Kotlikoff: Optimal Retirement Planning

The Major Technology Breakthrough to Guide Portfolio Choice


Optimizing retirement outcomes means funding the highest standard of living, both before and after retirement, with a smooth transition in between. Planning for that economics-based outcome, known as “consumption smoothing,” is computationally intensive. But a recent technological breakthrough, which does that smoothing using uncertain asset returns, gives advisors a tool that improves portfolio choice.

Economics-based financial planning differs markedly from conventional financial planning. Economics-based planning is grounded in consumption smoothing – the proposition that households want to have a stable standard of living through time as well across good times and bad times. Why else save for retirement? Why else buy life, homeowners, automobile, medical, or longevity insurance? Why else diversify your portfolio?

Physiology meets economics

The instinct to smooth our living standard over time is physiological. We get satiated. We realize that guarding against rainy days –when we can no longer work, when Joey totals the car and when the market crashes – beats splurging now.*

There are two big things that limit our ability to perfectly smooth consumption. The first is cash constraints. A young, middle-class couple with lots of mouths to feed, a large mortgage to pay, and college costs to cover will need to limit its discretionary spending until they get out from under their bills. The couple’s goal is still to smooth its living standard, but only to the extent possible without going into or taking on more debt.

The second reason is uncertainty. Things change. We lose our jobs, we face unexpected medical bills, or the market tumbles. How do we smooth consumption when our economic world is uncertain? First, we insure against downside risks to the extent possible and affordable. Second, we make our spending and saving decisions based on what we expect to happen, taking into account the potential for uninsured events, like losing our jobs, to happen. What about investing, particularly in the stock market, which offers a high average, but also highly risky return? Here we trade off the risk of a drop in our living standard against the potential for a rise.

Unlike the casino, where the bets are unfair, i.e., where we have a greater than 50-50 chance of losing money, the stock market and certain other risky investments are gambles worth taking – up to a point. That point is determined by our degree of risk aversion, which might better be called our coefficient of satiation. When our risk aversion is very high, we are very concerned about risk because we lose a lot more welfare from seeing our living standard fall by a given amount than by seeing it rise by the same amount.

Problems with target practice

Conventional financial planning bears some surface resemblance to economics-based planning. But on close inspection, it disrupts consumption rather than smoothing it. Conventional planning is goal/target-based and focused on retirement. Households are advised to spend 75% to 85% of their pre-retirement income in retirement and stick to that spending target through time.

This prescription is problematic. First, given the enormous number of factors involved in our finances, from our labor earnings to our retirement accounts to our Social Security benefits to our taxes, the financial industry’s rule-of-thumb target is invariably too high or too low, and often by a mile.

A retirement-spending target that’s too high or low implies a living standard before retirement that’s too low or high. This means your spending either jumps or plunges at retirement. That’s consumption disruption, not consumption smoothing.

Even small – 10%– mistakes in the target will produce massive consumption disruption. The reason? Households will be making a seemingly small mistake for 35 or more years. Adding that large a number of small mistakes means that we’ll spend a lot more or less in retirement than we should. This, in turn, means we’ll have to spend a lot less or more before retirement than we should. This, again, means consumption distribution.

If the advisory industry is wrong on the first leg of financial planning – saving/spending – what about the second leg, namely insurance? Here too, there are major problems. Life insurance is meant to smooth the living standards of spousal survivors from when their household is intact through when it isn’t. But if the living standard that needs to be insured isn’t correctly calculated, the life insurance advice will also be off base. Or take longevity insurance. If, as is generally the case, the financial industry focuses on your dying on time – at your life expectancy – it will ignore your financially worst-case longevity scenario – the one in which you live to or close to your maximum, not your expected age of life. This dissuades you from purchasing annuities from insurance companies, which, of course, leaves more money industry in the hands of the money advisor industry to manage for a fee.

