february 2017 design framework. - t. rowe price glide... · target date investing: t. rowe...

EXECUTIVE SUMMARY

■■ T. Rowe Price’s glide-path design framework is constructed to flexibly accommodate a broad range of plan characteristics and preferences. It supports both our proprietary off-the-shelf glide paths as well as customized designs for specific plans.

■■ Our approach embraces the principle of economic utility, a term that refers to the level of satisfaction or dissatisfaction derived from a good or service—an asset allocation glide path in this case.

■■ The primary goal is to find the glide path that robustly maximizes utility satisfaction as defined by investor preferences and constraints.

■■ We also seek to ensure the design is robust in satisfying the heterogeneous nature of participant demographics and risk preferences.

■■ The relative importance placed between the contravening objectives of consumption and account balance stability has perhaps the most significant effect on shaping the glide path. Risk preference also plays an important role, but demographics have a relatively minor influence.

Target Date Investing:T. ROWE PRICE’S GLIDE-PATH DESIGN FRAMEWORK.

Richard K. Fullmer, CFAAsset Allocation Strategist

James A. Tzitzouris, Ph.D.Director of Asset Allocation Research

Wyatt A. Lee, CFAPortfolio Manager, Target Date Solutions

Target date portfolios are the leading retirement saving vehicles within defined contribution (DC) plans in the United States. Asset allocation, the exercise of determining the relative share of various asset types to hold, is a key element in the design of these portfolios. By design, this allocation changes strategically over the portfolio’s life cycle, which may extend for 70 years or more to account for the span of a working career and potentially lengthy retirement. The change over time in the allocation to equities and bonds is known as a glide path. Because asset allocation is an important determinant of investment

outcomes, the suitability of the glide path to any given DC plan is a matter of utmost importance to plan sponsors in their role as fiduciaries.

Plan sponsors have many options when selecting a target date solution. One course is to select from among the wide variety of pre-assembled target date portfolios commercially available in the marketplace. An alternative course is to develop a custom portfolio, in which case the glide path could be tailored to the sponsor’s unique preferences and the plan’s unique characteristics. In acknowledging that both approaches

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have merits, the U.S. Department of Labor has encouraged plan fiduciaries to consider both approaches.1

As a leading provider of target date portfolios and DC recordkeeping services, T. Rowe Price has considerable experience in the areas of glide-path design and glide-path selection.2 Whether the purpose is to build a generalized or customized solution, our design framework is constructed to flexibly accommodate a broad range of plan characteristics and preferences.

GLIDE PATHS: A BEHAVIORAL SOLUTION TO A BEHAVIORAL PROBLEM

Glide-path design happens at the intersection of financial and behavioral economics. This is because retirement outcomes depend not only on investment returns, but also on the cash flow (i.e., the saving and spending) behavior of the investor. Accordingly, our glide-path design framework incorporates in tandem an Economic Scenario Model (ESM) and a Behavioral Scenario Model (BSM). Both models use Monte Carlo simulation to generate thousands of potential scenarios:

■■ The ESM models the economy and capital markets, including items such

as economic growth, interest rates, inflation, and asset class returns.

■■ The BSM models the factors that influence investor cash flow behavior such as population demographics, salary, salary growth, contribution saving rates, employer matching incentives, defined benefit (DB) pension income, Social Security benefits, retirement date, retirement spending, and mortality rates.

Since many of these behavioral elements are influenced by what happens in the economy and capital markets, the BSM draws upon the ESM.

Behaviors are also strongly driven by attitudes. Thus, our framework also incorporates a set of customizable preference parameters to account for attitudes toward risk, consumption, longevity, etc.

Behaviors and attitudes can vary widely across plans as well as among participants within plans. Glide paths must therefore be robust in satisfying the heterogeneous needs of different investors. For commercially available target date portfolios, this means satisfying the range of participants across many plans, including those

investing through individual retirement accounts. For custom portfolios, this can be done more specifically for the range of participants within a particular plan.

Addressing this kind of heterogeneity is vital to glide-path design. Even the definition of what risk means can vary significantly from person to person. For example, does it refer to:

■■ Falling short of a desired postretirement standard of living (an income-based view)?

■■ A drop in account balances caused by poor portfolio returns (a wealth-based view)?

