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

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

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

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

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.

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

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

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

Dramatic Growth in OBS Activities

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

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

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%

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 = 1.1566 or k = 15.66% compared to the cost of capital f1 + f2(1-t) + (BR+m)t t – [bt(1-R)] 0.00125+0.0025(0.25)+(0.12+0.02)0.75 0.75-[(0.1)(0.75)(0.9)]

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.

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

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.

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

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.

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.

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

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

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 =$970000 D= 9 years = 0.02(from 8% to 10% over the next three months) 1+R = 1.08

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

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

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

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

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 = = 249.59 contracts to be sold

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

Foreign Exchange Risk Hedging with Futures Assuming perfect correlation between spot and futures prices Loan principal=£100m interest = £15m = spot exchange rate($/£)=$1.4713 per £1 = futures price($/£)=$1.4640 per £1 = $1.4213 per £1 = $1.4140 per £1 = -5cents

Foreign Exchange Risk Hedging with Futures The size of each British pound futures contract is £62500 = £115000000/£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

Foreign Exchange Risk Hedging with Futures Assuming imperfect correlation between spot and futures prices = $1.4213 per £1 = -5cents = $1.4140 per £1 = -3cents let h be the ratio of to

Foreign Exchange Risk Hedging with Futures The number of futures contracts to be sold changes = £115m*1.66/£62500 =3054.4 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

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

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

Credit Risk Hedging with Forward

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

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

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

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

Calculating the Fair Value of the Option by Using the Binomial Model $100 zero-coupon bond with two years maturity P2=$80.45 →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

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)

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[88.5-87.86,0]=0.64 Max[88.5-89.14,0]=0 t=1 t=2 ⇒(0.5)($0.64)+(0.5)($0)=$0.32 ⇒P=$0.32/1.1=$0.29

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

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

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

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

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

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.

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

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

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.

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.

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

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