###### A robust quantitative framework can help plan sponsors manage pension risk through glide path design.

#### Summary

- The most effective approach to de-risking a defined benefit plan is to formulate a precise glide path that imposes a discipline of adjusting asset allocation as the funding ratio of the plan improves.
- The challenge for a plan sponsor is to develop a glide path that is most suitable for the plan, given the specific nature of the plan and the plan sponsor’s risk tolerance in terms of funded status.
- A quantitative framework is essential for this type of analysis. This paper introduces the dynamic glide path equivalent of standard mean-variance optimization, which solves for glide paths rather than static allocations.

- This quantitative framework can be used to answer many kinds of questions. For example, it can help plan sponsors manage specific allocations to risk-seeking asset classes. We give two examples. The first relates to allocations to global high yield, which includes emerging markets debt and high-yield bonds.
- We show that a standard, stand-alone global high-yield mandate is not optimal. Instead, plan sponsors should ensure that the global high-yield allocation is hedged to the liability duration and that the investments are made within the context of strategies that allow for some tactical flexibility.
- The second example relates to illiquid assets such as real estate and private equity. We show that such allocations have a significant impact on glide path design.

#### Introduction

A glide path describes how a plan sponsor will change its asset allocation as the plan’s funding ratio evolves. Exhibit 1 shows a sample glide path. In this example, the plan sponsor can employ U.S. stocks and global high-yield debt as return‑seeking assets. U.S. long credit is used for liability matching, with long governments providing an additional source of duration as well as a hedge against equity downside risk. Glide paths are assumed to be “one way,” i.e., there is no re-risking if the plan’s funded status falls.

There is no single best glide path that’s appropriate for all plans. Rather, the glide path that a plan sponsor adopts will depend on the nature of the plan and the particular circumstances of the plan sponsor. We develop a general framework that can be used to address many questions arising in glide path design.

First we introduce a base case model, using a small set of standard asset classes, which generates an efficient glide path at every different risk level. Then we use the model to explore the benefit of using (versus excluding) global high-yield bonds as a secondary return-seeking asset. Finally, we study the case where the plan sponsor has a predetermined allocation to an illiquid asset class.

Exhibit 1: Sample Glide Path

#### Efficient Glide Paths

Our approach is a direct analog of portfolio theory. Textbook standard portfolio optimization analysis looks at static asset allocations over a fixed time horizon, and defines an “efficient portfolio” to be an asset allocation that maximizes “return” (total portfolio return) for a given level of “risk” (standard deviation of portfolio return). The efficient portfolios then trace out an “efficient frontier” in risk/return space.

For glide path design, the standard approach needs to be modified in several ways. First, we are not looking for a static asset allocation, but a glide path that specifies how asset allocations should vary dynamically with asset and liability returns.^{1} Second, the standard definitions of risk and return need to be modified to ensure they are appropriate to the defined benefit plan context.

Portfolio analysis in the glide path setting uses Monte Carlo simulation, and we define risk and return in two stages. Let’s assume we are simulating asset and liability returns for a closed plan over a 10-year period. We first need to come up with simple definitions of “risk” and “return” that make sense for defined benefit plan sponsors. A straightforward approach is to define “return” to mean the expected average funding ratio over the next 10 years, and “risk” to be the expected tracking error of assets versus liabilities over the next 10 years.

More precisely:

- For a single path of simulated monthly asset and liability returns, the path-specific risk is defined to be the realized volatility of the funding ratio over the full simulation period (assuming no additional contributions by the plan sponsor), and the path-specific return is defined to be the average funding ratio over the full period.
- In the full Monte Carlo analysis, we define risk and return by averaging the above path-specific risk and return measures over all simulated paths.

These are somewhat broad definitions that are intended to capture the overall risk/return of a glide path strategy as a whole rather than its characteristics at any specific point in time. For example, the definition of risk abstracts away from the fact that along most simulated paths funded status volatility is not constant through time, but will tend to decline as we move through the 10-year period, funded status improves and the plan de-risks.^{2}

From here on, the methodology is conceptually similar to standard efficient frontier analysis, though more computationally complex: for a given level of glide path risk, we determine the glide path that has the highest measure of return, i.e., the highest expected average funding ratio. This is the “efficient glide path” for that risk level. As the level of glide path risk varies, the efficient glide paths trace out an efficient frontier.