These are very different perspectives and, as we will show, an emphasis on one or the other can lead to very different glide paths.

WHAT MATTERS MOST TO YOU?

These differing ways of viewing risk align closely with our research into the primary investment objectives of target date investors:

■■ To fund an adequate and sustainable level of consumption after retirement, and

■■ To promote the stability of retirement account balances by limiting the volatility of portfolio returns.

We refer to the first as the Consumption objective and the second as the Balance Stability objective.

These objectives are contravening in that glide paths with higher levels of equity assets aid the Consumption objective due to higher expected returns over the long run, but also detract from the Balance Stability objective due to higher expected volatility along the way. While both objectives are undoubtedly important, different sponsors may weigh their relative importance differently.

Behaviors and attitudes can vary widely across plans as well as among participants within plans. Glide pathsmust therefore be robust in satisfying the heterogeneous needs of different investors.

1 U.S. Department of Labor, “Target Date Retirement Funds: Tips for ERISA Plan Fiduciaries,” February 2013. http://www.dol.gov/ebsa/newsroom/fsTDF.html.2 We have previously written extensively on the topic of glide path selection (see, for example, the papers by Fullmer and Tzitzouris: Evaluation of Target-Date Glide

Paths Defined Contribution Plans and Target Date Glide Paths: Balancing Plan Sponsor Goals). Conversely, this paper discusses the topic of glide path design.


Some may weigh the objectives neutrally, others may lean toward emphasizing the Consumption objective, and still others may lean toward emphasizing the Balance Stability objective. Whether the task is to select an existing pre-assembled glide path or to design a customized glide path, it is essential to assess the relative importance that the plan sponsor places between these objectives because the answer may affect the glide-path design significantly.

FRAMEWORK FOR GLIDE-PATH DESIGN

Big Picture View: Modeling Outcomes and Measuring UtilityOur design framework embraces the economic principle of utility, a term that refers to the level of satisfaction or dissatisfaction derived from a good or service—an asset allocation glide path in this case. Because retirement outcomes are uncertain, this level of satisfaction must be judged in terms of the probability of potential outcomes. In this sense, we view glide-path design as a classic example of outcome-oriented investing.3

The ability to model outcomes appropriately (the job of the ESM and the BSM) is a critical first step in the process. The next step is to assess the level of satisfaction these outcomes provide, which is purely a matter of

personal preference. In economic terms, this preference set is referred to as the investor’s utility function.

While utility functions may be unique to each individual, a common trait is that they are typically nonlinear, exhibiting a characteristic known as diminishing marginal utility. For example, the satisfaction associated with gaining an additional dollar is typically much higher when the goal is underfunded rather than overfunded. Likewise, the dissatisfaction associated with losing a certain fraction of existing wealth or consumption is typically greater than the satisfaction associated with gaining that same fraction of new wealth or consumption.4

At a high level, our glide-path design framework consists of three interconnected models, with inputs as shown in Figure 1.

Defining the ObjectivesBecause assessing utility satisfaction involves measuring investment outcomes relative to the investor’s objectives, the definition of these objectives is an important determinant of which glide path will best satisfy them. For example, some glide-path designers define the Consumption objective as a fixed income replacement rate (e.g., 75% of final year salary). We prefer a somewhat

more flexible consumption function that allows for the fact that retirees can and do alter their consumption to a degree in response to investment returns in much the same way that preretirees alter their consumption in response to changes in salary. In this way, we also avoid the problem of assigning an unrealistically high replacement rate hurdle to participants with low savings rates. In addition to consumption, we also explicitly incorporate the objective of short-term balance stability. See the appendix for further discussion of these objectives.

Measure Separately, Then CombineEvery possible glide-path solution offers a level of satisfaction with regard to the Consumption objective, another level of satisfaction with regard to the Balance Stability objective, and an overall level of satisfaction with respect to both objectives. We:

1. Measure a “utility score” for each objective separately, then

2. Convert these scores to a common certainty equivalent scale (discussed further in the appendix), then

3. Combine them into an overall utility score by weighting each objective according to the relative importance assigned to it.

