Bond Immunization

RESEARCH ON

Bond Immunization

ESLESCA 32 C by: Yasser Abdul-Aziz Hassan

Content

1. WHAT IS "immunization" MEANING?

2. WHAT IS "Bond immunization" MEANING?

3. Effects of Bond Immunization

4. Variations on Bond Immunization

5. Bond immunization and arbitrage in the semi-deterministic setting

6. Bond immunization minimizes risk

7. Immunization strategy

8. Immunization Difficulties

9.Immunization Example – Life Insurance

10. International Finance Facility for Immunization (IFFIm)

11. Conclusions

1. WHAT IS "immunization" MEANING?

In finance, interest rate immunization is a strategy that ensures that a change in interest

rates will not affect the value of a portfolio. Similarly, immunization can be used to ensure

that the value of a pension fund's or a firm's assets will increase or decrease in exactly the

opposite amount of their liabilities, thus leaving the value of the pension fund's surplus or

firm's equity unchanged, regardless of changes in the interest rate.

Interest rate immunization can be accomplished by several methods, including cash flow

matching, duration matching, and volatility and convexity matching. It can also be

accomplished by trading in bond forwards, futures, or options.

Other types of financial risks, such as foreign

exchange risk or stock market risk, can be

immunized using similar strategies. If the

immunization is incomplete, these strategies are

usually called hedging. If the immunization is complete, these strategies are usually called

arbitrage.

The Immunization may be defined: as the protection of the nominal value of a portfolio

against interest rate changes. It has been shown that under idealized conditions this

objective can be attained by equating the length of the investment horizon with some

measure or measures of the time pattern of cash flows associated with the portfolio. This

measure is commonly referred as duration.

The initial basis for strategies of financial immunization was the measure of duration

introduced by F. Macaulay in 1938. In view of the limitations of the immunization model

based on this measure, and in a bid to achieve greater interest risk coverage, a number of

approaches have led to a good many models being proposed, which may be classified into

three groups:

- Unifactorial models based on the use of single duration immunization measures.

- Models based on dispersal measures. These seek to minimize the dispersal of bond

portfolio cash flows in relation to the investment horizon.

- Multifactorial models based on the simultaneous use of a set of immunizing measures of

duration.

The purpose of this paper is to explore empirically the potential for improved immunization

using those models. In the next section, we realize a literary review of the analyzed models.

Sources: GLOBAL JOURNAL OF BUSINESS RESEARCH

MODELS OF FINANCIAL IMMUNIZATION: BEHAVIOR ON THE SPANISH PUBLIC DEBT MARKET

Later we describe the database used to develop the empirical work. Finally, we show the

results of this study and the reached conclusion.

Immunization in practice

Immunization can be done in a portfolio of a single asset type, such as government bonds,

by creating long and short positions along the yield curve. It is usually possible to immunize

a portfolio against the most prevalent risk factors. A principal component analysis of

changes along the U.S. Government Treasury yield curve reveals that more than 90% of the

yield curve shifts are parallel shifts, followed by a smaller percentage of slope shifts and a

very small percentage of curvature shifts. Using that knowledge, an immunized portfolio

can be created by creating long positions with durations at the long and short end of the

curve, and a matching short position with duration in the middle of the curve. These

positions protect against parallel shifts and slope changes, in exchange for exposure to

curvature changes.

2. WHAT IS "Bond immunization" MEANING?

Bond immunization is an investment strategy used to minimize the interest rate risk of bond investments by adjusting the portfolio duration to match the investor's investment time horizon. It does this by locking in a fixed rate of return during the amount of time an investor plans to keep the investment without cashing it in.

Immunization locks in a fixed rate of return during the amount of time an investor plans to keep the bond without cashing it in.

Normally, interest rates affect bond prices inversely. When interest rates go up, bond prices go down. But when a bond portfolio is immunized, the investor receives a specific rate of return over

a given time period regardless of what happens to interest rates during that time. In other words, the bond is "immune" to fluctuating interest rates.