Ancient versus modern portfolio guidance

Now for financial planning’s third leg – portfolio advice. Unfortunately, here too conventional financial planning fails to connect with physiologically-based, i.e., common sense economic theory. Conventional portfolio advice entails simulating, via Monte Carlo draws of asset returns and life expectancies, whether a client will run out of money if they follow “the” plan. Unfortunately, as just described, “the” plan is the wrong plan. It entails saving the wrong amount when young, spending the wrong amount when old, and never adjusting one’s spending through time, regardless of the circumstances. Thus, conventional Monte Carlo simulates your chances of financial survival having made three major financial mistakes.

According to economics, proper investment guidance is based on having clients make the best decisions today knowing they’ll make the best decisions tomorrow as circumstances change, including earning more or less than expected on their assets. Proper investment guidance also requires accounting for your client’s risk aversion – how quickly they get satiated and how hungry they will get if they consume less, i.e., how the weight upside and downside risk.

This is known as “dynamic expected lifetime utility maximization.” “Dynamic” references changing one’s decisions over time. “Expected” references making decisions now based on what we expect will happen, including our expectations of changing course as circumstances dictate. “Lifetime” references considering our entire future. And “utility” references a mathematical formula that captures the welfare we enjoy from consuming. This formula for the utility function incorporates our coefficient of risk aversion – how quickly or slowly we become satiated from consuming more at a point in time.

The higher our risk aversion (the quicker satiation kicks in), the more we prefer portfolios with little downside standard-of-living risk, even if that means foregoing considerable upside risk — the potential for a much higher standard of living. The lower the risk aversion (the slower satiation kicks in), the more we prefer portfolios with high upside potential standard of living even if such portfolios come with greater downside living-standard risk.

Under expected utility maximization (EUM), there is nothing rigid about the spending, saving and portfolio decisions households make through time. To the contrary, under EUM, households adjust what they are doing through time. If they suffer (enjoy) a big loss (gain) in the market, they cut back (raise) their spending as dictated by consumption smoothing.

Super-quick expected utility maximization is finally possible!

Maximizing expected utility of a client’s remaining lifetime is a formidable computational challenge. Economists, myself included, have been able to solve simple EUM problems using a numerical computation technique called dynamic stochastic programming.** The challenge is getting the algorithms to work precisely enough to handle the interdependence between spending and taxation, to deal with cash/borrowing constraints, to accommodate required interpolation over kinky decision functions (arising from those constraints), and to produce a solution in a commercially acceptable amount of time.

Fortunately, over the past year, my company made a major computational breakthrough that has overcome each of those hurdles. The new computation method, included in our tool, MaxiFiPRO, is called “certainty equivalence.” It entails generating, within 30 or fewer seconds, 500 living standard trajectories given a client’s spending/investment strategy. The trajectories are produced simultaneously via parallel processing. The client’s living standard in each year on each trajectory is calculated on an as-if (for-sure) basis using our patented iterative dynamic programming technique. Specifically, we calculate what the client would spend each year in the future if they were to receive, for sure, a fixed safe real rate of return. (The default value, which can be changed, is 1%.) Then asset returns are drawn to advance the client to the next year on the trajectory, at which point we calculate that year’s spending based on the same as-if safe real rate of return. Proceeding in this manner to the client’s maximum age of life produces one of our 500 living standard trajectories. Meanwhile, the program is calculating, in parallel, the other 499 trajectories.

Once the 500 trajectories are computed, they are plugged into a lifetime utility function, whose risk aversion coefficient is specified by the client via simple questions about their risk tolerance. We then repeat the exercise for alternative spending/investment strategies and compare levels of expected (average) lifetime utility across the strategies.***

MaxiFiPRO compares expected lifetime utility for the client’s base strategy as well as for two alternative strategies. The strategy with the highest expected lifetime utility is the one the client will likely prefer.**** We present various comparisons of the sets of living-standard trajectories under the base strategy and the alternatives. But summarizing 500 living-standard trajectories in a single number – the client’s index of expected lifetime utility – makes portfolio guidance, in consultation with the client, quick and easy.

Illustrating expected utility maximization in MaxiFiPRO

To illustrate portfolio guidance based on expected utility maximization, consider a hypothetical 54 year-old couple, Martha and Sam. Martha earns $200,000, Sam $50,000. They will both retire at 62. Their combined retirement accounts total $1 million and they have $400,000 in regular assets. They also have a $1 million house with a $500,000 mortgage plus standard annual housing expenses.

