Dollar Duration Matching:, Lecture notes of Accounting

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Dollar Duration Matching:

A Framework for Evaluating

Liability Driven Investment (LDI) Strategies

by Jon Taylor, Managing Director, Principal Global Investors

Exhibit 1: Annual Changes in AA Corporate Bond Yields

Source: Citigroup Yieldbook, Principal Global Investors

0

50

100

150

200

250

19901991199219931994199519961997199819992000200120022003200420052006

Basis Point Change

Liability Values Increase

Exhibit 2: S&P 500 Annual Returns

Source: Bloomberg, Principal Global Investors

0

10

20

30

40

19901991199219931994199519961997199819992000200120022003200420052006

Percentage Change

Asset Values Decrease

Measuring the Interest Rate Exposure of a Typical Defined Benefit Plan

Let’s consider a typical, moderate sized retirement plan and assess the duration mismatch and possible liability driven investment (LDI) strategies that can be employed to mitigate the interest rate risk of the plan. We will assume that the plan is fully funded with liabilities of $10 billion funded by assets of $ billion. The duration of the liabilities is 15. For simplicity, we will assume that the plan has 60% of plan assets invested in the S&P 500 Index and 40% invested in the Lehman Aggregate Bond Index. Currently, the duration of the Lehman Aggregate is 4.7 years.

By computing the dollar duration of plan liabilities and plan assets, we can ascertain the dollar impact on the portfolio of changes in interest rates assuming other factors are held constant.

Dollar duration can be computed as follows:

• Liability dollar duration = ($10.0 billion) * (100.0 %) * 15 = $150.0 billion
• Asset dollar duration: ($10.0 billion) * (40.0%) * (4.7) = $18.80 billion

Assuming, as we do in this example, the plan has 40 % in bonds managed against the Lehman Aggregate, a 100 basis point (bp) drop in interest rates will result in a deterioration of the plan’s funding status of $1.312 billion (see Exhibit 3 below) computed as follows:

((Liability $ Duration of $150 bn) - (Asset $ Duration of $18.8 bn)) * 0.01 = $1.312 bn

Exhibit 3: Exposure to Interest Rate Risk

Source: Principal Global Investors

-100 -50 -25 0 25 50 100

-$1,500,

-$1,000,

-$500,

$

$500,

$1,000,

$1,500,

Interest Rate Change (bp)

Surplus Value Change (millions)

(^) Against the LehmanBonds Managed Aggregate Index

Dollar Duration Matching

The bonds in the portfolio only insulate 12.5% of the duration risk of the liabilities. In effect, the plan sponsor has an active bet that interest rates will remain static or increase, or that gains from equities will be sufficient to offset any increase in liability valuations due to a decrease in interest rates.

Txt Box

It should be noted that this dollar duration analysis does not factor in convexity and its impact on both liabilities and fixed income assets. For small moves in interest rates, the effect of convexity is modest, but for large moves it can be material.

Assessing the Duration of Non-Fixed Income Assets

So far, this analysis assumes that equities do not respond to moves in interest rates or that their response is offset by other factors as was the case in 2000 to 2002. Under most market conditions, this overstates the risk as equities are generally sensitive to interest rate changes and, as such, would offset some of this risk.

If you factor in the interest rate sensitivity of equities and other assets into the equation, the amount of fixed income duration needed to match the liabilities diminishes. For example, consider equities. Companies generate a stream of earnings out into the future that are discounted to determine a current fundamental or fair value for a company. The discount rate used to discount these earnings is determined, in part, from market interest rates and, as such, is sensitive to changes in market interest rates. Thus, because equities generate cash flow far out into the future, they are often considered to be long-duration assets.

(^1) Duration measures the approximate percentage change in value for a 100 basis point change in interest rates. Duration is a first approximation and is only accurate for small changes in interest rates. For large interest rate moves, the estimation of the percentage change in value for changes in interest rates can be improved by adding an adjustment for convexity. Convexity is an important consideration when considering LDI strategies. Liabilities possess positive convexity. That is, changes in value are greater for interest rate declines than for commensurate interest rate increases. A typical bond portfolio also possesses positive convexity, and as such, contributes positively to any liability hedge. It should be noted, however, that some fixed income instruments such as mortgage backed securities possess negative convexity which needs to be factored into the analysis when they are included in any LDI strategy.

