Building better pension plans with liability-driven investing

Serge Lapierre, FCIA, FSA, Global Head of Liability-Driven Investments, Financial Engineering, and Quantitative Research, Multi-Asset Solutions Team, Manulife Investment Management
Frédéric Kibrité, CFA, FCIA, FRM, FSA, Portfolio Manager, Head of Investment Strategy—Liability-Driven Investments, Multi-Asset Solutions Team, Manulife Investment Management

To help demonstrate the potential benefits of a multicomponent LDI approach to pension plan management, Manulife Investment Management’s Liability-Driven Investments team commissioned Bayes Business School to construct a model based on the latest academic research. The results of the model form the basis of this paper.

Key takeaways

• When it comes to addressing the unprecedented challenges faced by pension plans today, we believe a one-size-fits-all approach just isn’t enough.
• In this paper, Manulife Investment Management's Liability-Driven Investments team worked with a leading business school to develop a model representative pension plan and, using the latest simulation and modelling building technology, we aim to show the clear benefits of adopting LDI as a way of improving retirement outcomes.
• We believe the simulation results show that by incorporating key-rate duration matching, introducing Plus assets, and introducing a dynamic derisking strategy, we may be able to not only reduce the volatility of a plan’s funding position over time, but also improve the plan’s likelihood of being able to achieve a well-funded status.

Since the global financial crisis, pension plans have increasingly adopted an LDI approach to managing risk. Pursuing the goal of making all payments due to plan members in full and on time requires as robust an investment strategy as possible.

So what makes LDI so special?

Liability-driven investing (LDI) is a holistic investment strategy applied not only to the plan’s assets, but also to its liabilities. It recognizes that if the goal of a pension plan is to make all benefit payments in full and on time, then the success of any investment strategy should be judged against this goal and this goal alone. This in turn leads to a simple conclusion: The benchmark for a pension plan should be based on its own liabilities rather than on a financial market index or on any combination of such indexes. This approach means that all investment decisions and, more important, all related risk management decisions, should be undertaken with an eye firmly on the plan’s liability profile instead of market indexes. Designing an investment strategy that pays little or no attention to the shape and nature of plan liabilities would be a bit like a cobbler fashioning a very elaborate pair of shoes for a client without measuring the client's feet first.

Seen through this lens, the plan’s liabilities represent a negative asset. This negative asset has similar risk characteristics to a bond portfolio, since the liabilities comprise fixed payments (some linked to inflation) stretching out into the future. They can therefore be valued as we value a fixed-income portfolio comprising bonds issued by governments and corporations. It also means that the value of these liabilities will have the same inherent economic risks as a portfolio of bonds: The value of the liabilities will fall as interest rates rise and rise when interest rates fall. They’ll also rise with higher-than-anticipated inflation and fall with lower realized inflation.

These risks are often characterized as being unrewarded. If we assume that both interest rates and inflation rates tend to mean revert over time, then the financial position of the plan will be affected by the volatility of interest rates and inflation, but there will be no long-term gain for bearing these risks. This is in contrast to the risks associated with other investments, such as equities. Although equity prices rise and fall over time, we assume that there’s a positive, long-term risk premium that can be earned from holding equities that rewards investors for bearing this risk.

If interest-rate and inflation risks are unrewarded, why bear them?

An LDI investment strategy usually comprises two key elements. The first is to hedge, as far as possible, or as far as affordable, the unrewarded risks posed by the plan’s liabilities. This can be achieved with the construction of a bond portfolio and with the addition of derivatives such as swaps that have similar risk characteristics to the liabilities. When hedged perfectly (which isn’t always possible), any rise in the value of the liabilities will be matched by an offsetting rise in the fixed-income portfolio. In this way, the plan can get closer to the panacea of risk management.

But in the event that a plan is in deficit—that is, where the value of the assets is lower than the value of the liabilities—constructing a fixed-income portfolio that matches changes in the value of the liabilities may not, on its own, be sufficient to close this deficit. This is where the construction of an appropriate portfolio of return-seeking assets comes in as the second key element of an LDI strategy. Return-seeking assets are expected to grow in value over time, closing the gap between the value of the assets and liabilities and thereby helping ensure that there are sufficient funds to meet all retirement obligations. 

An alternative approach to LDI

The traditional growth asset class is publicly traded equities; however, this asset class can fall in value dramatically. Furthermore, there’s generally a negative correlation between equities and treasuries in times of crisis, so liabilities may rise just as equities are crashing, thereby compounding the problem.