Exhibit 2: The Efficient Glide Path Frontier, and Two Points on It

In our base case analysis, we use four asset classes: U.S. equity, long credit, long government bonds and duration-hedged global high-yield debt. Exhibit 2 shows the efficient frontier together with two specific efficient glide paths that lie on it: a low-risk glide path and a higher risk glide path.

These two sample points on the efficient frontier demonstrate the optimal or efficient glide paths for plans with risk levels of 50 basis points versus 400 basis points, i.e., for a plan with an extremely low risk tolerance and one with a moderate-to-high risk tolerance. The model confirms that the plan can de-risk more gradually into long credit when the plan sponsor has a higher risk tolerance.

Exhibit 3: The Efficient Glide Path Frontier, With and Without Global High Yield

#### Using High Yield and Emerging Markets Debt

Exhibit 3 compares glide paths constructed using global high yield (i.e., high-yield bonds plus emerging markets debt) on a duration-hedged basis, with glide paths that hold global high yield on an unhedged basis, and with glide paths that do not hold it at all. A comparison of the blue and gray lines shows that hedging global high-yield holdings to the liability duration results in an improved risk/return trade-off versus leaving global high yield unhedged.

Note that the benefit of including global high yield in the glide path in a formulaic way, while meaningful, is rather modest, even when this is done on a duration-hedged basis. Plan sponsors who rely on active managers may derive additional benefit from a strategy that can allocate tactically rather than unconditionally to global high yield. However, the benefits of tactical allocation will depend on manager skill.

Exhibit 4: The Efficient Glide Path Frontier, With A Fixed Allocation to Private Equity

#### The Role of Private Equity

The two other examples in this paper involve plan allocations to relatively illiquid asset classes. Many defined benefit plans have some direct investment in private equity. Given size limitations, the private equity investments held may not be highly diversified. But our analysis shows that a high degree of idiosyncratic risk in the private equity allocation can actually be beneficial, whereas when the private equity investment is highly correlated to U.S. equity, say with a correlation greater than 50%, it does not shift the efficient frontier appreciably upward.

Exhibit 4 assumes a 50% correlation between returns on private equity and returns on public equity. By imposing a fixed 5% private equity allocation (in the chart on the right), the average funding ratio is improved by only a quarter percentage point. This is a negligible boost in return when the risk level is 520 basis points.

In order to get more substantial benefits from a private equity allocation, plan sponsors should ideally select private equity funds that have a substantially lower correlation than 50% to public equity investments. In short, the lower the correlation is, the bigger diversification benefit the investor gets.

Exhibit 5: The Efficient Glide Path Frontier, With a Direct Investment in Real Estate

#### The Influence of a Real Estate Allocation

Many defined benefit plans have some direct investment in commercial real estate due to its attractive long-term expected real return and diversification benefit versus other return-seeking assets. This asset class is significantly less liquid than investments in financial assets, and it is often not feasible to vary the asset allocation dynamically. We consider the case where the plan already has 5% of its assets directly invested in commercial real estate, and must hold this allocation fixed over the next 10 years.

The analysis confirms that a 5% direct investment in commercial real estate can improve the average funding ratio at every level of targeted risk.

Both of these examples illustrate that, while alternative asset classes can play a useful role in a plan’s investment strategy, plan sponsors need to understand how such allocations influence glide path design as a whole.

#### Key Takeaways

A quantitative approach to glide path design can help answer questions regarding investment strategy for defined benefit plans.

- The framework is the analog of standard portfolio optimization theory, but in the defined benefit plan context.
- Instead of focusing on total return and absolute risk at a fixed horizon, we focus on return and risk relative to liabilities, over time.
- Instead of solving for optimal static allocations (efficient portfolios), we solve for optimal dynamic strategies (efficient glide paths).

We used the framework to investigate the role that specific asset classes can play in glide path design:

- High yield and emerging markets debt: should be held on a duration-hedged basis, and preferably allowing for tactical flexibility.
- Private equity: the case is only compelling if their correlation with public equities is low enough (less than 50%).
- Real estate: direct investments can add value, but only if the glide path is adjusted significantly from the base case.

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