# Interest rate risk

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Interest rate risk is the risk that arises for bond owners from fluctuating interest rates. How much interest rate risk a bond has depends on how sensitive its price is to interest rate changes in the market. The sensitivity depends on two things, the bond's time to maturity, and the coupon rate of the bond. [1]

Risk is the possibility of losing something of value. Values can be gained or lost when taking risk resulting from a given action or inaction, foreseen or unforeseen. Risk can also be defined as the intentional interaction with uncertainty. Uncertainty is a potential, unpredictable, and uncontrollable outcome; risk is a consequence of action taken in spite of uncertainty.

In finance, a bond is an instrument of indebtedness of the bond issuer to the holders. The most common types of bonds include municipal bonds and corporate bonds.

An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited or borrowed. The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited or borrowed.

## Calculation

Interest rate risk analysis is almost always based on simulating movements in one or more yield curves using the Heath-Jarrow-Morton framework to ensure that the yield curve movements are both consistent with current market yield curves and such that no riskless arbitrage is possible. The Heath-Jarrow-Morton framework was developed in the early 1991 by David Heath of Cornell University, Andrew Morton of Lehman Brothers, and Robert A. Jarrow of Kamakura Corporation and Cornell University.

In finance, the yield curve is a curve showing several yields or interest rates across different contract lengths for a similar debt contract. The curve shows 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. Treasury securities for various maturities are closely watched by many traders, and are commonly plotted on a graph such as the one on the right which is informally called "the yield curve". More formal mathematical descriptions of this relation are often called the term structure of interest rates.

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. When used by academics, an arbitrage is a transaction that involves no negative cash flow at any probabilistic or temporal state and a positive cash flow in at least one state; in simple terms, it is the possibility of a risk-free profit after transaction costs. For example, an arbitrage opportunity is present when there is the opportunity to instantaneously buy something for a low price and sell it for a higher price.

Robert Alan Jarrow is the Ronald P. and Susan E. Lynch Professor of Investment Management at the Johnson Graduate School of Management, Cornell University. Professor Jarrow is a co-creator of the Heath–Jarrow–Morton framework for pricing interest rate derivatives, a co-creator of the reduced form Jarrow–Turnbull credit risk models employed for pricing credit derivatives, and the creator of the forward price martingale measure. These tools and models are now the standards utilized for pricing and hedging in major investment and commercial banks.

There are a number of standard calculations for measuring the impact of changing interest rates on a portfolio consisting of various assets and liabilities. The most common techniques include:

1. Marking to market, calculating the net market value of the assets and liabilities, sometimes called the "market value of portfolio equity"
2. Stress testing this market value by shifting the yield curve in a specific way.
3. Calculating the value at risk of the portfolio
4. Calculating the multiperiod cash flow or financial accrual income and expense for N periods forward in a deterministic set of future yield curves
5. Doing step 4 with random yield curve movements and measuring the probability distribution of cash flows and financial accrual income over time.
6. Measuring the mismatch of the interest sensitivity gap of assets and liabilities, by classifying each asset and liability by the timing of interest rate reset or maturity, whichever comes first.
7. Analyzing Duration, Convexity, DV01 and Key Rate Duration.

## At banks

The assessment of interest rate risk is a very large topic at banks, thrifts, saving and loans, credit unions, and other finance companies, and among their regulators. The widely deployed CAMELS rating system assesses a financial institution's: (C)apital adequacy, (A)ssets, (M)anagement Capability, (E)arnings, (L)iquidity, and (S)ensitivity to market risk. A large portion of the (S)ensitivity in CAMELS is interest rate risk. Much of what is known about assessing interest rate risk has been developed by the interaction of financial institutions with their regulators since the 1990s. Interest rate risk is unquestionably the largest part of the (S)ensitivity analysis in the CAMELS system for most banking institutions. When a bank receives a bad CAMELS rating equity holders, bond holders and creditors are at risk of loss, senior managers can lose their jobs and the firms are put on the FDIC problem bank list.

The CELS ratings or Camels rating is a supervisory rating system originally developed in the U.S. to classify a bank's overall condition. It is applied to every bank and credit union in the U.S. and is also implemented outside the U.S. by various banking supervisory regulators.

In American finance, the FDIC problem bank list is a confidential list created and maintained by the Federal Deposit Insurance Corporation which lists banks that are in jeopardy of failing. The list is closely monitored, and if problems continue with a listed bank, the FDIC takes control of the bank; it may then sell the problem bank to a stronger one, or liquidate the bank and pay off the depositors.

See the (S)ensitivity section of the CAMELS rating system for a substantial list of links to documents and examiner manuals, issued by financial regulators, that cover many issues in the analysis of interest rate risk.

In addition to being subject to the CAMELS system, the largest banks are often subject to prescribed stress testing. The assessment of interest rate risk is typically informed by some type of stress testing. See: Stress test (financial), List of bank stress tests, List of systemically important banks.

