Immunization (finance)
Encyclopedia
In finance
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...

, 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
Bond duration
In finance, the duration of a financial asset that consists of fixed cash flows, for example a bond, is the weighted average of the times until those fixed cash flows are received....

 matching, and volatility and convexity
Bond convexity
In finance, convexity is a measure of the sensitivity of the duration of a bond to changes in interest rates, the second derivative of the price of the bond with respect to interest rates . In general, the higher the convexity, the more sensitive the bond price is to decreasing interest rates and...

 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
Hedge (finance)
A hedge is an investment position intended to offset potential losses that may be incurred by a companion investment.A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, many types of...

. If the immunization is complete, these strategies are usually called arbitrage
Arbitrage
In economics and finance, arbitrage is the practice of taking advantage of a price difference between two or more markets: striking a combination of matching deals that capitalize upon the imbalance, the profit being the difference between the market prices...

.

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
Bond (finance)
In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest to use and/or to repay the principal at a later date, termed maturity...

 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 can be difficult or expensive to achieve in practice. That meant that only institutional investors could afford it. But the latest advances in technology have relieved much of this difficulty. Dedicated portfolio theory
Dedicated Portfolio Theory
Dedicated Portfolio Theory, in finance, deals with the characteristics and features of a portfolio built to generate a predictable stream of future cash inflows...

 is based on cash flow matching and is being used by personal financial advisors to construct retirement portfolios for private individuals. Withdrawals from the portfolio to pay living expenses represent the stream of expected future cash flows to be matched. Individual bonds with staggered maturities are purchased whose coupon interest payments and redemptions supply the cash flows to meet the withdrawals of the retirees.

Volatility matching

A more practical alternative immunization method is duration matching. Here, the duration
Bond duration
In finance, the duration of a financial asset that consists of fixed cash flows, for example a bond, is the weighted average of the times until those fixed cash flows are received....

 of the assets is matched with the duration of the liabilities. Alternatively, the first derivative of the asset's price function with respect to the interest rate, is matched with the liabilities. To make the match more profitable, the assets and liabilities are arranged so that the convexities
Bond convexity
In finance, convexity is a measure of the sensitivity of the duration of a bond to changes in interest rates, the second derivative of the price of the bond with respect to interest rates . In general, the higher the convexity, the more sensitive the bond price is to decreasing interest rates and...

 of the assets exceed the convexity of the liabilities; alternatively, the second derivative of the assets is set to exceed the second derivative of the liabilities.

Calculating Immunization

Immunization starts with the assumption that the yield curve is flat. It then assumes that interest rate changes are parallel shifts up or down in that yield curve. Let the net cash flow at time t be denoted by Rt , i.e:




Rt = At - Lt
; t = 1,2,3,...,n



where At and Lt represent cash inflows (At) and outflows or liabilities (Lt)



We will assume that the present value of cash inflows from the assets is equal to the present value of the cash outlfows form the liabilities. Thus, we have:




P(i) = 0



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
Yield curve
In finance, the yield curve is the relation between the interest rate and the time to maturity, known as the "term", of the debt for a given borrower in a given currency. For example, the U.S. dollar interest rates paid on U.S...

. 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 a duration in the middle of the curve. These positions protect against parallel shifts and slope changes, in exchange for exposure to curvature changes.

Difficulties

Immunization, if possible and complete, can protect against term mismatch but not against other kinds of financial risk such as default
Default (finance)
In finance, default occurs when a debtor has not met his or her legal obligations according to the debt contract, e.g. has not made a scheduled payment, or has violated a loan covenant of the debt contract. A default is the failure to pay back a loan. Default may occur if the debtor is either...

 by the borrower (i.e., the issuer of a bond
Bond (finance)
In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest to use and/or to repay the principal at a later date, termed maturity...

).

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.

See also

  • Arbitrage
    Arbitrage
    In economics and finance, arbitrage is the practice of taking advantage of a price difference between two or more markets: striking a combination of matching deals that capitalize upon the imbalance, the profit being the difference between the market prices...

  • Asset liability mismatch
    Asset liability mismatch
    In finance, an asset–liability mismatch occurs when the financial terms of an institution's assets and liabilities do not correspond. Several types of mismatches are possible....

  • Bond convexity
    Bond convexity
    In finance, convexity is a measure of the sensitivity of the duration of a bond to changes in interest rates, the second derivative of the price of the bond with respect to interest rates . In general, the higher the convexity, the more sensitive the bond price is to decreasing interest rates and...

  • Bond duration
    Bond duration
    In finance, the duration of a financial asset that consists of fixed cash flows, for example a bond, is the weighted average of the times until those fixed cash flows are received....

  • Bond (finance)
    Bond (finance)
    In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest to use and/or to repay the principal at a later date, termed maturity...

  • Covered interest arbitrage
    Covered interest arbitrage
    Covered interest arbitrage is the investment strategy where an investor buys a financial instrument denominated in a foreign currency, and hedges his foreign exchange risk by selling a forward contract in the amount of the proceeds of the investment back into his base currency...

  • Duration gap
    Duration gap
    -Definition:The difference between the duration of assets and liabilities held by a financial entity.-Overview:The duration gap is a financial and accounting term and is typically used by banks, pension funds, or other financial institutions to measure their risk due to changes in the interest rate...

  • Hedging
    Hedge (finance)
    A hedge is an investment position intended to offset potential losses that may be incurred by a companion investment.A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, many types of...

  • Interest rate parity
    Interest rate parity
    Interest rate parity is a no-arbitrage condition representing an equilibrium state under which investors will be indifferent to interest rates available on bank deposits in two countries. Two assumptions central to interest rate parity are capital mobility and perfect substitutability of domestic...

  • Interest rate swap
    Interest rate swap
    An interest rate swap is a popular and highly liquid financial derivative instrument in which two parties agree to exchange interest rate cash flows, based on a specified notional amount from a fixed rate to a floating rate or from one floating rate to another...


External links


Recommended Reading

  • Wesley Phoa, Advanced Fixed Income Analytics, Frank J. Fabozzi Associates, New Hope Pennsylvania, 1998. ISBN 1-883249-34-1
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