This is why some pension plans have addressed this issue in two complementary ways that are consistent with the philosophy of LDI. First, plans can diversify their growth portfolio across a wider range of asset classes. Second, plans can invest in return-seeking assets such as infrastructure, commercial property, timber, and agriculture, which typically produce a reward over the long term. These assets classes, which are typically referred to in the asset management industry as private, real, or alternative assets, are what we call Plus assets for LDI portfolios, as we believe they can offer additional benefits from a liability-matching perspective, increase the diversification of a multi-asset portfolio, and can also provide a liquidity premium. We therefore believe that having Plus assets within a portfolio can help to close a deficit over time and, additionally, help to reduce the volatility of the plan’s liabilities. Focusing both the fixed-income portfolio and the growth portfolio on plan liabilities—with these same liabilities acting as the benchmark for these assets—is the essence of LDI.

Putting our theory to the test

To help demonstrate the benefits of a multicomponent LDI approach to pension plan management and to test the extent to which LDI can help improve the likelihood of meeting all retirement obligations in full and on time, we commissioned Professor Andrew Clare of Bayes Business School¹ to construct a model based on the latest academic research. The results of the model form the basis of this paper.²

Their research found that:

• A key rate duration (KRD) matching strategy produces better results in terms of risk management than those that can be achieved by investing in a traditional bond portfolio.
• An investment strategy that relies too heavily on the performance of equity markets, all else equal, will have a high probability of failing.
• Including Plus assets in the growth portfolio probably requires a more dynamic approach than can be achieved through straightforward annual rebalancing.
• A dynamic approach to asset allocation that combines a KRD-matching strategy and an allocation to Plus assets can improve the prospects of achieving a wide range of funding objectives.

The representative plan 

To demonstrate how an LDI approach to the management of pension plan assets can help reduce the risks that a typical plan faces, we’ve designed a representative pension plan. We’ll use this plan in the simulation experiments so that we can gauge the impact of different strategies on the financial health of the plan.³

Figure 1: the liability profile of the representative plan

Source: Bayes Business School, Manulife Investment Management, 2021. For illustrative purposes only.

The liabilities faced by this plan peak around 20 years’ time, and the last cash flow occurs in 80 years’ time. The cash flow in the first year is $16.25 million, which represents 2.71% of the total liability.⁴ While the benefits of LDI can be achieved regardless of a plan’s circumstances, we’ve set the duration of the liabilities for our plan to just over 17 years.⁵ This means that a one percentage point fall in the liability discount rate would cause the value of the liabilities to rise by approximately 17 percentage points. The present value of these liabilities at the start of the simulations is always $600 million. This present value has been calculated using FTSE Pension Discount Curve data.⁶ Finally, for simplicity, we assume that the plan is closed to both new entrants and future accrual.

Hedging

We can use the liability profile shown in Figure 1 to demonstrate different approaches to hedging the risks inherent in the liabilities. To do this, we assume that a bond portfolio has been constructed that has the same value (present value) as the liabilities at the outset of the 10-year simulation period. Using Monte Carlo techniques, we then simulate 10,000 paths for the bond assets and the liabilities over the course of this period.²

To establish the advantages and disadvantages of different approaches to hedging plan liabilities, we investigate the performance of three bond portfolios, where the liabilities are always discounted using the FTSE Pension Discount Curve. In addition, to keep the analysis simple, in these simulations we assume that the value of the bond assets, whatever their composition, matches the value of the liabilities at the start of the 10-year simulation period.

The bond portfolios are represented by:

• Market index—The Bloomberg Barclays U.S. Aggregate Bond Index (Agg)
• KRD matching with credit allocation—A 50% investment in a portfolio of treasuries and a 50% investment in the bonds comprising the FTSE Pension Discount Curve (KDM-50/50)
• KRD without credit matching—The portfolio comprises a 100% investment in the portfolio of bonds that makes up the FTSE Pension Discount Curve (KDM-100)

As we progress through the strategies listed above, we gradually increase the precision of the matching strategy. But what impact does it have on the plan’s funding position in 10 years’ time? To answer this question, we simulate the paths of the liabilities and assets described above 10,000 times in each case. This allows us to look at the consequences of each hedging strategy. To run the simulation exercises for each of the strategies, we used monthly data on all the key financial variables spanning the period from 2008 to 2019.⁷

Figure 2: liability hedging

Source: Manulife Investment Management, Bayes Business School, 2021.

Figure 2 presents some results that summarise the simulations.² The bars represent the 5^th percentile of the funding ratio distribution, where 95% of the funding ratio outcomes after 10 years were greater than this value. As expected, the figures show that the worst-performing strategy is the Agg: The 5^th percentile value for this strategy was found to be 66%, which means that 5% of all outcomes were worse than this value. With regard to the KDM-50/50 and KDM-100 strategies, we can see that the distribution of outcomes is now very narrow; for example, with KDM-100, the 5^th percentile is found to be 97.6%. 

