Engineering LDI: Circumspect Pension Planning

Western Asset

Executive Summary

  • It is not enough for a pension asset allocation merely to look good on paper. It must also function well within real-world regulatory constraints and alongside the real-world limitations of the instruments available to the pension plan.
  • Keeping a corporate pension plan integrated with and consistent with corporate financial standards means the plan should never be run at lower standards than are in place for corporate financial operations.
  • A pension plan can never remove all risks. The presence of residual risks imposes diminishing returns on risk-reduction efforts, in which case it is non-optimal for the plan either to maintain a minimum-risk allocation or to attempt to eliminate any specific source of risk. Instead, more balanced, diversified approaches to risk-reduction should be taken.
  • These principles imply that pension plans should avoid such common practices as dollar-duration matching, confining active allocation to only a few managers or asset classes, adopting finely-honed fixed-income benchmarks within a largely unmatched asset portfolio, or leaving substantial tracking error between asset benchmarks and liability-discounting mechanisms.

When a pension plan practices liability-driven investing, it matches the risks of plan assets to those of plan liabilities. The plan recognizes that its true risks arise from movements in assets relative to liabilities, and so it manages the risks of its funded balance (assets minus liabilities), not merely of its assets alone. This same level of perspective should be applied at both the macro and micro levels of plan management.1 At the macro level, the corporate plan sponsor should recognize pension plan assets and liabilities as part of corporate assets and liabilities, and pension plan management should be integrated into corporate financial management. At the micro level, asset allocation tactics should be coordinated within an aggregate plan strategy. The plan’s decision on how much interest rate risk to tolerate should be in balance with its decisions on how much equity market and spread risk to tolerate, and these decisions should be consistent with the real-world precision of the financial instruments available to the plan.

We call these various levels of pension decision-making the engineering aspects of plan management, as opposed to design aspects. An automobile designer sets out to create a car that is sleek and beautiful, but the conceptual design must be road-tested, and design compromises must be engineered in so that the car will actually function well on real-world roads. Similarly, pension design features should be balanced and workable alongside economic, regulatory, and practical considerations.

Rather than putting an aluminum engine on a cast-iron chassis or combining state-of-the-art steering with run-of-the-mill brakes, a designer keeps the various features of a production-model car in balance. In much the same way, a corporation should keep the financial standards of its pension plan in balance with those of its operating finances. Similarly, it should avoid taking heroic measures to eliminate interest risk when it is simultaneously tolerating large amounts of equity- or real-estate market risk, and before finely engineering a cash-flow matching swap, it should first determine whether that instrument will exhibit large tracking error against its plan liabilities. Risk can never be eliminated from pension plan design, and in practice there are diminishing returns to risk-reduction efforts. Rather than trying to eliminate any one type of risk, a plan should balance all types of risk, just as it should balance risk-reduction with return-enhancement.

A hallmark of a well-run plan is that the various strata of plan design are integrated with each other and managed with commensurate levels of effort. Stated at such a conceptual level, this principle should be obvious. However, applying it to the real world can reveal a number of insights that are not immediately obvious and that run counter to many popular practices. In this paper, we’ll apply the principle first to the basics of pension management as part of corporate financial management. From there, we’ll discuss the realities of risk management within LDI. Finally, we’ll drill down to more nitty-gritty issues of LDI tactics, such as the general sub-optimality of dollar-duration matching, the choice of active versus passive management across asset classes, and the fine points of asset benchmark selection.

Integrating DB Pension Plans into Corporate Finances

A corporation’s pension plan is merely one aspect of its financial structure.Pension liabilities are a debt of the sponsoring corporation, just as is any corporate bond or loan, and plan assets are merely part of corporate assets. Writers since Treynor (1973) have argued that this is the true financial economics of corporate plans, and the reforms of FASB, ASB (UK), and IASB have firmly embedded this concept in global pension accounting. It is imperative that plan sponsors operate accordingly.

Since pension assets and liabilities are merely aspects of overall corporate financial structure, they should be managed at no lower a level of financial standards than are applied to other areas of corporate finance. Many of the fine points of this principle are explored in the finance literature on corporate pensions. We raise one specific here which should hint at the tenor of that literature while also extending it.

