Manajemen Lembaga Keuangan Lindung Nilai Budi Purwanto Hedging
Manajemen Lembaga Keuangan: Lindung Nilai Budi Purwanto
Hedging § Derivative securities have become increasingly important as FIs seek methods to hedge risk exposures. The growth of derivative usage is not without controversy since misuse can increase risk. This chapter explores the role of futures and forwards in risk management.
Futures and Forwards § Second largest group of interest rate derivatives in terms of notional value and largest group of FX derivatives. § Swaps are the largest.
Derivatives § Rapid growth of derivatives use has been controversial § Orange County, California § Bankers Trust § As of 2000, FASB requires that derivatives be marked to market
Spot and Forward Contracts § Spot Contract § Agreement at t=0 for immediate delivery and immediate payment. § Forward Contract § Agreement to exchange an asset at a specified future date for a price which is set at t=0.
Futures Contracts § Futures Contract § Similar to a forward contract except § Marked to market § Exchange traded (standardized contracts) § Lower default risk than forward contracts.
Hedging Interest Rate Risk § Example: 20 -year $1 million face value bond. Current price = $970, 000. Interest rates expected to increase from 8% to 10% over next 3 months. § From duration model, change in bond value: P/P = -D R/(1+R) P/ $970, 000 = -9 [. 02/1. 08] P = -$161, 666. 67
Example continued: Naive hedge § Hedged by selling 3 months forward at forward price of $970, 000. § Suppose interest rate rises from 8%to 10%. $970, 000 $808, 333 = $161, 667 (forward (spot price) at t=3 months) § Exactly offsets the on-balance-sheet loss. § Immunized.
Hedging with futures § Futures used more commonly used than forwards. § Microhedging § Individual assets. § Macrohedging § Hedging entire duration gap. § Basis risk § Exact matching is uncommon.
Routine versus Selective Hedging § Routine hedging: reduces interest rate risk to lowest possible level. § Low risk - low return. § Selective hedging: manager may selectively hedge based on expectations of future interest rates and risk preferences.
Macrohedging with Futures § Number of futures contracts depends on interest rate exposure and risk-return tradeoff. E = -[DA - k. DL] × A × [ R/(1+R)] § Suppose: DA = 5 years, DL = 3 years and interest rate expected to rise from 10% to 11%. A = $100 million. E = -(5 - (. 9)(3)) $100 (. 01/1. 1) = -$2. 09 million.
Risk-Minimizing Futures Position § Sensitivity of the futures contract: F/F = -DF [ R/(1+R)] Or, F = -DF × [ R/(1+R)] × F and F = NF × PF
Risk-Minimizing Futures Position § Fully hedged requires F = E DF(NF × PF) = (DA - k. DL) × A Number of futures to sell: NF = (DA- k. DL)A/(DF × PF) § Perfect hedge may be impossible since number of contracts must be rounded down.
Payoff profiles Short Position Futures Price Long Position Futures Price
Futures Price Quotes § T-bond futures contract: $100, 000 face value § T-bill futures contract: $1, 000 face value § quote is price per $100 of face value § Example: 103 14/32 for T-bond indicates purchase price of $103, 437. 50 per contract § Delivery options § Conversion factors used to compute invoice
Basis Risk § Spot and futures prices are not perfectly correlated. § We assumed in our example that R/(1+R) = RF/(1+RF) § Basis risk remains when this condition does not hold. Adjusting for basis risk, NF = (DA- k. DL)A/(DF × PF × br) where br = [ RF/(1+RF)]/ [ R/(1+R)]
Hedging FX Risk § Hedging of FX exposure parallels hedging of interest rate risk. § If spot and futures prices are not perfectly correlated, then basis risk remains. § Tailing the hedge § Interest income effects of marking to market allows hedger to reduce number of futures contracts that must be sold to hedge
Basis Risk § In order to adjust for basis risk, we require the hedge ratio, h = S t/ f t § Nf = (Long asset position × h)/(size of one contract).
Estimating the Hedge Ratio § The hedge ratio may be estimated using ordinary least squares regression: § St = a + b ft + ut § The hedge ratio, h will be equal to the coefficient b. The R 2 from the regression reveals the effectiveness of the hedge.
Hedging Credit Risk § More FIs fail due to credit-risk exposures than to either interest-rate or FX exposures. § In recent years, development of derivatives for hedging credit risk has accelerated. § Credit forwards, credit options and credit swaps.
