Optimizing Life-Cycle Strategies for Savings Plans

Introduction

Thoughtful, long-term savings plan solutions are crucial for individual investors because they may help address the pension gap created by state pension systems in many countries. In the developed world, state pension systems face structural challenges due to low birth rates over several decades, and the resulting demographic changes. To close the pension gap for individual investors, policymakers globally are promoting savings plan solutions through occupational and private pension schemes.

In the academic personal finance literature, LC strategies are considered one of the most favored investment strategies for these savings plans. Many practitioners, including asset managers and independent financial advisors (IFAs), also advocate for LC strategies in these solutions.

Typically, LC strategies share a common principle: young individual investors with a long investment horizon until their retirement date, and a relatively small amount of financial assets in their savings plan, compared to their future lifetime savings, tend to have a more “return-seeking” allocation in their savings plan accounts. Middle aged investors tend to have a more “balanced” allocation in their accounts. Finally, older investors, with a short investment horizon until their retirement date, and a substantial amount of financial assets, typically have a more “conservative” allocation in their accounts. The key question today, therefore, is how to develop a prudent LC strategy that reduces the risk-return profile of the allocation in savings plan solutions as the investor ages. This reduction aims to achieve the investors' goals and objectives, which, in most cases, means closing the pension gap.

Practitioners, such as asset managers, banks, and individual financial advisers, typically derive LC strategies via several steps. They begin with a single-period portfolio optimization approach, such as mean-variance optimization, to create several optimized portfolios. The risk-return profiles these portfolios range from a risk-reduced to a return-seeking positioning.

Next, they construct different LC strategies using an age-based risk-reduction strategy - referred to as a “Glide-Path” in this paper. A Glide-Path determines the transition from a return-seeking to a risk-reduced portfolio over time by allocating the investor’s savings plan assets into these optimized portfolios over time. According to their multi-period nature these LC strategies are then evaluated using Monte Carlo simulations by projecting the development of various representative savings plans into the future. Finally, the simulation results are used to determine the overall risk-return profiles of the LC strategies and to benchmark them against the objectives, goals, and risk-return profiles of the individual investors.

From discussions with other practitioners this approach has shown effective  and has served us and other practitioners well in the past. We refer to this method as the “select and benchmark” (SB) approach because it involves selecting optimized portfolios and Glide-Paths, as well as benchmarking the resulting LC strategies against the objectives, goals, and risk-return profiles of the individual investors. We will call LC strategies derived using the SB approach “SB-LC-strategies” in this report.

Today however - driven by technological progress, digitalization, and a substantial increase in computational power - more systematic approaches such as dynamic programming (DP) can be used to derive optimal investment strategies in a multi-period investment context – approaches that still align directly with the goals and objectives of their individual investors. In this DP approach, the goals and objectives of the individual investor become the objective function. Then, through an optimization process performed in a multi-period investment environment, an optimized investment strategy is derived that maximizes the objective function of the individual investor in question.

As we will see later, for well-established objective functions - such as a Constant Relative Risk Aversion (CRRA) utility - these optimized investment strategies also exhibit an age-based de-risking pattern in the allocation of the savings plan. Compared to the SB approach, this method has the advantage of directly deriving optimized strategies by solving the multi-period investment problem, rather than selecting LC strategies and benchmarking their behavior against the investor’s objectives. We refer to LC strategies derived using this approach as “DP-LC-strategies” in this document.

Savings plan solutions with LC strategies are implemented in target date funds, also known as life-cycle funds (Viceira, 2008), or in individualized account-based solutions. Target date funds allow for very efficient implementation of a savings plan solution: investors select a target date fund whose target date aligns with the estimated end of their savings period as closely as possible, and then simply purchase shares over this period. In an individual account-based solution, each investor has their own account, which needs to be administered, but tailoring the LC strategy to the objectives of the account owner, i.e., the individual investor, is also possible.

The target date funds solution has the advantage of an efficient implementation as a one-size-fits-all solution. However, it has the disadvantage of not being able to account for the individual objectives and risk-return preferences of the investor. Conversely, the account-based solutions offer the advantage of customization to individual needs but require more administrative effort.

Historically, the trade-off between these two implementation approaches has often fallen in favor of target date funds due to the ease of their implementation. However, due to the technological progress mentioned above - which has led to efficient account platforms, web-based front-end solutions, investment apps, and investment engines providing rule-based and customized investment strategies – our view is that the trade-off will increasingly favor individualized account-based solutions for new savings plan solutions. This is why banks and asset managers are offering individualized asset management (IAM) platforms to provide more bespoke investment solutions.

This paper is organized as follows. In Section One, we will present the SB and DP approaches. In Section Two, we compare these two approaches by applying them to the savings plan of an individual investor who intends to maximize the expected CRRA-utility derived from the final value of the savings plan at the plan’s end date. The last section concludes and provides an outlook.

1 / Concepts

In this chapter, we take a closer look into the SB and DP approaches for constructing LC strategies. We first note that financial regulators in many jurisdictions have established frameworks to classify individual investors based on their financial knowledge, capacity, and willingness to bear financial risks, resulting in an overall risk profile for each investor. And practitioners, such as banks, asset managers, and financial advisors, must develop savings plan solutions that adhere to the key principles of these regulatory frameworks.

Typically, during the development process, product providers use a version of the SB approach. This involves heuristic selection of the investment universe, investment constraints, and glide paths, followed by benchmarking the solution against the overall risk profile in one of the final steps.

Conversely, the DP approach directly translates the overall risk profiles and objectives into an objective function. Once the objective functions for an investor are determined, the optimized investment strategy for the savings plan solutions can be derived by solving the optimization problem.