In order for a corporate sponsor to achieve at least the same level of integrity in its pension plan as in its corporate finances, the implicit rating of the plan should be no lower than that of the sponsor. For example, to maintain a AAA rating, the corporation must follow fastidious financial standards. Maintaining only, say, an A rated pension plan would detract from overall corporate financial standards, since pension finances are merely an aspect of corporate finances.2 In order to maintain a AAA rating overall while the pension plan is A, the non-pension aspects of corporate finances would have to be managed at better than a AAA level. The law of diminishing returns indicates that the company could more effectively relax non-pension financial standards and tighten pension standards until the two were comparable, leaving aggregate financial standards unchanged, but with less overall effort. This doesn’t mean that a AAA company’s plan should avoid risky assets. Rather, those risks should be taken within a diversified, well-funded allocation, just as corporate operations would pursue risky ventures in a diversified, well-funded manner.

FASB, ASB, and IASB all require that a corporate plan evaluate its pension liabilities using yields on “high quality” bonds. This is usually interpreted to mean AA yields. Should a AAA company opt for tighter standards than accounting protocols require: AAA instead of AA yields? Well, it wouldn’t borrow in the market at AA yields when it qualifies for AAA yields. Why should it effectively borrow in the pension plan at AA yields by using these for liability valuation? Using AAA yields would raise liability valuations over GAAP minimum levels and thus reduce corporate book value. However, that would not reduce the economic value nor the market cap of the corporation, as corporate finances are already being managed at AAA standards, and market valuations are based on those standards as well.3

On the other side of the spectrum, a speculative-grade corporation may want to operate its pension plan at a higher standard, partly because of regulatory constraints, but also in order to maintain credibility with its workforce. A corporation provides pension benefits in lieu of cash wages. If a corporation were to run its pension plan with speculative-grade standards, its workers would and should value their pension benefits at a lower level than what is reported on the firm’s financial statements (based on high-quality bond yields). In that case, the corporation might not be getting its money’s worth from the plan.

So a high-grade corporation should operate its pension plan at no lower a quality level than its corporate finances, but a speculative-grade corporation might want to run a more highly-rated plan. This asymmetry accrues from the asymmetric economics of pension plans. While a corporation is fully liable for plan under-performance, it has only limited ability to benefit from any over-performance. Regulatory strictures are similarly asymmetric.

To summarize this section, a firm’s pension plan structure should be consistent with overall corporate financial structure. Pension-plan standards should be maintained at least as high as corporate financial standards. Under-funding a plan makes sense only if this is a lower-cost method of funding corporate operations than viable alternatives. Over-funding the plan makes sense only if pension assets provide the best investment of corporate cash and if the sponsor has a viable strategy for repatriating excess plan assets.

Optimization Balances Competing Ends

It is impossible to eliminate risk from a pension plan. Even when liabilities are fully hedged, the plan will still be exposed to residual, non-hedgeable actuarial (and perhaps interest-rate and inflation) risks. The existence of these residual risks necessarily implies that there will be diminishing returns to risk-reduction efforts. Not only is there a trade-off between increasing return and reducing risk, but also that trade-off becomes more severe as a plan seeks either lower levels of risk or higher levels of return. In addition, the degree of these diminishing returns increases as residual risks proliferate.

Exhibit 1
Existence of residual risks introduces “diminishing returns’ to plans’ risk-reduction efforts.
If residual risks were zero (dark blue frontier), the trade-off between risk and return would not become more severe as risk was reduced or return increased. Return/risk ratios would actually increase along the frontier as risk was reduced. With the existence of residual risks, the frontiers become curved. Diminishing returns set in. Ever-larger losses of return are required to achieve successive reductions in risk, and return/risk profiles eventually deteriorate as risks are reduced. Also, the severity of diminishing returns increases as residual risks increase.
Source: Western Asset

As long as there is actuarial risk to liabilities (uncertainty of participants’ retirement-age and longevity), a plan faces a “deteriorating” trade-off between risk and return. Exhibit 1 shows efficient frontiers for pension allocations under different assumptions about residual risks. If actuarial risks were ignored, the efficient frontier would be the straight (dark blue) line emanating from the vertical axis. Once actuarial risks are considered, the efficient frontier becomes curved, with a vertical slope at the point of minimum risk (the fully-hedged allocation).4 The curvature of the frontier and its vertical slope at minimum risk mean that as the plan moves to reduce risk, moving left on the frontier, it sacrifices ever-larger returns for each successive reduction in risk. There are residual risk, the more curved the frontier, and so the more rapidly diminishing the returns from risk reduction efforts.

