Gap Analysis

Most banks use gap analysis to measure interest rate risk in their balance sheets. The gap is defined as the difference between the amounts of rate-sensitive assets and rate-sensitive liabilities maturing or repricing within a specific time period. In other words:

Gap = rate-sensitive assets (RSA) ? rate-sensitive liabilities (RSL)

A firm is said to have a positive gap within a specific time period when its rate-sensitive assets exceed its rate-sensitive liabilities—i.e., “assets reprice before liabilities,” in the professional jargon. It describes the case in which an institution’s short-term assets are funded by long-term liabilities. An increase (decrease) in interest rates leads to an increase (decrease) in Net Interest Income (NII).

When the gap is negative, we refer to it as “liabilities reprice before assets.” It describes the case in which the institution’s long-term assets are funded with short-term liabilities. An increase (decrease) in interest rates leads to a decrease (increase) in NII. This is typically the case for financial intermediaries operating in an interest rate environment where the yield curve has a positive slope. Financial institutions are then said to “ride the yield curve” by borrowing on short maturities and lending long-term: the positive spread between short-term and long-term rates generates a profit margin as long as rates remain stable. This profit margin is, however, at risk when rates start to move up.

Gap analysis is attractive because it is simple. It relies on accounting data and does not involve complex mathematics (such as duration and convexity) and statistics (such as volatilities and correlations). It is a very effective tool for balance sheets that are dominated by instruments that do not have options embedded in them.

However, the approach is prone to inaccuracies for several reasons:

• Gap reports identify only repricing risks. Various kinds of risk are not captured in the gap analysis framework. In particular, gap analyses do not consider basis risk and yield curve risk, such as a steepening of the yield curve. Gap reports also cannot capture foreign exchange risk or the correlation risk between interest rate changes in two currencies.
• Gap analysis does not consider the impact of offsetting positions in different buckets. For example, mismatches in the 1- to 3-month bucket may partially offset the mismatches in the 6- to 12-month bucket. It may be necessary to hedge only the net mismatch.
• Gap analysis ignores interest flows and the associated reinvestment risk of coupons and interest payments.
• Gap analysis uses only accounting data—i.e., book values—which may differ significantly from market value and therefore may bias the measurement of risk.
• Gap analysis may result in large discontinuities in reported positions when positions switch buckets. For example, a 194-day asset, which is in the 7- to 12-month bucket today, will move to the 3- to 6-month bucket after two weeks. This may cause a huge reported mismatch in both buckets.
• Gap analysis is static in nature; it cannot take into account the impact of new volumes on gap positions. However, dynamic gap reporting addresses this issue. Dynamic gap reporting accounts for the rollover strategy of the institution—i.e., its origination strategy and its funding policy. It deals with how maturing assets are replaced by new products, such as the incentives a bank might offer to new customers to take variable rate mortgages in a declining-interest-rate environment (while maturing mortgages are mostly fixed-rate).

Beyond Duration Analysis: Long-Term VaR

Duration gap analysis allows a more accurate assessment of interest rate risk in the balance sheet than simple gap analysis. However, both frameworks are static in nature and do not capture the stochastic nature of interest rates and foreign exchange rates and the fact that the balance sheet evolves over time. New retail products are originated, and maturing assets and liabilities are rolled over as they mature not necessarily into instruments with similar characteristics.

Long-term VaR (LT-VaR) is an extension of the classic VaR framework in the context of the trading book. The time horizon in a classic VaR framework is very short: one day for market risk management purposes and 10 days for regulatory capital reporting. For the banking book, the risk horizon is much longer, at least one year. The objective of LT-VaR is to generate the statistical distributions of Earnings at Risk (EaR) and Net Worth (NW) at different horizons, say next quarter and end of year for EaR and one and two years for NW, in order to produce the worst case EaR and NW at a given confidence level, say 99 percent.

This ambitious procedure can be achieved only by means of powerful Monte Carlo simulations of:

• The correlated term structure of interest rates, such as swap rates, cost- of-funds rates, and mortgage rates, over very long horizons
• Implied volatilities for various types of instruments
• Interest-rate-sensitive prepayment of mortgages and other loans, as well as changes in deposits and savings balances, including seasonal variations in demand for loans and deposits
• Loan defaults
• Renewals (retention rates) and new volume (new origination) for retail
• Products such as mortgages and other consumer loans, on the asset side of the balance sheet, and funding products on the liability side
• At each step of the simulation, pricing models must be used to assess the value of assets and liabilities at that point in time. The simulation should also trigger hedges, when required along a simulation path, in order to comply with any ALCO policy regarding maximum risk exposures (e.g., gap limits).