# Finance:Immunization

In finance, **interest rate immunization**, as developed by Frank Redington 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.

## Contents

## 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 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 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.

## Duration matching

A more practical alternative immunization method is **duration matching**. Here, the duration of the assets is matched with the duration of the liabilities. To make the match actually profitable under changing interest rates, the assets and liabilities are arranged so that the total convexity of the assets exceed the convexity of the liabilities. In other words, one can match the first derivatives (with respect to interest rate) of the price functions of the assets and liabilities and make sure that the second derivative of the asset price function is set to be greater than or equal to the second derivative of the liability price function.

## 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 [math]t[/math] be denoted by [math]R_t[/math], i.e.:

- [math]R_t = A_t - L_t \text{ for } t = 1,2,3,\ldots,n[/math]

where [math]A_t[/math] and [math]L_t[/math] represent cash inflows and outflows or liabilities respectively.

Assuming that the present value of cash inflows from the assets is equal to the present value of the cash outflows from the liabilities, then:

- [math]P(i) = 0[/math]
^{[1]}

## Immunization in practice

## 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). It might also be difficult to find assets with suitable cashflow structures that are necessary to ensure a particular level of overall volatility of assets to have a proper match with that of liabilities.

Once there is a change in interest rate, the entire portfolio has to be restructured to immunize it again. Such a process of continuous restructuring of portfolios makes immunization a costly and tedious task.

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.

## History

Immunization was discovered independently by several researchers in the early 1940s and 1950s. This work was largely ignored before being re-introduced in the early 1970s, whereafter it gained popularity. See Dedicated Portfolio Theory#History for details.

## See also

- Arbitrage
- Asset–liability mismatch
- Bond convexity
- Bond duration
- Bond
- Covered interest arbitrage
- Debt sculpting
- Duration gap
- Hedging
- Interest rate parity
- Interest rate swap

## References

- ↑ The Theory of Interest, Stephen G. Kellison, McGraw Hill International,2009

## External links

## Further reading

- Wesley Phoa,
*Advanced Fixed Income Analytics*, Frank J. Fabozzi Associates, New Hope Pennsylvania, 1998. ISBN:1-883249-34-1 - Stulz, René M. (2003).
*Risk Management & Derivatives (1st ed.)*. Mason, Ohio: Thomson South-Western. ISBN 0-538-86101-0.