In summary, these results demonstrate that the KRD strategies produce better results in terms of risk management than those that can be achieved investing in a traditional bond portfolio. 

The growth portfolio

Having demonstrated how different approaches to liability hedging strategies perform, we now turn our attention to the growth portfolio. The main purpose of the growth portfolio is to generate the returns needed to make up for the deficit when the plan is underfunded. In this next set of experiments, we therefore assume that the representative pension plan begins the 10-year simulation period with a funding ratio equal to 85%. Again, using data spanning the period 2008 to 2019, we investigate the performance of a combination of equities and bond portfolios. We also introduce the plan sponsor into these simulations. One of the most important assets of any pension plan is the financial support of the sponsor. We therefore assume that the sponsor pays a fixed sum of $12 million into the plan for the first 7 years of the simulation period. This contribution is equivalent to 13% of the deficit of the plan at the start of the simulations.

We combine the liabilities shown in Figure 1 with three alternative bond portfolios, but where the allocation to equities is always 60%. We also assume that the plan rebalances its asset portfolio back to a 60%/40% equity/bond at the end of each year in the simulation. The three alternative bond portfolios are represented by:

• An allocation of 40% to a portfolio of bonds—Represented by the Agg (40% Agg)
• An allocation of 20% to a portfolio of bonds—Represented by the Bloomberg Barclays U.S. Treasury index and an allocation of 20% to a portfolio represented by the bonds in the FTSE Pension Discount Curve (40% DM). This bond portfolio has been constructed to match the duration of the liabilities
• An allocation of 20% to a portfolio of bonds—Represented by the Bloomberg Barclays U.S. Treasury index and an allocation of 20% to a portfolio represented by the bonds in the FTSE Pension Discount Curve (40% KRD Match). This bond portfolio has been constructed to match the duration of the liabilities at 5-year intervals; that is, it’s a KRD-matching portfolio.

The results of these simulations are shown in Panels A and B of Figure 3. In Panel A, we again present the 5^th percentile of the distribution of funding ratios after 10 years. In sharp contrast to the results presented in Figure 2, where we started with a funding ratio of 100%, we see that the funding ratio 5^th percentiles of each strategy are now around 50% for all three strategies. This means that on more than 5% of our simulations, the funding ratio was as low as 50% or less. These results indicate that, although the hedging strategies—both duration matching and KRD—result in better funding ratio outcomes than would be achieved by investing in a conventional bond portfolio, represented here by the Agg, the volatility of equities dominates the benefits achieved from the hedging strategies.

As an additional way of looking at the results, Panel B presents the proportion of times that the representative plan’s funding ratio exceeds 110% in the investment period. In practice, a plan that reaches, for example, 110% funding after 4 years is unlikely to continue taking investment risk for the remaining 6 years. The chart shows that from year 5 onward, the matching strategies reach this threshold more often than is achieved with the traditional bond portfolio. However, the exposure to equities still makes the prospect of achieving this level of funding (or greater) relatively low, with all three strategies having less than a 40% chance of achieving this level of funding after 10 years. 

Figure 3: the growth portfolio, equities, and bonds

Source: Manulife Investment Management, Bayes Business School, 2021.

In summary, an investment strategy that relies too heavily on the performance of equity markets, other things equal, will likely experience higher funding volatility.

Introducing Plus assets 

So far, the results have demonstrated that a KRD approach to hedging liabilities produced excellent results in terms of risk management and that a reliance on equities to close this gap, even combined with a hedging strategy and with support from the plan sponsor, could still leave the plan underfunded after 10 years. Next, we’ll introduce Plus assets to the portfolio.

By diversifying across a range of asset classes, any shock to one of the components, such as the equity holding, might have less of an impact if other return-seeking asset classes are imperfectly correlated with the performance of the equity market. This is the benefit of diversification. Achieving this diversification by investing in alternative and real asset classes such as infrastructure, commercial property, timber, and agriculture—which we refer to as Plus assets for LDI portfolios—has the added benefit of bringing the risk characteristics of the growth portfolio more in line with the risk characteristics of the liabilities. By investing in Plus assets, pension plans are essentially killing two birds with one stone. On the one hand, they’re building a more robust growth portfolio, and on the other, they’re staying true to the LDI philosophy of aligning the risks inherent on the asset side of their balance sheet with those on the liability side.