3 An introduction to these concepts can be found in the companion paper by Fullmer: Risk and Utility in Outcome-Oriented Investing.4 Note that our approach does not directly measure the utility of wealth per se, but rather the utility of consumption and the utility of the effect of portfolio returns on participant account balances, which we believe are more directly associated with DC plan objectives.

Our design framework embraces the economic principle of utility, a term that refers to the level of satisfaction or dissatisfaction derived from a good or service...

FIGURE 1: Big Picture View

(ESM)Capital Markets

Model

(BSM)Savings and Consumption

Model

Utility SatisfactionModel

Capital markets historyOur long-term capitalmarket outlook

Plan record-keeping data

Employeebenefits data

Governmentregulations

Personal preferences


While the overall score is the primary concern, the commonly scaled scores for each objective are useful for understanding the trade-off in overall utility that occurs when placing different degrees of focus on one objective or another. For example, how much satisfaction in the Consumption objective must be given up to incrementally improve satisfaction in the Balance Stability objective, and vice versa? For sponsors interested in a customized solution, such insights can help assure that the ultimate design is well aligned with their intentions.

The next step is to solve for the glide path that maximizes this overall utility score.

Figure 2 illustrates the process in which many thousands of economic and capital market (i.e., asset class return) scenarios are generated by the ESM, which when applied to a glide path translates into a series of portfolio returns. The BSM generates many thousands of salary and saving scenarios which result in simulated cash flow scenarios for many thousands of participants. Each scenario can represent up to 1,200 monthly values representing a potential 100-year investment horizon.5 The actual life span assumed for each particular scenario is determined randomly, such that the distribution of participant life spans across all scenarios closely approximates that of a representative mortality table.

Note that glide-path utility considers:

■■ Many thousands of possible economic scenarios,

■■ Many thousands of possible investor behavior and life span scenarios,

■■ Lifetime income from sources other than the DC plan, such as DB pensions and Social Security,

■■ Customizable inputs of plan demographic characteristics (shown in orange), and

■■ Customizable preference settings (shown in teal).

Finishing Touches: Promoting RobustnessUtility maximization produces a highly specialized solution, which is fine when applied to a single investor or a homogenous group of investors. Retirement plan participants, however, are quite heterogeneous as a group. When divided into subpopulations, a different specialized (i.e., utility maximizing) solution may apply to

each. The final step of our process, then, is to take care that the solution is heterogeneously robust with respect to satisfying different segments of the participant population, as illustrated in Figure 3. The objective here is to minimize the degree to which the utility of certain subpopulations might otherwise be unfairly sacrificed for the sake of increasing the utility of other subpopulations.

DESIGN PARAMETERS

Our framework incorporates a number of parameters, which we categorize as environmental factors, demographic factors, and preference parameters.

5 Consider, for example, a working career that may start at age 21 and a possible life span as represented by a mortality table that extends through age 120.

FIGURE 2: Design Approach Flowchart

Overall Utility Satisfaction Score

Utility of Portfolio Returns(Balance Stability Objective)

Glide path

Objective:Find the glide paththat (robustly)maximizes overallutility satisfaction.

Custom Inputs Custom PreferencesStandard InputsKey

Output:

Certainty EquivalentUtility of Portfolio Returns

Output:

Certainty EquivalentUtility of Consumption

Relative GoalImportance

Determine Utility of Each Objective

Mortality Time preferenceRisk preference

Output:Consumption

BSMSalaries

Saving ratesMatching incentives

Retirement datePension benefitsSocial Security

Output:

Portfolio Returns

ESM

Economic growth Inflation Interest rates Asset class returns


Environmental Factors

Environmental factors are those that generally apply universally to all plans and all investors and therefore are not customized for individual plans. These include:

■■ All inputs into the ESM for generating economic and capital market scenarios.

■■ Rules governing Social Security taxes and benefits.

Demographic FactorsDemographic factors describe the targeted investor population. The goal is to incorporate as much relevant information about the plan and participants as possible. In the case of an off-the-shelf glide path targeting the general population, we calibrate demographic factors based on T. Rowe Price recordkeeping data that spans thousands of plans and millions of participants. In the case of a customized glide path for a particular plan, we calibrate these factors based on data associated with that specific plan.

Demographic factors include items such as salary, salary growth, employee contributions, and employer matching incentives. The assumed retirement date and provisions for DB plan income may also be customized, as may the mortality assumptions.

