Reducing the Cost of Implementation in Goal-Based Investing With an Integrated Multi-Period Approach

In the rapidly changing world, capital markets continue to face new uncertainties and pressures. But there are also opportunities for long-term investors who currently lean on time-tested investment principles—for example, a diversified mix of investments appropriate for their time horizon and risk tolerance—to consider the next generation of asset allocation strategies. Here is our newest article in a series about multi-horizon strategic asset allocation.

Investment strategies to help individuals achieve their financial goals typically change over the years as priorities, timeframes, and risk tolerance evolve. Likewise, the academic thinking behind optimal investment strategies has continued to evolve over the past several decades.

In this article, we explore a relatively new approach to goal-based investing (GBI). The premise is that instead of building a customized mix of investments for each financial goal among several (i.e., multiple portfolios), it could be more effective and could cost less to build one investment portfolio that supports multiple financial goals.

Diversification, time horizon, and risk tolerance remain factored in—along with an annual review to rebalance the portfolio and stay aligned with an investor’s priorities and target asset allocation.

The Evolution of Goal-Based Investing

Historically, a traditional long-term investment approach assumes specific returns on investments over time, possibly with respect to benchmarks such as the S&P 500 Index (equities) or the ICE BofA U.S. Broad Market Index (fixed income), for example.

An approach introduced in 1952 is Nobel Prize winner Harry Markowitz's Modern Portfolio Theory (MPT), in which a portfolio could include high risk/high reward and low risk/low reward investment selections, with risk expressed as volatility of investment returns.

An extension of this approach involves analyzing multiple timeframes to achieve several financial goals—what we call multi-period analysis in this article. It incorporates:

• Annual rebalancing of the investments back to the target allocations across equities, bonds, cash, and alternative investments.

• Dynamic strategies that account for market conditions changing over time, expressed in CMAs (capital market assumptions).

• Notions of risk, such as maximum drawdown (i.e., maximum estimated loss in a portfolio) that incorporate the full evolution of wealth over an investor’s collective time frame for all goals rather than only dispersion for one goal at a single time point; cf. our previous insight articles for details on those points.

Goal-based investing is a relatively new investment approach in wealth management. It emphasizes investing to achieve specific financial goals, each of which has a unique time horizon and priority. This could include, for example, short- and long-term goals to pay for a house, new car, vacations, college, and retirement. Achievement is conditional on accumulating a specific amount of money for each of the goals by specific future times.

In contrast to MPT, GBI risk is measured in terms of the probability of failure to achieve the goals. In other words, high-priority goals require a higher probability of financial success. Thus, one of the main differences between MPT and GBI is measuring risk as shortfall probability as opposed to volatility of portfolio returns, respectively.

GBI’s view of risk is a key ingredient for the Behavioral Portfolio Theory (BPT) that Hersh Shefrin and Meir Statman introduced in 2000 and is the basis for Goals-Based Portfolio Theory. BPT integrates an idea from Nobel Prize-winning Behavioral Economist Richard Thaler in 1985 that individuals are prone to subjectively dividing their money into separate “mental accounts.” Each mental account has its purpose, objective, risk tolerance, and monetary and emotional value. Mental-account bias can lead to ineffective financial decisions, such as accumulating cash in a low-interest savings account while maintaining balances on high-interest credit cards.

Single- vs. Multi-Period Models: Optimization for Goal Planning

A traditional investment approach typically assumes a buy-and-hold strategy for the entire amount of time needed to achieve the financial goals. Sanjiv Das, Harry Markowitz, Jonathan Scheid, and Meir Statman apply in 2010 mean-variance theory to investment models with a normal range of expected returns (i.e., Gaussian returns) but without annual rebalancing back to the allocation targets.

They also factor in the mental accounts approach: A mean-variance optimal portfolio is constructed for each goal. Given the assumptions of single-period Gaussian returns, this is possible because the probability of success is expressed in terms of an investment strategy’s mean and volatility.

Single-period models assume one rate of return for the entire timeframe, without intermediate changes. However, in economic cycles such as the past several quarters with downward market pressure and persistent inflation in the U.S., investors might expect a recession in the coming year, followed by a recovery period. In such circumstances, single-period analysis misses material intermediate information and is thus suboptimal.

On the other hand, dynamic asset allocation may be an optimal investment strategy given it uses a multi-period model (i.e., an annual portfolio review with rebalancing). It also accounts for changes over time in its capital market assumptions.

Multi-period approaches naturally yield dynamic strategies that may perform better than single-period approaches (cf. insight article 3). Moreover, multi-period models explicitly incorporate time in investment decisions. Time being a key dimension in any goal-based planning.

In the following section, we show how to concurrently analyze time horizons for several financial goals using multi-period optimization (MPO). This leads to interesting results about the cost to achieve all goals through their respective dynamic strategies.

Cost to Attain Multiple Goals Via Goal-Based Investing

To illustrate the difference between the separate mental accounts approach and the dynamic single-account approach, further below we considered two separate goals with different priorities and different time horizons.

In addition to identifying the specific goals and their priorities, GBI frameworks encompass two main analysis steps, namely the identification of the suitable investment universe and the identification of suitable decisions/strategies in terms of how to allocate to these separate investments.

We assume that identification of the suitable investment universe is already accomplished.

To this end, for the examples we have selected three investments with distinctive characteristics, namely Low Risk (LR), Medium Risk (MR), and High Risk (HR) investments. We also noted our assumptions for average annualized returns in Figure 1.

