Constructing A Liability Hedging Portfolio PDF
Constructing A Liability Hedging Portfolio PDF
Constructing A Liability Hedging Portfolio PDF
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Contents
Executive Summary 1
List of Figures
1. A Holistic Approach to Plan Assets:
Decisions in One Portfolio Impact the Other 2
2. The Value of Liabilities Is Different Under Each Discount Rate 5
3. Liability Hedge Ratio Formula 6
4. Long Credit Bonds Can Keep Up With Liabilities
Better Than Core Bonds 7
5. Liability Hedge Portfolio Using Core Bonds Can Erode
Funded Status in Periods of Steady or Falling Interest Rates 7
6. Distribution of Benefit Payments Creates Curve Risk 8
7. The Impact of One Issuer on a Bond Index Can Be Significant 11
8. With a Large Growth (Equity) Portfolio,
Additional Exposure to Credit May Increase Risk 13
9. Interest Rate Swap Example 17
10. The Marginal Payoff of Swaptions Mirrors That of Bonds 19
11. Swaption Collar Can Increase Protection at Reduced Costs 20
List of Tables
1. Identifying the Most Relevant Liability for the Sponsor’s Needs 4
2. Top Ten Constituents of Barclays AA Corporate Index 10
3. Equities Are Modestly Correlated to Credit Spreads 12
Executive Summary
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Liability Hedging
Figure 1. A Holistic Approach to Plan Assets: Decisions in One Portfolio Impact the Other
Role Role
Theoretical zero volatility asset Growth engine for portfolio
that “perfectly” immunizes
liability Objectives
Interaction Effect
The impact of decisions in Cover costs of administering
Objective one portfolio on the other the plan
Minimize impact of movements Reduce future contribution
in the market-based discount amounts of the plan sponsor
rate on the liability and funded
ratio Meet required return expectations
of the plan
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Liability Hedging
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Liability Hedging
plan’s health as measured by a threshold for Table 1 summarizes the variety of liability meth-
acceptable funding levels. The funding target odologies that are disclosed in a typical actuarial
methodology uses similar cash flows and report. Plan sponsors should identify for them-
assumptions as in the ABO calculation and selves which methodology is most pertinent when
impacts the sponsor’s cash contribution require- thinking about the risks of the plan. For instance,
ments. Recent legislation known as MAP-21 has if a sponsor’s primary concern is to mitigate the
materially impacted funding target calculations volatility of the plan’s liabilities on the balance
by allowing plan sponsors to use higher refer- sheet, the sponsor would pay close attention to the
ence rates (based on a 25-year moving average) PBO estimate of its liabilities. But if the sponsor
in the calculation. This lowers the present value wants to reduce the volatility of its annual cash
of pension liabilities and required contributions, contribution, the funding target liability would be
providing some relief to sponsors (the relief is the right metric to monitor and manage.
temporary as the effects of MAP-21 will fade
Although inflation has an indirect influence on
away over the coming years). However, because
the PBO in terms of assumed salary growth,
MAP-21 has created a more favorable treatment
inflation typically does not meaningfully influ-
of liability present values that deviates greatly
ence liability measurement for most US plans.
from a “mark-to-market” approach, some plans
Unless explicitly stated in the plan’s provisions,
have shifted to accounting-based methods
US defined benefit pension benefits are usually
(ABO or PBO) when evaluating the movement
defined as a nominal dollar value (e.g., based
and risks associated with their liability to better
on a percentage of an employee’s salary level).
account for necessary future contributions after
Since benefits are usually not subject to a cost of
the expiration of MAP-21 relief.
living adjustment, US plans emphasize nominal
corporate and Treasury bonds in their liability
Table 1. Identifying the Most Relevant Liability for the Sponsor’s Needs
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Liability Hedging
hedging portfolios. The present value of plan’s Capital Allocation and Hedging Ratio
liabilities, however, will change in response to For most plans, the strategic asset allocation
changes in perceived or expected inflation to is a customized mix between the growth and
the extent that interest rates are affected. liability hedging portfolios, taking into consid-
As referenced in Table 1, the particular defini- eration the sponsor’s tolerance for surplus risk.
tion of the liability determines what discount rate Surplus risk refers to the expected volatility of
the plan must use, and the choice of discount funded status, measuring the extent to which
rate impacts the present value of the liability. fund assets and liabilities will deviate from each
Figure 2 displays the various discount rates that other (a theoretical portfolio with no surplus
could be used and their impact on the present risk would be “immunized” as assets perfectly
value of the funding rate liability. The value of match liabilities). It can be used to measure
the liability increases moving from the top of the risk of failing to attain adequate long-term
the table in Figure 2 to the bottom, as there is returns consistent with the plan’s expected
an inverse relationship between the discount return—inability to mitigate surplus risk means
rate and the present value of the liability. For the sponsor will ultimately have to make up
example, there is an approximately $33 million the difference and kick in higher contributions
difference in the value of the liability between to keep the plan’s funding at a healthy level.