In effect, the plan sponsor has an active bet that interest rates will remain static

or increase, or that gains from equities will be sufficient to offset any increase in

liability valuations due to a decrease in interest rates.

Dollar Duration Matching

Exhibit 4: Rolling Three Year Correlation

of the Lehman Long Government/Credit Index

vs. the S&P 500 Index (Price Changes)

Source: Lehman Live and Principal Global Investors

-0.

-0.

-0.

0

Jan-83Jul-84Jan-86Jul-87Jan-89Jul-90Jan-92Jul-93Jan-95Jul-96Jan-98Jul-99Jan-01Jul-02Jan-04Jul-

Correlation

Average Correlation 0.

Exhibit 5: Interest Rate Risk Mitigation Strategies:

Moving to a Long-Duration Bond Mandate

and Factoring in the Interest Rate Sensitivity of Equities

Source: Bloomberg, Principal Global Investors

-100 -50 -25 0

-$1,500,

-$1,000,

-$500,

$

$500,

$1,000,

$1,500,

Surplus Value Change (millions)

Interest Rate Change (bp)

25 50 100

Derivatives Overlay Strategies

A possible next step for the plan will be to consider a derivatives overlay strategy to reduce the mismatch further.

The major attraction of a derivatives overlay strategy is that it can be implemented without radically disturbing underlying portfolios. This will be very attractive for multi-manager situations. There are many advantages to using derivatives to reduce the mismatch between plan liabilities and plan assets. First and foremost is efficiency. The interest rate derivatives market is deep, liquid, and highly efficient and has performed well during periods of financial market stress. Derivatives, such as Treasury futures, interest rate swaps, options and swaptions provide an efficient mechanism for extending asset duration and hedging inflation risk. Derivatives are also very cost effective and allow for a high degree of precision when implementing a liability driven investment strategy.

Exhibit 6: Interest Rate Risk Mitigation Strategies:

Moving to a Long-Duration Bond Mandate,

Factoring in the Interest Rate Sensitivity of Equities

and Adding a Derivatives Overlay Strategy

Source: Principal Global Investors

-100 -50 -25 0 25 50 100

-$1,500,

-$1,000,

-$500,

$

$500,

$1,000,

$1,500,

Interest Rate Change (bp)

Surplus Value Change (millions)

Long Duration Bonds, Equities &Derivatives Overlay

Derivatives entail cash flows and these cash flows need to be funded. Thus, there needs to be a source of liquidity that can be accessed. In the case of futures, initial and variation margin needs to be posted. 2 For swaps, while there is no initial cash outlay, interest payments are made periodically and collateral often needs to be posted between actual cash flow dates. With a typical interest rate swap, fixed payments are made semi-annually while floating rate payments are made quarterly. There are, however, many variations to the cash flow frequency. Collateral that can be posted generally consists of high quality bonds or cash. The amount of collateral required will be determined by changes in interest rates after the effective date of the swap and the quality of the securities posted. 3

Additionally, to the extent the pension plan’s asset portfolio is totally exposed to financial market risk already, any derivatives overlay will entail leverage.^4 Thus for the plan to preserve existing exposure to equities and other high expected return assets while at the same time reducing the duration mismatch further would entail some leverage.

Suppose that our hypothetical plan sponsor decides to reduce the asset and liability duration mismatch further by entering into an interest rate swap. For expositional purposes, lets look at 30-year zero coupon swap with a notional value of $1.0 billion. A 30-year zero coupon swap is selected because it will add meaningfully to the hedge because of the substantial duration afforded by the 30-year zero coupon structure. 5 On a dollar duration basis, this swap will add another $29.1 billion to the combined hedge. With this swap added to the duration mismatch mitigation strategies already employed, the plan now has over 50% of the plan’s interest rate risk hedged (see Exhibit 6). The dark blue bars represent the sensitivity of the plan’s funding status to changes in interest rates after imputing a duration estimate for equities and factoring in a move to long duration bonds and implementing an interest rate swap.

