NEWS: The Journal of Portfolio Management - Personalized Target-Date Funds

MULTI-ASSET STRATEGIES AND ASSET ALLOCATION

volume 50 number 5

MARCH 2024

pm-research.com

Personalized

Target-Date Funds

Kobby Aboagye, Sébastien Page, Louisa Schafer, and James Tzitzouris

Kobby Aboagye, Ph.D.

Kobby Aboagye is an investment quantitative analyst in the Multi-Asset Division. He is an assistant vice president of T. Rowe Price Associates, Inc.

Kobby has been with T. Rowe Price since 2021, beginning in the Multi-Asset Division. Prior to this, Kobby was employed by American Air Liquide, a global industrial gas company, as a senior research scientist in the Computational and Data Science Group. In this role, Kobby explored and developed new algorithms for Air Liquide to procure energy (electricity and natural gas) efficiently and optimally, in both the physical and financial markets. Kobby also modeled the health impact of COVID-19 in the Americas and, collaborating with researchers from the University of Washington, built a statistical model to predict the excess demand in oxygen for ventilators. Kobby also was employed by PricewaterhouseCoopers as an accountant in the auditing line of business, where he led medium-risk audit projects in a variety of sectors including banking, energy and mining, and telecommunications.

Kobby earned a B.Sc. in statistics and actuarial science from KNUST in Ghana and an M.Sc. and a Ph.D. in operations research from Princeton University.

Sébastien Page, CFA

Sébastien Page is Head of Global Multi-Asset and Chief Investment Officer. He oversees a team of investment professionals dedicated to actively managing a broad set of multi-asset portfolios representing more than $485 billion1 in assets, including the firm's target date franchise. He is a member of the Asset Allocation Committee, which is responsible for tactical investment decisions across asset allocation portfolios, and a member of the Management Committee of T. Rowe Price Group, Inc.

Sébastien's investment experience began in 2000, and he has been with T. Rowe Price since 2015. Prior to this, Sébastien was employed by PIMCO as an executive vice president where he led a team focused on research and development of multi-asset solutions. Prior to joining PIMCO in 2010, he was employed by State Street Global Markets as a senior managing director.

Sébastien earned a Master of Science degree in finance and a bachelor's degree in business administration from Sherbrooke University in Quebec, Canada. He also has earned the Chartered Financial Analyst® designation.

Sébastien coauthored award-winning research papers for The Journal of Portfolio Management in 2003, 2010, 2011 and 2022 and the Financial Analysts Journal in 2010 and 2014. He is the author of the book "Beyond Diversification: What Every Investor Needs to Know About Asset Allocation" (McGraw Hill, 2020) and the coauthor of the book "Factor Investing and

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1 As of December 31, 2023

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Asset Allocation" (CFA Institute Research Foundation®, 2016). Sébastien is a member of the editorial boards of The Journal of Portfolio Management and the Financial Analysts Journal, and he is a member of the Board of Directors of the Institute for Quantitative Research in Finance (Q Group). He regularly appears in the financial media, including Bloomberg TV and CNBC and was recently named amongst the 15 Top Voices in Finance for 2022 by LinkedIn.

CFA® and Chartered Financial Analyst® are registered trademarks owned by CFA Institute.

Louisa Schafer, CFA, Ph.D.

Louisa Schafer is a quantitative analyst in the Multi-Asset Division.

Louisa has been with T. Rowe Price since 2016, beginning in the Investment Fellowship Program.

Louisa earned a B.A. in economics and business administration from American University in Bulgaria and a Ph.D. in economics from Louisiana State University. Louisa also has earned the Chartered Financial Analyst® designation.

CFA® and Chartered Financial Analyst® are registered trademarks owned by CFA Institute.

James Tzitzouris, Ph.D.

James Tzitzouris is the director of Research, Retirement in the Multi-Asset Division. He is a member of the Multi-Asset Steering Committee and a vice president of both the Retirement Funds and Target Funds series. Jim is a vice president of T. Rowe Price Group, Inc., and T. Rowe Price Associates, Inc.

Jim's investment experience began in 1999 when he joined T. Rowe Price, beginning in the Fixed Income Division. He has been actively involved with the Investment Fellowship program at T. Rowe Price since its inception in 2006, serving as a rotational manager, interviewer, and key advisor.