the MAP-21 Discount Curve and IRS Full Generally, open and soft closed plans, as well
Yield Curve, as the MAP-21 legislation results as hard frozen plans that are underfunded, will
in higher discount rates than the IRS Full Yield assume some level of surplus risk to generate
Curve. This example highlights the funding excess return (above and beyond the liability’s
status and subsequent required contribution return) to increase funded status and reduce
relief that defined-benefit plans have received future contributions.
since the introduction of the legislation.
7%
6%
5%
Discount Rate
4%
3%
| 5
Liability Hedging
Analysis is possible to quantify the size of such as the Barclays Aggregate, serve as an all-
surplus risk (or surplus volatility), but on a more inclusive universe of investment-grade bonds,
simple and intuitive level, hedge ratios can be the Aggregate has a meaningful mismatch in
computed to assess how much the market value duration compared to most defined benefit
change for plan assets captures the change in pension liabilities. Even larger allocations
pension liabilities. Liability values and related to an Aggregate-based portfolio will embed
hedges are significantly driven by the level of significant surplus risk—potentially more than
interest rates, as well as changes in the credit the sponsor realizes. Lesser but still important
spread of corporate bond yields in excess of considerations of using core bond benchmarks
US Treasuries. Sponsors can compute a rate are their significant holdings in mortgage-
hedge ratio that provides an estimate of how backed and asset-backed securities, which are a
“protected” the plan would be given a move in poor hedge for a liability marked on the basis
interest rates (Figure 3). of corporate yields. Core bond benchmarks
also introduce additional tracking error as they
include securities with negative convexity.
Figure 3. Liabilities Hedge Ratio Formula
Similar calculations can be made for credit
LH Allocation % x LH Duration x Funded Status % spread metrics, as a credit hedge ratio estimates
Liability Duration how “protected” the plan is from tightening
(falling) credit spreads relative to the credit
sensitivity of the liability. As an extreme
For example, assume a defined benefit plan example, a plan with a 100% allocation to
with the following characteristics: duration-matched Treasuries would be effec-
tively 100% hedged to general rate sensitivity,
Funded Status: 85% but the plan would have a 0% credit hedge
Liability Hedging Allocation: 50% position, given no exposure to credit spreads.
Liability Hedge Duration: 5.5 years
Duration of the Liability Hedge
Liability Duration: 12 years Figure 4 ties the concepts of rate and credit
Despite a 50% allocation to fixed income, hedging together and indicates the benchmark’s
this hypothetical plan maintains an effective importance to the effectiveness of a liability
interest rate hedge ratio of 20%, suggesting the hedge. The chart displays the cumulative
plan is hedged on less than a quarter of its rate performance of a sample liability stream (with
exposure related to the liability. The rate hedge duration of 13 years—approximating typical
ratio is lower than the liability hedging alloca- pension plan duration), the Barclays US Long-
tion due to the plan being underfunded (not Term Credit Corporate Index, and the Barclays
enough assets available to match the size of the Aggregate Bond Index during a period of
liability) and the shorter duration of the assets falling interest rates (January 2010 through
relative to the liabilities. December 2013). The Long Credit index does
a significantly better job of keeping up with the
This example reveals an inherent weakness growth in liabilities, as its duration and yields
of using “core” or “core plus” approaches as are closer to those of the liability.
liability hedges. Though core bond benchmarks,
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Liability Hedging
The Aggregate’s inability to hedge the liabili- hedge is invested in long duration bonds. Said
ties can be very painful for pension plans. As another way, a pension portfolio with total
shown in Figure 5, a plan with a 50/50 alloca- assets of $1 billion whose liability hedge is
tion (growth/liability hedge), where the liability invested in long duration bonds would end
hedge is the Aggregate, would have a funded up with approximately $100 million more in
status of 80% at the end of the simulation funded status than the portfolio using the
period. This contrasts with a terminal funded Aggregate during this period of falling interest
status of 87% for the portfolio whose liability rates.