To immunize a bond portfolio, you need to know the duration of the bonds in the portfolio and adjust the portfolio so that the portfolio's duration equals the investment time horizon. For example, suppose you need to have $50,000 in five years for your child's education. You might decide to invest in bonds. You can immunize your bond portfolio by selecting bonds that will equal exactly $50,000 in five years regardless of interest rate changes. You can buy one zero-coupon bond that will mature in five years to equal $50,000, or several coupon bonds each with a five year duration, or several bonds that "average" a five-year duration.

Duration measures a bond's market risk and price volatility in response to a given change in interest rates. Duration is a weighted average of the bond's cash flows over its life. The weights are the present value of each interest payment as a percentage of the bond's full price. The longer the duration of a bond, the greater its price volatility.

Sources: http://news.morningstar.com/classroom2/course.as

p?docId=5397&page=3&CN=com

Duration is used to determine how a bond will react to changing interest rates. For example, if interest rates rise 1%, a bond with two-year duration will fall about 2% in value.

You needn't worry about doing the calculations as you can obtain a bond's (or bond fund's) duration from a broker or advisor. Using bonds' durations, you can build a bond portfolio immune to interest rate risk.

3. Effects of Bond Immunization

Changes to interest rates actually affect two parts of a bond's value. One of them is a

change in the bond's price, or price effect. When interest rates change before the bond

matures, the bond's final value changes, too. An increase in interest rates means new bond

issues offer higher earnings, so the prices of older bonds decline on the secondary market.

Interest rate fluctuations also affect a bond's reinvestment risk. When interest rates rise, a

bond's coupon may be reinvested at a higher rate. When they decrease, bond coupons can

only be reinvested at the new, lower rates.

Interest rate changes have opposite effects on a bond's price and reinvestment

opportunities. While an increase in rates hurts a bond's price, it helps the bond's

reinvestment rate. The goal of immunization is to offset these two changes to an investor's

bond value, leaving its worth unchanged.

A portfolio is immunized when its duration equals the

investor's time horizon. At this point, any changes to

interest rates will affect both price and reinvestment at

the same rate, keeping the portfolio's rate of return the

same. Maintaining an immunized portfolio means

rebalancing the portfolio's average duration every time

interest rates change, so that the average duration

continues to equal the investor's time horizon.

A more direct form of immunization, "dedicating" a portfolio not only matches its duration

to the investor's long-term time horizon, but also matches specific anticipated receipts of

cash to the investor's specific anticipated liabilities along the way. To pay for college, for

example, a parent might construct a bond portfolio so that interest and principal payments

will be paid each year in September, when tuition is due.

Bond immunization is a passive

investment strategy that takes

advantage of the duration of bonds.

Bond investors wanting to plan their

investments efficiently employ it

over the long term. As an educated

investor, you should know about this

investment strategy and how to

apply it to your portfolio.

4. Variations on Bond Immunization

When investors talk about the interest rate risk of bonds, they usually mean the risk to their

capital investment. Duration is used to measure risk, by letting them know how much a

bond's price should change for a small change in interest rates.

Suppose that an investor must make a $1,000,000 payment in five years. To simplify the

problem, suppose that he has three investment opportunities. He can buy four year zero

coupon bonds, five year zero coupon bonds, or six year zero coupon bonds.

If the investor buys the six year zero coupon bonds, he will have to sell it in five years to

make his payment. If rates are where he expects them to be, he should be able to make

that payment. If rates are lower, then the bond

will be worth more than he expected, and he will

have a surplus of cash after paying the liability.

But if rates are higher than he expected, then the

price of the bond will be lower than he thought, and he might not be able to make the

$1,000,000 payment. The Macaulay duration of the bond is 6 years. We can also calculate

the duration of the liability payment. Since it is a single flow due in five years, its duration is

5 years. Because the duration of the bond is longer than the duration of the liability, its

value will be more sensitive to changes in yield.