Credit Forwards § Credit forwards hedge against decline in credit quality of borrower. § Common buyers are insurance companies. § Common sellers are banks. § Specifies a credit spread on a benchmark bond issued by a borrower. § Example: BBB bond at time of origination may have 2% spread over U. S. Treasury of same maturity.
Credit Forwards § SF defines credit spread at time contract written § ST = actual credit spread at maturity of forward Credit Spread at End Seller Buyer S T> S F Receives Pays (ST - SF)MD(A) SF>ST Pays Receives
Futures and Catastrophe Risk § CBOT introduced futures and options for catastrophe insurance. § Contract volume is rising. § Catastrophe futures to allow PC insurers to hedge against extreme losses such as hurricanes. § Payoff linked to loss ratio
Regulatory Policy § Three levels of regulation: § Permissible activities § Supervisory oversight of permissible activities § Overall integrity and compliance § Functional regulators § SEC and CFTC § Beginning in 2000, derivative positions must be marked-to-market.
Regulatory Policy for Banks § Federal Reserve, FDIC and OCC require banks § Establish internal guidelines regarding hedging. § Establish trading limits. § Disclose large contract positions that materially affect bank risk to shareholders and outside investors. § Discourage speculation and encourage hedging
Derivatives § Derivative securities as a whole have become increasingly important in the management of risk and this chapter details the use of options in that vein. A review of basic options –puts and calls– is followed by a discussion of fixed-income, or interest rate options. The chapter also explains options that address foreign exchange risk, credit risks, and catastrophe risk. Caps, floors, and collars are also discussed.
Call option § A call provides the holder (or long position) with the right, but not the obligation, to purchase an underlying security at a prespecified exercise or strike price. § Expiration date: American and European options § The purchaser of a call pays the writer of the call (or the short position) a fee, or call premium in exchange.
Payoff to Buyer of a Call Option § If the price of the bond underlying the call option rises above the exercise price, by more than the amount of the premium, then exercising the call generates a profit for the holder of the call. § Since bond prices and interest rates move in opposite directions, the purchaser of a call profits if interest rates fall.
The Short Call Position § Zero-sum game: § The writer of a call (short call position) profits when the call is not exercised (or if the bond price is not far enough above the exercise price to erode the entire call premium). § Gains for the short position are losses for the long position. § Gains for the long position are losses for the short position.
Writing a Call § Since there is no theoretical limit to upward movements in the bond price, the writer of a call is exposed to the risk of very large losses. § Recall that losses to the writer are gains to the purchaser of the call. Therefore, potential profit to call purchaser is theoretically unlimited. § Maximum gain for the writer occurs if
Call Options on Bonds Buy a call Write a call X X
Put Option § A put provides the holder (or long position) with the right, but not the obligation, to sell an underlying security at a prespecified exercise or strike price. § Expiration date: American and European options § The purchaser of a put pays the writer of the put (or the short position) a fee, or put premium in exchange.
Payoff to Buyer of a Put Option § If the price of the bond underlying the put option falls below the exercise price, by more than the amount of the premium, then exercising the put generates a profit for the holder of the put. § Since bond prices and interest rates move in opposite directions, the purchaser of a put profits if interest rates rise.
The Short Put Position § Zero-sum game: § The writer of a put (short put position) profits when the put is not exercised (or if the bond price is not far enough below the exercise price to erode the entire put premium). § Gains for the short position are losses for the long position. Gains for the long position are losses for the short position.
Writing a Put § Since the bond price cannot be negative, the maximum loss for the writer of a put occurs when the bond price falls to zero. § Maximum loss = exercise price minus the premium
Put Options on Bonds Buy a Put Write a Put X X
Writing versus Buying Options § Many smaller FIs constrained to buying rather than writing options. § Economic reasons § Potentially unlimited downside losses. § Regulatory reasons § Risk associated with writing naked options.
Hedging § Payoffs to Bond + Put Bond X Put Net X
Tips for plotting payoffs § Students often find it helpful to tabulate the payoffs at critical values of the underlying security: § Value of the position when bond price equals zero § Value of the position when bond price equals X § Value of position when bond price exceeds X § Value of net position equals sum of individual payoffs
Tips for plotting payoffs
Futures versus Options Hedging § Hedging with futures eliminates both upside and downside § Hedging with options eliminates risk in one direction only
Hedging with Futures Gain Bond Portfolio 0 Bond Price X Loss Purchased Futures Contract
Hedging Bonds § Weaknesses of Black-Scholes model. § Assumes short-term interest rate constant § