Wednesday, April 19, 2017

Retirement Roulette

Phyllis loves to play roulette at the casinos. She knows there are games with better odds but there's something about the large spinning wheel and the big green table with its field of many bets that she finds irresistible.

Phyllis has a roulette strategy – she calls it a "system" – that she adheres to rigorously. Because a fair roulette game is totally random and the odds favor the house her strategy isn't statistically profitable but that isn't something that concerns a typical gambler. Watching a YouTube video of a roulette game, I heard one player say he watches for trends in the random winning numbers (humans are really good at seeing trends, even when they don't exist) and I hear another say that he seems to win a lot with the number 26.

Phyllis' strategy is to place several small bets on the first spin of the wheel and to double the bets each time she loses. After a winning bet, she bets the same amount on the next spin.

She places a bet on red, another bet on 36, a corner bet, and a street bet for each spin. (Watch a few minutes of this YouTube video[1] if you've never seen a roulette game. Notice the multiple bets placed by each player at each spin of the wheel.)

After each spin, she calculates the revised amount of her bankroll and places another set of bets on the next round. Her strategy is to stop playing should she double her initial bankroll and, of course, she will stop playing when she is ruined.

At this point, you may wonder what Phyllis and her roulette strategy have to do with financing retirement. The answer is that the mechanics of her roulette game are somewhat analogous to the way in which retirement should be played. Visualizing retirement funding as a roulette game can demonstrate the process as a whole as opposed to seeing a set of related but independent strategies for income generation, asset allocation, annuitization, and the like.


Life is like a box of chocolates. Retirement is like a game of roulette.
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We start with a grand strategy, hopefully one that is more profitable than a roulette strategy, and play one year at a time in the same way that Phyllis plays one spin of the roulette wheel at a time. We stop playing retirement when no one in our household is still alive.

It's not a perfect analogy. Phyllis stops playing roulette when she runs out of money but, unlike roulette players, we can't stop being retired when we go broke. We have to figure out how to continue playing retirement until the end, perhaps getting by on Social Security benefits alone – not a pleasant prospect[2].

Now, let's play a game of Retirement Roulette. Over my working life, I have accumulated wealth that I can use to pay for retirement. That wealth is represented by the three stacks of chips in front of me that constitute my "bankroll."

My financial capital (pink), social capital (red) and human capital (blue) at retirement. Image from designinstruct.com.

The first stack of chips represents my financial capital[3]. It represents my wealth held in taxable accounts, retirement accounts, home equity, etc. The second stack of chips represents my human capital, my ability to generate income from labor. Perhaps I can retire as a college professor and still teach a couple of classes each semester for a few years. This stack of chips will shrink over time whether or not I use it as my ability to generate income from labor diminishes.

The third stack of chips represents my "social capital" and includes my Social Security benefits and a small pension I earned from a previous employer. I have three chips. The first represents my pension, the second represents my wife's Social Security benefits and the third chip represents my own Social Security benefits.

My social capital.

On the "Retirement Roulette" table in front of me lies a broad array of potential retirement bets including:
  • a bet on a retirement date
  • a bet on an amount to spend this year
  • a bet on stocks
  • a bet on bonds
  • a bet on cash
  • a bet to claim or delay Social Security benefits
  • a bet to purchase an annuity
  • a bet to purchase long-term care insurance
  • a bet on a legacy for our heirs
I refer to these as "bets" because each has a cost, each has a payoff, and each payoff is uncertain.

I use my strategic retirement plan[4] to guide my bets in much the same way Phyllis uses her strategy to place roulette bets. That plan identifies my strategic objectives – the long-term financial retirement goals I'm trying to achieve. I now need to identify the best tactical moves I can make in the present round (this year) to further those long-term objectives. For example, I have a strategic goal to not outlive my savings so perhaps a good tactic for the current round is to not claim my Social Security benefits, yet.

First, I bet that I have enough retirement resources to retire this year at age 65.

I decide to wager the pension bet immediately because I am 65 years old and, unlike postponing Social Security benefits, delaying my pension claim has no financial benefit. The payoff for this bet is $1,000 of income monthly for as long as I live.

I have determined that the optimal Social Security claiming strategy for our household is for my wife to claim at age 66 and for me to claim at age 70. Since she is now 66, I will bet her Social Security benefits chip now and save mine for the year I turn 70. Of course, I can decide to bet my chip sooner should I need the money.

The payoff for this bet is some immediate income from my wife's benefit and maximum lifetime retirement and survivor benefits for both of us should we live longer than an average life expectancy at the claiming age.

I won't bet the home equity chips right away in case I need those for an emergency later in retirement.

My strategic retirement plan calls for a floor-and-upside retirement strategy so I will add a small pension bet to my wife's Social Security benefits to create the floor. I move chips from my financial capital pile to the pension bet.

After calculating the income from my floor bet, I decide that I will need to spend 3% of my remaining portfolio balance on expenses for the coming year. I move that amount of chips to the spending bet on the table.

I count the number of chips left in my financial assets pile and decide on an asset allocation. I move 5% of the chips remaining in that pile to the cash bet on the roulette table, 35% to the bonds bet, and 60% to the stocks bet. All of my chips are now on the table on eight different bets and they look something like this:


I am actually making 12 bets, not eight, because not buying Long-term Care Insurance (LTCi), for example, is also a bet. It's a bet that I won't need the insurance in the coming year and that I will have both the resources and the health to enable me to make that bet a year from now should I so decide.

I win this "non-bet" when I don't need to claim LTCi in the coming year and the payoff is a year of typically substantial premiums. I lose this non-bet when I do need to make a claim but don't have insurance or when my health deteriorates to the point that I can't qualify for the insurance in the future. I would lose a purchase bet if the insurer raises my future premiums so much that I am forced to let the policy lapse before I need it. And, of course, I lose the bet if delaying the purchase results in significantly higher premiums when I eventually do buy. Retirement bets can be very complicated and understanding them in their entirety is critical.

In Retirement Roulette, we bet all of our chips every year and we make every bet even if the bet is that we should wager nothing on it.

I "spin the wheel" and nature takes its turn. A year later the results are in.

The payoff on my stock bet will be about 8% with a standard deviation of about 12%, meaning that about two-thirds of annual returns will fall between a 4% loss and a 20% gain. The payoff on my bonds bet will be about 3% with a standard deviation of about 3%. My cash bet will return about the rate of inflation, or about zero in real dollars.

My pension bet will pay off $12,000 and my wife's Social Security benefit will pay off about $20,000. My cash will increase by about the rate of inflation but decrease by about the 3% I planned to spend. Of course, expenses are unpredictable and I may actually spend more or less. The "payoff" for the spending bet will be about a 3% loss.

My life expectancy and that of my wife have decreased by a little less than one year. (Life expectancy is a key factor in many retirement decisions.)

And so ends round one.

To prepare for round two I must evaluate the results of all my bets, changes in my life expectancy and my wife's, changes in our health, our expectations for the financial markets going forward, and other critical factors to decide which if any of my bets I should change for the coming round.

How will I bet in future rounds? I won't know for certain until I see how retirement unfolds between now and then, but my plan is to play my Social Security chip when I reach 70. My spending next year might go up or down a little depending on this year's market returns. I may move some chips from the stocks bet to the bonds bet after a really good run for stocks, or vice versa after a poor run, but only if the percentages get seriously out of whack. Most years I will tweak my bets just a little and spin again.