To investigate the value of integrating Plus assets into the growth portfolio, the plan can also allocate its funds to the following real assets represented by the related total return financial market indexes:

• U.S. real estate—The FTSE EPRA Nareit US Real Estate Index
• Global infrastructure—FTSE Global Core Infrastructure Index
• Global timber—S&P Global Timber and Forestry Index
• Global agriculture—NASDAQ OMX Global Agriculture Index

One of the drawbacks of these asset classes is that they’re generally less liquid than those that are traded on public exchanges, but this is only really a drawback for those investors who require their investments to be very liquid. For investors such as pension plans, with very long-dated financial commitments, this illiquidity represents less of a drawback and more of an opportunity. This is because investors in these asset classes can expect to earn a liquidity premium; that is, an addition to return in compensation for assuming this illiquidity.

However, it’s important to acknowledge in the modelling that higher transaction costs might be incurred when investing in or disinvesting from an illiquid Plus asset class compared with investment in and disinvestment from, say, publicly traded equities.² To deal with this real-world problem, we impose a transactions cost of 7.5%, which applies with any redemption of a holding in a Plus asset class. So, for example, if the investment is valued at $100 million, selling this amount of the asset class would only realise a value for the plan of $92.5 million.

To investigate the role that Plus assets can play in closing the funding gap, the representative plan again begins the 10-year simulation period with a funding ratio of 85%, but the plan’s portfolio is represented by:

• An allocation of 40% to a portfolio of equities, represented by the S&P 500 Index
• An allocation of 40% invested equally between a portfolio of treasuries and the bonds comprising the FTSE Pension Discount Curve, where the bond portfolio has been constructed to match the duration of the liabilities at 5-year intervals; that is, it’s a KRD-matching portfolio
• An allocation of 20% invested in four Plus asset classes: real estate, infrastructure, timber, and agriculture (5% invested in each one)

Figure 4: adding plus assets

Source: Manulife Investment Management, Bayes Business School, 2021.

In Panels A and B of Figure 4, we’ve presented the results of the simulation. In Panel A, we see that the 5^th percentile for the strategy that incorporates Plus assets is lower than the comparable simulation without Plus assets. The main reason why the Plus assets haven’t improved the final outcome for the representative plan is due to the rebalancing that occurs in the simulation at the end of each year, which, with the assumed higher transaction costs, has a detrimental effect on the performance of the growth portfolio.

Panel B of Figure 4 shows the probabilities of reaching a 110% funding ratio over the 10-year planning horizon. We see that the probability is lower at all points over the period with the inclusion of the Plus assets. This leads us naturally to another important conclusion: While rebalancing liquid asset classes such as government bond portfolios and equity portfolios, investors should not attempt to manage illiquid asset classes in the same way; instead, a more strategic, dynamic approach to the problem is needed. Using cutting-edge, modern simulation approaches, we’ll take a more detailed look at this issue later on in the paper.

In summary, we can say that including Plus assets into the growth portfolio requires a more dynamic approach to the management of the return-seeking assets than can be achieved through straightforward annual rebalancing.

Dynamic derisking and the introduction of a virtual plan manager

So far in our experiments, we’ve simulated outcomes in the absence of any intervention from what we might refer to as a virtual plan manager of the plan’s assets and liabilities. In this section of the paper, we introduce dynamic decision-making. We do this by using cutting-edge simulation technology known as multistage stochastic programming (MSP),³ which is widely used in operations research. MSP allows for more sophisticated financial market models and realistic constraints, such as constraints on assets, transaction costs, and taxes, compared with more conventional simulation methods. It also allows us to introduce specific objectives for the plan over the 10-year simulation period, objectives that could be thought of as representing a strategy implemented by its managers.²

The objectives⁸ that we model are as follows:

Objective 1—We assume that the plan’s planning horizon is 10 years and that the plan’s managers/sponsors would like to be in the position to afford a buyout at the end of this 10-year period.

Objective 2—We assume that the plan wishes to maximise the funding ratio over the 10-year planning ratio. This means that the plan’s management will try to ensure that the funding ratio is as high as possible, given the other constraints.

Objective 3—We assume that the plan’s managers wish to reduce the potential buyout cost at the end of 10 years.

These are realistic objectives for any real-world pension plan. Using this tool, we can, among other things, identify the optimal asset allocation over the 10 years and examine the likely dispersion of the representative plan’s funding ratio at the end of the 10-year period. We can also calculate the median funding level of the plan and the 5^th percentile of the funding ratio distribution at 10 years, which we present in Figure 5. Also note that the company’s contribution is again set to $12 million for each of the first 7 years of the simulation and that we impose the same illiquidity cost on investment and disinvestment in the Plus assets.