A stress test, in financial terminology, is an analysis or simulation designed to determine the ability of a given financial instrument or financial institution to deal with an economic crisis. Instead of doing financial projection on a "best estimate" basis, a company or its regulators may do stress testing where they look at how robust a financial instrument is in certain crashes, a form of scenario analysis. They may test the instrument under, for example, the following stresses:

## Related Research Articles

In finance, a high-yield bond is a bond that is rated below investment grade. These bonds have a higher risk of default or other adverse credit events, but typically pay higher yields than better quality bonds in order to make them attractive to investors.

Discounting is a financial mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee. Essentially, the party that owes money in the present purchases the right to delay the payment until some future date. The discount, or charge, is the difference between the original amount owed in the present and the amount that has to be paid in the future to settle the debt.

In finance, an interest rate swap (IRS) is an interest rate derivative (IRD). It involves exchange of interest rates between two parties. In particular it is a linear IRD and one of the most liquid, benchmark products. It has associations with forward rate agreements (FRAs), and with zero coupon swaps (ZCSs).

Bond valuation is the determination of the fair price of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. Hence, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate. In practice, this discount rate is often determined by reference to similar instruments, provided that such instruments exist. Various related yield-measures are then calculated for the given price.

A money market fund is an open-ended mutual fund that invests in short-term debt securities such as US Treasury bills and commercial paper. Money market funds are widely regarded as being as safe as bank deposits yet providing a higher yield. Regulated in the United States under the Investment Company Act of 1940, money market funds are important providers of liquidity to financial intermediaries.

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.

The bond market is a financial market where participants can issue new debt, known as the primary market, or buy and sell debt securities, known as the secondary market. This is usually in the form of bonds, but it may include notes, bills, and so on.

The Heath–Jarrow–Morton (HJM) framework is a general framework to model the evolution of interest rate curves – instantaneous forward rate curves in particular. When the volatility and drift of the instantaneous forward rate are assumed to be deterministic, this is known as the Gaussian Heath–Jarrow–Morton (HJM) model of forward rates. For direct modeling of simple forward rates the Brace–Gatarek–Musiela model represents an example.

The Z-spread, ZSPRD, zero-volatility spread or yield curve spread of a mortgage-backed security (MBS) is the parallel shift or spread over the zero-coupon Treasury yield curve required for discounting a pre-determined cash flow schedule to arrive at its present market price. The Z-spread is also widely used in the credit default swap (CDS) market as a measure of credit spread that is relatively insensitive to the particulars of specific corporate or government bonds.

The following outline is provided as an overview of and topical guide to finance:

Initially pioneered by financial institutions during the 1970s as interest rates became increasingly volatile, asset and liability management is the practice of managing risks that arise due to mismatches between the assets and liabilities.

The interest sensitivity gap was one of the first techniques used in asset liability management to manage interest rate risk. The use of this technique was initiated in the middle 1970s in the United States when rising interest rates in 1975-1976 and again from 1979 onward triggered a banking crisis that later resulted in more than \$1 trillion in losses when the Federal Deposit Insurance Corporation and the Federal Savings and Loan Insurance Corporation were forced to liquidate hundreds of failed institutions who had typically lent for long maturities at fixed interest rates and borrowed for much shorter maturities. The interest rate sensitivity gap classifies all assets, liabilities and off balance sheet transactions by effective maturity from an interest rate reset perspective. A thirty-year fixed rate mortgage would be classified as a 30-year instrument. A 15-year mortgage with a rate fixed only for the first year would be classified as a one-year instrument. The interest rate sensitivity gap compares the amount of assets and liabilities in each time period in the interest rate sensitivity gap table. This comparison gives an approximate view of the interest rate risk of the balance sheet being analyzed. The interest rate sensitivity gap is much less accurate than modern interest rate risk management technology where the impact of a change in the yield curve can be analyzed using the Heath-Jarrow-Morton framework based on the work of researchers such as John Hull, Alan White, Robert C. Merton, Robert A. Jarrow and many others.

An asset swap refers to an exchange of tangible for intangible assets, in accountancy, or, in finance, to the exchange of the flow of payments from a given security for a different set of cash flows.

Kamakura Corporation is a global financial software company headquartered in Honolulu, Hawaii. It specializes in software and data for risk management for banking, insurance and investment businesses.

Repricing risk is the risk of changes in interest rate charged (earned) at the time a financial contract’s rate is reset. It emerges if interest rates are settled on liabilities for periods which differ from those on offsetting assets. Repricing risk also refers to the probability that the yield curve will move in a way that influence by the values of securities tied to interest rates -- especially, bonds and market securities.

In finance, a zero coupon swap (ZCS) is an interest rate derivative (IRD). In particular it is a linear IRD, that in its specification is very similar to the much more widely traded interest rate swap (IRS).

## References

1. Ross, Westerfield, Jordan (2010). Fundamentals of Corporate Finance. New York: McGraw Hill / Irwin. ISBN   978-007-108855-8.