### Executive Summary

Given the myriad of products and services available to today’s prospective retirees, there are a lot of choices to consider about which retirement income strategy to pursue, from portfolio-based withdrawal strategies to annuities with income guarantees and more.

Yet as it turns out, what seems like a relatively simple question – which retirement income strategy is the best – is actually remarkably difficult to determine. Because as it turns out, which is “best” depends heavily on how you *measure *what “best” really means in the first place.

For instance, when evaluating by what produces the most wealth, the best retirement strategy is generally to just not spend very much (and ideally invest for growth along the way, too)! If the goal is to maximize retirement spending, then the “best” strategy is to invest as aggressively as possible in order to maximize the portfolio growth that will substantiate that spending. Yet portfolios with maximal growth can also produce the greatest catastrophes, which means a risk-averse retiree may not want that approach, even if it would otherwise have increased retirement spending!

What all of this ultimately means is that in framing different retirement income strategies – and the trade-offs they might entail – it’s important to give serious consideration to the measuring stick that will be used to evaluate the potential retirement outcomes. Because the “best” retirement income strategy may be very different depending on whether you measure based on wealth, spending, probabilities of success, magnitudes of failure, or utility functions that weigh both the upside and downside risks!

## Determining *How *To Measure The “Best” Retirement Strategy

Imagine for a moment that a 65-year-old couple is trying to decide how much to spend for a 30-year retirement from their $1,000,000 portfolio, and how that portfolio should be invested. The seemingly simple trade-off choices might include:

A) Spend an inflation-adjusting $30,000/year from the portfolio, by putting 90% of it into an immediate annuity and keeping the other 10% in cash reserves

B) Spend an inflation-adjusting $45,000/year from the portfolio, and invest it 50/50 in stocks and bonds

C) Spend an inflation-adjusting $60,000/year from the portfolio, and invest it 100% in stocks

While many advisors might intuitively lean towards one strategy or another as likely to be the “best”, it turns out that accurately assessing which is really the best depends heavily on how the outcome is measured in the first place.

## Measuring Retirement Outcomes By Projected Wealth

The first way these three strategies might be assessed – and the most common methodology for the first several decades of financial planning – is to project how wealth would accumulate and compound over the 30-year retirement time horizon.

For instance, the chart below graphs the remaining wealth in the portfolio across each of the three strategies, assuming inflation averages 3%, and that long-term 30-year investment returns are 3% for cash, 5% for (intermediate) bonds, and 10% for stocks. (The immediate annuity is assumed to have a principal refund feature if death occurs before the payments have been recovered, which winds down over time as the payments are made.)

As the chart illustrates, on the basis of this analytical approach – which strategy accumulates the most wealth in the long run – strategy C is the best. Ironically, this is true even though in general, long-term wealth would actually be maximized by spending the *least *(and allowing the most to compound for future growth), which would have been strategy A. Yet in this case, the long-term compounding return of stocks is *so *dominant, that strategy C creates the most long-term wealth, *even though* its growth is slowed by what are also the largest ongoing withdrawals.

## Measuring Retirement Outcomes Based On Cumulative Spending

Notwithstanding the fact that strategy C actually turned out to create the most wealth – despite taking the largest withdrawals – in practice, retirees who ultimately want to enjoy retirement should probably not measure outcomes based on final wealth alone. Otherwise, for any two strategies that have similar returns, the “better” one will always be the one with the *least* spending, which at the logical extreme would mean the “most successful” retirement strategy is the one where the clients never spend a dime of their retirement funds!

An alternative approach would be to look at the cumulative amount of dollars actually spent, which more accurately represents the retiree’s opportunity to actually *enjoy* the retirement portfolio. In this context, the “best” strategy will not be the one that leaves the most money in the portfolio at the end, but the one that allows the most money to be consumed while the retiree is alive.

In this case, evaluating outcomes based on cumulative spending once again supports strategy C as the “best”. As shown below, strategy C produces by far the largest amount of cumulative retirement income spending, in addition to the fact that it also produces the greatest wealth accumulation over time (as shown earlier), thanks again to the long-term compounding return of equities.

Of course, the caveat to this methodology is that it doesn’t just show projected wealth and cumulative spending, per se. It shows the projected levels of wealth and spending *if* *average returns are earned*. Moreover, it’s based on having returns average out to their long-term target *with no volatility along the way*.