In terms of volatility and correlations, we assume a constant covariance throughout time, although changing covariances could be easily accommodated. (Covariance is the directional movement between the returns of two assets.) We also set the volatility of LR, MR, and HR at 9%, 13%, and 33% on an annual basis, respectively, with positive correlation between the different investment vehicles (i.e., returns move together rather than inversely from one another).

Optimal Strategies and Cost of Funding Goals

For each approach below, we:

• Determine the cost of funding—the minimal initial capital sufficient to achieve each goal (i.e., separate accounts approach) and all goals (i.e., integrated approach) with the prescribed certainty

• Identify optimal trading strategies to achieve goals with the minimal initial capital

• Use a scenario-based, multi-period optimization framework like in our Multi-Period Portfolio Optimization white paper.

We analyze different approaches using optimization over admissible strategies that respect the following realistic constraints:

• In any rebalancing periods, investment in the high-risk portfolio shall be no more than 30% of the individual’s total investment.

• To prevent high rebalancing costs, we limit the turnover in each future rebalancing period to no more than 20% of the total investment, as measured against the previous rebalancing period.

Separate Mental Accounts Approach

Using Shefrin’s and Statman’s Behavioral Portfolio Theory for both goals in Table 1, each goal is supported with its own separately managed investment portfolio.

The house goal is achievable with initial capital of $476,280 (95% of the total required capital to fund the goal). As illustrated in Figure 2, there is gradually de-risking since the investment proportion in the low-risk portfolio increases over time. This is explained by the lack of utility for any remaining portfolio balance above the target level for the goal. This results in prioritizing wealth protection towards the end of the time horizon.

The car goal is achievable with initial capital of $126,500 (63% of the total required capital to fund the goal). This is due to the longer time horizon (10 years) and the lower probability (70%) required to achieve the goal. As illustrated in Figure 3, the phase with higher risk is relatively long (first seven years), followed by de-risking in the last three years.

Overall, for both goals, the individual needs initial capital of $602,780, separated into two different accounts.

To understand where the separate mental accounts approach might be suboptimal compared to an integrated approach, let us have a closer look at the value of investments in two disjoint events: the $500,000 required for the house goal is not attained (20% probability) or the house goal is attained (80% probability).

Failure scenario: It turns out that the expected portfolio value across all failure scenarios (20% probability) is $427,986, a shortage of slightly less than 15%.

Success scenario: On the other hand, the expected value across all success scenarios (80% probability) is $707,196, a 40% surplus.

It would have been mutually beneficial if both goals had been combined with one strategic investment portfolio. Here’s why:

• The value of allocations to the car goal throughout the first five years could have increased the likelihood of achieving the house goal

• The cash generated by the house goal (40% surplus) could have increased the likelihood of achieving the car goal

Integrated Accounts Approach

Here we assume a single investment strategy to achieve both goals from Table 1. To accommodate both goals in one multi-period framework, we must specify a rule for when to sacrifice the house goal to achieve the car goal. Continuing with our analysis, we assume that if the portfolio value is $500,000 at year five, the individual will buy the house.

The following results underline the advantage of integrating both goals with one investment strategy rather than the approach with separate accounts:

• To achieve both goals, $557,000 initial capital was sufficient. This is $45,780 less than needed with the separate accounts approach, an almost 7.5% improvement!

• An optimal strategy is shown in Figure 4. It is structurally like the one for the car goal in Figure 3 in that it starts with a period of higher risk followed by gradual de-risking toward the end. However, it differs from the overall strategy in the mental accounts approach in that the combination of the two mental accounts (Figures 2 and 3) results in de-risking beginning early, from year one. Such early de-risking is unnecessary since the additional cash for the car goal mitigates possible large losses and thus, in principle, serves as a de-risking component.

Conclusion

We compared two goal-based investing approaches for individual investors: a multiple mental accounts version and an integrated account version. In this study, both approaches make use of multi-period analysis, which is necessary to handle simultaneously any combination of different goals over different time horizons as in the latter approach.

The results indicate a substantial reduction of cost in advantage of the integrated version and different implementation strategies. A reason is that the multiple accounts approach overlooks correlations between different accounts and disregards any interaction between their corresponding strategies.

Chen Sui, CFA, Senior Principal Product Manager, Analytics and Trading Solutions, contributed to this article.

This blog post is for informational purposes only. The information contained in this blog post is not legal, tax, or investment advice. FactSet does not endorse or recommend any investments and assumes no liability for any consequence relating directly or indirectly to any action or inaction taken based on the information contained in this article.

References

FactSet’s White Papers and Insight articles:

1. Multi-Period Portfolio Optimization White Paper
2. Are You Incorporating Rebalancing In Your Strategic Asset Allocation Process? (January 27, 2022)
3. Stepping Into Dynamic Asset Allocation (March 21, 2022)
4. What is the Right Risk Measure for Long-Term Investors? (August 4, 2022)

S Das, H Markowitz, J Scheid, and M Statman (2010). “Portfolio Optimization with Mental Accounts.” Journal of Financial and Quantitative Analysis 45(2): 311-334

H Shefrin, and M Statman (2000). “Behavioral Portfolio Theory” Journal of Financial and Quantitative Analysis

35(2):127-151

R Thaler (1985). “Mental Accounting and Consumer Choice” Marketing Science 4(3):199-214