Preference Parameters

The environmental and demographic factors serve as a representation of facts rather than attitudes. The expression of attitudes is made through preference parameters, which include:

■■ Relative Goal Importance: This denotes the relative degree of importance between the Consumption objective and the Balance Stability objective. This may range from a

100% preference for the Consumption objective to a 100% preference for the Balance Stability objective or anywhere in between. Values near either end of this range are very rare.

■■ Risk Preference: This denotes the degree of risk aversion with respect to achieving each objective. With regard to the Consumption objective, a participant or plan sponsor who displays high risk aversion will seek to reduce the volatility of consumption cash flow and the possibility of outliving the portfolio’s assets. With regard to the Balance Stability objective, a participant or plan sponsor

who displays high risk aversion will seek to reduce the volatility of participant balances. Because participants exhibit a range of risk preferences, our framework does not force the selection of a single risk preference value. Rather, it allows for a weighted distribution of risk preference values to reflect a range in participant and sponsor attitudes.

■■ Time Preference: This denotes the degree to which one focuses on outcomes exclusively at retirement versus focusing on outcomes at all periods equally. With regard to the Consumption objective, time

FIGURE 4: Impact of Risk Preference on the Utility-Maximizing Glide Path

Age (Years)

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Least Risk Averse

Most Risk Averse

Source: T. Rowe Price.Note: This figure shows hypothetical illustrations of utility-maximizing glide paths under a given set of assumptions, including a neutral relative goal importance in which both objectives are given equal weight.

FIGURE 3: Outer Loop to Enforce Robustness Across Subpopulations

2

OverallUtility Score

3

Repeat forSubgroups to

Refine Solution

1

Utility Score:Consumption

Utility Score:Balance Stability

OUTCOME OUTCOME OUTCOMEAchieve

robustness Overall

satisfaction levelHighest satisfaction

glide path


preference has to do with the horizon over which the retirement account is to produce postretirement income. A plan sponsor or participant seeking to consume the entire account balance at retirement has an extreme value for the present. A plan sponsor or participant focused on long-term income distributions values cash flows equally across time for as long as participants may live. Thus, a “to versus through” preference can be expressed via this parameter.6 With regard to the Balance Stability objective, time preference has to do with the horizon over which the stability of portfolio returns is measured. A plan sponsor or participant who focuses on account balance stability exclusively at retirement has an extreme value for the present at the time of retirement. A plan sponsor or participant with a long-term focus evaluates account balance stability at all periods equally.

ILLUSTRATIONS

The following illustrations show the impact of three different types of parameters:

■■ Risk preference.

■■ Relative goal importance.

■■ Demographic factors of earnings and savings.

Each illustration makes the same underlying assumptions. Demographic data are represented by a large representative sample of actual participant data taken from the T. Rowe Price recordkeeping database. Common assumptions include:

■■ Retirement occurs at age 67, at which time Social Security benefits are initiated,

■■ No DB plan,

■■ A time preference that weights all periods equally, and

■■ A state-dependent consumption rule that seeks to maximize the utility of consumption given the risk and time preferences, taking into account factors such as portfolio returns, inflation, Social Security income, and remaining life expectancy.

Impact of Risk PreferenceFigure 4 shows the impact of risk aversion. As one would expect, lower risk aversion will typically result in glide paths that hold more equity.

Because participants express a wide range of risk preferences and the impact of risk preference is so significant, we find it unappealing to force the specification of a single risk aversion for everyone. Rather, our approach is to specify a range of risk preferences in which various risk preference values are assigned a given weight. Doing so helps to promote the robustness

of the resulting solution across a heterogeneous group of participants.

Impact of Relative Goal ImportanceFigure 5 shows the impact of relative goal importance. A greater emphasis on lifetime consumption results in glide paths that hold more equity, whereas a complete focus on balance stability results in a flat glide path since in that case the only thing that matters is keeping portfolio volatility steady.7

Keep in mind that all the glide paths shown in Figure 5, ranging from high equity to low equity, were produced using the same risk preference assumption. We highlight this to emphasize that the level of equity in the glide path is not merely a function of risk preference. In fact, compared with risk preference, relative goal importance can have just as much influence on the level of equity—and even more influence on the slope and curvature of the glide path as it evolves over time.