The game will continue as long as one of us survives. Unlike roulette, our game doesn't end if we deplete our bankroll, though our lifestyle is likely to be severely curtailed in that event.

The important perspectives of the roulette analogy are:

  • Like roulette, retirement funding has a very large element of uncertainty. This includes the length of our careers, how long we will live, market returns, interest rates, annuity payouts, inflation, discretionary spending and spending shocks, which is to say all of the critical factors are uncertain. Even households who generate retirement income completely with "risk-free" assets will be exposed to expense risk.
  • Like roulette, retirement funding is a series of "rounds"(typically years) during which the retiree makes a series of decisions (bets) and the universe responds. These first two characteristics define what game theorists refer to as a sequential stochastic game against nature[5].
  • Retirement ends with death; roulette ends when the gambler decides to walk away or is ruined. Retirees can't walk away but they can lose their standard of living.
  • Unlike roulette, a retiree plays all her wealth every round. Some bets, like cash, will have very little risk. Bets we don't make are as important as those we do. 
  • A "round" typically involves multiple bets that are separate, yet the ultimate result of the round is the sum of the bets won less the sum of the bets lost.
  • Critical factors can change from one round to the next and these must be considered when placing next year's bets. Retirement funding is dynamic, not set-and-forget.
Retirement Roulette ties back to my posts on strategic retirement planning; The Opening, the Middle Game and the Endgame[6]; and A Mission Statement for Retirement[7].

Next time, I'll tie these together.


REFERENCES

  1. YouTube video of a roulette game. [click here]
  2. The Tightwire Act of Living Only on Social Security, Washington Post.
  3. Sullivan and Sheffrin (2003) defined human capital as "the stock of competences, knowledge and personality attributes embodied in the ability to perform labor so as to produce economic value", in other words, our capacity to generate wealth from our labor. Social capital is defined as capital from "social structures" like Social Security and pensions. Financial capital consists of debt and equity.
  4. Strategic retirement planning, The Intersection of What's Desired and What's Possible, The Retirement Cafe´.
  5. Sequential stochastic games against nature, A Tiny Bit of Game Theory, The Retirement Cafe´.
  6. The Opening, the Middle Game and the Endgame, The Retirement Cafe´.
  7. A Mission Statement for Retirement, The Retirement Cafe´.

Friday, March 31, 2017

My Appreciation of Annuities Has Grown

I believe I've told this story before, but a friend once brought his wife, whom I'd never met, to my home to talk about retirement planning. As I tried to introduce myself, she interrupted me to say, “If you recommend a life annuity I will get up and walk out.”

Nice to meet you, too!

I have also received emails from readers saying they would never consider investing their hard-earned retirement money in the stock market.

And so it goes. People have strong opinions about both. Because I believe that the most important requirement for a good retirement plan is that the clients can sleep at night, I rarely try very hard to convince them to change their beliefs, though I do try to present fair assessments of both alternatives.

If you firmly believe that annuities or the stock market are not for you, you are probably right.

I have always believed that life annuities can play a critical role in many retirement plans but my appreciation for them has increased over the years. For anyone who is on the fence about life annuities, I'd like to share some different perspectives that may help you decide.

A life annuity is a contract typically sold by an insurance company to an “annuitant” (often a retiree) guaranteeing periodic payments for as long as the annuitant lives. In retirement planning, we use annuities to mitigate longevity risk, the risk of outliving our retirement savings.

The payout for a single male aged 65 today is about $560 per month, or $6,737 annually for a $100,000 annuity. That's about 6.7% annually. That is not equivalent to a 6.7% investment return because part of this payout is a non-taxed return of your own capital. The equivalent investment return will depend on how long you live. It will begin with a negative return and, should you live long enough, it will eventually exceed the payout rate. [1]

The insurance company invests the premiums you pay in bonds. It also uses premiums paid by annuitants who don't live a long time to pay annuitants who do live a long time using what are referred to as “mortality credits.” The payouts you receive come from bond interest, from a partial return of your own capital and, if you live longer than average, from mortality credits.

Perhaps the greatest objection to life annuities, and the one my wife's friend found unacceptable, is the fact that a life annuity typically has no value after the annuitant dies. True, some annuities offer riders that guarantee income for a number of years (period certain) or guarantee repayment of some principal to beneficiaries, but these riders are expensive and may not be worth the cost.

The fear is that the retiree will buy an annuity and die before enough payments have been received to cover the annuity's cost. This is what had happened to my friend's sister-in-law and why the return on investment for an annuity starts out negative.

This is the same “break-even” analysis that many use to justify claiming Social Security benefits as soon as possible and the problems are similar. Both Social Security retirement benefits and life annuities are insurance – not investments – that mitigate the risk of living a long, expensive retirement. If the annuitant doesn't live a long life, then he or she would clearly have been better off not purchasing the annuity, but that isn't something we can predict.

That insurance has value whether or not we make a claim. The retiree who purchases an annuity at age 65 but only lives to age 70 mitigates the risk of a long life even though he didn't happen to live to an old age. People who purchase car insurance but don't have an accident rarely argue that their premiums were wasted, nor do homeowners who buy insurance but don't have a fire of flood claim. Many retirees considering annuities apparently don't see longevity insurance in the same way as they view other policies but purchasing life annuities and delaying Social Security benefits provide a very real transfer-of-risk insurance benefit.

For every story of a relative who purchased a life annuity and didn't live long after the purchase there is a story of someone who benefited from mortality credits. You may do better or worse when purchasing an annuity, but in either case you were insured against a long, expensive retirement.


“Some prominent figures who are noted for their use of annuities include: Benjamin Franklin assisting the cities of Boston and Philadelphia; Babe Ruth avoiding losses during the great depression, and O. J. Simpson protecting his income from lawsuits and creditors. Ben Bernanke in 2006 disclosed that his major financial assets are two annuities.” —Wikipedia [2]


Liquidity is another concern for the purchaser of a life annuity. The annuitant takes a large sum of cash that could easily be spent and purchases a life annuity whose value can only be spent as periodic payments. Let's assume a retiree decides to spend $100,000 of cash on a life annuity that pays $6,000 a year. She no longer has access to the $100,000 to cover large bills; she only has $6,000 per year in liquid assets, albeit for the rest of her life.

One alternative to purchasing a life annuity is to “self-annuitize” with a “sustainable withdrawal rate.” SWR strategies work by over-saving. The funds that must be kept on hand to reduce the probability of depleting one's savings aren't really available for spending, either. They are needed to generate future income and to ride out periods of poor market returns. Furthermore, it has been shown that this strategy is economically inefficient (i.e, expensive).[3]

Liquidity is a valid concern and retirees need to consider their remaining liquidity should they purchase an annuity. This consideration, however, should take into account the true liquidity of alternative strategies. Those savings may not be as liquid as you thought.

For households that will fund retirement with a mixture of annuities and investments annuities will enable a more aggressive investment portfolio. A household that has a significant floor of Social Security benefits and life annuities can absorb market losses more confidently knowing that its base income is secure.

Different Perspectives on Life Annuities
  • The insurance has value even if we don't “make a claim” (live to an old age)
  • Annuity alternatives may not have the liquidity they appear to have
  • Annuities give the retiree more confidence to invest a market portfolio more aggressively
  • Some retirees lack interest in investing 
Lastly, I have come to appreciate life annuities more because my wife, despite her MBA, has little interest in investments. Should she survive me, she will probably be far happier with a secure base of income and less need to worry about investment results.

