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

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.


  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´.


  1. Life is actually full of bets the moment we leave the nest!

    A bet on education (more or none).
    A bet on college.
    A bet on degree.
    A bet on career.
    A bet on which job to take in that career.
    A bet on when to change jobs.
    A bet on salary/wage (with each job).
    A bet on to marry, or not.
    A bet on who to marry.

    I've missed many others - but you get the idea. And each bet also involves risk and financial reward.

    Where we are in each of our lives has been a string of lucky, or unlucky, bets in life. Each of us going along the same spectrum of wagers as we age. There's a standard deviation curve for that too ... the very unlucky (left tails - homeless), and the very lucky (right tails - one-percenters), with most in between.

    Nice post Dirk, I look forward to your "bringing it all together" post.

    1. Had this blog been around when I was much younger I would have been much "luckier" in life. I made many--too many--of the wrong choices in the factors you site. I made them not for lack of desire to make the right choices--but for lack of available information. Now, in retirement, it appears I am making as many of the correct choices as possible simply because the information is available.

      IIRC, Dirk Cotten has been referred to as a thought leader in retirement planning. I would wholeheartedly agree.

  2. Dirk: Excellent post. Too many people leave it to chance with disasterous results for their retirements plans.

  3. Fun/interesting/thoughtful post. I too am looking forward to the next iteration. However, I think of employer-sponsored retirement plans as either "financial capital" or as "deferred human capital". Invariably, the payout from my 401(k) and/or defined benefit pension plan is not "socialized", but is a function of the employment decisions I /my employer's made, the employers decision to sponsor the plan, my decision to participate/waive participation (or the employer's participation/eligibility decision if the plan was non-contributory), etc. So, why do you believe employer-sponsored pensions and retirement savings belong in "social capital"?

    1. Joe, that’s an interesting question and asked in an excellent way – why do I believe employer-sponsored pensions and retirement savings are "social capital.” That's important because there is no widely-accepted, precise definition of social capital.

      Let me answer the easy part first. I don’t believe retirement savings like 401(k) plans should be classified as social capital. As my post states, I believe they are financial capital.

      Regarding pensions, however, when Social Security was enacted there was a concern that it might be illegal to cover public employees so many of these employees, teachers for example, began to be covered under public pensions, instead. About 13 states, as I recall, still cover teachers with public pensions instead of Social Security. For that reason, I tend to lump public pensions under social capital.

      As for your employer-provided DB plan, its payouts are dependent upon the mortality rates of a group of employees and that seems social to me, as well, though it might not fit your definition.

      Regardless, I’m not sure it makes much financial difference if you personally choose to categorize employer-sponsored “pensions” differently than I do.

      Interesting question. Thanks for writing!

  4. The choice to never walk away from the game is also a bet. Another bet would be to save the last bullet just in case. Each bet has its own risks and potential rewards.