To shed more light on this, consider Figure 5 in terms of what happens to the glide paths after the targeted

FIGURE 5: Impact of Relative Goal Importance on the Utility-Maximizing Glide Path

Age (Years)

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100% Consumption Focus

100% Balance Stability Focus

Source: T. Rowe Price.Note: This figure shows hypothetical illustrations of utility-maximizing glide paths under a given set of assumptions, including a moderate level of risk aversion consistent with producing glide paths that approximate those commonly found in the marketplace today.

6 While we accept that the versus nomenclature has become accepted in the industry, we object to it as confusing and potentially misleading as explained by Fullmer in, Glide Path Classification: Sensibly Reframing “To Versus Though.”

7 Recall that the Account Balance objective has to do with the volatility of account balances and therefore is independent of the size of account balances or any other time-related effects when the time preference is to focus on all periods equally. The level of equity in the flat glide path that results when the focus is purely on balance stability will depend on the chosen value of the risk parameter.


retirement date. When the emphasis is on consumption with little or no regard for balance stability, the glide path turns upward, becoming U-shaped. While we are aware of no U-shaped glide paths in the marketplace today, a number of authors (including us) have written that such U-shaped glide paths are in fact theoretically optimal under certain assumptions.8 Here we see evidence of what is perhaps the most important of those assumptions: a strong preference for long-term consumption at the sacrifice of short-term balance stability. The fact that no U-shaped glide paths exist in the marketplace, however, suggests that plan sponsors and participants do care about balance stability.

It bears noting that when the two objectives are neutrally weighted, we find that the utility-maximizing solution is downward sloping all the way through retirement. This is the case even though we hold the risk preference steady over the entire horizon. We make this point because some authors have suggested that glide paths that continue to slope downward after retirement can only be justified if risk aversion is assumed to increase as people age. Our findings refute that argument because we make no such assumption.

Impact of Demographic FactorsFigure 6 shows the impact of earnings levels and savings rates. Here we have taken quintiles of both earnings and savings rates to form 25 demographic subpopulations.9 For readability, the chart shows only nine of these subpopulations representing the highest, middle, and lowest quintiles along each dimension.10

As can be seen, these demographic factors have a relatively small effect on glide-path design. This result may seem surprising at first given the significant differences in these subpopulations.

For example, the “High Earner, Low Saver” group is the worst funded not only because they save poorly, but also because Social Security will contribute a relatively smaller proportion of their preretirement level of consumption. Conversely, the “Low Earner, High Saver” is comparatively much better funded for the opposite reasons. Even so, the effect on the glide path is limited.

The limited effect of demographic factors is worth highlighting because it supports the idea that target date portfolios can be

sensible default options for all participants in a plan.

TOWARD PROMOTING ROBUSTNESS

As can be seen in the previous examples, the process of utility maximization leads to highly specialized solutions that will differ depending on the input parameters. This would seem to place a very high burden on getting all of the assumptions correct—a burden that sponsors may find unappealing

FIGURE 6: Impact of Demographics on the Utility-Maximizing Glide Path

Age (Years)

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Narrow Difference in Equity Weight at Retirement (Age 65)

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52.25 53.46 51.8256.00 54.59

51.9856.88 54.30

50.87

High Earner, High SaverHigh Earner, Median SaverHigh Earner, Low Saver

Median Earner, High SaverMedian Earner, Median SaverMedian Earner, Low Saver

Low Earner, High SaverLow Earner, Median SaverLow Earner, Low Saver

Source: T. Rowe Price.Note: This figure shows hypothetical illustrations of utility-maximizing glide paths under a given set of assumptions, including a moderate level of risk aversion consistent with producing glide paths that approximate those commonly found in the marketplace today and a neutral relative goal importance in which both objectives are given equal weight. High is defined as the top quintile, median is defined as the middle quintile, and low is defined as the bottom quintile of the participant population.

8 Please see the paper by Fullmer titled, Reflections on Recent Target Date Research, as well as the other papers that it references.9 Quintiles of two demographic variables (earnings and savings) combine as a Cartesian product to produce a 5x5 matrix, resulting in 25 demographic

subpopulations. 10 Note that the glide paths for the 16 demographic subpopulations not shown generally fall within the range of the 9 that are shown.


given that participants’ situations and preferences can vary widely.

