Definitions

# Interest rate risk

Interest rate risk is the risk (variability in value) borne by an interest-bearing asset, such as a loan or a bond, due to variability of interest rates. In general, as rates rise, the price of a fixed rate bond will fall, and vice versa. Interest rate risk is commonly measured by the bond's duration.

Asset liability management is a common name for the complete set of techniques used to manage risk within a general enterprise risk management framework.

## Calculating interest rate risk

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 1990s by David Heath of Cornell University, Andrew Morton of Lehman Brothers, and Robert A. Jarrow of Kamakura Corporation and Cornell University.

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. Duration is a stress test where the yield curve shift is parallel
• 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.

## Banks and interest rate risk

Banks face four types of interest rate risk:

1. Basis risk is the risk presented when yields on assets and costs on liabilities are based on different bases, such as the London Interbank Offered Rate (LIBOR) versus the U.S. prime rate. In some circumstances different bases will move at different rates or in different directions, which can cause erratic changes in revenues and expenses.

2. Yield curve risk is the risk presented by differences between short-term and long-term interest rates. Short-term rates are normally lower than long-term rates, and banks earn profits by borrowing short-term money (at lower rates) and investing in long-term assets (at higher rates). But the relationship between short-term and long-term rates can shift quickly and dramatically, which can cause erratic changes in revenues and expenses.

3. Repricing risk is the risk presented by assets and liabilities that reprice at different times and rates. For instance, a loan with a variable rate will generate more interest income when rates rise and less interest income when rates fall. If the loan is funded with fixed rated deposits, the bank's interest margin will fluctuate.

4. Option risk is presented by optionality that is embedded in some assets and liabilities. For instance, mortgage loans present significant option risk due to prepayment speeds that change dramatically when interest rates rise and fall. Falling interest rates will cause many borrowers to refinance and repay their loans, leaving the bank with uninvested cash when interest rates have declined. Alternately, rising interest rates cause mortgage borrowers to repay slower, leaving the bank with relatively more loans based on prior, lower interest rates. Option risk is difficult to measure and control.

## Hedging interest rate risk

Interest rate risks can be hedged using fixed income instruments or interest rate swaps. Interest rate risk can be reduced by buying bonds with shorter duration, or by entering into a fixed-for-floating interest rate swap.