personal finances are practically time-continuous, it is easier to think of them as a series of years, or “discrete-time states”, so that’s how we plan. The age of death for a healthy person is unpredictable, but we often think of people retiring around age 65 and living until age 100, or so. In that case, retirement would consist of one to 36 discrete time states representing ages 65 through 100.

 Following is a simple state diagram for a retiree who retires at age 65 and turns out to live to age 76. Of course, life span is unpredictable for a healthy retiree, so we don’t know beforehand if our own chain will contain one state or dozens.

An individual state can be identified by the age of the retiree, so we can use the terms “state” and “age” synonymously in this example. Each state has associated with it information about income, expenses, net worth, remaining lifetime, portfolio balance, desired standard of living, risk tolerance and other critical financial information.

This information is known with the most certainty in the state that is current, in other words, at our present age. For example, we can know our current portfolio balance, interest rates, current desired standard of living, and current risk tolerance fairly well. We can't know with as much confidence what these values will be for next year, and the uncertainty increases every future year.

For example, if state zero represented 2007, the market crash in October of that year might significantly change all future expectations for portfolio balance, portfolio spending, and net worth and it might even affect our decision to delay Social Security benefits. For some households, it postponed the planned retirement date.

The following table illustrates some of the plan's forecasted financial data for each year in the diagram above as of the starting state (age 65). Age 66 data is less certain when predicted at age 65, age 67 data predicted at age 65 is even less certain, etc. (Click to enlarge.)

Large changes in expectations might also result from out-sized market gains, unexpected medical expenses or the loss of a spouse. Our view of the future can change significantly in a short time. In 2006, our forecast for 2008 would not have included a 55% market crash and a housing crash.

Also, note that the state data we are forecasting are moving targets. Income changes when we claim Social Security benefits. Life expectancy decreases at each new state. Spending, our desired standard of living, tends to decline with age. The sustainable withdrawal percentage from our savings portfolio increases with age. The purchasing power of a dollar changes. Our forecasts constantly change, but so do our targets. We can't simply say we're going to spend $50,000 a year in retirement or receive $50,000 of income annually in retirement because those numbers change over time.

What about the past?

This series or “chain” of discrete states (ages) has the characteristic that the values of next year's state are dependent only upon the information provided in the current state and what happens this year. Anything that happened before reaching the current state is no longer relevant. (Mathematicians refer to this as a discrete-time Markov chain.)

A Monopoly board provides a simpler example of a Markov chain. If your race car or thimble is currently parked on Illinois Avenue, where you will end up next depends solely on where your thimble or race car currently sits and the next roll of the dice. It doesn't matter if you got to Illinois Avenue by sitting on New York Avenue and rolling a five or States Avenue and rolling eleven. That won't affect where you will move next.

This is an important concept that points out, for example, the absurdity of a fixed sustainable withdrawal strategy basing how much you can spend in year 12 of retirement on how much savings you had at the beginning of retirement. If you reach year 12 of retirement with a half million dollars in your savings portfolio, it doesn't matter if you got there by starting retirement with $1M and depleting half of it, or by starting retirement with $250,000 and doubling it. All that matters is where you are now and what happens next.

This is also an important concept in retirement planning because the states you “land on” will be a random walk through retirement-wealth “state space” resulting from those unpredictable incomes, expenses, market returns, and lifetimes, etc.

(State-space is simply the set of all possible future states of a dynamic system – or all possible states of retiree wealth in this explanation. In the simple game of tic-tac-toe, for instance, there are 765 essentially different states that can be reached. The state space for a coin-toss consists of only a head and a tail. There are only two possible future states. In reality, there are an infinite number of possible wealth states for a retiree and time is continuous. It simplifies the explanation, however, if we imagine time in discrete years (snapshots) and a finite number of essentially-different wealth states.)

The state diagram above shows the path moving forward in a straight line, but your path will actually wander through wealth “state space” depending on the draws from those random variables, incomes, expenses, market returns, etc., as illustrated in the following diagram.

When you reach the darker-blue state at age 67 in the above diagram, for example, it won't matter how much or how little wealth you had at ages 65 or 66. Those gray states and the information they contained will no longer be relevant. At age 67, we can only guess the future positions of the light blue states and when we reach age 68 and gray-out age 67, our predictions of the position of future light blue states may change then, perhaps dramatically.

This Markov-chain, or "Markovian", nature of retirement finance has a number of implications for the retirement model. First, since year three's finances depend solely on year two's financial state plus some unpredictable events, and year two's finances are also unpredictable, predicting our future finances with any accuracy quickly becomes untenable. We are trying to predict where we will be in the future by moving an unpredictable distance and direction from an unknown starting point.

