As retirement research has evolved, so too have ideas about what constitutes an optimal retirement strategy.

In fact, in a recent paper, researchers Patrick Collins and Francois Gadenne note that the three generally accepted retirement modeling approaches each have their own shape — from the curve of the efficient frontier, to the triangle of the Maslow-style hierarchy of retirement needs, to the rectangle of the household balance sheet with its assets and liabilities.

While each of the different forms may be shaped, as it were, by different recommendations, it’s not entirely clear which is best — or if we can even speak honestly about such a possibility. That may be just as well, as the best approach for retirement planning may incorporate all three shapes.

While his original paper was simply called Portfolio Selection, Harry Markowitz’s 1952 article in the Journal of Finance ultimately became the foundation of portfolio design, aptly dubbed Modern Portfolio Theory. Its key insight was that the investments of a portfolio shouldn’t be selected based solely on their individual return potential. Instead, effective portfolio design considers both the expected return and the risk — i.e., volatility — of the investment. Furthermore, it prescribed that a portfolio should be evaluated based on the overall risk of the entire portfolio, not just its component parts.

This Mean Variance Optimization approach to designing a portfolio was originally created to select investments on an annual basis, predicated on annual expected return and volatility metrics. However, it was ultimately adopted as an approach to fund longer-term goals such as retirement.

After all, if the MVO approach could effectively minimize risk for a given level of expected return, or maximize return for a given level of risk tolerance, then in theory buying and holding that portfolio for the long run should deliver the best path to achieving the retirement goal. The investor simply had to constrain the portfolio to a level of overall risk that was comfortable — that is, to pick a portfolio on the efficient frontier that was consistent with risk tolerance.

The shape of your retirement planning approach dramatically impacts the lens through which you evaluate what is a good or bad retirement strategy.

However, while the MPT approach was relatively straightforward to apply to a single portfolio pursuing a single goal — ideally over a single time horizon — it was more problematic in the context of a broad range of planning goals, each of which might have not only different time horizons and different comfort levels with risk, but also outright different priorities.

For instance, funding college for children in middle school might be a high-priority intermediate-term goal; funding retirement is a high-priority but longer-term goal; and funding a vacation home is another longer-term goal, but one with a much lower priority. Yet Modern Portfolio Theory didn’t give an effective means to construct a portfolio that covered each of these separate goals, with their distinct time horizons and varying levels of prioritization.

Thus emerged the concept of goals-based planning and the associated goals-based portfolios, where the portfolio in the aggregate may be comprised of mini-portfolios or buckets, each of which are tied to a particular goal. The investment allocations are set as appropriate for each particular goal and time horizon, and are kept consistent with the tolerance of risk for each specific goal.

Accordingly, essential expenses — the food, clothing and shelter kinds of needs — might be covered with a guaranteed income stream from an immediate annuity, while more flexible discretionary expenses might be invested via a growth portfolio. Meanwhile, short-to-intermediate-term needs might be invested with a series of laddered bonds that produce the requisite cash flows as needed.

Yet the problem with the goals-based planning approach is that it starts with the spending goal in mind, and then works backwards to the portfolio or other alternative product solution. An alternative approach may be to objectively consider the balance between available assets and spending goals — not to mention other current and future liabilities — to decide whether the best path forward is to adjust the portfolio to fit the goal, or to adjust the goal to fit the portfolio.

In other words, some retirement or other goals can’t be effectively funded, regardless of the portfolio, because the goal itself just isn’t economically feasible given the available assets. And for others, available assets may overfund the goal such that the investor could afford to pick new, higher goals. None of this is necessarily captured in an approach that simply focuses on allocating investment assets to match goals.

Instead, the necessary retirement model creates a household balance sheet that fully captures all current and future assets, along with current and future spending liabilities, to first determine whether the goals are feasible, and whether the household overall is overfunded, underfunded or right on track.

To the extent that the household is over- or underfunded, adjustments can then be made to the asset side of the balance sheet by adjusting the portfolio, or to the liability side of the balance sheet by changing the spending goals. This model takes into account the value of all current and future assets — from portfolio assets and future savings, to the remaining human capital of future years of work, and illiquid capital like the value of Social Security benefits along with all liabilities from current liabilities like credit card and mortgage debt. The future liability of spending goals themselves are calculated on a present value basis. Thus, the investor gets a pure, apples-to-apples comparison of whether the household is adequately funded or not.

In their recent paper The Shapes of Retirement Planning: Are You a Curve, a Triangle, or a Rectangle?, Collins and Gadenne suggest that the distinctions between these three models matter. Their different philosophical approaches mean that each model may take substantively similar inputs regarding the client’s goals and circumstances, but come up with different outputs and recommendations.

Viewed another way, each has its own shape that becomes the dominant lens through which retirement planning is viewed: The first is a curve based on the efficient frontier, the second a triangle akin to Maslow’s hierarchy of needs but applied in the context of a retirement portfolio, and the third is a rectangle, modeling the assets-and-liabilities ledger of a household balance sheet.

The fundamental challenge to these different shapes of retirement planning is that, in essence, they’re different models to analyze the possibilities, priorities and optimal portfolios for retirement. They all take in various inputs about the client’s retirement goals and circumstances to produce some outputs, but the way those inputs are analyzed will differ — such that the same inputs can produce different outputs and recommendations.

For instance, under the MPT framework, finding the right portfolio is about matching the portfolio that best fits the required return for the client’s goal, without violating his/her risk tolerance.

Yet Kahneman and Tversky’s work on prospect theory finds that people’s preferences regarding risk are impacted by where their finances stand when it comes to their goals in the first place. In other words, we experience more negative feelings about a loss than we do positive feelings about a gain, and whether something is a loss or a gain depends on where we financially stand at the moment.