Our approach to this dilemma is to wrap a final “robustness process” around the utility-maximization framework as discussed earlier. The idea is to help ensure that the final solution satisfies the objectives across the broad range of participants for which the glide path is designed. This involves evaluating how the utility-maximizing solution differs for various subpopulations defined along dimensions related to demographics and risk preferences and minimizing the degree to which the utility of any particular segment is sacrificed to the advantage of any other segment. Thus, our approach incorporates an inner utility maximization process surrounded by an outer relative utility minimization process. The inner process seeks the highest possible level of satisfaction for each of a number of different subpopulations. The outer process seeks robustness in the level of satisfaction attained across them.

CONCLUSION

Our framework for glide-path design strives to model the world as realistically as possible. It consists of three component models: an economic model of the economy and capital markets, a behavioral model of participant savings and consumption, and a utility satisfaction model of sponsor and participant attitudes. A set of parameters is designed to flexibly accommodate a broad range of plan characteristics and preferences, whether the intent is a customized solution for a particular DC plan or a generalized solution designed to accommodate multiple plans and individual retirement accounts.

While the ultimate goal is to find the glide path that maximizes overall utility satisfaction, we also strive to promote robustness in satisfying a range of demographic subsets of the participant population. The good news is that

demographic factors have a relatively muted effect. Factors such as risk preference and the relative importance assigned to different goals can affect the glide path more significantly.

T. Rowe Price has long stressed that because retirement requires a long-term outlook, investors should be encouraged to look past short-term portfolio volatility and instead focus on long-term lifetime consumption replacement. Yet we also recognize that people do care when their retirement accounts lose value, reflecting what behavioral economists refer to as “present bias”—the tendency to value near-term outcomes at the expense of long-term outcomes. For this reason, our glide-path design framework gives prominent attention to both objectives in crafting a behavioral solution to this behavioral problem.

APPENDIX

Utility of ConsumptionOur utility function employs the Arrow-Pratt measure of constant relative risk aversion (CRRA), which of the form:

where c is consumption, U(c) is the utility of consumption, and γ is a constant that indicates the degree of risk aversion as given by the risk preference parameter.

Our consumption model is very flexible and can be customized using a number of parameters. Postretirement consumption includes monies withdrawn from the DC plan, Social Security income, and DB pension income (if any). When the time preference is for lifetime income, the consumption function is made subject to the entire term structure of mortality as identified

by a representative mortality table. Other customization parameters for the consumption function include:

■■ Consumption Flexibility Preference: This has to do with the degree to which retirees are willing to alter one’s standard of living in response to changes in wealth that result from investment performance. We can allow the consumption function to be annuity-like in terms of maintaining a given standard of living (in real terms) or to be more endowment-like in terms of adjusting the standard of living up or down in response to the performance of the investor’s retirement account.

■■ Consumption Impatience Preference: This has to do with the degree of “personal impatience” with respect to postretirement consumption.11 For example, is the attitude to spend more early in retirement while people are more likely to be alive to spend it? Or is it to spend conservatively throughout retirement to guard against unplanned longevity or unexpected future spending shocks?

Through these parameters, our consumption model may take a number of different forms, such as:

■■ A fixed consumption replacement rate: For example, the level of consumption in the last year of employment is measured, and then 80% of this amount is withdrawn and consumed in the first year of retirement, and then this amount is adjusted every year for inflation.12

■■ An endowment spending rule: For example, the level of consumption is defined as a percentage of the rolling average balance over some defined period, in which case withdrawals will vary depending on portfolio returns.

11 This concept traces back to economist Irving Fisher’s seminal work, The Theory of Interest: As Determined by Impatience to Spend Income and Opportunity to Invest It.

12 A value less than 100% is commonly used with this rule because postretirement consumption need not replace that portion of preretirement salary directed toward certain items that no longer apply after employment ends, such as payroll deductions for DC plan contributions and FICA taxes.


■■ A required minimum distribution rule: For example, the level of consumption is based on the Internal Revenue Service table for the minimum amount participants must withdraw from their account each year.

