Investments & Securities Chapter 24 Liabilitydriven Strategies Summary This Begin With The Basic Principles

CHAPTER 24

LIABILITY-DRIVEN STRATEGIES

CHAPTER SUMMARY

In this chapter, we begin with the basic principles underlying the management ofassets relative to

liabilities, popularly referred to as asset/liability management. We then describe several

structured portfolio strategies, strategies that seek to match theperformance of a predetermined

GENERAL PRINCIPLES OF ASSET/LIABILITY MANAGEMENT

The nature of an institutional investor’s liabilities will dictate the investment strategy it will

request its portfolio manager to pursue.

Classification of Liabilities

A liability is a cash outlay that must be made at a specific time to satisfy the contractual terms of

an issued obligation. An institutional investor is concerned with both the amount and timing of

liabilities, because its assets must produce the cash to meet any payments it has promised to

A type I liability is one for which both the amount and timing of the liabilities are known with

certainty. Type I liabilities, however, are not limited to depository institutions. A major product

sold by life insurance companies is a guaranteed investment contract (GIC).

Liquidity Concerns

Because of uncertainty about the timing and / or the amount of the cash outlays, an institution

must be prepared to have sufficient cash to satisfy its obligations. Also keep in mind that the

entity that holds the obligation against the institution may have the right to change the nature of

the obligation, perhaps incurring a penalty.

Surplus Management

The two goals of a financial institution are to earn an adequate return on funds invested, and to

maintain a comfortable surplus of assets beyond liabilities. The task of managing funds of

a financial institution to accomplish these goals is referred to as asset/liability management or

surplus management.

The economic surplus of any entity is the difference between the market value of all its assets

and the market value of its liabilities; that is,

The economic surplus can be expressed as

economic surplus = market value of assets – present value of liabilities.

Accounting surplus is surplus of assets over liabilities as reported in financial statements based

on generallyaccepted accounting principles (GAAP) accounting. Institutional investors must

prepare periodic financial statements that include the reporting of assets and liabilities. With

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trading account. For all assets in the available-for-sale and trading accounts, market value

accounting is used.

Institutional investors that are regulated at the state or federal levels must provide financial

reports to regulators based on regulatory accounting principles (RAP). The surplus as measured

using RAP accounting, called regulatory surplus, may, as in the case of accounting surplus,

differ materially from economic surplus.

IMMUNIZATION OF A PORTFOLIO TO SATISFY A SINGLE LIABILITY

An immunization strategy refers to the investment of the assets in such a way that the existing

business is immune to a general change in the rate of interest.

Investing in a coupon bond with a yield to maturity equal to the target yield and a maturity equal

can be shown that the accumulated value and the total return are never less than the target

accumulated value and the target yield. Thus the target accumulated value is assured regardless

of what happens to the market yield. For this situation, the coupon issue has the same duration as

the liability.

The equality of the duration of the asset and the duration of the liability is the key to immunization.

will result in the duration wandering from the target duration, which will also reduce the

likelihood of achieving the target yield.

Immunization Risk

The sufficient condition for the immunization of a single liability is that the duration of the

portfolio be equal to the duration of the liability. However, a portfolio will be immunized against

the product of two terms. The first term depends solely on the characteristics of the investment

portfolio. The second term is a function of interest-rate movement only. The second term

characterizes the nature of the change in the shape of the yield curve. Because that change will

be impossible to predict a priori, it is not possible to control for it. The first term, however, can

be controlled for when constructing the immunized portfolio, because it depends solely on the

horizon or liability due date, y = portfolioyield, and n = time to receipt of the last cash flow.

The objective in constructing an immunized portfolio is to match the portfolio’s duration to the

liability’s duration and select the portfolio that minimizes the immunization risk. The immunization

risk measure can be used to construct approximate confidence intervals for the target yield and the

target accumulated value.

When the universe of acceptable issues includes corporate bonds, the target yield may be

jeopardized if a callable issue is included that is subsequently called. Call risk can be avoided by

restricting the universe of acceptable bonds to noncallable bonds and deep-discount callable

bonds.

Constructing the Immunized Portfolio

return is 12%. The 10% return is called the safety net return. The difference between the

immunized return and the safety net return is called the safety cushion. In our example, the

safety cushion is 200 basis points (12% minus 10%).

The three key factors in implementing a contingent immunization strategy are (i) establishing

accurate immunized initial and ongoing available target returns, (ii) identifying a suitable and

immunizable safety net return, and (iii) designing an effective monitoring procedure to ensure

that the safety net return is not violated.