Figure 5: dynamic derisking

Source: Manulife Investment Management, Bayes Business School, 2021.

Panels A and B of Figure 5 present the results of our optimised approach; they show a dramatic improvement in the funding ratio position compared with the equivalent nondynamic simulation, adding Plus assets, the results of which we include in the figure for purposes of comparison. Panel A of the figure shows that the 5^th percentile for the optimised approach is just over 60%. In practice, of course, a plan with very strong funding would likely seek a buyout; in other words, the sponsor and plan managers would be unlikely to have such a high funding ratio as an objective. Of more significance, Panel B of Figure 5 shows the probability of reaching a 110% funding position throughout the planning period. The figure shows that by year 5, there’s just over an 80% probability of reaching this level of funding (or greater), while the probability of reaching a 110% funding position is close to 100% by the end of the 10 years. We shouldn’t get carried away with this result, as significant as it is. This plan began with a funding position of 85% and received significant support in the form of contributions from the plan sponsor, but the results do demonstrate the combined value of Plus assets, a KRD-matching strategy, and a dynamic approach to the retirement problem.

With regard to this dynamic approach, in Figure 6 we present the median asset allocation of the representative plan over this 10-year period; we can think of this as being the optimal asset allocation of the plan.⁹ We see a decline in the allocation to equities over this period, from around 45% to 23%. With regard to the allocations to fixed income (a combination of KRD and a more conventional bond portfolio) and Plus assets, in the early years of the planning period, the allocation to Plus assets rises from around 5% to 25% and then gradually declines as the planning period progresses, while we see the allocation to fixed income stable at around 50% of total assets for the first 4 years of the planning period, before rising steadily to 70% by the end of this period.

Figure 6: asset allocation with dynamic derisking

Source: Manulife Investment Management, Bayes Business School, 2021.

In summary, these results show the important and dynamic role that can be played by Plus assets in a derisking journey as plans seek to achieve their funding objectives. 

A custom approach for facing the future

We live in a world of uncertainty. From the impacts of climate change, global pandemics, and increasing longevity to potential changes in the very nature of financial markets, all or any of these factors can bear on the ability of pension plans to become fully funded down the road. Rather than hoping for the best, plan sponsors must consider the worst scenario they can sustain. They must identify the risks, determine whether their current strategy allows them to sustain this uncertainty going forward, and use that as their basis for making strategic decisions for the future.

When it comes to addressing the unprecedented challenges faced by pension plans today, we believe a one-size-fits-all approach just isn’t enough. Today, pension plans large and small have access to custom approaches using a mix of LDI funds designed to closely match liabilities and calibrate their credit exposure.

In this paper, Manulife Investment Management’s Liability-Driven Investments team developed a model of a representative pension plan and, using the latest simulation and modelling building technology, we’ve shown the clear benefits of adopting LDI as a way of improving retirement outcomes.² The simulation results show that by constructing a fixed-income portfolio that matches the duration at key points along the liability profile (KRD matching), by integrating Plus assets, and, finally, by introducing a dynamic derisking strategy, we can not only help reduce the volatility of a plan’s funding position over time, but we can also improve the plan’s likelihood of being able to achieve a well-funded status. 

This paper was written by Manulife Investment Management in partnership with Professor Andrew Clare of Bayes Business School¹. The school is an integral part of City, University of London, and is consistently ranked amongst the best business schools and programmes in the world. Bayes holds the rare gold standard of 'triple-crown' accreditation from the Association to Advance Collegiate Schools of Business (AACSB), the Association of MBAs (AMBA) and the European Quality Improvement System (EQUIS).

1 Formerly Cass Business School. 2 “Liability-Driven Investment for Pension Funds: Stochastic Optimization with Real Assets,” https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3832434, April 23, 2021. 3 The model used in simulation experiments was built by Bayes Business School and commissioned by Manulife Investment Management, January 31, 2021. 4 Values are in USD throughout. 5 These results are applicable for various levels of duration and are not dependent on the assumptions used here. 6 Details of this data can be found at https://www.soa.org/sections/retirement/ftse-pension-discount-curve/; in addition, details about how the liabilities were generated can be found at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3832434. 7 For more information about the underlying data, please see https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3832434. 8 For more information about the specification of these objectives, please refer to https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3832434. 9 In the optimised simulation, we add an additional constraint on the allocation to real assets from year 5 onward to reflect the real-world consideration that a pension scheme would probably not want too high an allocation to illiquid asset classes at a point when it may also wish to proceed to a buyout. The maximum Plus asset allocations for years 5, 6, 7, 8, 9, and 10 were set at 60%, 50%, 40%, 30%, 20%, and 10%, respectively.