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Effective LDI: Does Your LDI Portfolio Have Enough Yield?

Michael J. Bazdarich, PhD
Product Specialist/Economist

Executive Summary

  • DB plans need to do more than merely minimize tracking error to liabilities. They must also ensure that their assets feature sufficient yield to sustain or improve funded status the way they intend.
  • Typically, the allocation which minimizes tracking error to liabilities will not provide sufficient returns to sustain funded status, so even a plan intent on de-risking still needs to target asset yields high enough to prevent slippage in funded status over time.
  • The yield on plan assets must exceed that on plan liabilities by enough to compensate for the credit risks plan assets face (that liabilities do not).
  • For underfunded plans, assets yields must exceed liability yields by an even greater amount, because for these plans, benefit payments take a bigger percentage bite out of assets than out of liabilities.
  • Because of these realities, sustaining or improving funded status is a daunting task for plans. We believe active management is a critical tool for plans to help address these challenges.

It is hard work for a defined benefit (DB) plan’s assets to keep up with or overtake its liabilities and especially so when the plan is underfunded. Granted, DB plans are typically locked onto the task of targeting plan asset returns, but it is our experience that plans often lose sight of this goal when they embark upon derisking. Yet, asset return considerations are crucial for these plans as well.

There are two facts that DB plan sponsors must be aware of to successfully balance risk-management and return-enhancement. First, the lowest-risk allocation for a plan will typically not provide sufficient asset returns to keep up with liability returns and thus sustain funded status. Therefore, even a plan that merely wants to sustain funded status at 100% with minimum risk still needs to target a higher yield on its assets than what its liabilities exhibit.

Second, the arithmetic of funded status is such that underfunded plans need to achieve higher returns on assets than those on liabilities merely to sustain funded status, let alone improve it. This is because benefit payments take a larger percentage bite out of assets than liabilities when funded status is below 100%. This puts further onus on plan asset returns.

These are incontrovertible facts of pension management. Yet, they often get lost in the shuffle when plans start homing in on increasing duration and customizing plan assets to better hedge liabilities.

We are in favor of plans improving their hedge performance and reducing tracking error. Our point is merely that tracking error reduction must be done in concert with establishing adequate return targets to achieve the plan’s other goals. Again, the trade-off between risk and return is relevant for well-funded, “de-risking” plans as well as for seriously underfunded, “return-seeking” ones. All plans must achieve sufficient yield and return on their asset portfolios.

The following sections delineate some of the inconvenient details that buttress this point. These concerns affect real-world plans. That they might be complex or underappreciated makes them no less relevant.

Tracking Error Is an Incomplete Measure of DB Risks

Tracking error in LDI is typically calculated as the standard deviation of changes in funded status. These changes are due mostly to the difference between asset returns and liability returns. Standard deviation measures volatility around the mean. So, tracking error measures how volatile funded status is around its expected rate of change. This calculation makes no allowance for whether the expected rate of change in funded status is satisfactory for a plan. Yet, surely this expected rate of change is of supreme importance for any real-world plan.

Consider the two profiles of funded status displayed in Exhibit 1. On Path 1, funded status declines steadily over time. Tracking error is zero on this path, because funded status does not deviate from its trend path. In contrast, on Path 2, funded status varies wildly around a steady 100% trend, with 12% annual tracking error.

Exhibit 1
Funded Status Under Two Paths: Which Is Riskier?
Source: Western Asset, hypothetical data

Which path is less risky, 1 or 2, zero tracking error or 12% tracking error? To put it more tellingly, under which path would a pension manager be more likely to keep his or her job?

The answer should be obvious. Yet, how many LDI analyses of pension risk begin and end with tracking error, including no discussion at all of expected returns? How many analyses of “de-risking” begin and end with analyses of duration and key-rate durations, never even mentioning the issue of portfolio yield?

Again, minimizing tracking error alone is not sufficient for a real-world plan. A plan must also target asset returns that can be expected to achieve its objectives, and minimum-risk allocations will generally be deficient on this count.

Minimum Tracking Error—Allocations Typically Imply Declining Funded Status

If you’ve read any LDI literature, you’ve come across depictions of efficient frontiers for DB allocations. This is an application of Markowitz mean-variance analysis to pension optimization. Because tracking error is a more relevant risk measure for a DB plan than total return volatility, the horizontal axis for an LDI efficient frontier is cast in terms of tracking error, as in Exhibit 2.