Yet a zero-volatility growth-in-a-straight line projection is not reflective of the real world. When the dynamics of real-world *are *considered – i.e., the “best” strategy is evaluated not based on linear projections but a different measuring stick – suddenly the optimal approach changes.

## Measuring Retirement Outcomes Based On Probability Of Success

Over the past 15 years, as computing power has continued to grow exponentially, it’s no longer necessary to project the financial outcome of a strategy by just measuring the economic impact based on *average *returns. Instead, we can now measure economic outcomes by modeling thousands of possible scenarios, each with randomized returns (based on the probability that they will occur), and instead quantify how often the results are “successful” (i.e., have money left at the end) or are not (i.e., run out of money before the end of the time horizon). This approach is commonly known as Monte Carlo retirement analysis.

When using this different methodology to quantify retirement outcomes, though, the relative benefits of each strategy begin to look very different as well. For instance, the chart below shows the Monte Carlo outcomes of our three retirement strategies, including the range of *possible *outcomes based on a 95% confidence interval (long-term returns that are plus-or-minus two standard deviations).

When measured earlier based on (median) final wealth and cumulative spending dollars, the “best” scenario was the all-stock strategy C and the worst was the immediate-annuity-based strategy A (with the latter coming in last in terms of *both *spending *and *wealth accumulation). Yet now when we observe the *range *of results, Strategy C has the best average but also includes the worst failures (including financial ruin as early as the 22^{nd} year of retirement), while Strategy A has an extremely narrow range of outcomes that are “mostly” well below the average of Strategy A… but *none *of them are failures!

In other words, based upon probabilities of success instead, annuity-based strategy A is now the “best” – a 100% probability of success, with no projected failures (presuming the annuity company is secure in the first place) – and strategy C is the worst (the lowest probability of success and highest frequency of depletions/failures). The entire sequence of which retirement strategies are “best” changes completely when using a different measuring stick, as the “best” for accumulating wealth and spending on average is the all-stock portfolio but the “best” for avoiding any risk of depletion is to spend less and annuitize assets to secure that spending goal!

## Measuring Retirement Outcomes Based On Magnitudes Of Failure And Adjustment

The charts in the prior section – based on probabilities of success – showed that strategy A was “best” and superior to both strategy B and strategy C. However, a more nuanced look reveals that just choosing the plan with the highest probability of success (and lowest probability of failure) may not be the ideal approach, either.

After all, the probabilistic “superiority” of strategy A (the $30,000/year annuity approach) over strategy B (spending $45,000/year from a diversified portfolio) was not by a large margin. For instance, if strategy B “only” spent $40,000/year adjusting for inflation instead of $45,000/year, the approach would have been successful with a 99+% probability of success. And to be fair, that is about the same as strategy A, which was shown as a 100% probability of success when looking the risk of market volatility, but is really only 99% (or perhaps 99.9%) when considering the small-but-not-zero default risk of the insurance company as well.

Of course, if strategy B were adjusted to spend “only” $40,000/year and have a 99% probability of success similar to strategy A, now the only difference between the two is the spending level: which is 33% higher, for life, with strategy B over strategy A, as shown below!

Viewed another way, the key distinction here is that while the original strategy B had a 95% probability of success and a 5% probability of failure, the *magnitude of *that failure wasn’t actually very severe, and it wouldn’t take much of an adjustment to stay on track (cutting from $45,000/year to $40,000/year of spending is sufficient). And even with poor returns, there is only a 5% chance the portfolio runs out of money* at all*, and those scenarios don’t run out until almost 28 years into retirement. Which means realistically spending would likely only need to be adjusted later – if at all – to stay on track for those final years if returns had been especially poor along the way.

Furthermore, for a 65-year-old couple, there’s a roughly 70% chance that both of them will have passed away by then anyway. Which means there’s a barely 30% probability that this 5%-failure risk is even relevant (i.e., the “joint probability” of *both* running out of money in their 90s *and *still being alive in their 90s is less than 2%). And again, if there’s *still* a fear that the bad returns are occurring or may occur soon, a “mere” 10% cut in spending is more than sufficient to ensure the plan stays on track, because the “failure” isn’t actually a very dramatic shortfall in the first place. Notably, even if the spending cut does have to occur, strategy B *still *produces more retirement spending cash flow than strategy A!

On the other hand, strategy C still turns out to be vastly inferior under the “magnitude of failure” approach, as the “bad” outcome can be *very *bad (flat broke by the 23^{rd} year), and the size of the adjustment necessary to get/stay on track would be far more than “just” a 10% spending reduction.