■■ A fixed percentage rule: For example, the level of consumption is set at 4% of the balance at the time of retirement, and then this amount is adjusted every year for inflation.

Although our model supports each of these rules-based approaches, our preferred approach is state dependent rather than rules-based because we believe this more accurately reflects how people actually behave. Under this approach, participants seek to maximize the utility of their consumption by adjusting it over time in response to their ever-changing situation. Consumption evolves as a function of variables such as past consumption, portfolio returns, inflation, remaining life expectancy, and the chosen level of aversion to the risk of sustaining the current rate of consumption into the future. For example, in states in which portfolio returns are stronger than expected, consumption may rise. Conversely, in states in which portfolio returns are weaker than expected, consumption may fall.

Utility of Portfolio Returns (Balance Stability)

We likewise employ a CRRA model for the utility of portfolio returns in evaluating the Balance Stability objective. We use the trailing three-year cumulative return for this measure, reflecting our view of the typical degree of present bias displayed by investors with regard to their DC account balances. The risk preference parameter specifies the degree of risk aversion to be applied. The time preference parameter is also applied as discussed previously.

Combining Utility Scores for Objectives with Different ScalesBecause consumption and returns are different things, the utility of consumption score and the utility of returns score have different scales. Thus, we need to convert them into a common scale. For this, we rely on a classic technique in economics known as the certainty equivalent and ensure that we do so using a common reference measure. The certainty equivalent represents the outcome the investor would require with certainty in order to be indifferent between that certain outcome and the set of the uncertain outcomes.

Our method is to compute the excess return (above cash) that would be required with certainty in order to give the equivalent utility score as measured under uncertainty. This is done for both the utility of consumption and the utility of returns. The result may be described as the “utility-equivalent excess return,” which brings both measures under a common scale. We could have chosen something other than a rate of return as the common reference variable for computing the certainty equivalents. The use of returns makes sense, however, given that glide paths are investment solutions and plan sponsors are generally familiar with the investment returns offered by various asset classes.

MONTE CARLO

Material Assumptions Include:Our analysis used Monte Carlo simulation to model the uncertainty of asset class returns and inflation, derived from a structural model of financial and economic factors. From this model, we generate 10,000 scenarios, representing a spectrum of possible monthly outcomes for each variable over a period of 1,080 months (a 90-year horizon corresponding to a starting age of 25 and a mortality table that runs to age 115). Portfolio glide paths were

modeled with equity/bond allocations that varied from quarter to quarter. All portfolios were rebalanced back to target weights at the beginning of each month.

For modeling plan characteristics and participant behavior, we used the T. Rowe Price Behavioral Scenario Model, which is based on actual participant data from DC plans for which T. Rowe Price provides recordkeeping services. Participants were assumed to begin working and saving at age 25 and to retire at age 67. Each participant was assigned a unique salary, contribution savings rate, and employer contribution match formula such that the distribution of these variables closely aligned with the actual participants in our database. Salaries were assumed to grow over time according to a model incorporating average wage growth for all workers as measured by the national Average Wage Index, as well as career salary growth. Postretirement withdrawal horizons were modeled according to the combined healthy RP-2000 mortality table using projection scale AA.

Monte Carlo SimulationMonte Carlo simulations model future uncertainty. In contrast to the use of average outcomes, Monte Carlo analyses produce outcome ranges based on probability, thus incorporating future uncertainty.

Material Limitation Include:■■ The analysis relies on certain

assumptions, combined with a return model that generates a wide range of possible return scenarios for these assumptions. Despite our best efforts, there is no certainty that the assumptions for the model will accurately predict asset class return rates going forward. As a consequence, the results of the analysis should be viewed as approximations, and readers should allow a margin of error and not place


too much reliance on the apparent precision of the results.

■■ Extreme market movements may occur more often than in the model.

■■ Some asset classes have relatively short histories. Actual long-term results for each asset class may differ from our assumptions, with those for asset classes with limited histories potentially diverging more.

■■ Market crises can cause asset classes to perform similarly, lowering the accuracy of our return assumptions and diminishing the benefits of diversification (that is, using many different asset classes) in ways not captured by the analysis. As a result, returns actually experienced by the investor may be more volatile than those used in our analysis.

■■ The analysis does not use all asset classes. Other asset classes may be similar or superior to those used.