Exhibit 2
Efficient Frontier, Funded-Status Optimization (LDI)
Source: Western Asset, hypothetical data

The other important difference between an LDI efficient frontier and a more standard one concerns expected returns. For a standard efficient frontier, there is no normative difference between return levels, at least not on the upward-sloping portion of the curve (the actual efficient frontier). True, everyone likes higher returns, but there is a trade-off between higher expected returns and higher risks, and the returns available at the point of minimum risk on the frontier may be perfectly acceptable to some investors.

In contrast, for an LDI efficient frontier, large portions of the efficient frontier are unacceptable. For the LDI frontier, returns are best cast in terms of expected change in funded status: expected asset returns less expected liability returns, adjusted for the level of funded status (much more on this later). And portfolios showing a negative expected change in funded status will be unacceptable, disastrous for all but the most overfunded plans.

For a 100% funded plan, the unacceptable portion of the efficient frontier includes all points for which expected change in funded status is negative. For an underfunded plan, the unacceptable portion includes all points where expected change in funded status is insufficient to bring funded status back to 100% prior to plan termination.

The fact is that the point of minimum risk on an LDI efficient frontier typically has negative expected change in funded status. DB liability valuations are determined using AA corporate bond yields to discount future benefit obligations. The “yield” on the liabilities then becomes the AA yield associated with this valuation.

Pension obligations “earn” this corporate bond yield, but they do not suffer downgrades or defaults. In contrast, a portfolio of AA bonds matching the duration characteristics of the liabilities will suffer occasional downgrades, even defaults, so that its realized return will fall short of its yield and, hence, short of the return on liabilities. With rare exceptions, Treasury bonds don’t suffer downgrades or defaults, but they provide a lower yield than the AA yields used to discount liabilities, so they can’t match the return on liabilities either.

In sum, the best available hedge of DB liability valuations—the minimum-risk point on the efficient frontier—will not be able to match the return on liabilities, which is equivalent to saying that at that minimum-risk point, the expected change in funded status is negative.1 These shortcomings are especially acute for projected obligations more than 30 years in the future, as current market structure provides little product or liquidity with maturities more than 30 years.

Finally, besides the interest rate and default risks involved, liability valuations also exhibit actuarial risks that likely cannot be hedged. While actuarial risks need not imply expected downward pressure on funded status, they do reduce chances of success at any given level of funded status and expected change in funded status.2

For all these reasons, the minimum-risk allocation on an LDI efficient frontier will not be an acceptable allocation for a DB plan. To successfully meet its obligations, a plan must consider both its tracking error and also the level of asset returns relative to liability returns.

This is right in line with the Markowitz criterion of minimizing risk subject to meeting some return target. It is not in line with analyses that focus only on minimizing tracking error or on matching durations of assets and liabilities. Our Western Asset LDI Optimizer is constructed specifically to minimize tracking error while also achieving the funded status improvement targets of our clients. You don’t have to use our Optimizer to construct LDI solutions with sufficient returns, but you do need to deal with the following considerations.

Portfolio Yield Must Compensate for Asset Credit Risk

As stated earlier, DB liabilities sport the yields of AA bonds, but suffer none of their default risks, let alone those of lower-rated bonds. In our construction of LDI solutions, we pay a lot of attention to the credit quality of plan assets relative to that of the liabilities. The essence of such deliberations boils down to one question: Does the yield on the assets exceed that on the liabilities by enough to fully compensate the plan for the credit risks of its assets?

If the yield premium for plan assets over plan liabilities is not sufficient to compensate for credit risks, then the expected return on assets will be less than that on liabilities, in which case funded status will be expected to decline over time. If the yield premium for assets over liabilities equals or exceeds expected credit losses, then the plan has a chance to succeed. (Even in the latter case, full discharge of liabilities is not guaranteed,3 but a chance at success beats the certainty of failure any time.)

How does a plan determine the yield on its liabilities? This is simple. Whatever discount method a plan uses to evaluate its liabilities, there will be a unique, accompanying discount rate or internal rate of return (IRR). When this IRR is used to evaluate liabilities, the resulting valuation equals that provided by the plan’s actual discount method. This IRR can be taken as the “yield” on the liabilities.

Once the yield on liabilities is so determined, we can calculate or estimate the yield on plan assets, subtract an amount for the expected credit losses the assets will suffer each year, and compare the two results. Again, if expected asset returns—that is, yields less expected credit losses—do not at least equal the yield on liabilities, then the allocation can be expected to fail, regardless of how well it reduces tracking error.