If he buys the four year zero, instead, then he can hold on to it until it matures. At that

point, he can reinvest it for a period of one year. If rates are high when the bond matures,

he should be able to make the liability payment. He will probably even have a surplus. If

rates drop, though, he might not have enough money to make the payment. The investor

has left himself open to interest rate risk, but in this case it is not the price risk that we saw

earlier. Reinvestment risk is another form of interest rate risk. Duration can still be used to

measure this risk, as long as there is either an investment horizon or a stream of liabilities

involved. In this case, we can look at the duration of the asset (4 years) and the duration of

the liability (5 years). Since the asset's duration is shorter than that of the liability, we can

infer that there is reinvestment risk rather than price risk.

If the investor bought a five year zero that paid $1,000,000, then he will be able to pay off

his liabilities no matter what happens to interest rates. If rates go up during that period, the

price of the bond will fall. But the investor is insensitive to this, because the present value

of the liability also falls by an equal amount. Similarly, if rates go down then he is insensitive

to the reinvestment rate, because he will not be reinvesting any cash flows during that

period.

Sources: http://www.duke.edu/~charvey/Classes/ba350/bon

dval/immune.htm

The above example is a simple one, but can be generalized. Bond portfolios are often set up

to provide the funds needed to pay off a stream of liabilities. The above analysis might lead

us to believe that zero coupon bonds should be bought to pay each of the liabilities. If the

schedule of payments goes for several years, and several payments must be made each

year, it might actually be cheaper to buy some

coupon bearing bonds. The final payment of a

bond could be used to pay off most of one

liability payment, while its coupons pay off a

smaller portion of earlier liability payments. This

type of problem lends itself to linear

programming techniques. A model can be set up

which picks the cheapest portfolio of bonds that

provides funds for the liability schedule. Such a

portfolio is often called a cash matched portfolio,

or a dedicated portfolio.

Matching the cash flows of assets and liabilities is

not the only way to avoid interest rate risk.

Suppose that we get rid of the simplifying

assumption used above to fund the $1,000,000 payment in five years. Suppose that the

portfolio manager is still restricted to investing in those three zero coupon bonds, but he is

now allowed to invest in a mix of the four year zero and the six year zero. We saw that

when rates went up, that was good for reinvesting the four year zero, but bad for the price

of the six year. On the other hand, when rates went down, it was bad for reinvesting the

four year but good for the price of the six year. If the portfolio manager could figure out

some way to set up his portfolio so that the reinvestment risk associated with the four year

bond exactly canceled out the price risk of the six year bond, then it would be immune to

interest rate shifts. He might be interested in doing this if it is a cheaper way to fund the

liability payment.

In a world where short and long term interest rates shift in parallel, he could do this by

matching the duration of his assets with the duration of his liabilities. If he bought equal

present values of the four and six year zeros, then the Macaulay duration of his portfolio

would be five years. If interest rates shifted, the present value of liability would shift by the

same amount as the value of the portfolio. But the world of interest rates is not ideal. If

short term interest rates drop, but longer interest rates rise, we would have the worst of all

possible situations. He would not get the reinvestment that he needs from the four year,

and would get less than he expects from the price change on the six year.

The most common way to immunize a bond

portfolio is called combination matching

To get around this problem, we might also try matching up the convexity of the assets with

the convexity of the liabilities. This is difficult to do with a one payment liability, unless it is

funded with a zero coupon bond. But if there are multiple liability payments, then it is

possible to match the duration and convexity of the assets with the liability schedule. As

with the dedicated portfolio, this can be done easily with a linear programming model. A

portfolio with these properties is called an immunized portfolio. It is also sometimes

referred to as a duration-matched portfolio.

Dedicating or immunizing portfolios are considered passive strategies. The portfolio

manager who dedicates a portfolio can almost forget about managing it. Cash will always

be there when he needs it. It is a good idea to rebalance the portfolio occasionally.

Sometimes new bonds that are cheaper or a better fit will become available. When this

happens, cash can be taken out of the portfolio.