She doesn't actually feel that way, though. She's not that keen on handing over part of our savings to insurance companies for annuities. Still, she hasn't threatened to walk out if I mention them.

Yet.


David Blanchett, Michael Finke and Wade Pfau published a paper entitled “Planning for a More Expensive Retirement[4] in the March issue of Journal of Financial Planning. The paper contains a wealth of data explaining why funding retirement is quite expensive today. The following chart from that paper shows that the cost of buying one dollar of real annuity income at age 65 has more than doubled since 1982.


The cost of a dollar of real annuity income increased as the result of two trends: a long-term decline in interest rates and an increase in life expectancy, both of which tend to increase the cost (lower the payout) of annuities. While interest rates are historically low and may revert to the mean going forward, life expectancies should continue to increase, though perhaps at a slower rate than over the past three decades. In other words, while two factors lowered annuity payouts only one is likely to reverse.



REFERENCES

[1] Payout Rates and Returns on Income Annuities, Wade Pfau.



[2] Annuity (American), History, Wikipedia.



[3] The 4% Rule—At What Price?, Jason S. Scott, William F. Sharpe, and John G. Watson, April 2008.



[4] Planning for a More Expensive Retirement, Blanchett, Finke, Pfau, 2017.





Tuesday, March 21, 2017

Annuities: Anything Anytime

In my previous post, Annuities: All or Nothing, I discussed a paper entitled, "Annuitization and Asset Allocation" [1], written by Dr. Moshe Milevsky and Dr. Virginia Young in 2007. The authors developed models for two annuity markets. The first, referred to as “All or Nothing”, calculates an optimal age for purchasing a life annuity one time in retirement, but the authors also found that there is a better way.

The second analysis in that paper identifies an optimal way to purchase annuities when the retiree can choose to purchase any amount of annuity at any time. The authors refer to this as an “Anything Anytime” annuity market and it is the scenario in which most Americans will find themselves.

While most Americans can choose to purchase life annuities in pieces rather than being limited to a single purchase in an All or Nothing market, we can't generally undo these transactions because there isn't a healthy secondary market where we can sell life annuities. We can annuitize but we can't economically un-annuitize.

Second, Anything Anytime considers public and private pension income including Social Security and similar benefits equivalent to income from life annuities from insurance companies so they all meet the optimal income-purchase requirement. A household that needs $100,000 in annuity income and expects $5,000 in Social Security or pension benefits, for example, needs only purchase another $5,000 of life annuity income. (All or Nothing largely ignored private and public pension income.)

Third, if the math for All or Nothing seems challenging, Anything Anytime quickly dives into complex utility functions and differential calculus so I suggest you do what I do in these cases: trust the math and concentrate on the conclusions.

The Anything Anytime analysis of Milevsky [2007] explores whether there is an optimal strategy for annuitizing when a utility-maximizing [2] retiree can purchase more annuities at any time in any amount but cannot “un-annuitize.” It determines that there is an optimal strategy and that it is roughly (I paraphrase here) as follows:
Retirees should annuitize some amount of their wealth at the beginning of retirement (recalling that Social Security and other pensions count). Should their wealth increase as they age relative to their annuity income they should then annuitize more but if wealth remains steady or declines they should “stand pat” with existing annuity income.
In other words, this research finds that the optimal annuitization path for a utility-seeking retiree is to start with a base of annuity income at the beginning of retirement and ratchet it upward if and when her wealth increases relative to her annuity income.

Anything Anytime recommends an immediate purchase of some amount of annuity income (or claim of pension or Social Security benefits) early in retirement and that is a major difference from All or Nothing. The latter sought the optimal age for a one-time purchase of annuities and found that it is typically later in retirement. The paper recommends that everyone needs some amount of annuity income, but since nearly all Americans are covered by Social Security or a public pension, nearly everyone will have some annuity income.

The optimal amount of annuity income to purchase at a given age is determined by a ratio, w/A (wealth relative to annuity income), in which w is total liquid wealth and A is total annuity income. Note that A is annuity income and not the face value of the policy. (For example, if you purchase a $100,000 annuity that pays out $4,000 per year, A refers to $4,000, not $100,000.) "Liquid wealth" means wealth exclusive of the face value of annuities. In my example, a retiree whose wealth was $500,000 and who purchased a $100,000 annuity would be left with $400,000 of liquid wealth.

Calculating this ratio (w/A) and determining a household's utility function account for the difficult math. This wealth-to-income ratio is determined by solving a differential equation of a utility function for a given time in retirement. Since utility functions are quite difficult to identify for an individual the calculation would be difficult even if the math weren't.

It is important to note that the wealth-to-income ratio is a function of time and wealth so it changes as we age. It isn't a fraction, like 50%, that we can calculate and assume that our annuity income should always equal half our wealth, but rather a fraction that needs to be calculated periodically as we age and our wealth changes. We can't know it accurately in advance because we can't predict our future wealth accurately.

Setting aside the difficulty of calculating an optimal wealth-to-income ratio for an individual household, there is much to be learned from this study. To begin with, there exists a mathematically optimal strategy for annuitizing wealth in retirement that involves establishing an initial amount of annuity income early in retirement and adding to annuity income as we age and our wealth increases. If our wealth does not increase, purchasing more annuity income is suboptimal.

This strategy fits well with a number of annuity strategies, noting that these strategies come more often from the Safety-first school and economists than from the Probabilists school and stock market devotees. Annuity-laddering strategies to avoid locking in the worst payouts during times (like these) of low interest rates work well with this strategy. The strategy to purchase multiple annuities from multiple insurers to mitigate the default of a single insurer does, as well.

Many households will be reluctant to hand over a large chunk of retirement savings to an insurance company. Establishing some annuity income early in retirement and planning to possibly buy more income later should ease this anxiety by making the purchases smaller and reducing regret.

In the paper's conclusion the authors state:
"In this case which we label anything anytime, individuals annuitize a fraction of wealth as soon as they have opportunity to do so – i.e. they do not wait – and they then purchase more annuities as they become wealthier."
Not waiting somewhat contradicts the advice of many economists and planners to delay claiming Social Security benefits as long as possible. Given the benefits of delaying those claims, perhaps waiting just a few years might be better advice.

The difficult calculation of the initial wealth-to-income ratio can be approximated by applying floor-and-upside principles and buying a “comfortable” amount of flooring. That amount may not be mathematically optimal but we know that owning some amount of annuity income early in retirement is part of an optimal strategy.

Should our wealth increase and our floor no longer feel adequate, we know that purchasing more is also part of an optimal strategy. Should our wealth not increase, instead, purchasing more income is likely to be sub-optimal. Though we may not be able to calculate the precise optimal amount to purchase, we have a better understanding of when to buy more.

I do have concerns with this strategy as it might apply to households at the bottom end and top end of wealth. A household whose retirement savings become so large that they need only spend a small percentage each year probably has enough safety margin to stop buying more annuity income when wealth increases. At some point, the fortunate retiree will probably feel that his floor is adequately sized.

At the other extreme, there may come a time when the retiree's wealth declines so significantly that she wishes to divert more assets from investments to annuities, which is contrary to the Anything Anytime strategy of standing pat on annuity income when wealth declines.

Recall that the paper addresses utility-maximizing retirees, those that seek the greatest economic satisfaction given diminishing marginal returns. A real-life retiree who amasses enough wealth might change his goal from utility maximization to growing a legacy portfolio and a retiree who loses much of her wealth might begin to value bankruptcy avoidance more than optimal utility.