A plan could go through this process in greater detail. For example, our LDI Optimizer calculates a measure of option-adjusted spread (OAS) for the liabilities. This could be compared to the OAS on plan assets, and this asset OAS could be adjusted for expected credit losses.

Still, this comparison provides an initial litmus test. If asset yield less expected credit losses is less than liability yield, the allocation won’t do. If asset yield less expected credit losses meets or exceeds liability yield, the allocation has passed a first test, and the plan can move on to more demanding criteria.

Granted, expected credit losses on a portfolio are difficult to determine precisely. Exhibit 3 lists our rough estimates of historical average annual credit losses for various (passive) fixed-income indices.4 Alternatively, a plan might construct its own estimates of likely credit losses. In the final analysis, some estimate of these should be attempted, or else the plan has no criterion by which to determine whether plan yields (expected returns) are sufficient to match those on plan liabilities.

Exhibit 3
Estimated Annualized Credit Losses by Quality Index (bps per Year)
Source: Bloomberg Barclays Live, Western Asset. Estimates are for Jul 1989–Feb 2018 sample, except for High Yield, where sample period is Feb 1994–Feb 2018.

Similarly, when non-fixed-income asset classes are included in the plan asset allocation, some estimate of realized return on these should be constructed. Equities don’t default, but companies do fail, as do other types of investments. Estimates of expected returns on assets will include some allowance for likely losses due to corporate/venture failures. These return expectations can be folded in with loss-adjusted yields on fixed-income assets to determine whether projected asset returns are sufficiently high relative to liability returns to match the goals of the plan.

Underfunded Plans Need Further Boosts to Asset Returns

Funded status is the ratio of plan assets to the valuation of plan liabilities. If the return on assets equals the “return” on liabilities, funded status will remain constant, right? Wrong. In order for funded status to remain constant, the rate of change of assets must equal the rate of change of liabilities. These rates of change depend not only on “returns,” but also on the effects of benefit payments on asset and liability valuations.

One dollar of benefit payment reduces both assets and liability valuations by one dollar. However, the effects of benefit payments on the rates of change in assets and liabilities depend on the respective sizes of assets and liabilities. When a plan is underfunded, assets are less than liabilities, so each dollar of benefit payments takes a bigger percentage bite out of assets than out of liabilities. Therefore, in order merely to sustain funded status, asset returns must exceed liability returns by an amount sufficient to offset the erosion caused by benefit payments.

This is not just an accounting artifact. If asset returns merely match liability returns in percent terms, and the plan is underfunded, then the dollar return on assets must be less than that on liabilities, so the funded deficit is deteriorating in dollar terms as well.

To sustain funded status, it must be that:

ROA = ROL + (BEN/PBO)*(1-FS)/FS,

where ROA and ROL are returns on assets and liabilities, respectively, BEN is benefit payments, PBO is the liability valuation, and FS is funded status.

We saw in the previous section that in order for ROA to match or exceed ROL, the yield on assets must exceed the yield on liabilities by enough to compensate for expected credit losses on assets. When the plan is underfunded, assets must return a further premium over liabilities to match the term BEN/PBO*(1-FS)/FS.

For most plans we work with, benefit payments are around 5% of liability valuation. So, for an 80% funded plan with current benefits 5% of liability valuation, asset returns must exceed liability returns by 1.25% per year, just to sustain that 80% funded status.

To improve funded status by X percent, it must be that:

ROA = ROL + (BEN/PBO)*(1-FS)/FS + (X/FS)*(1+ROL-BEN/PBO).

ROL-BEN/PBO is the rate of change in liability valuation. So, to achieve an X percent improvement in funded status, return on assets must exceed return on liabilities by enough to offset the erosion in funded status caused by benefit payments plus a premium X that is “magnified” by the underfundedness of plan and by the rate of change in the liabilities.

So, for an 80% funded plan, with benefits payment equal to 5% of liabilities, in order to achieve a 2% per year improvement in funded status, asset returns must exceed liabilities returns by about 375 basis points (bps) per year (by a little more if the return on liabilities—ROL—exceeds the 5% benefit payment as a fraction of PBO).

Notice that even with a 2% annual improvement in funded status, it would still take the plan 10 years before it could hope to achieve fully funded status. Shorten the projected time to five years, and a 4% annual improvement in funded status is necessary, in which case, asset returns would have to exceed those on liabilities by 625 bps per year!