STRUCTURING A PORTFOLIO TO SATISFY MULTIPLE LIABILITIES

Multiperiod Immunization

Multiperiod immunization is a portfolio strategy in which a portfolio is created that will be

capable of satisfying more than one predetermined future liability regardless if interest rates

change. Even if there is a parallel shift in the yield curve, it has been demonstrated that matching

the duration of the portfolio to the duration of the liabilities is not a sufficient condition to

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immunize a portfolio seeking to satisfy a liability stream. Instead, it is necessary to decompose

the portfolio payment stream in such a way that each liability is immunized by one of the

component streams. The key to understanding this approach is recognizing that the payment

stream on the portfolio, not the portfolio itself, must be decomposed in this manner. There may

be no actual bonds that would give the component payment stream.

Cash Flow Matching

An alternative to multiperiod immunization is cash flow matching. This approach, also referred

to as dedicating a portfolio, can be summarized as follows. A bond is selected with a maturity

that matches the last liability stream. An amount of principal plus final coupon equal to the

amount of the last liability stream is then invested in this bond. The remaining elements of the

liability stream are then reduced by the coupon payments on this bond, and another bond is

EXTENSIONS OF LIABILITY-DRIVEN STRATEGIES

Deterministic models assume that the cash flows from assets and liabilities are known with

certainty. However, most non-Treasury securities have embedded options that permit the borrower

or the investor to alter the cash flows.

COMBINING ACTIVE AND IMMUNIZATION STRATEGIES

In contrast to an immunization strategy, an active/immunization combination strategy is a mixture of

two strategies that are pursued by the portfolio manager at the same point in time. The immunization

component of this strategy could be either a single-liability immunization or a multiple-liability

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The following formula can be used to determine the portion of the initial portfolio to be managed

actively, with the balance immunized:

active component =

immunization target rate minimum return established by client

immunization target rate expected worst case active return

−

.

In the formula it is assumed that the immunization target return is greater than either the

minimum return established by the client or the expected worst-case return from the actively

managed portion of the portfolio.

LIABILITY-DRIVEN STRATEGIES FOR DEFINED BENEFITPENSION FUNDS

Whilea defined benefit plan can use an immunization or cash flow matching strategy that

hasbonds only, the problem is that the liabilities are uncertain due to factors such as changes

inthe contractual benefits provided by the plan sponsor, the decision by plan beneficiaries toretire

early, and the impact of inflation on benefits.

Ross, Bernstein, Ferguson, and Dalio of Bridgewater Associates propose the following

liability-driven strategy for a pension plan, which involves two steps.First, create animmunizing

portfolio.The purpose of this portfoliois to hedge the adverse consequences associated with the

exposure to the liabilities. Second,create what they refer to as an “excess return portfolio.” The

purpose of that portfolio is togenerate a return that exceeds the return on the immunizing

portfolio. The total return forthe pension plan is then

KEY POINTS

• The nature of their liabilities, as well as regulatory considerations, determines the investment

strategy pursued by all institutional investors. By nature, liabilities vary with respect to the

amount and timing of their payment.

• The economic surplus of any entity is the difference between the market value of all its assets

and the present value of its liabilities. Institutional investors will pursue a strategy either to

maximize economic surplus or to hedge economic surplus against any adverse change in

market conditions.

• When there are multiple liabilities to be satisfied, either multiperiod immunization or cash

flow matching can be used. Multiperiod immunization is a duration-matching strategy that

exposes the portfolio to immunization risk. The cash flow–matching strategy does not impose

any duration requirement. Although the only risk that the liabilities will not be satisfied is that

issues will be called or will default, the dollar cost of a cash flow–matched portfolio may be

higher than that of a portfolio constructed using a multiperiod immunization strategy.

• Liability-driven strategies in which the liability payments and the asset cash flows are known

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• The liability structure of a defined benefit pension plan is uncertain. There are two

liability-driven strategies advocated for defined benefit pension plans. One approach argues

that only bonds should be acquired and a dedicated portfolio strategy should be used. The

other approach is a liability-driven strategy that uses bonds and equities but uses the liabilities

as a benchmark in determining the best asset allocation.

ANSWERS TO QUESTIONS FOR CHAPTER 24

(Questions are in bold print followed by answers.)

1. What are the two dimensions of a liability?

2. Why is it not always simple to estimate the liability of an institution?

3. Why is asset/liability management best described as surplus management?

4. Answer the below questions.

(a) What is the economic surplus of an institution?