Our ability to predict future states decays quickly. We can perhaps predict a year in advance with a little accuracy, but this foresight decreases with each year beyond that and quickly becomes unpredictable. No one predicted the 2008 financial disaster in 2006.

Our ability to predict our financial future decays quickly. No one predicted the 2008 financial disaster in 2006.
[Tweet this]

Second, thinking of retirement as a Markov chain that renders past information irrelevant means each new year of retirement becomes a new puzzle to solve, possibly quite different than the one we faced the previous year, so dynamically updating our plans becomes an obvious necessity. It also rids us of the notion that our financial situation years ago remains relevant.

The top-level model for retirement finance, then, should look something like this.
"Retirement finance is a random walk of unpredictable length ranging from one year to several decades. At a given age, only the present financial data are known with any certainty. Data from previous years can be known but are irrelevant. The reliability of forecasts of data for future states decays rapidly with time and forecasts beyond five years are probably sheer conjecture. The key determinants of retirement wealth are random variables: income, expenses, life span, and risk tolerance. Retirees can choose to spend more or less, within a reasonable range, depending on their risk tolerance. Retirees with high risk tolerance can increase spending early in retirement and consequently increase the risk of a lower standard of living in late retirement while more risk-averse retirees can decrease spending early in retirement and consequently decrease the risk of a lower standard of living in late retirement.”
Retirement finance is a random walk along a Markov chain, or to a game theorist, a sequential game against nature. Each year we make forecasts based on what we know (our current financial status and the financial environment), what we expect to happen in the future, and what unexpected outcomes we believe we might experience in the future (risks). We make our move based on this analysis and our risk tolerance. Then nature takes its turn and we repeat.

Once we have a high-level model of retirement finance, we can start to think about how to plan for it. Surprisingly, I have been able to find very little literature that addresses the best way to develop a plan. A good place to start, I think, would be to answer this question: How can you know a good plan when you see one?

Friday, April 22, 2016

Adding Risk to the Model, Part 2

In my last post, A Model of Retirement Planning, Part 1, I suggested that “The challenge of retirement income planning is to best position our available resources to maintain our desired standard of living throughout an unpredictable length of retirement with somewhat-predictable future income but largely unpredictable future expenses.” 

Let me break that down. "Best positioning our available resources" means placing our best bets because retirement is unpredictable and we can't know in advance which strategy will outperform the others. "Maintaining our desired standard of living throughout retirement" is typically the retiree's first goal, but it may not be the only one.

I began building a high-level view of retirement finance and the main point of that post was that the three most critical factors of retirement finance are lifespan, income, and spending and all three are largely unpredictable.

Once we lay out an estimate of the cost of the standard of living we desire in retirement (the expenses), estimate the amount of income we might be able to generate from all available wealth resources, and choose a life expectancy for planning purposes, there will be a large range of potential retirement strategies still at our disposal. Different households with virtually the same expected income, expenses, and lifetimes may plan very differently because their risk tolerances differ. We need to add risk tolerance to the model.

The primary risk of retirement is that of losing our standard of living. (Notice I didn’t say the primary risk is depleting our savings. It’s possible to deplete our savings – or even to not have savings –  and still maintain our standard of living. The latter is more important.)

Risk tolerance refers to how much risk we can tolerate emotionally and psychologically. Nearly everyone is risk-averse, meaning that, when exposed to uncertainty, we attempt to reduce that uncertainty. But, some of us are more risk-averse than others, and some are more risk-tolerant, so we tend to choose whatever strategy “lets us sleep at night.”

Given identical expectations of future expenses and income, two households might choose very different retirement strategies because one household is significantly more worried about the prospects of losing their standard of living than the other. Generally, the higher standard of living one chooses, the greater the risk of outliving savings.

Because income can be a range and not a single amount and expenses are a range and not a single amount, there is a budget range within which we can plan. Say we expect annual expenses to range from $30,000 to $35,000 and income to range from $40,000 to $42,000. We can take some risk and plan on $42,000 of income and $30,000 of expenses, be conservative and plan on $40,000 of income and $35,000 of expenses, or choose something in between.

The amount a household will spend in retirement depends somewhat on how much risk they are willing to accept that they will run short of money late in life. Consequently, risk tolerance is a key factor in the basic retirement finance model.

A household that finds that it doesn't have enough expected income to pay for the expected cost of their desired standard of living has three levers to pull in any combination. The household can reduce expenses, increase income, or take more risk of a lower standard of living late in life.