■■ Income taxes are not taken into account, nor are early withdrawal penalties.

■■ The analysis models asset classes, not investment products. As a result, the actual experience of an investor in a given investment product (e.g., a mutual fund) may differ from the range generated by the simulation, even if the broad asset allocation of

the investment product is similar to the one being modeled. Possible reasons for divergence include, but are not limited to, active management by the manager of the investment product or the costs, fees, and other expenses associated with the investment product. Active management for any particular investment product―the selection of a portfolio of individual securities that differs from the broad asset classes modeled in the analysis―can lead to the investment product having higher or lower returns than the range used in this analysis.

Modeling Assumptions:■■ The primary asset classes used for

this analysis are stocks and bonds. An effectively diversified portfolio theoretically involves all investable asset classes, including stocks, bonds, real estate, foreign investments, commodities, precious metals, currencies, and others. Since it is unlikely that investors will own all of these assets, we selected the ones we believed to be the most appropriate for long-term investors.

■■ Results of the analysis are driven primarily by the assumed long-term, compound rates of return of each asset class in the scenarios. Our corresponding assumptions are as follows:

— Annual mean: for inflation, 3%; for stocks, 8.0%; and for bonds, 5.3%.

— Standard deviation: for inflation, 3%; for stocks, 18.0%; and for bonds, 6.5%.

— Correlation: 0.4 between stocks and bonds.

■■ Investment expenses, such as those in the form of an expense ratio, are not considered.

IMPORTANT: The projections or other information generated by our analysis regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results, and are not guarantees of future results. The projections are based on assumptions. There can be no assurance that the projected results will be achieved or sustained. The charts present only a range of possible outcomes. Actual results will vary with each use and over time, and such results may be better or worse than the projected scenarios. Clients should be aware that the potential for loss (or gain) may be greater than demonstrated in the projections.

The results are not predictions, but they should be viewed as reasonable estimates. Source: T. Rowe Price Associates, Inc.


Important InformationThis material is directed at institutional investors only and is not intended for distribution to retail investors.

It has been prepared by T. Rowe Price for informational purposes only. This information is not intended to be investment advice or a recommendation to take any particular investment action.

The views contained herein are those of the authors as of February 2017 and are subject to change without notice; these views may differ from those of other T. Rowe Price associates.

This information is not intended to reflect a current or past recommendation, investment advice of any kind, or a solicitation of an offer to buy or sell any securities or investment services. The opinions and commentary provided do not take into account the investment objectives or financial situation of any particular investor or class of investor. Investors will need to consider their own circumstances before making an investment decision.

Information contained herein is based upon sources we consider to be reliable; we do not, however, guarantee its accuracy.

Past performance cannot guarantee future results. All investments involve risk. All charts and tables are shown for illustrative purposes only.

T. Rowe Price Investment Services, Inc.

T. Rowe Price Associates, Inc.

REFERENCES AND FURTHER READING

Clark, Jerome A. and Wyatt A. Lee. “T. Rowe Price’s Approach to Target Date Portfolio Design.” T. Rowe Price Perspective, January 2016.

Fisher, I. The Theory of Interest: As Determined by Impatience to Spend Income and Opportunity to Invest It. New York: Macmillan (1930).

Fullmer, Richard K. “Reflections on Recent Target Date Research.” T. Rowe Price Asset Allocation Insights Report, February 2014.

Fullmer, Richard K. “Glide Path Classification: Sensibly Reframing ‘To versus Through’.” T. Rowe Price Perspective, April 2015.

Fullmer, Richard K. “Risk and Utility in Outcome-Oriented Investing.” T. Rowe Price Perspective, February 2017.

Fullmer, Richard K. and James A. Tzitzouris, Jr. “Target Date Glide Paths: Balancing Plan Sponsor Goals.” T. Rowe Price Investment Dialogue, October 2013 (updated January 2016).

Fullmer, Richard K. and James A. Tzitzouris, Jr. “Evaluation of Target-Date Glide Paths within Defined Contribution Plans.” Journal of Retirement, Vol. 1, No. 4 (Spring 2014), pp. 75–94.

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T. Rowe Price focuses on delivering investment management excellence that investors can rely on—now and over the long term.

To learn more, please visit troweprice.com.

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