The economic surplus of any entity is the difference between the market value of all its assets

and the market value of its liabilities; that is,

(b) What is the accounting surplus of an institution?

Accounting surplus is surplus of assets over liabilities as reported in financial statements based

on generally accepted accounting principles (GAAP) accounting. The accounting treatment for

(c) What is the regulatory surplus of an institution?

Institutional investors that are regulated at the state or federal levels must provide financial

reports to regulators based on regulatory accounting principles (RAP). RAP accounting for

(d) Which surplus best reflects the economic well-being of an institution?

Economic surplus best reflects the economic well-being of an institution because these values are

market values and thus best reflect investor’s beliefs about the true financial condition of a firm.

(e) Under what circumstances are all three surplus measures the same?

5. Suppose that the present value of the liabilities of some financial institution is

$600 million and the surplus $800 million. The duration of the liabilities is equal to 5.

Suppose further that the portfolio of this financial institution includes only bonds and the

duration for the portfolio is 6.

Answer the below questions.

(a) What is the market value of the portfolio of bonds?

We rearrange the equation of “economic surplus = market value of assets – market value of

liabilities” to get:

(b) What does a duration of 6 mean for the portfolio of assets?

Duration is a measure of the responsiveness of cash flows to changes in interest rates. Duration

can be calculated for liabilities in the same way in which it is calculated for assets. Because the

duration of the assets is 6, the market value of the assets will change by about 6% for a 100 basis

(c) What does a duration of 5 mean for the liabilities?

If the duration of the liabilities is 5, the present value of the liabilities will increase by 5% or

(d) Suppose that interest rates increase by 50 basis points; what will be the approximate

new value for the surplus?

Given that we have a 50 basis point change instead of a 100 basis point change, we divided the

duration by 2. Doing this gives causes the decrease in assets to be

( )

0.06 $1.4 billion

2

−

= −$42

( )

0.05 $600 million

−

(e) Suppose that interest rates decrease by 50 basis points; what will be the approximate

new value for the surplus?

Given that we have a 50 basis point change instead of a 100 basis point change, we divided the

duration by 2. Doing this gives causes the increase in assets to be

( )

0.06 $1.4 billion

2

=

$42 million. Similarly, the increase in liabilities will be

( )

0.05 $600 million

2

= $15 million. Thus,

the net change in surplus value is:

6. Answer the below questions.

(a) Why is the interest-rate sensitivity of an institution’s assets and liabilities important?

Knowing the interest-rate sensitivity reveals steps that a firm’s manager can perform to avoid

financial difficulties caused by being short of assets relative to liabilities. More details are given

below.

(b) In 1986, Martin Leibowitz of Salomon Brothers Inc. wrote a paper titled “Total Portfolio

Duration: A New Perspective on Asset Allocation.” What do you think a total portfolio

duration means?

One would think that total portfolio duration refers to the duration of all assets together. If bonds

in the portfolio are all assumed to be option-free bonds, total portfolio duration means modified

7. If an institution has liabilities that are interest-rate sensitive and invests in a portfolio of

common stocks, can you determine what will happen to the institution’s economic surplus

if interest rates change?

The stock market is generally influenced like bonds and other fixed-income securities when

interest rates change. That is, stock values fall when interest rates increase and values rise when

8. The following quote is taken from Phillip D. Parker (Associate General Counsel of the

SEC), “Market Value Accounting—An Idea Whose Time Has Come?” in Elliot P. Williams

(ed.), Managing Asset/Liability Portfolios (Charlottesville, VA: Association for Investment

Management and Research, 1991), published prior to the passage of FASB 115:

“The use of market value accounting would eliminate any incentive to sell or retain

investment securities for reasons of accounting treatment rather than business utility.”

Explain why this statement is correct. (Note that in historical accounting a loss is recognized

only when a security is sold.)

Accounting treatment that occurs in annual reports is concerned with making the firm’s book

9. Answer the below questions.

(a) Indicate why you agree or disagree with the following statement: “Under FASB 115 all

assets must be marked to market.”

As explained below in more detail, FASB 115 does not require that all assets must be marked to

market even though many have to be marked to market.

Institutional investors must prepare periodic financial statements prepared in accordance with

GAAP. Thus the assets and liabilities reported are based on GAAP accounting. The accounting

treatment for assets is governed by FASB 115. However, it does not deal with the accounting

treatment for liabilities.