First, we can lower our expenses, reducing discretionary expenses like travel for example, or accept a lower standard of living. We might relocate to someplace where our desired standard of living is less expensive. We can also lower expenses in retirement by working longer and thereby shortening the length of our retirement.

Second, we can increase income by delaying retirement and working and saving longer (the most effective strategy). We may also be able to increase income through part-time employment. We can increase income by delaying the claiming of our Social Security benefits. We may even increase it by changing our funding strategy. A life annuity, for instance, might generate more lifetime consumption than investing in stocks and bonds.

Third, we can spend more early in retirement if we are willing to accept more risk of a lower standard of living at the end of retirement. One way to do this is to bet a lot on the stock market. If the market performs very well during our retirement, we will have more money to spend. Unfortunately, if the market performs only moderately well or poorly, we will have less to spend later in retirement. Many people seem willing to make that bet.

We can also take risk with our life expectancy. Some people bet that they won't live a long life and they increase spending accordingly. That seems like a risky bet for a healthy person, the downside being a low standard of living in old age, but people tell me frequently that they “won't live past 80.” I have no idea how they know that. Once again, this allows us to increase spending in early retirement at the risk of a lower standard of living late in retirement.

Regardless, if you are willing to take more risk of a lower standard of living in late retirement, of not reaching late retirement, or of not encountering many large, unexpected expenses, you can increase your spending in early retirement. Spending won’t depend solely on your income and expenses, it will also depend on your risk tolerance.

Imagine two married households with identical financial resources on the eve of retirement, but with vastly different risk tolerances.

The risk-tolerant household can assume that they won’t live much past median life expectancy, that they won’t need long-term care or have other large unexpected living expenses and that the market will return 8% after inflation throughout their retirement, so they invest most of their savings in a stock and bond portfolio and spend 4% of it each year.

The more risk-averse household will assume the husband will live to age 90 and the wife to 100. They will work as long as they are able and delay claiming Social Security benefits. They will purchase long-term care insurance and use their savings to purchase a life annuity so they maximize consumption and avoid market risk entirely. They will relocate to an area with a lower cost of living. They will spend less early in retirement and hold some back for a possibly long retirement.

Risk tolerance is critical to retirement planning, but can vary over time with risk capacity and risk perception.
[Tweet this]

The risk-tolerant household will feel comfortable spending significantly more in early retirement than the more risk-averse household, which is to say that they will choose a higher standard of living with a greater risk of dying broke. If the more risk-tolerant household is too conservative, they will have a lower standard of living than they would have otherwise had. If the more risk-tolerant household loses the bet, they will have a higher standard of living in early retirement than in late retirement.

One last important point about risk tolerance should be considered. We might imagine that risk tolerance is constant for a given retiree, but that isn't always the case. Like most other key factors of retirement planning, risk tolerance can be unpredictable. It can change situationally or with age.

William Bernstein has written often about investors who feel quite risk tolerant during a bull market only to find during a market crash that they fear losses much more than they expected. He recently wrote that investors who take measure of their risk tolerance during good times should probably halve it. It is difficult to predict how you will feel in a gut-wrenching crash like 2007 until you have lived through one or two.

Research differs on the correlation between age and risk tolerance. This 1997 study (download PDF) concluded that “Risk tolerance increases with age when other variables are controlled”, while a 2010 study reports that “Risk tolerance generally decreased as people age.” In both cases risk tolerance changed significantly with age, but the direction of the change differed.

Interestingly, the study that showed older people become more risk tolerant concluded during the Tech boom and the study reporting that risk tolerance generally declines with age concluded just after the Great Recession, consistent with Bernstein's observation.

Regardless, the important point for a retirement model is that risk tolerance is critical to planning but it can vary over time as our risk capacity and perception of risk change. Like most critical factors of retirement finance, it isn’t something we can establish at the beginning of retirement and assume will remain unchanged. And, because we frequently can’t predict our future risk capacity with any certainty, nor our future perception of risk, our risk tolerance over time can be somewhat unpredictable.

To plan for retirement, we need to estimate future expenses, estimate future income, establish a life expectancy for planning purposes and understand how much risk we are willing to take with those estimates. We add the risk of losing our standard of living to the basic retirement model as follows.
The challenge of retirement income planning is to best position our available resources to maintain our desired standard of living throughout an unpredictable length of retirement with somewhat-predictable future income but largely unpredictable future expenses. Retirees can choose to spend more or less, within the range of available resources, depending on their risk tolerance. Retirees with high risk tolerance can increase spending in early retirement and consequently increase the risk of a lower standard of living in late retirement while more risk-averse retirees can decrease spending in early retirement and consequently reduce the risk of a lower standard of living in late retirement.”
Once we have an estimate of expected retirement income and expenses, choose a “comfortable” level of the risk of losing our standard of living late in life, and choose a life expectancy parameter for planning, we have gone a long way toward bounding a set of retirement finance strategies appropriate for our household. Choices of details like asset allocations, withdrawal rates, construction of a safe floor portfolio, and annuity considerations will flow from these basic decisions.