Figure 4. Long Credit Bonds Can Keep Up With Liabilities Better Than Core Bonds
150
140
Asset/Liability Growth (US$)
136.57
135.09
130
120
117.37
110
Barclays Agg
100 Barclays Long Credit
Sample Liability Stream
90
Dec-09 Jun-10 Dec-10 Jun-11 Dec-11 Jun-12 Dec-12 Jun-13 Dec-13
Figure 5. Liability Hedge Portfolio Using Core Bonds Can Erode Funded Status
in Periods of Steady or Falling Interest Rates
90%
50% MSCI ACWI/ 50% Barclays Agg 87%
50% MSCI ACWI/ 50% Long Credit
85%
Funding Status
80% 80%
75%
70%
65%
Dec-09 Jun-10 Dec-10 Jun-11 Dec-11 Jun-12 Dec-12 Jun-13 Dec-13
Sources: Barclays and MSCI Inc. MSCI data provided "as is" without any express or implied warranties.
| 7
Liability Hedging
Pitfalls of “Matching” the Liability and mitigated, but several of which are not
possible to eliminate.1 Specifically, we note the
A plan’s liability present value calculation is following chief challenges in perfectly hedging
subject to many complexities, and as a result, a liability stream: curve matching, credit spread
plans will encounter numerous implementa- constraints, high-quality concentration, and
tion challenges and trade-offs. It is virtually downgrade decay. Because many of these chal-
impossible to perfectly mimic the behavior lenges are unsolvable, we advise plans to devise
of a discounted liability stream through an the most effective liability hedge that mitigates
investable bond portfolio. The assumption is these trade-offs and manage surplus risk to an
a discrete set of annual cash flows discounted acceptable level, rather than try to attain a false
at a corporate bond rate could be perfectly sense of precision at a greater cost.
“immunized,” but in reality, the achievement 1
In this section, we focus on liability precision chal-
of complete liability replication is elusive. lenges related to interest rates and credit spreads, but we
In this section, we discuss the most notable note additional challenges exist such as those generated
challenges—some of which can be controlled by changes in mortality tables, future demographics
gains and losses, actuarial changes, etc.
14
12
Hypothetical Liability Cash Flows (Duration=14 Years)
0
1 10 19 28 37 46 55 64 73 82 91 100
Years Until Maturity
Source: Barclays.
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Liability Hedging
| 9
Liability Hedging
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Liability Hedging
and actuarial assumption changes), the sole recent downgrade. As indicated in Figure 7,
mechanism of change in the liability present after Verizon announced plans to issue debt
value is driven by applying a dynamic discount and acquire the Verizon Wireless interests it
rate. did not already own from Vodafone, Verizon
However, the asset side is not blessed with such bonds widened substantially (widening spreads
a static cash flow structure—individual under- mean the yield of a bond rises and the price of
lying bonds held by the plan may fall in value. the bond falls, all else equal) due to investor
Even worse, if an issuer is downgraded below concerns. Ultimately, Verizon and Verizon
the minimum quality permitted by index rules Wireless bonds were downgraded from low A
(or defaulted in a worst case scenario), the plan to BBB in September 2013.
sponsor sustains losses, while the index eventu- From November 30, 2012 (when Verizon
ally ejects the downgraded/defaulted bond(s) had issued its previous benchmark bonds)
and re-prices the discount rate as if the index to September 30, 2013 (the effective date of
never held the bonds in the first place. Verizon’s removal from the A or Better Index),
The recent downgrade of Verizon and Verizon Verizon’s underperformance caused a drag of
Wireless illustrates this disconnect. Verizon 16 bps on the total index. But more importantly,
and Verizon Wireless constituted about 3% Verizon’s ultimate removal from the A or Better
of the Barclays A or Better Index until their Index (a proxy for many liability valuations)
-10
130
120
Verizon bonds -15
widened meaningfully
110 in anticipation of the
downgrade
100 -20
Nov-12 Jan-13 Mar-13 May-13 Jul-13 Sep-13 Nov-12 Jan-13 Mar-13 May-13 Jul-13 Sep-13
Source: Barclays.
| 11
Liability Hedging
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Liability Hedging
markets, credit spreads tend to “widen.” The the “0 Growth /100 Liability Hedge” (fully
credit/equity alignment is intuitive, as the hedged) plan is helped by maximizing credit,
healthy economic/profit conditions that drive as the portfolio is devoid of equity risk, which
equity returns are also conducive to better reduces surplus volatility by better mimicking
performance among corporate bonds, as well as the behavior of the liability on a much larger
improved risk sentiment. slice of the portfolio. If a plan maintains
As a result of this relationship, plans must significant equity exposure, devising a complex
take into account the relative level of equity customized credit solution that tries to imitate
beta (market sensitivity) in their growth port- the liability may actually accentuate existing
folio when determining the right mixture of equity risks rather than help manage overall
corporate and Treasury bonds in their liability portfolio risk. For the “60 Low Beta Growth /
hedging portfolios. 40 Liability Hedge” portfolio, greatly reducing
equity beta (in this example, assumed to be
Figure 8 demonstrates equity risk can have 0.4) controls surplus volatility with a consis-
substantial implications for implementing a tent amount across the government/credit
liability hedge, plotting the appropriate govern- spectrum. Such an allocation comes with a
ment/credit ratio against surplus volatility for return trade-off. In most long-term periods,
a few sample portfolios. The “60 Growth /40 credit will typically outperform Treasuries
Liability Hedge” plan is better served, from (when adjusted for duration), given the excess
a surplus volatility perspective, with higher credit spread earned over time.