Besides actuarial risks, obligations of the plan beyond thirty years cannot be perfectly hedged with available financial instruments, and this will result in residual interest risk. Similarly, for open plans where benefits rise with wages, there is no available instrument that can perfectly hedge this “inflation” risk. Such considerations magnify the residual risks any plan faces, even hard-frozen plans.

Because the efficient frontier is curved and vertical at the minimum-risk, fully-hedged position, no plan with any risk tolerance will move to a fully-hedged position. The diminishing returns so incurred are too onerous. Similarly, diminishing returns accrue to attempts to eliminate any one particular type of risk, so completely eliminating any one type of risk—such as interest-rate duration—is also a sub-optimal policy.

In managing risk, a pension plan must be circumspect. With diminishing returns occurring in every direction it might move, rather than making extravagant risk-reduction efforts in any one direction, a plan is better off making balanced risk-reduction efforts on all fronts. This principle can be better understood by applying it to various popular LDI tactics.

Specifics of LDI Engineering

Dollar-Duration Matching Is Non-Optimal.

Exhibit 2
Dollar-duration matching produces an unbalanced risk profile.
Source: Western Asset

Dollar-duration matching means matching plan asset dollar duration to that of plan liabilities. A duration-matching position is sub-optimal, because the instruments used to boost asset duration most typically incur spread and curve risk as well.5 It is all but inevitable that at the point of duration-matching, the spread risks of assets and liabilities will be mismatched. Rather than stopping asset interest duration at the point of duration-matching, a plan should reduce or increase interest-rate duration from there, depending on whether asset spread duration is greater than or less than liability spread duration.6

The optimal position is where interest-rate and spread duration are balanced.7 Since dollar-duration matching means eliminating interest-rate duration risk, duration-matching cannot be optimal because it leaves other risks outstanding. This result holds regardless of the instrument used to increase interest-rate duration, so long as its spread duration differs from that of plan liabilities. This spread mismatch effectively imposes diminishing returns on duration-matching efforts. A balanced risk profile would dominate the duration-matching position.

We have derived this result under an analysis considering only interest-rate duration and spread duration. In the real world, interest-rate risk also occurs due to various types of yield-curve shifts: slope, convexity, etc. With these other risks in play as well as interest-rate and spread duration, not to mention equity-market risk, a dollar-duration matching program becomes even more sub-optimal, as it leaves all of these risk mismatches on the table while obsessing on interest-rate duration mismatches.

Spread Active Management Across Sectors.

The same principle of balancing risks applies to the choice of active asset allocations. Many plans choose to confine active management to just a few asset classes or managers. However, active management should be concentrated within one or two managers or asset classes only if the information ratios for those managers/classes dominate others’. If information ratios were more or less equal, then concentrating active management would necessarily leave the plan’s active risk undiversified.8 The plan could improve performance by properly diversifying active allocations.

In a risk-efficient allocation, the extent of active allocations across managers and asset classes will vary directly with the information ratios of asset managers, with high information-ratio managers receiving large active allocations and vice-versa. Ironically, some real-world plans restrict active mandates to the equity market, where manager information ratios are commonly found to be lower than elsewhere.9

Keep Benchmark Selection Commensurate With Asset Allocation.

Balancing pension risks includes “engineering” asset benchmarks to keep them consistent with the overall risk of a plan. For example, in a plan with a “traditional” 60% equities and 40% fixed-income allocation, it is not risk-efficient to pursue a precise cash-flow matching benchmark for fixed-income assets when the plan maintains such a large mismatch on its equity allocation. A highly-engineered fixed-income benchmark would be long past the point of severely diminishing returns to risk-reduction. The plan would do better to sharply scale back fixed-income matching efforts and incrementally reduce the risks of the rest of its portfolio.