Immunized portfolios need more nurturing. As time passes, the duration and convexity of

the portfolio and the liabilities will shift. They must be checked periodically to make sure

that they are still matched. The immunization process also relies on the fact that bonds will

have to be sold occasionally in order to make payments. Because of this feature, another

constraint is often added when creating an immunized portfolio to make sure that the first

several liability payments can be made without selling securities.

For more information, see the chapters on "Bond Immunization and Dedicated Portfolios"

in The Handbook of Fixed Income Securities, edited by Fabozzi and Pollack. The second year

course Money and Capital Markets deals with these concepts in much more detail.

Finally: The most common way to immunize a bond portfolio is called combination

matching. In combination matching, the portfolio not only matches its duration to its time

horizon, but also its cash flow and goals. For the first several years of the portfolio, the cash

flow from any maturing principal (plus coupon and reinvestment income) is made to equal

the intermediate investment goals set for the portfolio. Cash flow is paid out to fund

intermediate goal payments, giving the portfolio very little cash to reinvest and thus little

reinvestment risk. The low reinvestment risk helps the portfolio to lock in a rate of return

regardless of interest rate changes.

5. Bond immunization minimizes risk

The financial community has witnessed a wide variation of interest rates in recent years. It is virtually impossible to invest a portfolio of fixed income securities to a certain maturity without paying the price of interest rate changes.

One strategy that healthcare organizations can use to eliminate the uncertainty of interest rate changes is bond immunization.

A major problem often encountered in managing a bond portfolio is assuring a given rate of return over specified future periods.

Classical immunization is defined as the process by which a fixed income portfolio is created that has an assured rate of return for a specific time horizon irrespective of interest rate changes.

Bond immunization requires a portfolio structure that balances the change in value (prices) of the portfolio at the end of the investment horizon with the return from the reinvestment of the portfolio cash flows.

Immunization may be appropriate to the cash manager who seeks a high degree of assurance of compounded return over a specified investment horizon.

Immunization is especially appropriate where the time horizon is not extremely long or where the investor's tolerance for risk is low.

By accepting a more modest return, the manager is more likely to realize the desired return.

Reinvestment rate risk is critical in a bond or a portfolio that is accumulating value over a period of time.

The coupon reinvestment risk arises because the yield to maturity computation assumes that all coupon flows will be reinvested at the promised yield to maturity.

Unfortunately, the level of interest rates is constantly changing.

6. Immunization strategy

Multi period immunization 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.

Cash flow matching

Conceptually, the easiest form of immunization is cash flow matching. For example, if a

financial company is obliged to pay 100 dollars to someone in 10 years, it can protect itself

by buying and holding a 10-year, zero-coupon bond that matures in 10 years and has a

redemption value of $100. Thus, the firm's expected cash inflows would exactly match its

expected cash outflows, and a change in interest rates would not affect the firm's ability to

pay its obligations. Nevertheless, a firm with many expected cash flows can find that cash

flow matching is difficult or expensive to achieve in practice.

Combination matching

Also called horizon matching, a variation of multi period immunization and cash flow

matching in which a portfolio is created that is always duration matched and also cash-

matched in the first few years.

Passive portfolio strategy

A strategy that involves minimal expectational input, and instead relies on diversification to

match the performance of some market index. A passive strategy assumes that the

marketplace will reflect all available information in the price paid for securities, and

therefore, does not attempt to find mispriced securities.

Contingent immunization An arrangement in which the money manager pursues an active bond portfolio strategy until an adverse investment experience drives the then-available potential return down to the safety net level. When that point is reached, the money manager is obligated to pursue an immunization strategy to lock in the safety-net level return.

Safety cushion

In a contingent immunization strategy, the difference between the initially available Immunization level and the safety-net return.

Barbell strategy A strategy in which the maturities of the securities included in the portfolio are concentrated at two extremes.

Bullet strategy A strategy in which a portfolio is constructed so that the maturities of its securities are highly concentrated at one point on the yield curve.

Buy-and-hold strategy A passive investment strategy with no active buying and selling of stocks from the time the portfolio is created until the end of the investment horizon.

Combination strategy A strategy in which a put and with the same strike price and expiration are either both bought or both sold.