Jim earned an S.B. in mathematics from the Massachusetts Institute of Technology and an M.S.E. and a Ph.D. in mathematical sciences from Johns Hopkins University. In addition to his responsibilities at T. Rowe Price, he held an appointment as lecturer in the Department of Applied Math and Statistics in the Whiting School of Engineering at Johns Hopkins University, where he regularly taught classes in mathematical finance and quantitative investments. He also helped to design the curriculum and degree requirements for the master's degree in mathematical finance offered by that department.

Kobby Aboagye

is a quantitative investment analyst at T. Rowe Price

in Baltimore, MD. kobby.aboagye@troweprice

.com

Sébastien Page

is head of global multi- asset and chief investment officer at T. Rowe Price

in Baltimore, MD. sebastien.page@

troweprice.com

Louisa Schafer

is a senior quantitative investment analyst

at T. Rowe Price in Baltimore, MD. louisa.schafer@troweprice

.com

James Tzitzouris

is director of research, retirement at T. Rowe Price in Baltimore, MD. jim.tzitzouris@troweprice

.com

Personalized Target-Date Funds

Kobby Aboagye, Sébastien Page, Louisa Schafer, and James Tzitzouris

KEY FINDINGS

• The authors argue in defense of target-date funds and suggest several ways to improve upon them now that recordkeeping technology has evolved.
• A utility-based model expands upon traditional target-date funds, making the life-cycle investing strategy more dynamic and personalized.
• Analysis supports a substantial potential gain in risk-adjusted retirement spending from the suggested improvements, especially when including dynamic spending rules.

ABSTRACT

The simplicity and regulatory protection (when used as a default investment) of target-date funds (TDFs) offer advantages to both employers and employees saving for retirement in defined-contribution plans. But despite their commercial success, TDFs have faced criticism. The authors review the attacks on TDFs, argue in defense of them, and build a model to accommodate important extensions to traditional TDFs: further personalization and dynamic allocations and spending. They estimate that the benefits of these improvements average an additional 5%-6% in annual, risk-adjusted spending.

Target-date funds (TDFs) may be the most successful investment product of all time. While many academics and practitioners love to hate them, there is no doubt that their simplicity and regulatory protection provide advantages to

employers (plan sponsors) and employees who are saving for retirement (plan par- ticipants). In 2000, total assets under management (AUM) invested in TDFs stood at $5 billion. As of 2021, TDF AUM had reached a staggering $3.27 trillion.1

In the United States, as defined-contribution plans have grown, we have given individuals responsibility for portfolio construction. Individuals are presented with a menu of investment options, and they must choose how much to allocate to stocks versus bonds. Then, within each asset class, they must choose how much to allocate between different strategies and subasset classes. These choices aren't easy to make for noninvestment professionals. Most people do not have the expertise required to make these investment choices. Would your surgeon ask you to perform surgery on yourself?

Most individuals do not make a choice. Those involved with defined-contribution plans in the United States know that inertia seems to be the most powerful force that

1This number includes trusts (CITs). Source: Morningstar, "2023 Target-Date Funds and CITs Land- scape," report: https://assets.contentstack.io/v3/assets/blt4eb669caa7dc65b2/blt879461b1430db de5/6442b988398bc14b3cffe380/Target_Date_Landscape.2023.pdf.

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Multi-Asset Special Issue 2024	The Journal of Portfolio Management  |  3

drives portfolio construction. The do-nothing, default option drives how individuals invest because they do not engage in the process.

For many years, the default was cash. But this default led to poor returns. If an individual has a long time horizon before retirement, it is hard to argue that cash is a good investment. In fact, it may be the worst choice. It is not even the "risk-free" choice, because cash needs to be reinvested along the way, at uncertain rates.2 We cannot predict the cumulative return for cash over multi-year horizons. In theory, the "safest choice" is a long, inflation-protected bond that delivers cash flows that match what we want to spend in retirement. Such an asset does not exist, but long bonds are typically used as a proxy. Long bonds are also a suboptimal choice, however, when individuals are underfunded (and they cannot afford risk-free).

Stocks can deliver a higher compound rate of return over time, but they also expose investors to significant short-term losses. How much should individuals allocate to stocks throughout their life cycle? This key portfolio construction decision affects investment outcomes perhaps more than any other decision.

