rsa n rsl

Bank Financial Management: Hedging Interest Rate Risk

The GAP

The manageme management nt of a bank s assets and liabili liabilities ties focuses focuses on controlling the GAP between between RSA and RSL. Generally defined, defined, a rate-s rate-sensitive ensitive instrument is one that can be re-priced re-priced in 90 days or less. GAP = RSA

RSL

GAP Ratio = RSA / RSL GAP Management Strategies Zero GAP

A zero GAP or GAP Ratio of one (1.0) attempts to maturity match assets and liabilities. liabilities. However, this strategy does does not eliminate completely completely the risk of interest interest rate movements. movements. Why? Because there is not a perfect synchronization between the rates which affect assets and liabilities. Positive GAP

] RSA > RSL Positive GAP management is desirable when the yield curve is shifting from a flat position to a negative or humped shape.

DERlec12: Interest Rate Risk in Banking

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Negative GAP

RSA < RSL Negative GAP management, where RSL > RSA, has been the normal approach for depository institutions. Why? Because banks tend to borrow short and lend long. Given an upward sloping yield curve, a negative GAP is profitable as banks borrow at low cost and lend at higher yields. However, when rates are rising, a negative GAP involves considerable liquidity and interest-rate risk. The Building Blocks of ALM

1. Measurement of dollar GAP determining the amount of assets and liabilities being re-priced. 2. Estimating the rates at which dollars will be re-priced. 3. Projecting future income. 4. Testing different strategies.

FIN 420 / 618 Class Notes Warning!! These notes contain direct references to copyrighted material Do not quote, copy, or replicate without permission.

Prepared by: Dr. Gordon H. Dash, Jr. Last Update: 26-APR-99


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Positive Gap RSA > RSL

The Risk Losses if rates fall as the bank s net interest margin will be reduced

Possible Responses 1. Do nothing rates may remain stable or even improve. 2. Extend asset maturities or shorten liability maturities. 3. Increase RSL or reduce RSA. 4. Move toward a position where asset duration equals liability duration.

Negative Gap RSA < RSL

The Risk Losses if interest rates rise as the bank s net interest margin will be reduced.

Possible Responses 1. Do nothing rates may be stable or may actually fall. 2. Shorten asset maturities or lengthen liability maturities. 3. Decrease RSL or increase RSA. 4. Move toward a position where asset duration equals liability duration.




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Duration GAP Management

This method provides bankers with a single number that presents the bank s overall exposure to interest rate risks. Note that the net worth of a bank is: NW = A L. As interest rates change, the value of both a bank s assets and liabilities will change, resulting in a change in the bank s net worth: NW = A - L. Duration measures the sensitivity of the market value of

financial instruments to changes in interest rates. Def: the percentage change in the market price of an asset or a

liability is roughly equal to its duration times the relative change in interest rates attached to that particular asset or liability: P P

D

i

1 i

Where the left-hand-side captures the percentage change in market price; on the right-hand-side the bracketed term is the relative change in interest rates associated with the asset or liability. D is duration. The negative sign attached to duration is to remind us that market prices and interest rates on financial instruments move in opposite directions.




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For example, consider a bond held by a bank that carries duration of four years and a current market value (price) of $1,000. Market interest rates attached to comparable bonds are about 10 percent. Recent forecasts suggest that market rates may rise to 11 percent. If this forecast is correct, by what percentage will the bond s market value change? A: -3.64% (proof left to the reader). NOTE: the interest rate risk of financial instruments is directly proportional to their durations. A bank could hedge by durations such that: The dollar-weighted duration of the bank s asset portfolio

Duration GAP =

The dollar-weighted duration of bank liabilities

Dollar weighted duration of the bank s asset portfolio

-

(L/A) x (Dollar weighted duration of bank liabilities)

Because the dollar volume of bank assets usually exceeds the dollar volume of bank liabilities (or the bank would be insolvent), a bank seeking a duration GAP of zero would need to make sure that:




Dollar weighted duration of bank asset portfolio

Assets

U.S. Treas uries MuniBonds Com. Loans Consu mer Loans Real Estate Loans Total

=

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Dollarweighted duration of bank liability portfolio

$ Value

i Avg. rate Duration % 90 10.0 7.49

20

6.0

1.50

100 12.0

0.60

50 15.0

1.20

40 13.0

2.25

$300

Duration GAP = 3.047

3.047 yrs.

x

Total Liabilities / Total Assets

Liab. & $ i Avg. Equity Value rate Duration Negot. CDs

100

6.0

1.943

Other Time Dep. Sub. Notes

125

7.2

2.750

50

9.0

3.918

Stockholders Equity Total

25

$300

2.669 x ($275/$300) = 0.60 years.