government bond allocations. Conversely,
Figure 8. With a Large Growth (Equity) Portfolio, Additional Exposure to Credit May Increase Risk
Duration Matched Plan with ACWI Equity Exposure
5
100/0 90/10 80/20 70/30 60/40 50/50 40/60 30/70 20/80 10/90 0/100
Government/Credit Ratio
Sources: Barclays and MSCI Inc. MSCI data provided "as is" without any express or implied warranties.
Notes: Low beta growth portfolio assumes a 0.4 beta to the MSCI All Country World Index. Returns from October 2003 to October 2013.
| 13
Liability Hedging
| 14
Liability Hedging
| 15
Liability Hedging
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Liability Hedging
Figure 9. Interest Rate Swap Example to sign trade confirmations and understand
all terms of the contract. These processes
Party A Party B (particularly the ISDA) can be lengthy and also
Paying Fixed, Paying Floating,
Receiving Floating Receiving Fixed involve a fair amount of legal and administra-
tive expense.
We would be remiss not to mention the element
Notional Amount of counterparty risk associated with swaps. To
the extent a plan has earned profit on a swap,
it is vulnerable (and is taking “credit risk”)
with the financial institution that acts as the
needs to add duration for a liability hedge, or counterparty to the swaps. While this risk can
may take a position similar to party A if it needs be mitigated by proper collateral and netting
to lighten up duration in a specific instance. agreements, it must be monitored very closely.
Operationally, the plan must have the proper
A significant advantage of employing swaps resources and procedures in place to handle the
for duration/curve management approach is the periodic payments. Particularly in volatile rate
capital efficiency of the position. Since neither environments, ample cash or very liquid assets
party in an interest rate swap is required to pay should be set aside to meet such payments.
any upfront amounts, investors can increase the Also, most swaps contracts have strict collat-
duration of their portfolios without having to eral provisions and investors must be able to
tie up a significant amount of capital.2 Another manage any potential collateral calls.
positive is that there is a large and liquid market
for swaps of varying maturities (e.g., five-year, Since the underlying reference rates in swaps
ten-year, 30-year), and as such they can be cheap are heavily tied to US Treasury rates, a liability
to trade, particularly when compared to physical hedging portfolio constructed solely out of
corporate bonds. In particular, the market for swaps has no exposure to credit spreads. This
ultra-long swaps (above 30 years) is more liquid mismatch exposes the plan to tightening spreads,
and active than that for long-term bonds. as liabilities grow in value while the hedging
portfolio’s value remains unchanged. The lack
Plans must be aware of key considerations of exposure to credit spreads also exposes the
related to swaps. First, swap position sizing, plan to credit slippage, as the hedging portfolio
sensitivity analysis, trading, and reporting can misses out on the extra yield earned by the
all be more complex than plain vanilla bond liabilities. This effect causes the funded status
portfolios. Second, since interest rate swaps are to deteriorate since the hedging portfolio is not
OTC derivatives, investors must negotiate and earning the liability’s annual interest expense.
sign ISDA agreements with counterparties and
establish adequate back-office procedures to Finally, swaps (like bonds) are discrete invest-
handle the swap implementation. For specific ments that inherently target one point of the
swap transactions, plan investors are required maturity spectrum; thus, a plan would take on
significant curve risk if it only purchased swap
exposure to a single reference point. The curve
2
As the swap position valuation moves based on the
passage of time and change in interest rates, the position mismatch risk can be mitigated by entering
may require mark-to-market infusions. into multiple swaps with different underlying
| 17
Liability Hedging
rates (i.e., five-year, ten-year, etc.), though this hedge ratio, and the plan intends to increase its
approach introduces additional operational hedge ratio to 50% if discount rates rise by 100
complexity into the portfolio. bps. The plan can express that objective today
Swaptions. Swaptions are essentially options by selling a payer swaption, with the strike
on interest rate swaps, allowing plans to price set to the rate at which the plan wishes
obtain asymmetric payoff profiles in differing to increase the hedge ratio. The plan collects a
rate environments. Swaptions can either be premium in expressing this view, which creates
a receiver swaption or payer swaption, with an additional yield for the portfolio while still
the word “receive” or “pay” referring to what staying consistent with the strategic objec-
happens with the fixed rate leg of the swaption. tives of the plan. Effectively, the plan can take
For instance, a receiver swaption gives the buyer advantage of its structural need for duration by
the right to enter into an interest rate swap “selling” that action in advance and generate
(whose terms have been specified at purchase additional funds for the portfolio.