Tables 4a and 4b from Milevsky [2007] are shown here for your convenience. z0 is that difficult-to-calculate ratio of optimal wealth-to-income (w/A). Recall from my previous post that γ (gamma) is the coefficient of relative risk aversion. (Higher gammas are more conservative investors.)

The first table assumes existing annuity income of $25,000 and the second assumes $50,000. Compare the optimal annuity spending for existing annuity income, current wealth, and risk aversion. For example, the retiree who already has $25,000 of annual annuity income in Table 4a should spend more money on annuities than the retiree in Table 4b who already has $50,000 of annuity income – at any level of risk aversion.



As Milevsky [2007] notes, with other conditions remaining the same, retirees will tend to purchase more annuity income when they perceive greater market risk, are less risk-tolerant, have better health, and have greater wealth relative to annuity income. The paper also shows the value of purchasing annuities with low fees and the value of a retiree's own person health assessment (subjective hazard rate) compared to the insurance company's opinion (objective hazard rate).

A more practical approach that incorporates the findings of Milevsky [2007] might be to purchase enough annuity income early in retirement to provide a comfortable floor when added to Social Security and pension income. As your wealth increases, assuming it does, purchase more annuity income if the floor no longer feels adequate. Purchasing multiple, smaller annuities over time from multiple insurers may help overcome reluctance to "hand over your savings to an insurance company."

The strategies of establishing a floor of secure income early in retirement with Social Security benefits, pensions and life annuities, laddering annuity purchases over time, and diversifying among multiple insurers gain an economic endorsement from this research.

When is the best time to purchase a life annuity? Annuitization and Asset Allocation suggests that the answer to this question depends on whether the retiree will make a one-time purchase or can stagger purchases as she ages. For the latter, the answer is not an age but a path that may involve multiple smaller purchases.

No matter what the research says some retirees are never going to buy an annuity and some are never going to invest their savings in the stock market. I'll share some thoughts on that in my next post.



REFERENCES

[1] Annuitization and Asset Allocation, Moshe Milevsky and Virginia Young, 2007.

[2] Utility maximizing. Economists use the term "utility" as a measure of satisfaction, joy, or happiness. Utility is based on individual preferences and not solely on dollar value as one individual might value an additional dollar of income differently than another individual would. A single individual might also value a dollar differently in different situations. A utility-maximizing retiree seeks maximum satisfaction, which may not be the same as maximum consumption.





Monday, March 6, 2017

Annuities: All or Nothing

I recently reviewed recommendations for the optimal age to buy a life annuity and found that a number of sources recommend that men purchase in their mid-70s and women about six years later. Some of the recommendations could be traced back to a paper entitled, Annuitization and Asset Allocation [1], written by Moshe Milevsky and Virginia Young in 2007. You can find a link to the paper below in the References section, but be forewarned that it isn't for the mathematically faint of heart.

The authors develop models for two annuity markets. The first, referred to as “All or Nothing”, calculates an optimal age for purchasing a life annuity once in retirement. This single-purchase limitation might be the result of a retiree preferring to make a single annuity purchase, a pension plan that limits the participant to a single purchase, or a country's annuity market.

The second analysis identifies an optimal way to purchase annuities when the retiree can choose to purchase any amount of annuity at any time. The authors refer to this strategy as “Anything Anytime” and it is the scenario in which most Americans will find themselves. In this post, I'll review All or Nothing and save the more complex Anything Anytime analysis for next time.

For those of you who are not interested in the math, I provide a link to an Excel spreadsheet[2] at Github in the References section below that does the heavy lifting for you. If you're even less interested in the math, skip down to the last five paragraphs beginning with "How can an individual use this information?" No one will know.

Milevsky [2007] shows that the optimal age to purchase a life annuity is when the retiree's “force of mortality”[4] – more on that in a minute – is greater than the following constant:
where γ (gamma) is the coefficient of relative risk aversion, μ (mu) is the expected market return, σ (sigma) is the standard deviation of those returns and r is the risk-free rate[6].

γ, the coefficient of relative risk aversion, is difficult to know for an individual but research shows that it is often between 1 and 2 for the typical investor. An investor with a high risk tolerance will have a low coefficient of risk aversion like γ=1. A more conservative but still typical investor might have risk aversion γ=2. An individual with a γ=5 has very low risk tolerance.[7] A γ=1 retiree is far more likely to invest in the stock market than a γ=5 retiree.

The equity risk premium is the excess return demanded by stock investors above the risk-free rate. When the market returns 9% and a risk-free bond returns 5%, the equity risk premium is 4%. It is the expected market return less the risk-free rate (μ - r in the equation above). This would simply mean that an investor could get a 5% return with no risk and that he might earn 4% more than that by taking on the risk of investing in stocks. Historically, the equity risk premium has ranged from about 3.5% to 5.5%.

Think of M in the equation above as the return you expect from your investments (the term in square brackets) adjusted by your risk aversion (the term 1/(2γ) ). M considers not only your expectations of future market returns but also how much you value those returns based on your level of risk aversion. A risk-taker would value a 12% return, for example, more highly than a conservative investor would value that same 12% return.

If your risk aversion is γ =1, meaning you're a typical risk-taker, then the hurdle you need to exceed to convince yourself to annuitize is one-half (1/2γ) your expected risk-adjusted market return, but if you're less of a risk-taker (γ =2), the hurdle is a much lower one-fourth of that return, meaning you will probably annuitize sooner than an investor with γ =1.


When to purchase annuities with the All-or-Nothing strategy.


People who expect higher returns on their investments and value those returns more (because risk bothers them less) will annuitize later in retirement than those who don't because they think they can do better investing than buying an annuity. They expect to do so well in the market that they won't need to annuitize as early. Some are so confident in their investment prowess that they won't buy an annuity ever. Retirees with lower market expectations and a higher aversion to risk will annuitize sooner. Some won't ever invest in the stock market.

Milevsky [2007] identifies the optimal age to annuitize in the All-or-Nothing scenario as the age at which retirees will expect to do as well in the annuity market with mortality credits[5] as in the investment market. This introduces the second half of the optimization equation as well as the paper's big idea regarding All-or-Nothing purchases:
"One can then think of the hazard rate [force of mortality] as a form of excess return on the annuity due to the embedded mortality credits and the fact that liquid wealth reverts to the insurance company when the buyer of the annuity dies."
While M quantifies how much the retiree values expected excess returns from her investment portfolio after adjusting for her risk aversion, the force of mortality quantifies how much he or she can expect as a similar “excess return” from an annuity. When the retiree values his expectation of investment returns equally with an annuity's excess return he has reached the optimal age to annuitize.

Let me try to say all of this more simply.

Milevsky [2007] shows that the optimal age to buy an All-or-Nothing annuity is when the retiree values the return on an annuity the same as she values the return that she expects from her investments. In order to get a fair comparison, the paper uses the excess return on investments (expected return less the risk-free rate) to compare to the excess return on an annuity. Since some investors don't mind a lot of risk and some do, the excess return on investments is adjusted to reflect the risk tolerance of individual investors. (The annuity has no market risk.) And lastly, the excess return on an annuity is considered to equal the individual retiree's force of mortality, which is determined primarily by the retiree's gender and age.

