Interest Rate Risk

Interest Rate Risk: Income Side

• Interest Rate Risk – The risk to an institution's income resulting from adverse movements in interest rates

• Many bank liabilities are of very short maturity (such as saving deposits) whose interest changes with market interest rates.

• Many bank assets are long-term and interest income may not change as market interest rate rises.

• When market interest rates rise, bank income will decline.

Net Interest Margin: HK

Mar-1998 Mar-2000 Mar-2002 Mar-2004 Mar-2006

2.4

2.3

2.2

2.1

2.0

1.9

1.8

1.7

1.6

1.5

HK: Net Interest Margin: Local & Foreign Retail Bank%

Source: CEIC Database

What is the impact of monetary policy on bond markets?

Treasury Interest Rates By Maturity

0.001.002.003.004.005.006.007.008.00

Jan-

00

Jul-0

0

Jan-

01

Jul-0

1

Jan-

02

Jul-0

2

Jan-

03

Jul-0

3

Jan-

04

Jul-0

4

Jan-

05

Jul-0

5

Jan-

06

Jul-0

6

1

3

5

10

Interest Rate Risk: Balance Sheet Perspective

• An asset (or a liability) represents a set of payments that must be made at times in the future.

• Define PVT as the present value of a future payments made to an asset or a set of assets in T periods.

• Useful Approximation

PVFACE T i= .1 I = .11 Δi/(1+i) ΔPV ΔPV/PV ΔPV/PV/Δi/(1+i)

100 1 90.90909 90.09009 0.009091 -0.819 -0.00901 -0.99099100 2 82.64463 81.16224 0.009091 -1.48238 -0.01794 -1.97305100 3 75.13148 73.11914 0.009091 -2.01234 -0.02678 -2.94627100 4 68.30135 65.8731 0.009091 -2.42825 -0.03555 -3.91072100 5 62.09213 59.34513 0.009091 -2.747 -0.04424 -4.86648

(1 ) 1T

FACE PV iPV T

i PV i

Duration Measure of Interest Rate Risk

• Define market value, MV, of an asset or a set of assets as the sum of present values derived from payments made in each future period.

• Define the duration of an asset as d

• The % change of the market value of an asset to a change in the interest rate is approximately proportional to the duration of an asset.

T

ttPVMV

1

T

t

t

MV

PVtd

1

i

id

MV

MV

1

Example

• 5 period fixed payment loan of 100.

• Interest rate: 10%• Rises to 11%

Period Payment i=.1 i=.11

1 100 90.90909 90.090092 100 82.64463 81.162243 100 75.13148 73.119144 100 68.30135 65.87315 100 62.09213 59.34513

PV 379.0787 369.5897Duration 2.810126Δi 0.01

Duration×Δi/(1+i) 0.025547ΔMV/MV -0.02503

Measuring Interest Exposure

• Calculate the duration of a banks assets, dA. Calculate the duration of a banks liabilities, dL.

• An increase in the interest rate will have the following effect on assets and liabilities.

• Calculate the GAP as a function of duration of assets and liabilities.

i

id

A

AA

1

i

id

L

LL

1

A L

LD GAP d d

A

An increase in interest rates changes the value of a banks assets

and liabilities.

i

i

A

Ldd

A

L

i

id

i

id

A

L

L

L

A

A

A

L

A

A

A

NW

LALA

111

1

1

NW NW NW iGAP

A NW A iNW i

EM GAPNW i

Managing Interest Rate Risk

• A bank which has a large stock of assets which will pay a fixed interest rate may face losses if market interest rates rise.

• Since deposits must be redeemed at any time, the bank must offer market interest rates. If market interest rates rise, loan spreads will be cut.

• Banks may use asset and liability management to match the sensitivity of assets and liabilities to interest rates.

Responses to a perceived risk of a rise in interest rates.

• If interest rates are expected to rise, banks would like to reduce their long-term fixed interest rate assets and lock in current low interest rates by increasing their stock of long-term liabilities– Asset Management: Increase holdings of

short-term loans or securities.– Liabilities Management: Sell long-term

certificates of deposit.

Floating Rate Loans

• Fixed payment loans have a constant payment based on a fixed interest rate.

• Floating rate loan payments are based on an interest rate that changes as some benchmark interest rate changes

• A HK$ floating rate loan will be quoted as a spread over Hong Kong InterBank Offered Rate (HIBOR), the rate at which banks lend aggregate balances to each other.

• A US$ floating rate Euroloan will be typically quoted as a spread over London InterBank Offered Rate (LIBOR).

Swaps

• Basic (plain vanilla) interest rate swap is agreement by two parties to exchange interest rate payments on a notional principal.

• One party pays a fixed interest rate for a pre-determined period of time. Another party pays a floating rate equivalent to some benchmark interest rate (LIBOR, etc.)

