Uses of Derivatives for Risk Management

Charles Smithson

Copyright 2004 Rutter Associates, LLC

Assessing, Managing and Supervising Financial RiskThe World Bank, Washington, DC

May 19, 2004

2Rutter Associates

Outline

1. Tool Box – Derivatives being used by financial institutions

2. Asset-Liability Management: Using interest rate derivatives to manage the ‘maturity gap’ and/or ‘duration and convexity’

3. Managing Risks in the Investment Portfolio

4. Managing Credit Risk

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1. The Tool Box

+

+

=

=

Forwards, Futures, Swaps Options

Short Put/“Floor”

Short Call/“Cap”

Long Call/ “Cap”

Long Put/“Floor”

Long

Short

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• Managing Cash Flow Risk

• Managing Value Risk

– Changing the “Duration” of the Portfolio

– Changing the “Convexity” of the Portfolio

2, Asset Liability Management

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“Maturity Gap” measures exposure on a net interest income basis

r

NIIGap =

(Net Interest Income) = (Gap) x r

Gap = RSA - RSLwhere RSA = Rate sensitive assets

RSL = Rate sensitive liabilities

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Gap = $600 - $900 = - $3001 year

ABC Bank($ Millions)

< 3 mo. 100 6 mo. 100 12 mo. 400> 12 mo. 400

< 3 mo. 400 6 mo. 300 12 mo. 200> 12 mo. 100

Assets Liabilities

1,000 1,000

{RSA =

$600

{

RSL =$900

If interest rates rose by 100 basis points, NII would be expected to decline by $3 million

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Gap = $600 - $800 = -$2001 year

ABC Bank($ Millions)

< 3 mo. 100 6 mo. 100 12 mo. 400> 12 mo. 400

< 3 mo. 400 6 mo. 300 12 mo. 200> 12 mo. 100

Assets Liabilities

1,000 1,000

Suppose ABC enters into a 3-year, $100 million Interest Rate Swap in which it receives the 6-month rate and pays a 3-year rate.

$100 million of the 6-month liabilities now have an effective maturity of 3 years

200

200

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~ ~ ~ ~ ~

NP = Notional Principal = $100 millionR = 3-year Fixed RateR = 6-month Rate

_

~

ABC Bank’s Interest Rate Swap

PN R_

xPN R_

xPN R_

xPN R_

x PN R_

xPN R_

x

~xN P R4xN P R3

xN P R2xN P R1

xN P R5xN P R4

Month 0 6 12 18 24 30 36

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• Managing Cash Flow Risk

• Managing Value Risk

– Changing the “Duration” of the Portfolio

– Changing the “Convexity” of the Portfolio

2. Asset Liability Management

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DURATION

Shading represents the present value of the nominal cash flow at time t.

Duration

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Timet

CashFlow

0.5

1.0

1.5

2.0

2.5

90

90

90

90

90

DiscountRate7.75%

8.00%

8.25%

8.35%

8.50%

Calculation of Duration for Fixed Income Securities

PresentValue 86.70

83.33

79.91

76.66

73.40

400.00Price

*Weight = PV(CFt)/Price

Weight*0.22

0.21

0.20

0.19

0.18

1.00

Duration(Weight x t)

0.11

0.21

0.31

0.38

0.45

1.46 years

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Duration can also be expressed as an elasticity:

Percent change in price

Percent change in (1+ r)

Duration can be used to estimate percentage change in price:

Percent change in price

~ r

r1

D

D

Duration as a Measure of Interest Rate Sensitivity

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Bank holds a $50,000,000 loan with a duration of 13.183.

Loan is funded with debt that has a duration of 9.38.

The bank is not comfortable with a mismatch between the duration of the loan and the duration of the debt funding the loan.

Bank wants duration of asset position to match that of the debt. - Bank could sell the existing asset and replace it with one that has a duration of 9.38 - Bank could use an interest rate swap to modify the duration of the existing asset.

Changing the Duration of the Portfolio

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PN R_

xPN R_

xPN R_

xPN R_

x PN R_

x

~ ~ ~ ~xN P R4xN P R3

xN P R2xN P R1

xN P R5

~

NP = Notional PrincipalR = Fixed RateR = Floating Rate

_

~

Interest Rate Swap

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R_

R_

R_

R_

R_

~ ~ ~ ~R4R3R2R1 R5

~

An interest rate swap can be viewed as equivalent to long and short positions in fixed- and floating- rate bonds.

Lending FixedRate

Borrowing FixedRate

NP x NP x NP x NP x NP x

NP x NP x NP x NP x NP x

DurationSWAP = DurationFIXED - DurationFLOATING

- Fixed side of a 5-year swap paying 7% semi-annual has a duration of 4.3 - Floating side has a duration of 0.5. - Swap duration is 3.8

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Duration of the $50,000,000 loan is 13.183

Duration of swap is 3.83

By paying the fixed rate on a $50,000,000 swap, the bank will reduce the duration of the asset position to 13.183 - 3.8 = 9.38

Changing the Duration of the Portfolio

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• Managing Cash Flow Risk

• Managing Value Risk

– Changing the “Duration” of the Portfolio

– Changing the “Convexity” of the Portfolio

2. Asset Liability Management

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“True” Price Risk

Duration provides a linear estimate of the change in value of a security given a change in the interest rate.