The second half of the optimization equation is the retiree's force of mortality that can be calculated with the Gompertz function[3]:
Force of mortality is the instantaneous probability of a person's death at a given age conditional upon reaching that age. It is the probability that a person who reaches the age of 75, for example, will die before his or her next birthday. You can play with force of mortality parameters a bit at the web page in References[4].

The following graph shows the optimal age for the retiree used in the All-or-Nothing example in Milevsky [2007], a female with risk-aversion coefficient λ=1. The tables that follow and include this example are taken from that paper. The optimal age to annuitize in the All-or-Nothing scenario occurs when the blue curve of the force of mortality for this individual crosses the “M” red line of the value of expected market returns (the hurdle). This intersection is the age at which the retiree expects to do as well purchasing an annuity as investing the same amount of money.


When the retiree values expected investment returns more the red line (M) moves up and the optimum annuitization age (the intersection of the two curves) increases. When the retiree is less optimistic about doing well in the market, is more risk averse, or both the red line moves lower and the optimal annuitization age moves left. The green "M" line in the graph below shows the result for a retiree with the same market expectations but greater risk aversion (λ=2). (This can also be seen by altering market return and risk-aversion inputs in the aforementioned spreadsheet[2].)


Using these same inputs, Milevsky[2007] provides a range of examples in Tables 1a and 1b provided below for your convenience.



Notice the column labeled “Value of Delay.” These entries show that the longer you wait before the optimal age the more value you receive from purchasing an annuity. Once you pass the optimal purchase age, delaying longer means an annuity would provide less value than an earlier purchase would have provided, but still more than the adjusted portfolio return (M). You can see this on the graph but the tables show only that the value of delaying becomes negative.

To calculate the optimal annuitization age directly in the All-or-Nothing model I'll simplify the math just a bit. The optimal age (x) for purchasing an All-or-Nothing annuity is:
How can an individual use this information for their own annuity purchase decision in an All-or-Nothing scenario?

Economic studies are much better at teaching us how things work than at predicting outcomes for an individual household. The coefficient of risk aversion is difficult to tie down for an individual household and future market returns are at best a guess, so calculating an optimal annuitization age isn't nearly as exacting a process as these equations might seem to imply.

So, what can we learn from playing around with these equations?
  • The optimal age for annuitizing in the All-or-Nothing strategy is rarely much less than age 70 or much greater than 80 unless you are highly risk-averse, in which case you should simply ignore the math and buy an annuity early in retirement.
  • Males will purchase sooner than females because males of the same age have a shorter life expectancy than females
  • Retirees less tolerant of market risk will purchase annuities sooner
  • Retirees who are less optimistic about future market returns will annuitize sooner.
Play around with the spreadsheet[2] to see how the parameters affect the optimal age to annuitize.

Before you invest a lot of time in the All-or-Nothing analysis, though, Milevsky [2007] follows it with an analysis of an “Anything Anytime” strategy in which the retiree buys some initial amount of annuity upon retiring and then buys more if and when wealth increases. This strategy better fits the U.S. annuities market and my instincts about retirement finance.  See that analysis at Annuities: Anything Anytime.

The math gets a lot harder, though.





If Obamacare Exits, Some May Need to Rethink Early Retirement, New York Times, February 27, 2017. 



REFERENCES

[1] Annuitization and Asset Allocation, Moshe Milevsky and Virginia Young, 2007.


[2] Download Excel spreadsheet to calculate the optimal age for annuitization in the All-or-Nothing model.


[3] The Gompertz function can estimate continuous life expectancy by fitting a curve to a discrete life expectancy table. The fit is achieved by manipulating the m and b terms. Milevsky [2007] fits the curve to the Individual 2000 basic Annual Mortality table with projection scale G. For females m= 92.63 and b=8.78 and for males, m=88.18 and b=8.78 using this table.


[4] 
Force of mortality explained. It is analogous to hazard rate in reliability engineering. It is the probability, for example, that you will die at age 70 conditional upon your having lived to age 70.


[5] Understanding The Role Of Mortality Credits – Why Immediate Annuities Beat Bond Ladders For Retirement Income, Michael Kitces.


[6] Examples in this post and Milevsky [2007] assume γ=1 or 2, μ=0.12, σ=0.20 and r= 0.06.


[7] Estimating the Coefficient of Relative Risk Aversion for Consumption from Gordon Irlam's AACalc website.




Tuesday, February 21, 2017

Retirement Decisions with Expiration Dates

In a series of posts beginning with The Opening, The Middle Game and the Endgame, I mentioned that some retirement decisions have “expiration dates.” Some expiration dates are rigid and regulated while some are fuzzy and more practical. When you develop a retirement plan, it's important to understand when and how these decisions can disappear.

Claiming ages for Social Security retirement benefits range under current law from age 62 to age 70. We can delay the decision past age 70 but there is no benefit from doing so – benefits won't increase when we claim after age 70. The expiration dates for this decision are mandated and fixed.

In contrast, asset allocation decisions have no expiration date. We can change our asset allocation any time we see fit for as long as we live. In fact, I believe we should update our asset allocation whenever our changing financial situation warrants it. Likewise with spending rates.

Other decisions are neither firmly set in statutes or contracts, nor precisely delineated but at some point, they may no longer be available as a result, for example, of deterioration of our health or depletion of our retirement savings.

Most insurers set a maximum age for purchasing a fixed annuity but it is typically age 90 or age 95, neither of which is particularly restrictive. A major risk of delaying the purchase of a fixed annuity is that by the time you want to purchase one you may no longer have enough remaining savings to do so.

Let's say you plan to live off stock market investments and Social Security benefits until you will purchase a fixed annuity at age 80. Should your investments perform poorly or you overspend from savings, you may find at age 80 that you no longer have enough savings to purchase the amount of annuity income you had hoped.


Delaying some retirement decisions too long can take them off the table.
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Another risk of fixed annuities is that interest rates may fall significantly while you wait, making that future annuity income more expensive. (You can lock in payments with a deferred annuity but you still have inflation risk and need good portfolio returns in the interim.)

Whether it results from lost wealth or increased annuity costs, the expiration date for purchasing a life annuity can become the time when you no longer have enough savings to purchase the amount of annuity you wanted. That expiration date is practical and fuzzy. It can arrive quickly with a bear stock market or precipitous interest rate decline, or it can creep up on you with gradually declining savings because there are two things you cannot predict: how much real future annuity income will cost (i.e., what future interest and inflation rates will be) and how much savings you will have left when you decide to purchase.

Milevsky and Young [2006] [4] shows that there is a theoretical optimal age to purchase annuities depending on several factors such as gender and risk aversion and that waiting longer than this age to buy them has negative value. While the 90 to 95 maximum age for some insurers means that the option of buying an annuity can disappear, Milevsky[2006] suggests that the value of purchasing a life annuity may begin to decline well before then.

Long Term Care Insurance, it seems not widely known, is subject to medical qualification. Conditions that increase the likelihood of a claim will increase premium rates or may leave you unable to purchase coverage, at all. These conditions are not all age-related so some relatively young people may not qualify for LTC insurance. Regardless, as we age we may suddenly develop conditions that exclude its purchase.

Tom Morris [1], a retirement planner and wealth management advisor who also sells LTC insurance, wisely notes that the best time to buy insurance is when you can qualify for it. Purchasing in your 40s or 50s may be the best bet as premiums can start to rise quickly around age 60. His experience was that about half of applications for LTC insurance were denied when applicants were in their mid-to-late 60s. This is a decision you can put off too long. By the time you retire, it might already be too late.

The expiration date for LTC Insurance insurability is fuzzy and unpredictable because it depends on our health. As with fixed annuities, there are risks associated with delaying the purchase of LTC insurance and the risks grow with age until purchasing it will eventually no longer be practical.

There is no maximum age for obtaining a HECM reverse mortgage (both spouses must be at least 62), but there are reasons you could be denied. Let your house fall into disrepair, for example, and you might need to spend a lot to bring it up to FHA standards. You also need to show that you can afford to maintain the home and pay property taxes. Should your financial situation deteriorate to the point that you can no longer meet these requirements then you might be denied a loan.

Similarly, we might be able to use home equity to fund more appropriate housing in late retirement. Retirees who begin spending home equity too early, though, might not have enough equity left to make that decision when the time comes.

Lastly, if you have a financial crisis late in retirement you might not only be unable to maintain your home and pay property taxes but also find yourself needing the loan much sooner than you can get one approved. The process is a lot like borrowing a regular mortgage and can take months – not something you want want to do in the middle of a crisis.

(Full disclosure – I recently closed a HECM standby reverse mortgage line of credit, although I hope I never need to spend any of it. Mine took about three months.)

You may find you have waited too long to borrow a HECM if your wealth has declined too far, your home has fallen into disrepair, or you have an immediate financial emergency. If your goal was to fund late-retirement housing, you may have waited too long if you already spent too much of your current home's equity. If you live in an area with rapidly declining home values, your borrowing capacity is declining along with it.

Fortunately, with HECMs, we can financially separate the act of opening a HECM line of credit from spending the money. There's isn't much risk – or cost, if you shop around – to opening the loan. The risks are related to spending equity now that you might need later. There is little risk to deciding to open the loan now and delaying the decision to spend from it and there are benefits, like a growing line of credit, locked-in home valuation, and immediate access to an existing line of credit in the aforementioned crisis.

Two tiers of income tax might also limit some retirement options. You might fund early retirement from your savings alone. When you begin receiving Social Security benefits, a portion of them will be taxed (the first tier, up to 50% of your benefits taxed) so your income tax rate may increase. At age 70½, you will need to begin making Required Minimum Distributions (RMDs) from your IRAs and this can push your Social Security tax rate even higher (the so-called “tax torpedo", up to 85% of benefits taxed[3]”).

Before receiving Social Security benefits and withdrawing RMDs you may experience a period of very low income tax rates during which it is attractive to use Roth conversions to lower IRA balances, reduce future RMDs and avoid taxes. This strategy is less appealing once you receive taxable Social Security benefits and even less so if RMDs subsequently push your tax rate higher at age 70½.

In summary, some financial decisions can be made or changed at any time in retirement, including:
  • Annual spending rates
  • Asset allocation
Some financial decisions have "expiration dates" and at some point may no longer be available or attractive options:


Some "expiration dates" are firm but others are a function of declining health, depleted wealth, life expectancy, future interest rates or expected market returns, all of which are difficult or impossible to predict, i.e., they're risky. These are not factors that can be considered at the beginning of retirement and forgotten. They must be monitored and our plans revised as retirement progresses.

While I generally believe it is wise to delay decisions until you have to make them, that is not the same as delaying decisions as long as you possibly can. Delaying a decision to spend home equity as long as you can is safer and more conservative, as is deciding to delay claiming Social Security benefits (safer, though not necessarily optimal). Delaying a decision to purchase LTC insurance or to do Roth conversions, on the other hand, may take these options off the table.

It's important to understand which retirement funding options can be here today but gone tomorrow.




Medicare Part B premiums are eating a growing percentage of Social Security benefits. A Bigger Bite Out of Social Security, Center for Retirement Research.



REFERENCES

[1] Tom Morris, Wealth Management Advisor, Raleigh, NC.


[2] 
Retirement Planner: If You Change Your Mind, SSA.gov.


[3] Will Your Social Security Benefits Be Taxed? The Retirement Cafe´.


[4] See Table 1a, Annuitization and Asset Allocation, Milevsky and Young, 2007.



Saturday, January 28, 2017

The Endgame

In The Opening Game, The Middle Game, and the Endgame, I compared the structure of financing retirement to the structure of a chess game. Having covered The Middle Game in my last post, I'll describe retirement's Endgame in this one.

The Endgame is dramatically different than the Opening game. The typical retiree has changed from a mentally sharp, physically active person with many decisions ahead, many options from which to choose, and an enormous range of potential outcomes in the Opening Game to one who is typically less active, perhaps has lower mental acuity and less interest in finance, has already locked in most of the important financial decisions, and whose range of potential outcomes has narrowed. Expecting to establish a strategy at the beginning of retirement that is optimal for both of these scenarios and one between is often a fool's errand.

Following is a simplified state diagram for visualizing the narrowing of options. At the beginning of retirement, the retiree has the most options. Initially, any of the blue circle "states" are possible in the future depending on the retiree's decisions and factors beyond her control, like her health and market returns.



The retiree follows the decision path in black (below) and arrives at the Middle Game. It may help to think of each row as a year. By the Middle Game (the row with one red circle), many future outcomes (light gray) are no longer likely to be achieved. A retiree who nearly depletes his portfolio by the Middle Game, for instance, makes ending retirement at a state that includes an enormous portfolio less likely, though not impossible.

Some future states may be impossible to achieve because, for example, the retiree's Social Security claim has already been finalized or Long Term Care insurance was or was not purchased and no longer can be. Once a retiree claims Social Security benefits at age 65, for example, all future states in which the retiree claimed at a different age are no longer possible. In other words, future Social Security benefits were locked in at age 65 under current law.


The retiree's range of possible final outcomes is represented by the bottom row of the pyramid. There are fewer red circles in that row than there were blue circles in the bottom row of the Opening Game pyramid above, indicating that the range of likely final outcomes has shrunk as time passed and decisions were made.

Several more decisions bring the retiree to the Endgame, where the range of possible final outcomes and the number of available options is the smallest, yet.


One benefit of breaking down retirement into sub-games is that it enables us to consider these different life stages simultaneously. Comparing the Endgame side-by-side with the Opening Game, for example, clarifies why retirement planners often recommend delaying Social Security benefits. Households that delay claiming and live into the Endgame will have a larger floor of Social Security benefits late in life. Delaying also lowers income in the Opening Game and visualizing the two stages side-by-side provides a clearer understanding of the tradeoffs.


In retirement's Endgame, the range of possible final outcomes and the number of available options is smallest.
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I set the beginning of the Endgame at age 86, again somewhat arbitrarily. It ends when there is no surviving spouse.

The median remaining life expectancy for an 86-year old male is about 4½ more years, 6 more years for a female and 8 years for either spouse of a couple. Life expectancy has taken another significant decline from the beginning of the Middle Game.

For every 100 women who begin the Opening Game in 2017 at age 65, about 53 will survive to play the Endgame and about 13 of those will likely live to 95 or older. For every 100 men, about 41 will survive to play the Endgame with about six reaching at least age 95.

    Our physical activity will typically follow another steep decline resulting in lower discretionary spending, but we are also likely to experience higher medical costs to offset the lower discretionary spending. Typical retiree expenses will decline about 25% after 20 years of retirement, but an individual household's spending may not be typical and even for those that are typical the spending doesn't decrease smoothly. In other words, spending over time is very difficult to predict for an individual household and it's even difficult to predict year-to-year.

    We may have lost significant mental acuity by the Endgame, though I have met people in this age group who are far sharper than I. Eventually, however, that mental acuity will likely begin to fade and we may no longer be able to manage our finances or have the desire to. We should anticipate this in our retirement plans.

    Investing in stocks just before and immediately following retirement (the Opening Game) exposes us to maximum probability of depleting our savings as a result of exposure to sequence of returns risk. Investing in stocks in the Endgame can also be tricky because, though the probability of depleting our portfolio due to a poor sequence of returns has declined with a shorter life expectancy, we will now have limited time to recover from bear markets. Investing only those funds intended for our heirs, if that is possible, eliminates this problem. Investing funds we may need to live on is highly risky during this game.

    We had to claim Social Security benefits no later than age 70 (or more correctly I should say that delaying past 70 would have provided no additional advantage) back in the Opening Game. If we die before reaching median life expectancy for the age at which we claimed then we made a fortunate choice. Should we live longer, we would have been better off delaying the benefits claim. Regardless, our remaining lifetime was unpredictable and that decision was locked in during the Opening Game.

    HECM reverse mortgage [1] borrowers who spent home equity early in retirement may wish they had waited, but those who borrowed early and delayed spending may well find that their credit line now exceeds their home's market value. HECM borrowers who chose tenure payments may be well ahead of the game.

    Regardless, HECM borrowers may now need to deal with the transition out of the home, as the loan will become payable unless a surviving spouse still lives in the home.

    By the Endgame, purchasing a fixed annuity or Long Term Care insurance are no longer viable options.

    The number of elder bankruptcy filings becomes negligible in the Endgame [4]. Though bankruptcies have generally declined across the board due to changes in bankruptcy law, the percentage of bankruptcies has been lower for those 75 and older for some time.

    U.S. Bankruptcy Filing Rates per 1,000

    Age Range
    1991
    2001
    2007
    18-24
    3.9
    3.7
    1.4
    25-34
    10.2
    12.7
    5.5
    35-44
    9.3
    14.4
    6.5
    45-54
    7.3
    11.4
    5.5
    55-64
    3.5
    5.5
    4.9
    65-74
    1.2
    3.1
    2.7
    75-84
    0.3
    2.3
    1.6
    85+
    neg
    neg
    neg

    The “Tax Torpedo”, as I discussed in a previous post, can become a long-term tax problem after age 70½ and will last until retirement account balances become low enough that RMDs no longer trigger higher Social Security benefit taxation.

    Sequence of returns risk is still a risk in the  Endgame, but it may have declined significantly along with our life expectancy. (It's always a risk, but a shorter life expectancy makes it less likely that sequence risk will result in portfolio depletion.) Hopefully, the retiree has implemented a variable-spending strategy rather than having tried to spend a fixed percentage of initial savings each year. This will act to mitigate the risk of portfolio depletion over time. In my simulations, few retirees deplete their savings before the Middle Game (see Death and Ruin) but portfolio depletion accelerates at about age 85.


    The probability of outliving an investment portfolio is dependent upon the size of the portfolio, the percent of the portfolio spent annually, the portfolio's volatility, market returns, and the retiree's life expectancy. Because the retiree now needs to fund a retirement that will be on average half as long as the retiree in the Opening Game, his chances of outliving savings relative to his life expectancy have decreased (a good thing).

    On the other hand, a smaller portfolio than the retiree expected with which to begin the Endgame increases the probability of portfolio depletion (a bad thing) and, as I have stated repeatedly, we won't know how much money is left in our portfolio for the Endgame until we almost reach it. To say this differently, an older retiree with a shorter life expectancy can spend a larger percentage of his remaining portfolio value each year, but we can't predict the portfolio's future value. The question then becomes, "spend a larger percentage of what?"

    Regardless, for retirees who do reach the Endgame, fixed annuities, maximized Social Security benefits, and pensions will feel quite warm and cuddly.

    The range of possible remaining-lifetime spending costs of a shorter retirement is usually smaller (less risky) than that of a longer retirement. The monkey wrench in the spending machine is end-of-life costs, which can be huge or near zero. According to both Banerjee and Blanchett [2, 3], however, even yearly spending with high end-of-life costs are often lower than initial retirement spending in real dollars.

    We may think that end-of-life costs are a function of age but they are not. End-of-life costs don't appear in your nineties unless you live into your nineties. Lots of people die in the Opening and Middle Games and many of them will have high end-of-life costs. Actor Christopher Reeves had enormous end-of-life costs in his late forties. High end-of-life costs are a risk in all three games. They are a function of when you die and not necessarily one of age.

    Remaining life expectancy, mental acuity, decreasing options, and the unavoidable effects of Opening and Middle Game decisions make this a different game. The best strategy for the End Game can't be determined until the Middle Game is nearly over because we won't know until then what market returns, interest rates, and life have done to our resources and our cost of living.

    Updating the characteristics table to include the Endgame gives us this:



    This series of posts was not intended as a comprehensive comparison of the three games. I have only tried to establish that retirement resources, options and challenges are different enough for a 65-year old, a 75-year old and an 85-year old to warrant perhaps three separate strategies.

    Our Endgame will be affected both by immediate financial decisions we make or others make for us but also by decisions we made a decade or two earlier. This is why we need to begin retirement by, as Stephen Covey says, "starting with the end in mind." Both our time and our mental acuity will likely be shortened by the Endgame. Our resources may be dwindling and that leaves the Endgame particularly fraught.




    REFERENCES


    [1] The Mortgage is Dead; Long Live the (Reverse) Mortgage, Cotton, D., The Retirement Cafe blog.



    [2] Banerjee, S. (2012). Expenditure patterns of older Americans, 2001-2009.



    [3] Blanchett, D. (2013, November 5). Estimating the True Cost of Retirement. Morningstar. 



    [4] Generations of Struggle. Deborah Thorne (Ohio University), Elizabeth Warren (Harvard Law School), Teresa A. Sullivan (University of Michigan)


    Friday, January 27, 2017

    The Middle Game

    I suggested that retirement is similar to a chess game in The Opening Game, The Middle Game, and the Endgame. Having covered the Opening Game in my last post, I'll describe retirement's Middle Game in this one.

    Here are a couple of quotes I found at chess websites regarding the Middle Game [1].
    “[A] Principle of the middle game is to enter into a comfortable endgame.” 
    “Most of our games are decided in the middle game. Sometimes because of tactical mistakes and often because we don’t chose the right plan in the middlegame. That is why it’s immensely important to understand middlegame positions.”
    As in chess, the Middle Game of retirement has its own distinct risks and rewards. It is difficult to strategize either the chess or the retirement Middle Game until we almost reach it because our options in the Middle Game depend largely on how the Opening Game ends. How many pieces will we have remaining in play? What will their positions be? How did the market treat our investments in the Opening? How is our health? Did we lose a spouse or do we still need to plan for two?

    An important difference between the two Middle Games is that we can lose at chess in the Middle Game by making the wrong moves then, but when we lose in retirement's Middle Game it is most often the result of decisions made in our Opening Game. Retirement mistakes in the Middle Game may not show up until the Endgame. Mistakes in chess' Middle Game may entirely eliminate the Endgame. We concede the game and move on to a new one.

    There are no conceded games in retirement. Assuming we are still alive (or our spouse is), we have to play retirement's Endgame with whatever resources we have left.