We should note that “return on liabilities,” as we have used it here, is the change in liabilities that would hold were no benefit payments made. This return can be calculated by aggregating the effects on liability valuation of changes in the liability discount method and of maturation of benefit flows. Alternatively, and more simply, return on liabilities is the observed percent change in liabilities plus benefit payments as a percent of (previous) liability valuation. Of course, when using this method, actuarial changes, service costs, and prior service costs should be accounted for as well.


We often hear that failing to plan is planning to fail. Granted, the concepts discussed here may be unfamiliar to pension managers and rarely mentioned in LDI analyses. However, they concern real-world effects on funded status. Failure to account for them could be fatal to your plan.

If the analysis here seems complicated to you, that is so because you are a human being, not a computer. But being a human being, Path 1 in Exhibit 1 probably looks more risky to you than Path 2, in which case you do need to pay attention to the issue of the yield and expected return on your assets.

Certainly, if your plan is substantially underfunded, then you need aggressive asset returns to improve funded status as quickly as desired. But even if you are fully funded and desiring to de-risk, you still need sufficient returns to prevent funded status from eroding back to underfunded levels.

The conceptual points made in sections titled “Tracking Error Is an Incomplete Measure of DB Risks” and “Minimum Tracking Error—Allocations Typically Imply Declining Funded Status” emphasize the fact that even for a fully funded plan, tracking error minimization alone is not an optimal—or even a sustainable—tactic. To make sure your allocation provides the desired sustenance of or improvement in funded status, you need to be aware of the effects of credit losses on fixed-income returns, and you need to be aware of the additional hurdles arising from the arithmetic of underfundedness and benefit payments.

Does your fixed-income allocation feature sufficient yield premium over that of your liabilities to cushion for the effects of credit losses? Does your asset allocation provide sufficient expected returns to deliver the desired rate of change in funded status? If you answer no to either of these questions, you need to beef up yields and/or expected returns on assets or else consider additional cash contributions to the plan.

Because of the various “stresses” underfundedness and prospective credit losses pose to a plan, we believe active management should be pursued in all sectors of the asset allocation. Every possible source of return should be considered when attempting to insure that asset returns are sufficient to deliver desired rates of change in funded status.

Similarly, this late in a business/market cycle, it may be overly risky to pursue the return levels necessary to achieve rapid improvements in funded status. In this case, cash contributions may be the most sensible strategy, however bitter that avenue might be to plan sponsors.


  1. Our definition of “best hedge” here is the allocation that minimizes tracking error, the leftmost point on the efficient frontier. While we have already asserted that tracking error is an incomplete measure of DB risk, we follow convention in this case by describing the minimum tracking error allocation as the “best hedge” of liabilities.
  2. With 100% funded status and zero expected change in funded status, the expectation is that the plan will have sufficient assets, but there is always the chance that adverse outcomes lead to plan failure. The higher the chances of adverse actuarial shocks, the higher this risk.
  3. This is the same point that was made in footnote 2. In a previous Western Asset white paper, Why All Defined-Benefit Plans Are Short-Term Investors, November 2014, available on our website, we dealt with this issue in detail. Because a DB plan has to make benefit payments even when assets are depleted, sufficiently adverse experience on realized returns results in such a loss of funded status that the plan never recovers, even when asset returns revert to expected levels (because the higher returns accrue to a depleted set of assets).
  4. These were estimated by comparing historical excess returns for these indices to the excess returns implied by OAS, duration and spread changes. For fixed-income securities or indices, excess return is return over and above that on a portfolio of Treasuries duration-matched to the security or index question. To a first-order approximation, excess return should equal the OAS—carry—less change in spread times duration less credit losses. So, credit losses can be approximated by taking excess returns, then subtracting OAS and the effects of spread changes. This estimate ignores second-order changes and the effects of convexity, and there are other conceptual problems, including the problem of aggregating returns, OAS, and duration across securities to provide measures for a fixed-income index. However, the process described here provides at least ballpark estimates of credit losses on investment-grade credit securities. For high-yield indices and securities, downgrades are not an issue, and credit losses can be calculated directly from default incidence and expected recovery rates. Note from the table that “observed” credit losses do not decrease uniformly as quality increases, at least not for long duration indices. This is an historic anomaly of long credit performance and is another topic best addressed at another time.
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