of the swaption) as the receiver of the fixed rate Though the plan could pocket the premium
at the expiry of the swaption. Alternatively, the from selling a payer swaption, it can alterna-
buyer of a payer swaption has the right to enter tively use the premium to fund purchases of
into an interest rate swap as the payer of the receiver swaptions as previously discussed. For
fixed rate on the expiration date. instance, suppose a plan sells payer swaptions,
If structured properly, payer swaptions can collecting premiums worth $1 million. The
provide a plan some protection from funded funds generated can be used to buy receiver
status deterioration if rates were to fall. swaptions that would give plans extra protec-
Specifically, a plan could hedge against a tion if interest rates fall. This strategy is known
decline in funded status due to falling rates by as a swaption collar. The collar’s pricing, payoff
purchasing out-of-the-money receiver swap- profile, and other characteristics will vary
tions. Because the swaption is customizable, the widely based on the level of rate volatility in the
plan can determine the rate at which it would marketplace, as well as the level and shape of
like to have protection by setting the strike the spot and forward yield curves.
equal to that rate. If rates fall below the strike, Similar to plain vanilla interest rate swaps,
the swaption becomes “in-the-money” and will swaptions are capital efficient and allow plans
have a positive payout to the buyer—in this to hedge their interest rate exposure without
case, the pension plan. Therefore, while the having to tie up a large amount of their capital
plan’s liability grows due to a drop in rates, its in the liability hedging portfolio. To better
assets grow along with it since the swaption illustrate this point, Figure 10 depicts the
has a positive payout. There is no free lunch, instantaneous change in value of a physical
of course, and the plan must pay a premium to bond and a swaption collar payoff in response
obtain this beneficial optionality. to changes in interest rates at expiry. Both
Another application of swaptions for a pension instruments give investors exposure to interest
plan is the possibility of earning extra income rates with certain duration (in this case $7.2
on the portfolio by monetizing a decision to million of exposure with duration of 14 years).
increase the plan’s hedge ratio if rates rise. For For every 50 bp change in interest rates both
instance, suppose a plan currently has a 40% the swaption’s final payout at expiry (once in
| 18
Liability Hedging
the money) and bond’s market value change by tion against falling rates. Figure 11 shows the
$500,000. With the swaption collar, however, funded status of a plan with swaption collar
the entire principal amount does not have to structured so that the payer leg kicks only when
be used up to gain exposure and the investor is funded status is anticipated to go above 100%.
free to use the funds elsewhere in the portfolio. At that point or above, the sponsor’s utility (or
This figure is only an estimate as it ignores use) for any further gains is limited, and any
changes in the swaption’s market value as it further potential upside gains in funded status
reaches expiry. Furthermore, the swaption can be used to fund downside protection.
collar has no payoff if interest rates at expiry
The swaption approach has similar drawbacks
fall in between the strikes (i.e., both legs are out
to interest rate swaps, including potential
of the money), whereas bonds would.
counterparty risk, collateral and cash flow
Swaptions can be particularly attractive to plans management, ISDA negotiation, and trade
not too far from becoming fully funded. Such confirmations. Swaptions also encounter the
plans can put on swaption collars, with the same caveats of swaps in terms of potential
payer leg struck at rates that result in funded curve mismatch and a lack of corporate yield
status being at or above 100%. Since the plan’s spread. One additional drawback is the high
sponsor cannot access excess assets (i.e., the level of complexity of swaptions (even relative
portion of assets in excess of the present value to swaps). Since swaptions combine elements
of the liabilities), any upside gains from rising of both options and interest rate swaps, plan
rates beyond fully funded can be sold and investors may need time to become comfortable
the proceeds can be used to increase protec- with their risks and benefits.
2,000,000
Payer Strike
Payout at Expiry (US$)
1,000,000
-1,000,000
-3,000,000
-4,000,000
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50
Spot Rate at Expiry
| 19
Liability Hedging
Payer Swaption
80% Kicks In Only When
Plan Becomes
Fully Funded
70%
60%
1.8% 2.6% 3.3% 4.1% 4.8% 5.6% 6.3% 7.1%
Interest Rates
| 20
Liability Hedging
| 21