In other words, when weighing the magnitudes of failure (and the small or large adjustments to stay on track) against the higher spending levels, strategy A turns out to be inferior to strategy B, but strategy C is worse than all of them!

## Measuring Retirement Outcomes Based On Utility Functions And Risk Aversion

Notably, the conclusions of the prior section – which determined that strategy B was superior to strategy A because it provided for greater spending, and the likelihood of even needing a spending adjustment was “small”, and the magnitude of the adjustment required to get back on track was also “minor” – still presumes that the retirees are comfortable with those “small” and “minor” risks. In reality, not *all *retirees will be comfortable facing such trade-offs, even if the requisite spending adjustments in strategy B are likely “minor” and of remote likelihood. Or viewed another way, just because they have the financial capacity to take the risk still doesn’t mean they have the tolerance or desire to do so!

Conversely, the magnitude of potential adjustments for strategy C – which could fall seven years short on a 30-year retirement goal and possibly need 20%-30% spending cuts to get back on track – were already deemed untenable, despite the materially higher initial spending amount. Yet again, in reality at least *some *retirees might be willing to risk such trade-offs, and are willing to face the possibility of a “big” spending cut in order to enjoy a “big” spending increase up front.

In theory, these scenarios could be weighed against each other by trying to quantify how much “happiness” the retiree derives from greater spending, and weigh it against the “unhappiness” of having a spending cut, along with how risk-averse the retiree is to the possibility such a cut would have to occur.

And in point of fact, this is exactly what a retirement planning “utility function” is meant to measure. A concept derived from economics, the purpose of a utility function is specifically to assign a measuring unit – “utils” – to potential outcomes. More positive outcomes (e.g., higher spending levels) have higher utils. Adverse outcomes (e.g., spending cuts necessitated by the depletion or near-depletion of assets) have negative utils. On this basis, we can then compare and contrast widely-differing strategies that have a complex range of outcomes by adding up the positive and negative “utils” over time to determine which creates the most satisfying net or cumulative outcome.

Another key advantage of using a utility function is that it becomes possible to give *different *weights to positive versus negative outcomes – specifically, to assign greater negative weight to negative outcomes than positive weight to positive outcomes. In theory, this shouldn’t matter, because a “rational” human being should be equanimous in the face of gains or losses. In point of fact, though, the recognition that as human beings we have greater aversion to losses (more “negative utils”) than the enjoyment we gain from favorable results (relatively fewer “positive utils”) is the “Prospect Theory” first discovered by Daniel Kahneman and Amos Tversky, for which Kahneman won the Nobel Prize.

If investors were indifferent to relative gains and losses, the utility function (shown below) should be a straight diagonal line that goes from the bottom left to the top right. Instead, though, it is not. To the upper right, the line begins to flatten, revealing that we have “diminishing marginal utility” for additional wealth. In practical terms, increasing your wealth by $1,000,000 if your prior net worth was $0 is a big deal (from poverty to being a millionaire!); increasing your net worth by $1M if you already had $99M is not such a big deal (it’s not as exciting for net worth to rise from $99M to $100M). Notably, *both* are a $1M increase in wealth, but we weigh the latter one less favorably because its value is diminished by the prior millions already accumulated.

On the other hand, as the Prospect Theory graphic shows, when we *lose *money, we show a more “consistent” level of distress with both initial and extended losses (though the initial losses still appear to sting a little bit more).

Given that behaviorally, we do *not *weigh gains in the same manner as offsetting losses (and vice versa), this makes it even *more *important to give each its appropriate weighting in the first place.

## Risk Aversion And Optimal Retirement Strategies

In the context of our three strategies, this means that the relative order of which is “best” or “worst” will depend heavily on how the retiree weighs the positive utils of having more spending and wealth, versus the negative utils of being forced to cut spending in order to avoid running out of wealth altogether.

For the *highly *risk-adverse retiree, who assigns an outsized negative weight (e.g., 5:1 or even 10:1) to spending cuts over spending gains, the “best” strategy is the all-annuity strategy A, which (if you believe in the security of the annuity company at least) has the smallest danger of any spending cuts, nor does it face any market volatility either (and thus no negative utils from bear markets along the way). For this retiree, anything that decreases wealth – temporarily with market volatility or permanently and necessitating spending cuts – will be inferior, and end out with a negative utility result (because of the huge weighting of any negative utils).

On the other hand, for the risk-tolerant retiree who is far more sanguine about potential losses (or simply feels more flexible to accommodate them with spending adjustments) and places a greater weighting on upside potential and enjoying more money today, strategy C could actually still be the optimal result. While as noted earlier, this strategy has a “whopping” 25% probability of failure (or at least, a 25% probability of necessitating a spending adjustment), and could require a 25%+ spending cut to get back on track, for the retiree with flexible spending who doesn’t mind the downside risk if it means a better-than-50% chance of just getting to spend more, this may be an appealing trade-off. For this retiree, strategy A once again goes from being best to worst, and strategy C is superior.

And for the retiree in the middle – who perhaps is “rather” negative about spending cuts but is willing/able to tolerate them as long as they’re “likely to be rare” and infrequent – strategy B turns out to be the “best” strategy after all, because it has the most appealing balance. For this retiree’s utility function, strategy A doesn’t bring enough upside happiness, strategy C exposes the retiree to too much downside unhappiness, and the ideal Goldilocks outcome (not too much risk, nor too little upside) is strategy B.

The ultimate point: in order to determine which strategy is “best”, given both the potential for upside wealth, and downside spending cuts, and the trade-offs entailed in pursuing greater upside at the risk of more downside, it’s necessary to “score” both the upside *and *the downside to objectively find the best balance between the two. And how those upside and downside outcomes are weighted will in turn depend on the retiree, and his/her preferences for managing downside risk and enjoying upside return in the first place (i.e., his/her personal utility function).

## Determining The “Best” Retirement Strategy Depends On How It’s Measured

As the examples in the preceding sections have shown, determining which option is the “best” financial planning strategy can be heavily reliant on the measuring stick used to quantify the outcomes in the first place. In our choice between three strategies – annuitizing most of a portfolio for guaranteed income, taking ‘moderate’ distributions from a moderate growth portfolio, or taking large distributions from an aggressive portfolio – each strategy’s outcomes were variously best, second, or worst, depending on how the outcome was measured, as shown in the summary below.

This means that careful thought about *how *a strategy will be evaluated is actually an essential aspect of the process in crafting financial planning recommendations. The issue is akin to what any scientist analyzing any problem has to consider: the research methodology used to analyze an issue can impact the conclusion about it, *so it’s crucial to vet not just the results but the methodology itself*. Otherwise, a flawed design to a research study can yield a flawed conclusion about its results.

For instance, imagine a medical study analyzing a weight-loss drug in the hopes that reducing obesity will cut down on deaths from complicating factors such as diabetes and high blood pressure. The research focuses on whether the drug leads to weight reduction, and finds that it does, concluding it’s a good drug. However, in reality, side effects of the drug itself include a significant increase in the risk of cancer and stroke! As a result, the drug does “cure” obesity but actually increases the ultimate risks of death that losing weight was meant to help minimize. In this context, if you measure “impact on weight loss” the drug is a success, but when measured by “impact on overall health” it’s actually a failure.

Of course, when it comes to financial planning, the situation is complicated by the fact most clients have multiple and complex goals and preferences. Accordingly, it’s almost impossible to establish financial planning strategies that are “objectively” dominant and superior in all situations. At best, some products or solutions might be better than others *for a particular goal,* or subject to particular constraints and client risk tolerance or other preferences. For instance, an emergency savings fund invested in a money market that yields 1% is clearly better than one that only yields 0.1%, and for the “core” indexing portion of a retirement account an S&P 500 index with an expense ratio of 0.1% is better than one with an expense ratio of 1%. Nevertheless, whether the high-yield money market or the low-cost index fund are “best” in the first place depends on the goals to be pursued (accumulating for retirement versus saving for an emergency fund) and tolerance for risk. With the caveat that because of our behavioral biases, even with stable risk tolerance our *perceptions of *these risks may be distorted in a way that inappropriate impacts our decisions (which is a discussion for another day!).

Nonetheless, the fundamental point remains that evaluating which retirement strategy is best requires a combination of *both *a quality process to objectively analyze the scenarios, *and *a careful consideration of what tools will be used to *do *the measuring and evaluate the outcomes in the first place, to properly fit them into a client’s preferences and tolerance for risk!

**So what do you think? How do you evaluate the outcomes of potential retirement income strategies with clients? Is it based on projected wealth, cumulative spending, Monte Carlo analysis, probabilities of success, magnitudes of failure, utility functions, or something else? How do you explain these concepts to your own clients? Please share your thoughts in the comments below!**