Following the Pension Protection Act of 2006 (PPA), plan sponsors can automatically enroll employees for monthly contributions to their retirement plan. They can use a multi-asset fund as the default option. These measures make inertia work in favor of employees. They can opt-out or change their asset allocation, but if they do nothing (which is often the case), they automatically get exposure to a diversified portfolio with a healthy allocation to stocks. TDFs are a popular default option in great part because they are designated by the Department of Labor as one of the so-called qualified default investment alternatives (QDIAs). TDFs starts with a high allocation to stocks when the employee (or "plan participant" in defined-contribution jargon) is early in their career and gradually shift from stocks to bonds as they approach retirement (the glide path). Participants are assigned a TDF vintage based on their retirement date.

TDFS HAVE DETRACTORS

Despite (or perhaps because of) their commercial success, arrows have been shot at TDFs. The four most common critiques are the following:

1. The downward glide path is not optimal.
2. TDFs are not well diversified.
3. Adaptive strategies deliver better outcomes.
4. TDFs are not personalized.

The Downward Glide Path Is Not Optimal

Detractors across academia and industry argue that there are better ways than a TDF to invest across one's life cycle. Credible research suggests that an inverse glide path-in which the allocation to stocks rises rather than decreases as the employee approaches retirement-produces better outcomes than traditional, downward-sloping glide paths (see Arnott, Sherrerd, and Wu 2013; Estrada 2014). Other research suggests that glide paths should have flexible shapes, including a peak, with rising then declining allocation to stocks (Mindlin 2016); a trough, with declining then rising allocation to stocks in retirement (Pfau and Kitces 2013; Pfau 2017); or a flat section in retirement (Cohen 2010). In an article with the provocative title "The False Promise

2For an intuitive description of how to think about the risk-free rate as a function of your time horizon, see Allison Schrager's book An Economist Walks Into a Brothel and Other Unexpected Places to Understand Risk (Penguin Random House, 2019).

4|  Personalized Target-Date Funds	Multi-Asset Special Issue 2024

of Target Date Funds," Esch and Michaud (2014) even suggest that maintaining a fixed stock/bond allocation throughout the life cycle may be a superior to any glide path. The limit appears to be one's imagination when it comes evaluating glide path success and ipso facto what an optimal glide path should look like.

TDFs Are Not Well Diversified

Others maintain that most TDFs deliver too much equity risk (Dhillon, Ilmanen, and Liew 2016). Private equity firms continue to lobby to get into 401(k) plans, arguing they can provide the needed diversification (Schoeff 2020; Ramsey 2022), although some might take issue with this claim (see, for example, Page 2020). Detractors often shoot this "too much equity risk" arrow at TDFs following market crashes. Following the financial crisis of 2008-2009, the SEC held public hearings on TDFs, asking, essentially, whether they were too risky.3 Zvi Bodie (2021) argues that stocks are risk- ier in the long run than most people think. He claims that the "fallacy" of time diversification has led to excessive risk-taking in defined-contribution and defined-benefit plans. Bodie has even gone so far as to suggest that most individuals should ignore the siren call of high stock returns and instead invest 100% of their retirement savings in a TIPS portfolio, to safely match their retirement spending goal. For unfunded individuals who would otherwise rely on stock returns for wealth accumulation, this type of advice must lead to larger contributions or lower expectations.

Adaptive Strategies Deliver Better Outcomes

The third critique targets the precooked-that is, deterministic-nature of the glide path. Shouldn't we adjust the glide path to the market environment?4 Or, a related question, shouldn't asset allocation change as a function of the individual's financial position? Yoon (2010) suggests a dynamic strategy that responds to prevailing market risks. Sharpe (2010) proposes an adaptive strategy that reacts to the relative size of the stock and bond markets in the market portfolio. Basu, Byrne, and Drew (2011) adjust the asset mix based on cumulative portfolio performance relative to a set target. They conclude that "the dynamic allocation strategies exhibit almost stochastic dominance over strategies that unidirectionally switch assets without consideration of portfolio performance." Kobor and Muralidhar (2020) propose an extension of this strategy, focusing on funded status relative to a retirement income goal. Similarly, Forsyth and Vetzal (2018) introduce adaptive strategies that consider the individual's accumulated wealth and argue that "investors are not being well served by the strategies currently dominating the marketplace."