(^2) The notional value of a Treasury bond futures contract is $100,000 and the initial margin for institutional hedgers is $1000 or 1.0 percent of the notional value. Variation margin is transferred daily and reflects the gain or loss on the futures contracts. The duration on the Treasury bond futures contract tracks the cheapest- to-deliver bond that can be delivered to settle the contract at maturity. When this paper was written, the 3 duration of the cheapest-to-deliver was 9.85. Swaps are traded within the legal framework of the International Swaps and Derivatives Association (ISDA) master agreement. As part of the standard ISDA, there is a Credit Support Annex that is negotiated between the counterparties which specifies the thresholds that trigger the posting of collateral when the value of the swap changes because of changes in interest rates. In addition, the Credit Support Annex also specifies 4 crediting rates for different securities posted as collateral. 5 In this case, leverage is defined as market exposure greater than one. A 30-year zero coupon swap, because of its 30-year term, provides a duration of nearly 30. In this case, the duration of the fixed side is 30, and the modified duration is 29.35. Netting out the floating rate side of the swap leaves a net modified duration of 29.1. Moreover, while the tenor of the swap is 30 years, the swap can be terminated at any time. Typically, the swap is assigned to a dealer who quotes a price for cancelling the swap. The cost of unwinding the swap will be driven by the change in interest rates since the effective date of the swap.

Dollar Duration Matching

While a long-duration bullet hedge such as the 30-year zero coupon swap explored here offers a very high duration per dollar of notional value, it can create a large mismatch with the duration profile of plan liabilities, thus making the plan vulnerable to twists in the yield curve. A more precise approach is to match key rate durations along the term structure (see Exhibit 8 below). This ensures that twists and non-parallel shifts in the yield curve result in minimal slippage in the hedge.

Exhibit 8: Optimize on Key Rate Durations

Source: Citigroup Yieldbook, Principal Global Investors

To the extent that the plan is exposed to inflation risk in the form of CPI linked benefits, a part of any derivatives overlay strategy should be comprised of inflation linked derivatives.^6 Inflation sensitive liabilities can be broken out and hedged separately with inflation sensitive derivatives.

In considering various duration mismatch mitigation strategies, one must be careful not to over hedge and recognize that liability estimation is an inexact science and that the interest sensitivity of non-fixed income assets varies over time. Thus, a full, exact hedge of plan liabilities is often not justified.

The use of leverage is a major issue for many plans. Presumably, the prohibition most plan sponsors have against employing leverage is driven by risk considerations. Ironically, employing leverage in an asset-liability management framework may, in fact, reduce surplus variability, and, thus, by implication reduce plan risk. Leverage is inherently a risk measure and needs to be evaluated in the context of the entire portfolio configuration.

(^6) Inflation risk embedded in a plan’s liabilities can be hedged using TIPS (out to 20 years), iSTRIPS and inflation swaps (liquid out to 10 years).

KRD Hedge Liabilities

0

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12

14

1 Yr 2 Yr 3 Yr 5 Yr 7 Yr 10 Yr 15 Yr 20 Yr 30 Yr Total Duration

Years

Dollar Duration Matching

Conclusion

A duration mismatch between plan assets and plan liabilities constitutes an active bet on the part of a plan sponsor. That is, if a plan’s asset duration is less than the duration of the liabilities that these assets are earmarked to fund, then the plan is betting that interest rates will increase or, if interest rates fall, that the return on other assets in the portfolio will more than offset the increase in the value of the liabilities due to the decline in interest rates. Dollar duration matching provides an intuitive and effective framework for assessing the magnitude of the duration mismatch and the potential impact this mismatch will have on the plan’s surplus position. With dollar duration matching, a plan sponsor can assess various duration mitigation strategies and their impact on surplus volatility.

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While this communication may be used to promote or market a transaction or an idea that is discussed in the publication, it is intended to provide general information about the subject matter covered and is provided with the understanding that The Principal is not rendering legal, accounting, or tax advice. It is not a marketed opinion and may not be used to avoid penalties under the Internal Revenue Code. You should consult with appropriate counsel or other advisors on all matters pertaining to legal, tax, or accounting obligations and requirements. Insurance products and plan administrative services are provided by Principal Life Insurance Company. Principal Life and Principal Global Investors are members of the Principal Financial Group® (The Principal®), Des Moines, IA 50392.