The plan could efficiently reduce risk by extending fixed-income allocations to long duration, but that is about as far as it should go.10 It needn’t even worry about duration-matching—let alone cash-flow matching, until its asset/liability mismatch has been sharply curtailed. It is not that a custom benchmark would fail to reduce risk. Rather, that risk reduction would be achieved at too great a cost. In terms of the earlier analogy, it would be like putting an aluminum engine on top of a cast-iron chassis. Flailing away at the last few basis points of interest risk, while leaving thousands of basis points of equity risk in play, is unbalanced and inefficient.

Exhibit 3
Pursuing cash-flow matching on a 40% fixed-income benchmark, while leaving an unmatched 60% equity allocation leaves funded-balance risks unbalanced.
Source: Western Asset

Match Your Liability Discount Instrument To Your Fixed-Income Benchmark.

If your plan is considering LDI, be aware that a considerable element of funded-balance risk arises from the tracing error between long-duration benchmarks and common liability valuations. For the purpose of discounting plan obligations, accounting and regulatory guidelines allow use of either a single, high-grade corporate bond yield or a high-grade yield curve. As we will detail in a follow-up to this paper, liability valuations utilizing a single discount rate show tracking errors of 400 bps per year with standard long-duration cash and swap benchmarks. The divergences among these reach the 1000-bp level during years of business cycle transition (from expansion to recession and vice-versa). Furthermore, switching to curve-based liability valuations generally fails to materially reduce the magnitude of these “basis risks”. (Yes, these tracking errors occur for benchmarks that are duration-matched to liability valuations.)

With such large basis risks looming, it makes little sense for a plan to finely tune asset allocations or benchmarks until basis risk issues have been addressed. The choice of liability discounting instrument should be coordinated with benchmark selection. For any fixed-income benchmark, a corresponding yield curve can be extracted. The curve corresponding to a plan’s specific benchmark should be used to discount its liabilities. Alternatively, if the discounting mechanism is fixed, a suitable asset benchmark should be chosen to match it. We will work through the specifics of this process in the forthcoming paper.


A pension allocation should make conceptual sense. It should also be workable in a real-world environment. Various optimization strategies look fine on paper, but typically feature practical shortcomings that detract from their real-world performance. Even on paper, some stratagems are suspect because they obsess on addressing particular aspects of risk, rather than taking a more circumspect approach. Plan managers must engineer pension design, both by balancing various aspects of risk and by making allowances for the practical shortcomings of available financial instruments.

A well-managed pension plan balances risks not only across asset classes, active allocations, and benchmarks, but also across the operational and pension-plan components of corporate finances. In some instances, this will result in the pension plan being run at a higher financial standard than is required by accounting or government regulations. In no instance should a pension plan be run at a lower standard than that applied to corporate finances.

Risk can never be completely removed from a pension plan or from a corporate structure, and the diminishing returns involved in risk-reduction efforts indicate that a plan should not pursue drastic risk-reduction efforts in any one area. Dollar-duration matching will typically be a non-optimal position. Similarly, active allocations should be spread across asset classes unless any one particular manager or asset class can be shown to enjoy a vastly higher information ratio than the rest. A plan should not over-engineer its asset benchmark to a degree of precision inconsistent with its overall risk budget. Finally, a plan should coordinate its choices on liability-discounting mechanism and asset benchmark.

These are just a few of the “road tests” that a serious and balanced, but straightforward approach to effective risk reduction would impose. LDI principles can work for real-world pension plans. However, precise conceptual plan designs must be road-tested to ensure satisfactory real-world performance, and myopic applications of LDI principles should be replaced with balanced, more comprehensive practices.


Bazdarich, M. (2007), “Separability and Pension Optimization,” Journal of Fixed Income, Winter pp.1-8.

Jin, Li, Robert C. Merton, and Zvi Bodie (2006), “Do a Firm’s Equity Returns Reflect the Risk Of Its Pension Plan,” Journal of Financial Economics, July 2006, pp. 257-92.

Treynor, Jack. (1973), “The Principles of Corporate Pension Finance,” Journal of Finance, pp. 627-38.

