1. Off-Balance-Sheet Activities
陳秀蘭
楊雅智
翁明祥

2. Off-Balance-Sheet Activities
Outlines
Definition, types
How to be valued and effect on FIs
Returns and Risks of OBS Activities
Loan commitments
Commercial letters of credit / Standby letters of credit
When issued securities
Futures and forwards
Interest rate risk
Foreign exchange risk
Credit risk
Catastrophe risk
Options, caps, floors, and collars
Swaps
Loans sold

3. Off-Balance-Sheet Activities
Definition, types
How to be valued and effect on FIs
Dramatic growth and related regulations
Returns and Risks of OBS Activities
The Role of OBS Activities in Reducing Risk

4. Off-Balance-Sheet Activities
In accounting terms – appear below the bottom line, frequently just as footnotes to financial statements
In economic terms – contingent assets and liabilities that affect the future, rather than the current shape of as FI’s balance sheet

5. Off-Balance-Sheet Activities
Off-Balance-Sheet Asset
- Contingent Gain
- When an event occurs, this item moves onto the
asset side of the balance sheet.
Off-Balance-Sheet Liability
- Contingent Loss
- When an event occurs, this item moves onto the
liability side of the balance sheet.

6. Valuation of OBS Activities
Option features
Contingent asset / liability value
(Delta Equivalent)
= Notional value × Delta of an option
Delta = ————————————————————
ex. An FI has an OBS asset of call option on bonds with a notional
value of $100million and the delta is 0.25
Contingent asset value = $25million
Change in the option’s price
Change in price on underlying security

7. Valuation of an FI’s Net Worth
Assets Liabilities
Market value of assets A Market value of liabilities L
Net worth *E
Market value of Market value of
contingent assets CA contingent liabilities CL
*E = A + CA - L - CL

8. Incentives to Do OBS Activities
Earn more fee income to offset declining margins or spreads on traditional lending business
Avoid regulatory costs or taxes since reserve requirements and capital adequacy requirements were not levied on off-balance-sheet activities
Hedge on-balance-sheet interest rate, foreign exchange, and credit risks

9. Dramatic Growth in OBS Activities

12. Regulations 1983 Quarterly Call Report (Schedule L) 1993 BIS Framework
List notional size and variety of OBS activities.
1993 BIS Framework
Impose capital requirements on OBS activities and explicitly recognize FI’s solvency risk exposure from pursuing OBS activities.
1994 DSSSA
Derivatives Safety and Soundness Supervision Act
1994 GAO’s report

13. Returns and Risks of OBS Activities
Loan commitments
Standby letters of credit and letters of credit
Futures, forward contracts, swaps, and options
When issue securities
Loans sold

14. Loan Commitments
A certain maximum amount, at given interest rate terms, in a period of time
Up-front Fee
Back-end Fee
Example Maximum amount = $10million
BR = Interest on the loan = 12%
m = Risk premium = 2%
t = Expected takedown rate = 75%
f1 = Up-front fee = 0.125% ( of $10million )
f2 = Back-end fee = 0.25% ( of $2.5million )
b = Compensating balance = 10%
R = Reserve requirements = 10%

15. Loan Commitments f1 + f2(1-t) + (BR+m)t t – [bt(1-R)]
The promised return (1+k) of the commitment is :
1 + k = 1+ ————————————
1 + k = 1 + —————————————————————
1 + k = or k = 15.66%
compared to the cost of capital
f1 + f2(1-t) + (BR+m)t
t – [bt(1-R)]
(0.25)+( )0.75
0.75-[(0.1)(0.75)(0.9)]

16. Loan Commitments Interest Rate Risk Takedown Risk Credit Risk
This exposes the FI to future liquidity risk or uncertainty.
Credit Risk
Aggregate Funding Risk
In credit crunches, spot loans may decline but loan- commitment-takedown not. However, cost of funds rise above than normal level in this time.

17. Commercial Letters of Credit
A contingent payment guaranty for domestic and international trade
Letter of credit fee
Default risk on letter of credit

18. Standby Letters of Credit
A contingent payment guaranty for CP issuing firm onto maturity
Standby Letter of credit fee
Default risk on standby letter of credit
The LC or SLC fees should exceed the expected loss from default risk, after adjusting for reclaiming and any monitoring costs.

