Managing Interest Rate Risk: GAP and Earnings Sensitivity

FINC 4320

Fall 2004

Interest Rate Risk

First, some basic ideas:• Interest rate risk is defined to be potential

variability in net interest income (NII) or market value of equity (MVE) due to changes in interest rates.

• Why the concern?

• Recall some interest rate/bond price fundamentals

Interest Rate Risk

• Why do we care about interest rate exposure? Recall the fundamental nature of a bank’s balance sheet:

– reinvestment risk

– refinancing risk

– price risk

Interest Rate Exposure and Earnings• First we will to look at a model that focuses on the

bank’s earnings stream. Here we will look at the effects of interest rate changes on interest income and interest expense. To do this, we need to look at rate sensitive assets and rate sensitive liabilities. Using these, we will compute a dollar measure, the GAP, of interest rate exposure.

• Method:– Group assets and liabilities into time "buckets” according

to when they mature or are expected to re-price– Calculate GAP for each time bucket– Funding GAPt

= $ Value RSAt - $ Value or RSLt

• where t = time bucket; e.g., 0-3 months

The GAP Model• Rate-Sensitive Assets

– Short-Term Securities Issued by the Government and Private Borrowers

– Short-Term Loans Made by the Bank to Borrowing Customers

– Variable-Rate Loans Made by the Bank to Borrowing Customers

• Rate-Sensitive Liabilities– Borrowings from Money Markets

– Short-Term Savings Accounts

– Money-Market Deposits

– Variable-Rate Deposits

Traditional static GAP analysis

1. Management develops an interest rate forecast2. Management selects a series of “time buckets” (intervals) for

determining when assets and liabilities are rate-sensitive3. Group assets and liabilities into time "buckets" according to

when they mature or re-price– The effects of any off-balance sheet positions (swaps, futures,

etc.) are added to the balance sheet position– Calculate GAP for each time bucket– Funding GAPt = $ Value RSAt - $ Value or RSLt

4. Management forecasts NII given the interest rate environment

Factors affecting NII

• Changes in the level of interest rates NII = (GAP) * (i exected)

• Changes in the slope of the yield curve

• Changes in the volume of assets and liabilities

• Change in the composition of assets and liabilities

Rate, Volume, and Mix Analysis

• Many banks publish a summary of how net interest income has changed over time.

• They separate changes over time to shifts in assets and liability composition and volume from changes associated with movements in interest rates.

• The purpose is to assess what factors influence shifts in net interest income over time.

Yield/ Net Yield/ NetRate Change Rate Change

Taxable loans, net $ 149,423 -117,147 32,276 161,222 36,390 197,612

Tax-exempt loans, nett 1,373 -586 787 1,108 -450 658

Taxable investment securities -5,313 -916 -6,229 4,507 2,570 7,077

Tax-exempt investment securitiest 2,548 74 2,622 2,026 -206 1,820

Interest earning deposits with 223 -176 47 28 48 76Federal funds sold 406 -1,745 -1,339 1,447 1,410 2,857Mortgage loans held for sale 7,801 -1,680 6,121 -113 549 436 Total interest income 156,461 -122,176 34,285 170,225 40,311 210,536

Interest bearing demand deposits $ 6,074 -12,517 -6,443 1,537 5,433 6,970Money market accounts 21,380 -36,244 -14,864 4,654 13,888 18,542Savings deposits -369 -3,307 -3,676 -660 -67 -727Time deposits 32,015 -22,545 9,470 38,824 32,812 71,636Federal funds purchased and -6,165 -29,744 -35,909 23,148 15,870 39,018Other borrowed funds 21,318 -4,272 17,046 21,960 3,361 25,321 Total interest expense 74,253 -108,629 -34,376 89,463 71,297 160,760 Net interest income $82,208 ($13,547) $68,661 $80,762 ($30,986) $49,776

Interest earned on:

Interest paid on:

Volume Volume

2001 Compared to 2000 2000 Compared to 1999Change Due to * Change Due to *

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The GAP Model

• An Asset-Sensitive Bank Has:– Positive Dollar Gap…indicates a bank has more rate

sensitive assets than liabilities, and that net interest income will generally rise (fall) when interest rates rise (fall).

• A Liability-Sensitive Bank Has:– Negative Dollar Gap…indicates a bank has more rate

sensitive liabilities than rate sensitive assets, and that net interest income will generally fall (rise) when interest rates rise (fall).

Optimal value for a bank’s GAP?

• There is no general optimal value for a bank's GAP in all environments.

• The best GAP for a bank can be determined only by evaluating a bank's overall risk and return profile and objectives.

• Generally, the farther a bank's GAP is from zero, the greater is the bank's risk.

• Many banks establish GAP policy targets to control interest rate risk by specifying that GAP as a fraction of earning assets should be plus or minus 15%, or the ratio of RSAs to RSLs should fall between 0.9 and 1.1.

Important Decisions in the GAP Model

1. Management must choose the time period over which NIM is to be managed.

2. Management must choose a target NIM.3. To increase NIM management must either:

a. Develop correct interest rate forecast; orb. Reallocate assets and liabilities to

increase spread.4. Management must choose dollar volume of

interest-sensitive assets and liabilities.

rates interest in change % Expected

NIM) tedNIM)(Expec in change % (Allowable

assets Earning

GAP Target

Target NIM and GAP

• A better risk measure relates the absolute value of a bank’s GAP to earning assets. – The greater is this ratio, the greater the interest rate risk

– The ratio of GAP to earning assets has the additional advantage in that it can be directly linked to variations in NIM.