TDFs Are Not Personalized (Enough)

While they automatically adjust portfolio risk exposure based on the individual's age (or more precisely, the individual's time to and since retirement), detractors argue that within a given age cohort, TDFs should be further personalized (see, for example, Tang and Lin 2015; Janssen, Kramer, and Boender 2013; Drew and West 2021; Duarte et al. 2022). It is common knowledge that an individual's risk tolerance depends on a lot more than their age. Turner and Klein (2021) provide a succinct review of the

3 https://www.sec.gov/spotlight/targetdatefunds/targetdatefunds061809.pdf.

4To clarify, TDFs are "dynamic" in that the stock/bond mix changes over time. Also, many TDF managers implement tactical asset allocation around the glide path to take advantage of transitory relative valuation opportunities. But tactical decisions rarely deviate more than 5% or 10% from the target glide path.

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Multi-Asset Special Issue 2024	The Journal of Portfolio Management  |  5

literature on the importance of such factors as wealth, income, education, race, gender, and personality. There is even a strand of research that correlates hormone levels, such as testosterone and cortisol, to risk tolerance (Nofsinger, Patterson, and Shank 2018). But much of the needed data for personalization are not readily available. Individuals may find blood tests and personality tests somewhat invasive. More practically, Li and Webb (2012) focus on the participant data that are available to the employer. They introduce three additional data fields, beyond an individual's retirement date: salary, savings rate, and plan balance. The recordkeeper can provide these data; hence, engagement from the individual is not required. They conclude that such "semi-personalized TDFs generally outperform the one-size-fits-all fund by more closely matching an optimal portfolio."

Such arrows have been shot at TDFs from the ivory tower for over a decade, yet the giant is still standing. Detractors have been asking the following question: "Your product works in practice, but does it work in theory?" In the real world, one in which employees are not investment professionals and employers prefer to focus on their core business, simplicity confers tremendous advantages to TDFs.

IN DEFENSE OF TDFS

The benefits of TDFs become more obvious if we compare them with the real-world alternative of self-allocated portfolios in 401(k) plans, rather than theoretically superior alternatives. Mitchell and Utkus (2022) explain that the adoption of TDFs has led individuals to hold more age-appropriate portfolios. They show that many non-TDF investors hold too little in stocks when they start their career or too much at retirement. There is a debate on the optimal shape of the glide path, but it is hard to argue that an 80% or higher allocation to cash for someone in their early 20s or an 80% or higher stocks allocation for someone near retirement are appropriate allocations. Yet one record- keeper confirmed that such allocations are surprisingly frequent for individuals who do not use TDFs. The same recordkeeper also explained that non-TDF investors are more likely to panic and sell stocks at the bottom rather than stay the course during a crisis.5 Mitchell and Utkus add that TDFs have "curtailed cash and company stock holdings and reduced idiosyncratic risk" and conclude that "the adoption of low-costtarget-date funds enhance retirement wealth by as much as 50% over a 30-year horizon."

Regarding the debate on the shape of the glide path, it's common sense that individuals become more risk-averse as they approach retirement. With decades to go until retirement, most young professionals are willing to tolerate the month-to-month volatility of stocks in exchange for a higher long-term expected return. But as they approach retirement, they become less willing to put money at risk. Large losses could mean a delayed retirement. Besides, those approaching retirement have larger account balances, such that a given percentage loss means a larger dollar loss than earlier in their life cycle.

Beyond common sense, the downward-sloping glide path stands on solid theoretical foundations. Decades of research on utility theory and hundreds of articles on life-cycle investing support the downward-slop glide path, going as far back as Samuelson (1969) and Merton (1969). The implications of Samuelson (1969) are reinforced two decades later in Samuelson (1989):

The capitalized (present discounted) value of [my] human capital declines as I age and as my time to retirement shrinks. Therefore, if I hold equities in constant fraction of my total wealth-defined as portfolio wealth plus

5Source: T. Rowe Price. Data available upon request.

6|  Personalized Target-Date Funds	Multi-Asset Special Issue 2024

human capital-my observed fraction in equities will be seen to decline rationally with age.