19. When Issued Securities
Commitment to buy and sell securities before issue
Sell the yet-to-be-issued securities in the secondary market at a small margin above the price expected to pay at the primary auction
Risk of mistake regarding the tenor of the auction

20. Nonschedule L Off-Balance-Sheet Risks
Settlement Risk
An FI is exposed to a within-day or intraday credit risk that does not appear on its balance sheet.
Affiliate Risk
The failure of an affiliated firm or bank imposes affiliate risk on another bank in a holding company structure.

21. The Role of OBS Activities in Reducing Risk
When used to hedge on-balance-sheet risks, OBS instruments can actually reduce overall insolvency risk.
Regulatory costs of hedging have risen, and caused FIs to underhedge, thereby increasing, rather than decreasing, their insolvency risk.
Noninterest fee income from OBS activities can potentially compensate for risk exposure for some FIs.
Optimum is always the point.

22. Futures and Forwards Interest rate risk Foreign exchange risk
Credit risk
Catastrophe risk

23. Interest Rate Risk Hedging with Forward
Change in bond values
= Capital loss on bonds
= Initial value of bond position
= Change in forecast yield
D = Duration of the bonds
1+R= 1plus the current yield

24. Interest Rate Risk Hedging with Forward
Suppose an FI holds a 20-year, $1million face value bond
As interest rates rise, the FI makes a capital loss on these bonds
=$ D= 9 years
= 0.02(from 8% to 10% over the next
three months)
1+R = 1.08

25. Interest Rate Risk Hedging with Forward
Capital loss:
Hedging: selling $1 million face value of
20-year bonds forward delivery
in three months’ time

26. Interest Rate Risk Hedging with Futures
Microhedging versus Macrohedging
Microhedging : Using a futures (forward)contract to hedge a specific asset or liability
Macrohedging : Hedging the entire duration gap of an FI

27. Interest Rate Risk- Macrohedging with Futures
FI’s net worth exposure to interest rate changes
= change in an FI’s net worth
= duration of its asset portfolio =5 years
= duration of its liability portfolio =3 years
k = ratio of on FI’s liability to assets =0.9
A = size of an FI’s asset portfolio=$100million
= shock to interest rates = (from 10% to 11%)
Loss on balance sheet: = -$2.091million

28. Interest Rate Risk- Macrohedging with Futures
Gain off balance sheet on selling futures
= change in dollar value of futures contract
= duration of the bond to be delivered
against the futures contracts
= the number of contract bought or sold
= the price of each contract
= expected shock to interest rates
1+RF= 1 plus the current level of interest rates

29. Interest Rate Risk- Macrohedging with Futures
How many futures ( )do we sell to fully hedge the interest rate risk
Assume the interest changes of the cash asset position match those of futures position
=5years, =3years, k=0.9, A=$100m,
=9.5years, =$970000 =
= contracts to be sold

30. Foreign Exchange Risk Hedging with Forward
Example:All assets and liabilities are 1 year
Assets Liabilities
U.S loans $100m U.S CDs $200m
U.K loans$100m
Risk : The pound will depreciate against the dollar
Hedge: Selling both the pound loan principal and
interest forward

31. Foreign Exchange Risk Hedging with Futures
Assuming perfect correlation between spot and futures prices
Loan principal=£100m
interest = £15m
= spot exchange rate($/£)=$ per £1
= futures price($/£)=$ per £1
= $ per £1
= $ per £1
= -5cents

32. Foreign Exchange Risk Hedging with Futures
The size of each British pound futures contract is £62500
= £ /£62500 = 1840 contracts to be sold
Loss on British pound loan
£115m*($1.4713/£-$1.4213/£) = $5.75m
Gain on futures contracts
(1840* £62500)* ($1.4640/£-$1.4140/£)= $5.75m

33. Foreign Exchange Risk Hedging with Futures
Assuming imperfect correlation between spot and futures prices
= $ per £ = -5cents
= $ per £ = -3cents
let h be the ratio of to

34. Foreign Exchange Risk Hedging with Futures
The number of futures contracts to be sold changes
= £115m*1.66/£62500 = contracts
Loss on British pound loan
£115m*($1.4713/£-$1.4213/£) = $5.75m
Gain on British pound futures position
(3054.4*£62500)* ($1.4640/£-$1.4340/£)=$5.75m

35. Credit Risk Hedging with Forward
FIs are afraid of the decline in credit quality of a borrower
Solution: They could buy a credit forward to hedge against an increase in default risk on an loan after the loan rate is determined and the loan is issued