Retirement planning should be a top-down process, rather than choosing from a menu of strategies.
[Tweet this]

The previous paragraph has significant implications for retirement planning. It suggests that planning should be a top-down process driven by the choices identified initially within the high-level model, rather than a process of choosing from among a menu of all possible strategies. By identifying the key factors first, we immediately eliminate many inappropriate or irrelevant strategies from consideration.

There is at least one more important top-level characteristic of retirement finances our high-level model must incorporate – retirement's “chained state” nature. Retirement planning isn't a one-time decision.  It's a series of moves in a sequential financial game.  (A sequential game against nature, in the vernacular, and a little more game theory.)

I'll get to that in A Random Walk, A Sequential Game, Part 3.

Friday, April 15, 2016

A Model of Retirement Planning, Part 1

The details of retirement financial planning are easier to understand once you imagine the big picture and can see what the pieces are and how they fit together. It's easy to get stuck in the weeds.

Most retirement literature, unfortunately, doesn’t start with the big picture. It often jumps right into asset allocations or sustainable withdrawal rates. So, let’s take a step back and build a basic model of retirement finance, starting with how much the bills will be and how we will pay them.

Funding retirement begins with the simple observation that after one retires, the bills keep coming but the paychecks stop.

We then need to find the “best” way to pay the bills, with “best” being defined from an individual household's perspective. The plan one household considers best might be completely unacceptable to a different, even quite similar household. Given two households with identical finances, for example, one might find a life annuity to be "the best" solution while the other might not trust insurance companies and refuse to even consider annuities.

Paying for the expenses of retirement is the basic problem, so let's start with the cost. Expenses are also sometimes referred to in a retirement planning context as spending or consumption. I'll use them synonymously here.

One way to estimate retirement expenses is to assume that we will maintain our pre-retirement standard of living after we retire. We can subtract FICA taxes and retirement savings amounts from our pre-retirement paychecks because those are two items we will certainly not need to pay after retirement. The result is an estimate of the amount of retirement income needed assuming no changes to our standard of living. But, it isn’t a very good estimate for two reasons. First, our spending will change as we age (it typically declines). Second, living expenses aren’t entirely predictable.

Some living expenses are fairly predictable but some are random. I can predict that I will have a grocery bill, a housing bill and a Netflix bill next month and I can predict the amounts fairly accurately.

When my son needed $500 a while back to repair his car's ignition switch, we didn't see that coming. When my daughter needed an emergency appendectomy, that wasn’t in the plan. Living expenses have both unpredictable and predictable components, which means that your total annual living expenses are unpredictable.

The predictable part is simply the minimum. I can be pretty sure that my living expenses will be $50,000 next year, but I might also have a large unpredictable expense or two next year. So, my total expenses next year will actually be somewhere between $50,000 and some amount that could be much larger but is unpredictable.

This “expense risk” is the fallacy in looking at retirement planning simply as an income problem, such as a sustainable withdrawal amount from a portfolio of volatile investments.

Retiring for an unpredictable number of years with unpredictable expenses and somewhat-predictable income.
[Tweet this]

Let’s say a planner (or an online calculator) tells you that you can spend 4% of your savings each year and your savings will likely last at least 30 years. That 4% provides you with a nice standard of living when added to your Social Security benefits until one day someone in your family becomes quite ill and you have $100,000 of uninsured medical bills or your adult child becomes unemployed and moves back home. Your retirement plan – and perhaps your retirement – is destroyed.

What went wrong? Your planner (or that online calculator) promised that you could spend 4% of your portfolio balance annually and your savings probably wouldn’t be depleted for at least 30 years. He (it) didn’t say what would happen if you should need to spend more than the 4% you planned. You thought 4% spending was safe, but how can you know that your retirement finances are “safe” without knowing how much you might have to spend? The income side of the equation alone doesn't show all the risk.

How long you will live in retirement is more critical than spending. If your desired standard of living costs $60,000 a year, you retire at 65 and die at 66, your entire retirement will cost about $60,000. If you live to 100, retirement will cost about $2.1M. (Those totals don’t include the aforementioned unpredictable expenses and the longer you live, the more likely you are to be hit with them.) A healthy person can't predict how long he or she will live and that means the total cost of retirement is highly unpredictable even without large, unexpected costs.