Merton (1971) also concludes that the allocation to stocks should be high when human capital is abundant (i.e., early in life) and that it should decrease over time. Here, the assumption is that human capital is bond-like rather than equity-like, which can be debated (Page and Tzitzouris 2016). But ultimately, almost all serious life-cycle research points to the downward-sloping glide path. Researchers have kicked the tires on its theoretical foundations in a variety of ways, for example, introducing nuances such as habit formation (Lax 2002), flexible labor supply (Gomes, Kotlikoff, and Viciera 2008), international evidence from 17 countries (Pfau 2011), advances in stochastic optimal control (Konicz, Karolina, and Weissensteiner 2016), investor behavior (Fagereng, Gottlieb, and Guiso 2017), and the inclusion of annuities (Shoven and Walton 2023). Despite all this tire-kicking, the downward-sloping glide path still stands as theoretically superior to alternative strategies proposed by TDF detractors, such as the upward-sloping glide path. And, as mentioned, it dominates all other alternatives in terms of adoption by plan sponsors. One might argue that most plan sponsors adopt a downward-sloping glide path merely because of regulatory considerations. Plan sponsors do not want to stray from regulatory guidance and standard industry practice because they fear lawsuits from participants. However, recent research shows self-directed participants' risk aversion increases with age as well (Egan, MacKay, and Yang 2023). Hence, the downward-sloping glide path occurs naturally, "in the wild."

As for the argument that TDFs aren't well diversified, it depends on the provider, but a quick look at publicly available information from various TDF managers reveals that these portfolio are indeed well diversified across domestic and international markets, style and size (value and growth, small and large), and credit asset classes (core bonds, high yield, international bonds).The only asset classes that are not typically included are illiquid alternatives, such as private equity, due to liquidity constraints on the defined-contribution plan platforms.

The related question as to whether equity risk is too high in TDFs is more difficult to debate because it also relates to risk tolerance and, ultimately, to how the life-cycle investing model is constructed. The credible research that supports a downward-sloping glide path also generally supports a high allocation to stocks or the "risky asset," especially early in one's career. The reality of capital markets is that equity risk is difficult to diversify away (see, for example, Page 2020). And the reality of life-cycle investing is that most individuals need a healthy compound rate of return because they either do not earn or save enough (or both) to meet their retirement goals.

OUR CONTRIBUTION: AN ADAPTIVE AND PERSONALIZED

TDF STRATEGY

While the optimality of the downward glide path and the level of diversification in TDFs can be debated, prior research offers more of a consensus that adaptive and personalized strategies can improve the investor's lifetime experience. We propose to extend TDFs by adding these two features and thereby address critiques #3 and #4 from the earlier discussion. Recent advances in personalized accounts-so-called managed accounts-on 401k platforms make these improvements possible.

Like Li and Webb (2012), our model uses data from the recordkeeper, thereby eliminating the need for the individual to engage in the process (401(k) participants have extremely low engagement levels). Our personalized TDFs can be used as a

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Multi-Asset Special Issue 2024	The Journal of Portfolio Management | 7

qualified default, like traditional TDFs. And for participants willing to engage, our model accepts detailed user inputs, for example, on their risk tolerance and any assets they might own outside of the 401(k), including their spouse's assets.

Our key contribution is to introduce a novel, multi-attribute utility function that incorporates the individual's aversion to deplete wealth. To set the stage, let us ask the most basic of questions: What goal are we trying to achieve when we design a TDF strategy?

The answer is far from obvious. "To make the most money" ignores risk. "To maximize my pot of money at retirement, while controlling for risk" ignores what happens after the investor retires. Besides, how should we define "risk"? Is it the month-to-month volatility of the investment portfolio? Or is it the uncertainty around the size of the pot of money the individual can retire with? Or, perhaps, should it be the probability of not achieving the desired consumption level in retirement? But then, how do we account for consumption during the accumulation phase? No wonder Nobel laureate William Sharpe described life-cycle investing as the "nastiest, hardest problem in fi nance."6

Ultimately, most investors want to maximize risk-adjusted consumption over their life cycle, from accumulation to decumulation … to death. Most of the studies we mentioned previously focus on this goal, starting with Merton (1969). In such classical utility functions, wealth is represented by a terminal value, what's "leftover" for bequest motives. Our innovation is to also account for the fact that most individuals also derive utility (or satisfaction or security) merely from holding wealth along their journey. Consider how most retirees want to live off the income generated by their retirement savings, without touching the principal. Their desire to hold on to wealth often goes beyond lifetime consumption considerations, or the desire to leave an inheritance. They display an explicit reluctance to deplete wealth, even if that means consuming less. Hence, in our model, wealth provides intrinsic utility, beyond its traditional interpretation as the present value of future consumption.

What Is The Individual's Goal?

Our study involves a set of models and simulations. To generate an adaptive and personalized glide path, we solve for the optimal allocation to stocks and bonds that the individual should hold at any point in time. We simultaneously optimize consumption decisions, which allows us to provide spending advice, should it be needed.

Here, we begin with our answer to the question: What goal is the individual is trying to achieve? In any period indexed by t = 1, …, T, we denote an investor's investment balance by bt, current period income by yt, consumption by ct, and allocation to equity by wt. We use a multi-attribute utility function. We optimize the individual's lifetime experience based on these basic preferences:

1. The individual wants more lifetime consumption,
2. She wants to hold more wealth along the way,
3. She wants less risk around each of these objectives.

For some relative risk aversion coeffi cient γ > 1 and depletion aversion coeffi cient

• ∈ (0,1), our single-period utility function is given by the following:7

	(c	b	y	)1 − γ − 1
u ct , b yt =		t	t		(1)
		1 − γ

1. https://www.benefitspro.com/2017/06/09/tackling-nastiest-hardest-problem-in-finance/?slreturn=20240016110306.
2. This utility function was originally derived by James A. Tzitzouris; see SSRN:https://papers.ssrn
   .com/sol3/papers.cfm?abstract_id=4693176.

8 | Personalized Target-Date Funds	Multi-Asset Special Issue 2024

This function is a composition of a constant relative risk aversion utility function (CRRA) and a Cobb-Douglas production function.

Our goal is to maximize the discounted expected aggregate utility over the investor's lifetime. To that end, we seek to maximize

(2)

where

bt+1 = Rt · (bt + yt − ct),

yt+1 = Gt · yt,

subject to the following constraints:

0	≤ wt,	No short sales
wt ≤ 1,	No leverage
0	≤ ct,	Consumption is a positive number
ct ≤ bt + yt	Individual cannot consume more than their account balance

We include the discount factor β ∈ [0,1] and the probability of being alive at the beginning of period t, denoted by pt ∈ [0,1]. We use standard mortality probabilities from the Society of Actuaries.8 T is the last year on the mortality tables (120th year).

It is important to distinguish the behavioral discount factor β from a traditional fi nancial discount factor. The behavioral discount factor refl ects an individual's preference to consume more in the present rather than defer consumption to the future. In this sense, it refl ects an investor's impatience. In contrast, a fi nancial discount factor refl ects the interest or growth rate of an alternative investment. In this case, we are not discounting future cash fl ows but, rather, expected utility-future satisfaction. We assume stochastic processes denoted by Rtb, and Rts describe the real returns of

investment-grade bonds and the broad stock market, respectively, with; yt denotes the real income (salary) received at the beginning of the period; and Gt is the stochastic real growth factor that governs the evolution of income between the current time period and the next.

The subscripts ct and wt under the Max operator indicate that we are solving for the asset allocation and consumption decisions simultaneously. Our framework applies to the individual's entire lifetime, across their working years (accumulation) and retirement (decumulation). The challenge is that asset allocation and consumption are multi-stage decisions. The decisions the individual makes now will have an impact on their future decisions. Such problems must be solved by working backwards, from the future to the present. Hence, we use the Bellman equation to solve Equation (2), as shown in Appendix A.

While computationally intensive, this framework is straightforward: The individual earns a salary, saves part of it, and spends the rest. Their retirement account balance grows with accumulated savings and market returns. In retirement, the individual enters the so-called "decumulation" phase. Their salary goes to zero, but they earn other sources of income, such as pensions and Social Security. From a mathematical modeling point of view, there is nothing special about reaching retirement age.

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8 This mortality information is available online: www.soa.org/resources/experience-studies/2014/ research-2014-rp/.