2.669 yrs.


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The management interpretation follows. The positive GAP of +0.60 years means that the bank s net worth will decline if interest rates rise and increase if interest rates fall. The key question is: by how much will the value of the bank s net worth change for any given change in interest rates? NW

DA

r

1 r

A

DL

r

1 r

L

Where A is total assets, DA is the average duration of assets, r the initial rate of interest, r the change in interest rates, L is total liabilities, and DL is the average duration of liabilities. If interest rates increased from 8% to 10%, on average, the bank s net worth would fall by approximately $3.34 million. This would carry with it the assumption that all interest rates both those attached to the bank s assets and its liabilities increased by 2 percentage points. Just the opposite should rates decline by 2%, on average.




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Hedging GAPs with Interest Rate Futures

Three problems act to restrict the application of this ALM method: 1. basis risk makes perfect hedges difficult to construct. Basis risk is the instability in the expected movements between spot and futures prices (b = s-f). 2. marking-to-market tends to destabilize earnings and present accounting problems/issues. 3. Hedged positions must be monitored and adjusted to market changes (requires skilled personnel).

The Hedge Ratio

As a tool of ALM (asset-liability-management), short-hedge strategies may be used to provide liquidity (see DC, xx), whereas a long hedge may be used to lock in current market yields (see DC, xx). A bank would use the futures market to hedge rate-sensitiveassets (RSA) and rate-sensitive-liabilities (RSL). For example, a Treasury-bill futures contract could be employed.




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To hedge a negative GAP (interest rates are expected to rise), a

Nf

$GAP N X 2 M

T-Bill futures contract can be sold. Compute the hedge ratio as follows: Where N is the number of months the GAP is to be hedged, and M is the maturity in months of the instrument used to hedge the GAP. For example, if a bank observed a $48 million negative GAP, and the bank felt that over the next 3 months rates would increase, the bank would sell 8 contracts: ($48/2)(1/3) = -8. To hedge a positive GAP (rates are expected to decline), T-Bill futures would be purchased. The hedge ratio would remain the same. A Hedge Based on Duration DA

Nf

TotalLiabi lity TotalAsset s

DL TotalAssts

Dus F

Where DA is the average asset duration; DL is the average duration of liabilities; Dus is the duration of the underlying security named in the futures contract; and, F is the price of the futures contract. FIN 420 / 618 Class Notes Warning!! These notes contain direct references to copyrighted material Do not quote, copy, or replicate without permission.



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Macro Hedges Versus Micro Hedges

The hedging strategy described above is a macro hedge. This type of hedge is designed to hedge the bank s net duration position. If successful, this strategy brings the entire asset/liability portfolio into balance so that the interest rate sensitivity of the assets and liabilities are matched. The macro hedge requirements

Detailed knowledge of the bank s total exposure to interest rate risk. Relatively large transactions in the futures market (designed to protect the entire portfolio). A significant effort must be devoted to interest rate forecasting. The Micro-Hedge Comparison

The micro hedge, by contrast, ties the futures position to a specific category of asset(s) or liability(s) rather than to the net interest rate exposure. The macro hedge is theoretically more effective, but the micro hedge is intuitively more practical.




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Information Requirements

The amount needed to monitor total GAP continuously may be prohibitive. Managers often find it more feasible to select a group of assets or liabilities. Futures trades are most often chosen to hedge a specific category of accounts. Accounting Standards FASB recommends more favorable accounting methods for futures hedges linked to identifiable cash market instruments (micro hedge). When an institution cannot link a hedge to a specific asset (liability) accounting rules require the hedge to be reported as gains or losses on the income statement before the final futures position is closed out. Because changes in interest rates during the course of the hedge may produce temporary losses which are ultimately recovered, reporting hedging results before the position is closed can increase variability in reported earnings. The results of micro hedging must be reported only when closed out, and they can be amortized over the remaining life of the hedged asset or liability. FIN 420 / 618 Class Notes Warning!! These notes contain direct references to copyrighted material Do not quote, copy, or replicate without permission.



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Managerial Flexibility Borrowers who demand fixed rate loans can be accommodated as the lender can limit interest rate risk by structuring a futures position (e.g., if rates rise, a short position in futures is required). Lending institutions can offer variable rate loans that are indexed to an instrument on which futures contracts are traded. The lender then helps the borrower in structuring a futures position that hedges against changes in the loan rate.



rsa n rsl

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