Thus, a prospective retiree who has no wealth may look aspirationally toward accumulating $1 million for retirement, while someone who already has $1.2 million would be highly distressed by going down to $1 million — despite the fact that they can both afford the same retirement at that point. At the same time, the prospective retiree with no wealth who accumulates $1 million experiences more happiness than the retiree who already has $1.2 million and accumulates another $1 million to grow the portfolio to $2.2 million.

These distinctions matter because it suggests the best portfolio with the traditional curve approach is simply the one that maximizes the risk-return tradeoff for a given level of risk. At the same time, under the triangle approach, it may be OK to invest more conservatively after achieving enough to cover the goals — and ensure that the retiree doesn’t go backward. Viewed another way, the triangle approach recognizes that maximizing risk-adjusted return is not the sole goal, as it is with the curve approach.

Similarly, the MPT curve approach has limited tools to evaluate the trade-offs between using guaranteed income streams like a lifetime immediate annuity in lieu of a risk-based portfolio altogether. It takes a triangle approach to recognize that it might be a good idea to satisfy certain essential needs with guaranteed income, and then plan to fund discretionary expenses by building a riskier portfolio on top.

In turn, even a goals-based triangle approach struggles to recognize and plan around all the assets that actually exist on the household balance sheet. For instance, the decision to delay Social Security can be especially effective at stabilizing the household balance sheet against low market returns or high inflation. Those factors benefit the delay of Social Security, even as they adversely affect other parts of the household balance sheet. That said, a goals-based framework has no effective tools to evaluate such trade-offs.

In contrast, with the rectangle approach, the household balance sheet’s Social Security asset would rise in value as inflation increases, helping offset the potential decline in the value of other fixed-income assets and the rise in the cost of retirement. More generally, it takes a household balance sheet approach, where all assets and liabilities are discounted to a consistent present value basis, to truly understand whether the household is effectively funded in the first place, given all the different income and expense cash flows that may occur at different times throughout retirement.

And at the most basic level, even defining what is a safe investment will vary depending on the approach. After all, safe in the context of the curve approach — the efficient frontier of MPT — is simply a portfolio that is 100% cash. But with the triangle approach, safe would take the form of a lifetime immediate annuity that covers all the essential expenses of retirement. And with a rectangle approach, safe would be a laddered TIPS portfolio that immunizes all future spending obligations against any changes in inflation or interest rates.

The bottom line: The shape of your retirement planning approach dramatically impacts the lens through which you evaluate what is a good or bad retirement strategy.

Given the varying retirement planning recommendations and conclusions depending on the curve, triangle or rectangle shape to the analysis, what is the optimal shape of retirement planning?

Collins and Gadenne suggest that the rectangle approach, utilizing the household balance sheet framework, is the most comprehensive approach that allows for effective procedural prudence in the retirement planning process — an important issue in a fiduciary future. Notably, Gadenne is the executive director of the Retirement Income Industry Association, which has built the curriculum of its own Retirement Management Analyst designation around the household balance sheet approach. Thus, Gadenne has some incentive to promote the rectangle approach. Though obviously, if the rectangle approach really is the most comprehensive and effective, that simply means the RMA has built around the optimal approach.

That being said, it’s not entirely clear that the rectangle approach really is the most effective to formulate retirement recommendations — at least not on its own. For instance, in calculating the household balance sheet, where all future cash inflows and outflows are discounted back to their present value, the results can be highly sensitive to the discount rate that is used in those time-value-of-money calculations. How funded the household is can vary significantly, with a higher discount rate generally improving funded-ness, as it implicitly increases assumed growth rates on assets and reduces the discounted cost of future liabilities. Even so, nothing on the household balance sheet directly conveys the greater risk that is inherent in assuming a higher discount rate.

More generally, there’s still very little agreement about what an appropriate discount rate may be for analyzing various retirement strategies. This means that two advisors using the same rectangle approach may come up with substantively different conclusions and recommendations about whether the prospective retiree is on track.

Similarly, there’s nothing about showing multiple goals on a household balance sheet that inherently prioritizes one goal over the other. The rectangle approach assumes that if the present value of all assets doesn’t add up to the present value of all liabilities, then the household is underfunded. But in the real world, if a prospective retiree doesn’t have enough money to retire and achieve all of their goals, saving more or working longer to shore up the asset shortfall aren’t the only answers.

The retiree can also choose to settle for less, selectively eliminating lower-priority goals. He may, for example, retire now but with a plan to take fewer vacations. He may rent instead of own a second vacation home, or downsize the retirement home and the associated cost of living. The rectangle approach is helpful to reflect if the current goal is feasible, but it is a weak framework for prioritizing which goals to cut.

And once the goals are selected and funded, it’s still necessary to actually allocate the assets to fund the plan, which entails some investment decisions and trade-offs. In this case, the rectangle approach would imply a form of asset-liability matching — for example, liability-driven investing. To the extent a portfolio is used even if just for certain long-term goals, at some point an MPT-style approach still remains relevant to allocate the diversified portfolio. In other words, the rectangle approach still doesn’t eliminate the need for the curve approach; it just recognizes that the curve should be applied to allocate the portfolio at the end of the process.

Ultimately, the rectangle, triangle and curve approaches all offer relevant contributions to the retirement planning process. The rectangle may help determine whether the plan is feasible and what’s possible, but the triangle approach is better for actually prioritizing goals. Meanwhile, the curve is still relevant when it comes time for portfolio implementation.

At a minimum though, Collins and Gadenne’s shape approach to retirement is an interesting way to think about different philosophical views and different modeling approaches when it comes to retirement planning.

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