Schedule of Dealer Quotes

Interest Rate Swap Dealer Quotes for Basic Swaps: Fixed Rate vs. 3 Month LIBORMarch 10. 2005 Swap Rates (Fixed Payer Pays)Term US Treasuries Bid Asked

2 years 3.83 4.04 4.053 years 3.72 4.18 4.194 years 3.81 4.3 4.335 years 4 4.52 4.557 years 4.18 4.71 4.7410 years 4.3 4.87 4.9120 years 4.51 5.13 5.1730 years 4.58 5.2 5.28

Source: Koch and Macdonald, Management of Banking

The dealer will pay LIBOR for the next 2 years to the customer if the customer will pay a fixed interest rate of 4.05%. The dealer will pay a fixed rate of 4.04% if the customer will pay LIBOR.

Swaps and Hedging

• If a bank has long-term fixed rate assets and short-term liabilities, they face interest rate risk. Solution: Swap income from fixed rate assets for floating rate from dealer.

• A pension fund with long-term obligations may like to lock in fixed income at a higher rate than LT treasuries. They may also swap income from floating rate assets for fixed income from a dealer.

Interest Rate Swaps are Quickly Growing in Importance

Interest rate swaps: Notional Principal

0

50000

100000

150000

200000

250000

Jun.

1998

Dec.199

8

Jun.

1999

Dec.199

9

Jun.

2000

Dec.200

0

Jun.

2001

Dec.200

1

Jun.

2002

Dec.200

2

Jun.

2003

Dec.200

3

Jun.

2004

Dec.200

4

Jun.

2005

Dec.200

5

Jun.

2006

Bil

lio

ns

US

$

Source: BIS International Financial Statistics http://www.bis.org/statistics/derstats.htm

Advantages of Swaps vs. Futures

• Swap terms can be tailored to individual needs whereas futures are standarized. OTOH, futures markets usually more liquid than swap.

• Swaps typically available for longer-terms while Futures are short-term.

• Exchange guarantees futures while

Market Risk

• Market Risk : Risk to banks liquidity and/or assets from movements in asset prices

1. Exchange Rate Risk– The potential fluctuations in the value of assets or liabilities denominated in foreign currencies due to fluctuations in the exchange rate.

2. Collateral Risk - The risk to the value of assets used as collateral for loans.

Exchange Rate Risk

• International banks often issue liabilities and assets in a variety of different currencies. If there is an imbalance, a change in the exchange rate can affect firms balance sheets.

• Example 1 : In Hong Kong, banks accept large foreign currency deposits but less demand for US$ loans in Hong Kong.

• Example 2: In Argentina, fixed exchange rate with the US dollar (EX = 1) has led Argentine banks to engage in large scale off-shore borrowing denominated in dollars and on-shore borrowing in pesos. What happens to Argentine banks if the peso is devalued?

• Balance Sheets Prior to Devaluation

• Balance Sheets After Devaluation (EX = .8)

Assets Liabilities

Loans P$125

Borrowings US$100 (= P$100)

Net Worth P$25

Assets Liabilities

Loans P$125

Borrowings US$100 (= P$125)

Net Worth P$0

Managing Exchange Rate Risk

• Asset and Liability Management: Hong Kong Banks Borrow and Lend to Foreign Banks to Match Currencies of Liabilities and Assets..

Total Assets 6241252 Total Liabilities and Capital 6241252HK$ Assets 2662668 HK$ Liabilities 2849549 -Loans to Customers 1502813 -Deposits 1830474 -Advances Due from Banks 120477 -Due to Banks Abroad 171007 -Securites and Other 1039378 -Other 848068Foreign Currency Assets 3578585 Foreign Currency Liabilities 3391704 -Loans to Customers 606001 -Deposits 1605443 -Advances Due from Banks 2160909 -Due to Banks Abroad 1349723 -Securites and Other 811675 -Other 436537

Source:HKMA Millions of HK$ ,2001.

Foreign Currency Forwards

• Forward Contracts: Agreements made today (t) for an exchange of currency to be made at some future date (in T periods).– Price, Ft,T determined at time t

– No money exchanged until time T

• Forward contracts are Over-the-Counter (i.e. not traded on an organized exchange)

• Banks are major dealers of FC Forwards.

Pricing Forward Contracts• Spot Rate, St = #DCU

per FCU• Foreign interest rate

for maturity period T, it,T

• Domestic interest rate for maturity period T, it,T

• Two strategies to invest for two periods1. Deposit in domestic

economy, return in DCU = (1+it,T)

2. Buy foreign currency, deposit in FC account, sell FC forward at rate, Ft,T.,

return in DCU, ,

1(1 )F T

t T t Tt

i FS

• Arbitrage implies equal returns for these two strategies.

,, , , ,

,

(1 )1(1 ) (1 )

(1 )

Tt TF T T

t T t T t T t T tF Tt t T

ii F i F S

S i

Currency Forwards: Mostly short-run

0

5000

10000

15000

20000

25000

30000

Jun.

98

Dec

.98

Jun.

99

Dec

.99

Jun.

00

Dec

.00

Jun.

01

Dec

.01

Jun.

02

Dec

.02

Jun.

03

Dec

.03

Jun.

04

Dec

.04

Jun.

05

Maturity over 5 years

Maturity over 1 year and up to 5years

Maturity of one year or less

Source: BIS International Financial Statistics http://www.bis.org/statistics/derstats.htm