– In particular, management can determine a target value for GAP in light of specific risk objectives stated terms of a bank’s target NIM:

Advantages of the GAP model

• The primary advantage of GAP analysis is its simplicity.

Problems with GAP Management

• Interest rates paid on liabilities tend to move faster than interest rates earned on assets

• Interest rates attached to bank assets and liabilities do not move at the same speed as market interest rates

• Point at which some assets and liabilities are repriced is not easy to identify

• GAP does not consider impact of changing interest rates on equity (capital) position. That is, it ignores the time value of money.

• GAP further ignores the impact of embedded options.

Exercise of embedded options in assets and liabilities

• Customers have different types of options, both explicit and implicit:– Option to refinance a loan– Call option on a federal agency bond the bank

owns– Depositors option to withdraw funds prior to

maturity

Interest rate risk and embedded options

Example: $10,000 Car loan 4 year Car loan at 8.5%

1 year CD at 4.5%Spread

4.0%But for how long?

Funding GAP GAP = $RSA - $RSL In this example: GAP1y = $0.00 - $10,000 = - $10,000

This is a negative GAP.

Implied options:10,000 4yr loan, financed by a 1 yr CD

-3 -2 -1 base +1 +2 +3

-1,000 -2,000 -8,000 -10,000Gap

-10,000 -10,000 -10,000

Re-finance the auto loans All CD’s will mature

3 month GAP is zero by definition:

-3 -2 -1 base +1 +2 +3

+8,000 +6,000 +2,000 0Gap

-1,000 -3,000 -6,000

Re-finance the auto loans, and less likely to “pull” CD’s

People will “pull” the CD’s for higher returns

1 year GAP position:

The implications of embedded options

• Is the bank the buyer or seller of the option– Does the bank or the customer determine when the option is

exercised?

• How and by what amount is the bank being compensated for selling the option, or how much must it pay to buy the option?

• When will the option be exercised?– Often determined by the economic and interest rate

environment

• Static GAP analysis ignores these embedded options

Earnings sensitivity analysis

• …allows management to incorporate the impact of different spreads between asset yields and liability interest costs when rates change by different amounts.

• Shifts in the yield curve are rarely parallel.• It is well recognized that banks are quick to increase

base loan rates but are slow to lower base loan rates when rates fall.

Earnings sensitivity analysis consists of six general steps:

1. Forecast future interest rates, 2. Identify changes in the composition of assets and

liabilities in different rate environments, 3. Forecast when embedded options will be exercised, 4. Identify when specific assets and liabilities will

reprice given the rate environment, 5. Estimate net interest income and net income, and 6. Repeat the process to compare forecasts of net interest

income and net income across rate environments.

2

(.5)

1.0

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ALCO Guideline

Board Limit(1.0)

(1.5)

Cha

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II($

MM

)

(2.0)

(2.5)

(3.0)- 300 -200 -100 +100 +200 +300ML

Ramped Change in Rates from Most Likely (Basis Points)

Sensitivity of Earnings: Year Two

1.0

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ALCO Guideline

Board Limit(1.0)

(.5)

(1.5)

Cha

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(2.0)

(2.5)

(3.0)

(3.5)-300 -200 -100 +100 +200 +300ML

Ramped Change in Rates from Most Likely (Basis Point)

Sensitivity of Earnings: Year One

Earnings at risk

• …the potential variation in net interest income across different interest rate environments, given different assumptions about balance sheet composition, when embedded options will be exercised, and the timing of repricings.

• Demonstrates the potential volatility in earnings across these environments.

• The greater is the potential variation in earnings (earnings at risk), the greater is the amount of risk assumed by a bank.

Income statement gap

• For smaller banks with limited off-balance sheet exposure, one procedure is to use Income Statement GAP analysis, which is a simplified procedure that takes some of the factors into account.

• This model uses an all encompassing Earnings Change Ratio (ECR).– This ratio attempts to incorporate information on each asset

and liability.

– This ratio indicates how the yield on each asset, and rate paid on each liability, is assumed to change relative to a 1 percent drop in the prime rate.

Steps that banks can take to reduce interest rate risk

• Calculate periodic GAPs over short time intervals.• Match fund repriceable assets with similar repriceable

liabilities so that periodic GAPs approach zero.• Match fund long-term assets with noninterest-bearing

liabilities.• Use off-balance sheet transactions, such as interest

rate swaps and financial futures, to hedge.

Various ways to adjust the effective rate sensitivity of a bank’s assets and liabilities on-balance sheet.

Objective Approaches

Reduce asset sensitivity

Buy longer-term securities.Lengthen the maturities of loans.Move from floating-rate loans to term loans.

Increase asset sensitivity

Buy short-term securities.Shorten loan maturities.Make more loans on a floating-rate basis.

Reduce liability sensitivity

Pay premiums to attract longer-term deposit instruments.Issue long-term subordinated debt.

Increase liability sensitivity

Pay premiums to attract short-term deposit instruments.Borrow more via non-core purchased liabilities.