FASB 115 specifies which of these three methods must be followed for assets. Specifically, the

accounting treatment required for a security depends on how the security is classified. There are

three classifications of investment accounts: (1i) held to maturity, (ii) available for sale, and

(iii) trading.

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classified as in the available-for-sale account if the institution does not have the ability to hold

the asset to maturity or intends to sell it. An asset that is acquired for the purpose of earning

a short-term trading profit from market movements is classified in the trading account. For all

assets in the available-for-sale and trading accounts, market value accounting is used.

(b) Indicate why you agree or disagree with the following statement: “The greater the price

volatility of assets classified in the held–to-maturity account, the greater the volatility of the

accounting surplus and reported earnings.”

In general one might agree that if there is volatility in assets, there might be volatility in the

account numbers that reflect this volatility. However, under FASB 115, the accounting treatment

for any unrealized gain or loss depends on the account in which the asset is classified.

10. What is meant by immunizing a bond portfolio?

Immunizing a bond portfolio means that the portfolio’s value is protected against a general

change in the rate of interest. More details are given below.

Investing in a coupon bond with a yield to maturity equal to the target yield and a maturity equal

to the investment horizon does not assure that a portfolio’s target accumulated value will be

achieved. This is because an increase in the market yield causes the market value to fall and the

portfolio can fail to achieve the target accumulated value. This can occur when the fall in

11. Answer the below questions.

(a) What is the basic underlying principle in an immunization strategy?

The basic underlying principle in an immunization strategy is to have the duration of the asset

equal the duration of the liability. Generalizing this observation to bond portfolios from

(b) Why may the matching of the maturity of a coupon bond to the remaining time to

maturity of a liability fail to immunize a portfolio?

Investing in a coupon bond with a yield to maturity equal to the target yield and a maturity equal

to the investment horizon does not assure that a portfolio’s target accumulated value will be

achieved. This is because an increase in the market yield causes the market value to fall and the

12. Why must an immunized portfolio be rebalanced periodically?

The key to immunizing a portfolio of assets is to match the duration of the assets with the

liabilities. Because market yields can change periodically affecting the duration of the assets, the

portfolio of assets must be rebalanced periodically to insure immunization. More details are

given below.

There is the question of how often the portfolio should be rebalanced to adjust its duration. On

13. What are the risks associated with a bond immunization strategy?

As described below, there are risks that can upset various types of bond immunization strategies.

A first risk involves uncertainty as to how the yield curve might shift. For example, if there is

a change in interest rates that does not correspond to the shape-preserving shift, matching the

portfolio’s duration to the liability’s duration will not assure immunization. The sufficient

condition for the immunization of a single liability is that the duration of the portfolio be equal to

A second risk involves the reinvestment rate. For example, consider the example in the text

where the accumulated value for a barbell portfolio at the liability due date misses the target

accumulated value by more than a bullet portfolio. There are two reasons for this. First, the lower

reinvestment rates are experienced on the barbell portfolio for larger interim cash flows over

14. “I can immunize a portfolio simply by investing in zero-coupon Treasury bonds.”

Comment on this statement.

If all the cash flows are received at the liability due date, the immunization risk measure is zero.

In such a case the portfolio is equivalent to a pure discount security (zero-coupon security) that

matures on the liability due date. If a portfolio can be constructed that replicates a pure discount

security maturing on the liability due date, that portfolio will be the one with the lowest

immunization risk. Typically, however, it is not possible to construct such an ideal portfolio.

More details are given below.

15. Three portfolio managers are discussing a strategy for immunizing a portfolio so as to

achieve a target yield. Manager A, whose portfolio consists of Treasury securities and

option-free corporates, stated that the duration of the portfolio should be constructed so

that the Macaulay duration of the portfolio is equal to the number of years until the

liability must be paid. Manager B, with the same types of securities in his portfolio as

Manager A, feels that Manager A is wrong because the portfolio should be constructed so

that the modified duration of the portfolio is equal to the modified duration of the

liabilities. Manager C believes Manager B is correct. However, unlike the portfolios of

Managers A and B, Manager C invests in mortgage-backed securities and callable

corporate bonds. Discuss the position taken by each manager and explain why they are

correct.

Manager A wants to use the Macaulay duration for his Treasury securities and option-free

corporates. This measure is an acceptable measure if assets and liabilities are option-free.

However, Manager A wants the duration of assets to equal the number of years until the liability

must be paid. Suppose the duration of the assets is 5 and the duration of the liabilities is not 5 but

say 3. If interest rates increase by 100 basis points then the market value of the assets will