Martha and Sam’s Base strategy is to hold half of all their assets in stock and half in bonds. But they also want to consider both “safe” (20% stock and 80% bonds) and “risky” (80% stock and 20% bonds) strategies. In all three cases, they specify, for their spending strategy, a 1% “as-if” safe real rate of return.

The chart below shows the couple’s expected utilities for their specified degree of risk aversion. Note that expected utility from the safe strategy is highest when the client is very risk averse and can tolerate almost no risk. The risky strategy produces the highest expected utility when the client can tolerate a lot of risk. And the base strategy is best if the client is moderately risk averse.

How do you read the values in the chart? Take the 111 index value in the last column. This means that choosing the risky strategy when you can tolerate a lot of risk provides the same lifetime utility, on average, as adopting the base strategy, i.e., investing 50-50 in stocks and bonds, but enjoying an 11% higher living standard under all outcomes.*****

MaxiFiPRO doesn’t recommend particular spending or investment strategies. It simply lets planners explore options with their clients based on the modern finance theory of consumption smoothing. Expected utility maximization has been the Holy Grail when it comes to portfolio guidance.****** It’s good to know that we’ve finally found it.

Index of Expected Lifetime Utility

How Much Risk Can You Tolerate?

Almost None Very Little Moderate Some A Lot
Base Strategy

50-50 Stocks/Bonds

100 100 100 100 100
Safe Strategy

20-80 Stocks/Bonds

102 101 99 96 89
Risky Strategy

80-20 Stocks/Bonds

92 94 97 101 111

Laurence J. Kotlikoff is a William Fairfield Warren Professor at Boston University, a Professor of Economics at Boston University, a Fellow of the American Academy of Arts and Sciences, a Fellow of the Econometric Society, a Research Associate of the National Bureau of Economic Research, President of Economic Security Planning, Inc., a company specializing in financial planning software, and the Director of the Tax Analysis Center. Professor Kotlikoff received his B.A. in Economics from the University of Pennsylvania in 1973 and his Ph.D. in Economics from Harvard University in 1977.

* Mathematically, economists capture satiation via what’s called a utility function. The simplest formulation posits a separate utility function, albeit with the same form, for each year’s consumption. The form of the function captures our physiology. As consumption in a given year increases by a fixed amount, utility increases, but the increase is smaller the higher consumption was to begin with. This property is referred to as diminishing marginal utility. The degree to which the increment to utility gets smaller is, again, in the simplest formulation, controlled by a single parameter called the degree of risk aversion. People that are more risk averse gain a lot of utility from getting to eat steak when they are starving, but very little when they’ve already eaten three steaks. People that are less risk averse get pretty much the same kick (pleasure) from an extra steak no matter the number of steaks they’ve already eaten.

** See, for example, https://www.kotlikoff.net/sites/default/files/w13966.pdf

*** Let me state, in different words, what I mean by a spending/investment strategy. An investment strategy is familiar. It involves specifying the assets you’ll hold in each future year and their portfolio shares. To set their spending strategy, our users set an “as if” safe real rate of return for their clients. If the safe rate is set at, say, 1 percent real, it means that their clients will, each year, spend as if they will earn 1 percent for sure on their investments. Note that the spending and investment strategies chosen can be set up to change over time and also change based on the situation the clients find themselves.

**** We assume the standard constant relative risk aversion form for annual utility. If the client values consumption differently, our expected utility calculations and strategy comparisons will, obviously, be biased.

***** There is no absolute measure of welfare (happiness). Hence, economist compare different levels of lifetime utility via what they call consumption equivalent variations. The 11 percent difference is such a consumption equivalent variation. It says that the expected utility of the risky strategy is equivalent to what the client would experience under the base strategy were the client also able to consume 11 percent more in all circumstances.

****** In its absence, the advisory industry has developed all manner of alternative, ad hoc portfolio-decision frameworks, including life-cycle funds, bucketing, value investing, goal-based investing, dynamic withdrawal strategies, variants of static, and mean-variance optimization.