Covered call writing strategy A strategy that involves writing a call option on securities that the investor owns in his or her portfolio. See covered or hedge option strategies.

Dollar safety margin The dollar equivalent of the safety cushion for a portfolio in a contingent immunization strategy.

6. Immunization Difficulties

Immunization, if possible and complete, can protect against term mismatch but not against other kinds of financial risk such as default by the borrower (i.e., the issuer of a bond).

Users of this technique include banks, insurance companies, pension funds and bond brokers; individual investors infrequently have the resources to properly immunize their portfolios.

The disadvantage associated with duration matching is that it assumes the durations of assets and liabilities remain unchanged, which is rarely the case.

7. Immunization Example – Life Insurance

Assume: You are required to invest $936, You are to ensure that the investment will grow

at a 10 percent compound rate over the next 6 years

$936 x (1.10)6 = $1,658.18

The funds are withdrawn after 6 years.

If interest rates increase over the next 6 years: Reinvested coupons will earn more interest

The value of any bonds we buy will decrease; our portfolio may end up below the target

value.

Reduce the interest rate risk by investing in a bond with duration of 6 years

One possibility is the 8.8 percent coupon bond shown on the next two slides:

Interest is paid annually

Market interest rates change only once, at the end of the third year.

8. International Finance Facility for Immunization (IFFIm)

The IFFIm is a large-scale pre-financing mechanism which is based on a system of guaranteed bonds. It guarantees that close to €4 billion will be raised over 20 years to undertake far-reaching immunization projects. The funds, guaranteed by donors, are provided by private investors on financial markets.

It may seem to take a long time to set up development assistance programmes when certain development issues must be addressed immediately. In the health sector particularly, any delay affects human lives and funding must be predictable if it is to be effective.

The International Finance Facility for Immunization (IFFIm) was set up at the United Kingdom and France’s initiative in 2006 to deal with these problems. It is a large-scale pre-financing mechanism which is based on a system of guaranteed bonds. Spain, Italy, Norway, Sweden and the Bill and Melinda Gates Foundation decided to take part in the IFFIm alongside France and the United Kingdom. They were then joined by South Africa (in March 2007) and various talks are being held so that other countries, like Brazil, follow suit. Donors have pledged close to €4 billion over 20 years to fund far-reaching immunization programmes.

Funds are raised by issuing bonds on the basis of donors’ pledges (countries or private foundations). The bonds are bought on financial markets and issued regularly on the basis of the scheme drawn up when the pledges are signed. Funds are perfectly predictable and stable and can be used directly for projects in the health sector.

The first issuance in November 2006 reflects this solid commitment because it raised nearly $1 billion in addition to $200 million raised from Japanese investors in March 2008. The Global Alliance for Vaccines and Immunization (GAVI) manages the funds allocating them to immunization projects it has shown to be reliable. As a result, $862 million was disbursed in 2007 to various immunization and health system improvement programmes, such as the pentavalent vaccine initiative. This should save over 500 million children in the future.

Other important initiatives are also being carried out against measles, yellow fever, polio and tetanus contracted during births by mothers and their children.

9. Conclusions

Financial sustainability planning for immunization in Cambodia has demonstrated some important early successes. More resources are being mobilized for health, and there is improved co-ordination of finance, particularly in reference to strengthening links between financial planning and programme planning.

Sources: Official IFFIm-website

The use of the FSP as a programme management tool has increased the capacity of the NIP to negotiate more long-term and hence reliable financing, while at the same time alerting the national government and international health agencies to the need for addressing significant financial gaps in the coming years, particularly in relation to procurement costs for new vaccine introduction and the funding of basic health services.

Despite these successes, the national programme still faces formidable financial challenges in the coming years that will require strengthened management, planning and advocacy approaches.

Of particular note is the requirement to address the issues of decentralization, macro-economic analysis and links between financial planning and programme planning.

This will position the MOH to more effectively address the major goal of financial sustainability planning – which is to mobilize national and international resources more efficiently and effectively in order to achieve programme goals of improved service coverage and equity.