Life expectancy and spending are the two largest determinants of retirement cost and, as I have pointed out, both are unpredictable. So, when someone asks how much money they will need to retire or how much retirement will cost, the correct answer is, “We can't say with any certainty, at all. We can tell you what typically happens, but your retirement may not be typical.” That rules out waiting until you're certain you can afford it to retire. Certainty is absurd.

This doesn't imply that because retirement is largely unpredictable retirement planning has no value. We can't say with certainty that it won't rain June 2nd of next year but we can plan an outdoor wedding that has a better chance of success than simply hoping for nice weather.

Where will we find the income to pay our bills after we retire? It typically comes from Social Security benefits, pensions, part-time employment, and personal savings invested in income-producing assets like stocks, bonds, and real estate.

Income is more predictable than expenses or it can be if retirement is funded appropriately. Spending from pensions, life annuities, TIPS bond ladders and Social Security benefits is pretty predictable. Investments are less predictable, but the most you can lose from your investment portfolio is its total balance. Unexpected expenses can cost much more than your savings.

Imagine, for example, that you have saved $100,000 and have it invested in stocks and bonds. The most you can possibly lose in the market is $100,000 and it is extremely unlikely that you will lose all of it. On the other hand, it’s easy to imagine a medical bill exceeding $100,000.

This large amount of risk inherent in retirement finance is an unavoidable reality. Even if you fund retirement entirely with Social Security benefits and life annuities, making your expected income more predictable, retirement will still be very uncertain because some expenses are highly unpredictable. If you are very wealthy relative to your spending, of course, this matters much less.

Here, then is the first part of a retirement finance model:
The challenge of retirement income planning is to best position our available resources to maintain our desired standard of living throughout an unpredictable length of retirement with somewhat-predictable future income but largely unpredictable future expenses.
Note that the primary goal is to maintain a desired standard of living throughout retirement and not to maximize wealth, income or an inheritance. Once the standard of living goal is achieved– itself alone a massive challenge for most households – any uncommitted resources can be applied to the other goals.

Standard of living, by the way, is also a moving target. We naturally become less active and spend less as we age. As David Blanchett showed, however, spending typically declines as retirees age when they spend appropriately for their savings level. Retirees who under-save tend to spend less over time and retirees who over-save tend to spend more as they age. The latter two tend to "correct" spending as they recognize that they are depleting savings too quickly or have more money to spend.

This is the beginning of the “big picture” and one of the reasons questions like “how much money do I need to retire” and “when can I retire?” are so difficult to answer and why retirement planning is so challenging. It also points out that most retirement planning focuses too narrowly on investment results.

Lastly, it points out just how risky retirement is. As financial planner, Larry Frank, frequently reminds me, “everything is stochastic.” By stochastic he means random or unpredictable. And, by everything he means the market, interest rates, inflation, expenses, taxes, Social Security benefits, how long we will live and most other significant factors of retirement financial success.

But, unpredictable life spans, income, and expenses aren’t the entire “big picture” of the retirement finance model. I'll expand the model in future posts, starting with Adding Risk to the Model, Part 2.

Friday, April 8, 2016

Certainty is Absurd

Sometimes I read an excellent column somewhere and refer my readers to it while trying to build on the author's ideas a bit. I read a column today by Adam Butler posted at Advisor Perspectives that is such a column, but it is so well written that I don't find much to add.

The information in Adam's column isn't new research. It is, instead, a well-laid-out argument consisting of prior research showing that no one, not even those identified as experts, can reliably pick winning stocks or time the stock market, or predict the future in any of a broad range of disciplines, for that matter. He includes a wonderful quote from Voltaire, “Doubt is not a pleasant condition, but certainty is absurd.”

Adam suggests as an alternative to attempting to predict future market returns, advisers use “forecast-light methods.” In other words, if we can’t predict the future, our plans should minimize sensitivity to critical predictions.

Voltaire's quote is spot on. Accepting uncertainty in retirement planning is uncomfortable (Do I have enough savings to retire? Should I work another year just in case? What if I buy an annuity and only live a few more years?) but unavoidable. Retirement finances are so unpredictable that certainty is, indeed, an absurdity.

I find the framing of this argument intriguing. If a fortune teller told us he could predict the future, we would say, “Prove it.” In the investment world, people claim they can predict the future and say, “Prove I can't.”

It usually doesn't work that way and there is scarce credible evidence that anyone can outsmart the market for more than just a few years. (My favorite example is Bill Miller, see “Losing Money with the Best Mutual Fund Manager of All Time.”)

I'll stop talking now and send you to Adam Butler's post. Enjoy!