Western Asset (2006a), “Which Alpha Would You Choose?” January 2006

Western Asset (2006b), “The Impact of Active LDI On Portfolio Selection,” May 2006

Western Asset (2006c), “Effective LDI: When Do Bond Swaps Help,” October 2006

  1. The principles prescribed in this paper are the opinions that we have formed based upon our research and experience. We believe their application would generally be beneficial to pension plans. However, we are not recommending they be applied to any specific pension plan, and they should not be construed as legal advice on plan structure.
  2. Also, the analysis of Jin et al. (2006) found that even before FAS 158, financial markets already were incorporating pension plan finances into corporate valuations. They found that the financial metrics of plans were fully reflected both in market cap and bond yields. So when a corporation explicitly integrates pension management within corporate financial management, it is merely acknowledging the discipline that market forces have already imposed upon it.
  3. As stated in footnote 2, market pricing has been found to already reflect the integrated financial practices of the corporation, both operational and pension aspects. If the corporation’s marketable debt is priced to a AAA yield, that must be because the market views the overall corporate finances as being of AAA quality. That valuation wouldn’t be valid unless it included pension liabilities as part of the AAA debt structure, in which case the mere accounting artifice of using AA yields for liability valuation would be inconsequential for corporate valuation.
  4. As discussed in Western Asset (2006b) and Bazdarich (2007), any point on the efficient frontier can be decomposed into a full hedge of plan liabilities (beta) and some allocation to an opportunistic overlay portfolio (alpha). Different points on the frontier differ only by the extent of allocation to the opportunistic portfolio. The volatility of the fully-hedged portfolio is merely the residual risk of the liabilities, so the volatility/risk of the allocation is (σr2α2)1/2, where σr is residual risk and σα is opportunistic risk. (Because the hedge portfolio removes all systematic risk, the hedged funded balance will have zero correlation with any available alternate strategy, including the opportunistic allocation, hence there is no covariance term in the bracketed expression.) Were σr=0, plan risk would be σα and would decline proportionally with opportunistic risk. However, as long as σr>0, successive reductions in opportunistic risk effect smaller and smaller reductions in total risk. Also, the larger residual risk, the smaller the reduction in total risk from any given reduction in opportunistic risk.
  5. While LDI analyses typically ignore the spread risk of long-duration swaps, swaps do exhibit such risks. In previous papers (cf. Western Asset [2006c]), we have critiqued the over-reliance on swaps in LDI efforts. Those results hold even without reference to the spread issues involved with swaps. Incorporating spread risk into the analysis further strengthens the results of our previous analyses.
  6. That is, suppose the bond or swap used to increase interest-rate duration has greater spread duration than the liabilities and that at the point of interest-rate duration-matching, the funded balance has positive spread duration. Then reducing exposure to the bond or swap—away from the duration-matching position—would increase interest-rate duration risk only slightly, because funded-balance interest-rate duration is starting from zero, but it would reduce spread risk substantially, thus reducing total funded-balance risk. Suppose instead that funded-balance spread duration is negative at the point of interest-rate duration-matching. (That is, suppose asset spread duration is less than liability spread duration.) Then increasing exposure to the bond or swap would raise interest risk only slightly, while lowering spread risk substantially. As long as spread durations of some assets are different from that of the liabilities, it will be sub-optimal to subject the plan to zero interest risk, but substantial spread risk. Instead, a more balanced exposure to interest- and spread-risks will more effectively reduce funded-balance risks.
  7. This is a standard result of optimization theory. When either objective function or constraints are convex/concave, optimization will typically result in an interior solution: non-zero values for all input variables. A “corner solution” is when some input is chosen at either minimum (zero) or maximum levels. Optimization problems can exhibit corner solutions when both objective and constraint functions are linear. In the present context, elimination of, say, interest risk is a corner solution. Such a policy will typically be non-optimal in real-world situations, because the presence of residual risks introduces diminishing returns within objective functions. So, optimized results will be interior solutions, with balanced exposure to all risks.
  8. We are assuming, of course, that the alphas of various managers are not perfectly correlated.
  9. See Western Asset (2006a). The well-known unreliability (low information ratio) of equity-managers’ alpha is the main reason the portable alpha approach has gained popularity in recent years.
  10. See Western Asset (2006c).
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