36. Credit Risk Hedging with Forward
:the actual credit spread on the bond in maturity
: the credit spread originally agreed to
MD : modified duration on the benchmark BBB bond
A : the principal amount of the forward agreement

37. Credit Risk Hedging with Forward

38. Catastrophe Risk Hedging with Futures
Who need to transfer the catastrophe risk
Property-casualty insurers are allowed to hedge the extreme losses
Example: Payoff= loss ratio*nominal value of futures
0.8*$25000=$20000
Insurer Investor
1.5*$25000=$37500

39. Options , Caps ,Floors ,and Collars
Writing versus buying options
Calculating the fair value of the option by using the binomial model
Using options to hedge risks
Caps, floors, and collars

40. Writing Versus Buying Options
-Writing a Call Option to Hedge the Interest Rate Risk on a Bond
Payoff function of a bond in an FI’s portfolio
Payoff gain
Bond price X
Payoff function from writing a call on a bond C -C A
Payoff loss

41. Writing Versus Buying Options
-Buying a Put Option to Hedge the Interest Rate Risk on a Bond
Payoff gain
Bond Price
Payoff function from buying a put on a bond
Payoff function of a bond in an FI’s portfolio X -C
Payoff loss

42. Calculating the Fair Value of the Option by Using the Binomial Model
$100 zero-coupon bond with two years maturity
P2=$ →R2=11.5%
R1=10%
r1=13.82% or 12.18% with equal probability
⇒[E(r1)]=(0.5)(0.1382)+(0.5)(0.1218)=0.13
⇒E(P1)=$100/1.13=$88.5

43. Calculating the Fair Value of the Option by Using the Binomial Model
Binomial Model of Bond Prices:Two –year Zero-Coupon Bond
$100
(.25)
$80.45
(.5)
$87.86
$89.14
t=1
t=2
(.25)

44. Calculating the Fair Value of the Option by Using the Binomial Model
The Value of a Put Option on the Two-Year Zero-Coupon Bond
(.25)
$0=Max(0,0) ?
(.5)
Max[ ,0]=0.64
Max[ ,0]=0
t=1
t=2
⇒(0.5)($0.64)+(0.5)($0)=$0.32
⇒P=$0.32/1.1=$0.29

45. Using Options to Hedge Interest Rate Risk on the Balance Sheet
With no Basis Risk

46. Using Options to Hedge Interest Rate Risk on the Balance Sheet
DA= 5 , DL= 3 ,k=0.9 ,A=$100 million
Rate:10%→11%
⇒ △E= – $2.09 million
δ=0.5, D=8.82 ,B=$97,000

47. Using Options to Hedge Interest Rate Risk on the Balance Sheet
With Basis Risk

48. Using Options to Hedge Interest Rate Risk on the Balance Sheet
br=0.92

49. Using Options to Hedge Foreign Exchange Risk
Value($s)
Exchange rate(US$/C$)
Value of C$ asset in U.S.dollar terms
Payoff of put option on C$s
$0.6367/C$
X=$0.63/C$1
$0.5821/C$1
-Hedging FX Risk by Buying a Put Option on Canadian Dollars

50. Using Options to Hedge Credit Risk
Credit spread call option
-A call option whose payoff increases as a yield spread increases above some stated exercise spread.

51. Using Options to Hedge Credit Risk
Digital Default Option
-An option that pays the par value of a loan in the event of default.
Repayment performance
Payoff gain
Option premium
Default
Par value of FI’s loan portfolio
Payoff loss

52. Using Option to Hedge Catastrophe Risk
Catastrophe Call Spread option
- A call option on the loss ratio incurred in writing catastrophe insurance with a capped ( or maximum) payout.
Loss ratio
Payoff
50%
80%
Option premium
Maximum payoff

53. Caps,Floors,and Collars
- A call option on interest rates , often with multiple exercise dates.
Floor
- A put option on interest rates , often with multiple exercise dates.
Collar
- A position taken simultaneously in a cap and a floor.

54. Calculating the Premium on an Interest Rate Cap
FI buys a 9 percent cap at time 0 with a notional face value of $100 million.

55. Calculating the Premium on an Interest Rate Cap
Fair premium= P = PV of year 1 option + PV of year 2 option

56. Collars
After an FI buys a cap and sells a floor, its net cost of the cap is;