    Even when we make poor retirement finance decisions it usually takes several years to deplete a portfolio. Did we invest too heavily in equities in the Opening and lose our savings to sequence risk? Did we claim Social Security benefits early and lock in lower benefits? Did we build an inadequate floor?


    We have to think about the Middle Game and Endgame during the Opening Game, and the Endgame during the Middle Game.
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    I set the beginning of the Middle Game at age 76, again somewhat arbitrarily, and repeat that the start and finish of these games are fuzzy ranges rather than specific ages. I choose age 85 as a representative end of the Middle Game. Picking a different age based on specific household conditions doesn't alter the principles.

    The median remaining life expectancy for a 76-year old male is 9 more years, 12 more years for a female and 15 years for either spouse of a couple. Life expectancy has a strong impact on retirement finances. Remaining life expectancy is dramatically lower during the Middle Game than in the Opening Game and this fact alone makes the Middle a significantly different game.

    As I previously mentioned, about 7 of 10 Americans born in 1952 will live to age 65 in 2017 to play the Opening Game. The following diagram shows how many women and men age 65 in 2017 are likely to live to each game beginning at about ages 75 and 85, and very old age 95. The areas of the circles are proportional to the number of survivors.


    Our physical activity is typically much lower beginning with the Middle Game and this may mean lower living expenses as, for example, we travel less. Typical retiree expenses will decline about 15% after 10 years of retirement, but an individual household's spending may not be typical and even for those that are typical the spending doesn't decrease smoothly.

    Investing in stocks in the Middle Game may still be wise because you might have several years of life remaining, depending on your household's unique financial circumstances. But, if you manage your own investments you should prepare for a likely decline in mental acuity and perhaps a waning interest in managing money as the Middle Game progresses.

    We had to claim Social Security benefits by age 70 (or more correctly I should say that delaying past 70 would have provided no additional advantage) back in the Opening Game. If we die before reaching median life expectancy for the age at which we claimed then we made a fortunate choice. Should we live longer, we would have been better off delaying the benefits claim. Regardless, that decision was locked in during the Opening Game.

    The real risk of reverse mortgages is that a retiree will spend most of her home equity early in retirement and then be forced to repay the mortgage because she can no longer afford the home. A HECM reverse mortgage guarantees only that the loan will not come due so long as the borrower or a spouse continues to live in the home. It does not protect a borrower who decides to move out because he or she can no longer afford the home.

    By the time a retiree reaches the Middle Game, she will likely have a better idea where she will want to spend the rest of her life and whether a reverse mortgage fits those plans. She will also have a better handle on her financial situation than she would have had if she had borrowed in the Opening Game. And, she may have a greater need for that home equity than she had in the Opening Game. Spending a reverse mortgage is a less risky proposition in the Middle Game.

    At some point around the middle of the Middle Game, purchasing a fixed annuity will become a less viable option. Also, because Long Term Care insurance requires medical qualification it may no longer be a viable option. In fact, medical issues can be a disqualifying factor even in the Opening Game.

    Elder bankruptcies decline in the Middle Game [4]. Though bankruptcies have generally declined across the board due to changes in bankruptcy law, the percentage of bankruptcies has been lower for those 65 and older for some time.


    U.S. Bankruptcy Filing Rates per 1,000

    Age Range
    1991
    2001
    2007
    18-24
    3.9
    3.7
    1.4
    25-34
    10.2
    12.7
    5.5
    35-44
    9.3
    14.4
    6.5
    45-54
    7.3
    11.4
    5.5
    55-64
    3.5
    5.5
    4.9
    65-74
    1.2
    3.1
    2.7
    75-84
    0.3
    2.3
    1.6
    85+
    neg
    neg
    neg

    ("neg" = negligible)

    Of course, forced retirement is no longer a huge risk in the Middle Game because nearly everyone will have retired by then.

    The “Tax Torpedo”, as I discussed in the previous post, can become a long-term tax problem after age 70½ and may well last all through the Middle Game and beyond. Avoiding it requires actions in the Opening Game, like spending down IRA's or executing Roth conversions.

    Sequence of returns risk is still a risk in the Middle Game, but it may have declined significantly along with our life expectancy. (It's always a risk, but a shorter life expectancy makes it less likely that sequence risk will result in portfolio depletion.) Hopefully, the retiree has implemented a variable-spending strategy rather than having tried to spend a fixed percentage of initial savings each year. This will act to mitigate the risk of portfolio depletion over time. In my simulations, few retirees deplete their savings before well into the Middle Game (see Death and Ruin).


    Because the retiree now needs to fund a retirement that will be on average half as long as the retiree in the Opening Game, his chances of outliving savings have diminished along with his chances of amassing a huge portfolio to leave to heirs. Shorter retirements have a smaller range of possible outcomes.

    The same logic applies to a large degree to spending. The range of possible spending costs of a shorter retirement is usually smaller than that of a longer retirement. The monkey wrench in the spending machine is end-of-life costs, which can be huge or near zero. According to both Banerjee and Blanchett [2, 3], however, even yearly spending with high end-of-life costs are often lower than initial retirement spending in real dollars.


    We may think that end-of-life costs are a function of age but they are not. End-of-life costs don't appear in your nineties unless you live into your nineties. Lots of people die in the Opening and Middle Games and many of them will have high end-of-life costs. Actor Christopher Reeves had enormous end-of-life costs in his late forties. High end-of-life costs are a risk in all three games. They are a function of when you die and not necessarily how old you are.

    According to health economist Austin Frakt [5], typical retirees in the Middle Game will spend about twice as much on health care as those in the Opening Game.

    Remaining life expectancy and the unavoidable results of Opening Game decisions make this a different game. The best strategy for the Middle Game can't be determined until the Opening Game is nearly over because we won't know until then what market returns, interest rates, and life have done to our resources and our cost of living.

    Updating the characteristics table to include the Middle Game gives us this:


    As in chess, the primary objective of the Opening Game in retirement finance is to set up a winnable Middle Game. The best strategy for a retired household's Middle Game will depend largely on how well they were positioned coming out of the Opening Game and they won't know that until they get there. That position will be the result of decisions made in the Opening Game, like Social Security claiming and spending decisions, and luck, like health, mortality, and market returns.

    Decisions made during the Middle Game will also affect the Endgame. These include the decision to spend a reverse mortgage, how we will invest and how much we will spend discretionarily.

    An objective of the Middle Game is to set up the Endgame, but some of the Endgame is set up during the Opening Game, like claiming Social Security benefits and building a floor. That means we have to think about the Middle Game and the Endgame while playing the Opening Game, and the Endgame while playing the Middle Game.

    Luck plays a very limited role in chess, but a much greater role in retirement. Retirement is more like backgammon in that respect, part skill and part luck, but that's a different post.




    Health economist Austin Frakt says, "Technology change is responsible for at least one-third and as much as two-thirds of per capita health care spending growth." Blame Technology, Not Longer Life Spans, for Health Spending Increases.


    REFERENCES


    [1] Chess Improvement, Middle Game Training



    [2] Banerjee, S. (2012). Expenditure patterns of older Americans, 2001-2009.



    [3] Blanchett, D. (2013, November 5). Estimating the True Cost of Retirement. Morningstar. 



    [4] Generations of Struggle. Deborah Thorne (Ohio University), Elizabeth Warren (Harvard Law School), Teresa A. Sullivan (University of Michigan)



    [5] Austin Frakt, Blame Technology, Not Longer Life Spans, for Health Spending Increases.