Interest Rates

LinearApproximation

EstimationError

Price

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Interest Rates

“True” Value Profile

Estimation Error--after convexityadjustment

Price

Convexity adjusts the linear measure to compensate for the change in the slope of the price risk curve between two points

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Interest Rate

Value

#1Linear Profile

#2Positive

Convexity

V0

r0

#3Negative

Convexity

The Impact of Positive and Negative Convexity

Sources of Convexity

• Borrowers have prepayment and/or rate cap options

• Depositors have withdrawal options

Suppose the bank’s debt portfoliohas a shorter duration thanit’s assets

V

r

Suppose the bank gave borrowersthe right to prepay with nopenalty

V

r

The result would beNEGATIVE CONVEXITY

V

r

Changing the Convexity of the Portfolio

A bank can reduce the effects ofNEGATIVE CONVEXITY . . .

V

r

. . . and buying out-of-the-moneyinterest rate caps

V

r

The net interest rate exposurewould be reduced.

V

r

V

rand floors.

V

r. . . by entering into pay fixed-receive floating swaps . . .

Changing the Convexity of the Portfolio

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Assets in a Bank’s Investment Portfolio

• Government Bonds (Domestic and Foreign)

• Mortgage-Backed Securities

• Corporate Bonds (Domestic and Foreign)

– Standard

– Convertible

– Asset-Backed

• Equity

• Structured Notes

3. Managing Risk in the Investment Portfolio

RisksInterest Rate RiskForeign Exchange Rate RiskEquity Price RiskCredit RiskCommodity Price Risk

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A U.S. bank is considering investing in a GBP-denominated bondthat matures in one year

Face Value: GBP 1,000,000Coupon: 8.00%Price: 100.3%

The YTM in GBP is 7.67%

The YTM to the U.S. bank would be 7.63%, after taking into account the bid/ask spread on the current USD/GBP spot rate,and assuming the FX rate does not change.

The U.S. bank is concerned about the foreign exchange rate riskthat is inherent in this investment.

Managing FX Risk

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If the U.S. bank wished to eliminate the foreign exchange risk,it could enter into a foreign exchange forward contract

USD/GBP Bid AskSpot 1.6175 1.61811-Year Forward 1.5895 1.5904

By locking in the exchange rate at the one-year horizon, theU.S. bank has locked in a YTM of 5.77%.

Data as of August 14, 1998

Managing FX Risk

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Alternatively, the U.S. bank could protect against the GBPweakening against the USD by purchasing a foreign exchangeoption -- a put option on GBP.

Suppose the U.S. bank elects to strike the option at the currentspot rate. The premium for the option is USD 0.06132.

Multiplying the premium with the GBP cash-flow at maturity,the cost to the U.S. bank for the option would be USD 66,226.

Factoring the cost of the option into the investment, the U.S.bank has guaranteed itself a minimum YTM of 3.45%.

But the U.S. bank’s YTM could rise if the GBP appreciates relative to 1.6181.

Managing FX Risk

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-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

1.40

0

1.47

5

1.55

0

1.62

5

1.70

0

1.77

5

1.85

0

Spot USD/GBP at Maturity

Yie

ld-t

o-M

atur

ity

No Hedge

FX Forward

FX Option (Spot Strike)

Managing FX Risk

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Does your institution have a formal Credit Portfolio Management function?

No20%

Yes80%

4. Managing Credit Risk

Source: 2002 Rutter Associates Survey of Credit Portfolio Management Practices, Sponsored by IACPM, ISDA, and RMA

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Rank the following tools in order of their importance to the management of your credit portfolio. (“1” denotes the most important and “4” denotes the least important.)

Management of new business and renewals of existing business

Loan sales and trading

Credit derivatives

Securitizations

1.11.1

2.72.7

3.03.0

3.23.2

4. Managing Credit Risk

Source: 2002 Rutter Associates Survey of Credit Portfolio Management Practices, Sponsored by IACPM, ISDA, and RMA

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Credit Default Swap

X basis points per year

ProtectionSeller

ProtectionBuyer

PaymentCredit event

ZeroNo credit event

or it could be bankruptcy, downgrade, failure to pay, repudiation or moratorium, acceleration, or restructuring

Materiality conditions may be specified

The credit event could be defined as default on a specific “reference” obligation, or an enumerated group of obligations, or all obligations in a specified class (e.g. “foreign currency bonds”) …

Cash settlement: Payment of the post-default market value of the asset against receipt of the strike price (usually par)

Physical delivery: Delivery of the reference bond or loan--or other acceptable instrument as agreed in the confirm--against receipt of the strike price (usually par)

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BANK

$20mm Exposure to XYZ Inc.

ProtectionSeller

$20mm x (x basis points)

If credit event does not occur

$20mm - Recovery

$0

If credit event occurs

Reducing the Portfolio’s Exposure to a Specific Obligorwith a Credit Default Swap

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Uses of Derivatives for Risk Management

Charles Smithson

Copyright 2004 Rutter Associates, LLC

Assessing, Managing and Supervising Financial RiskThe World Bank, Washington, DC

May 19, 2004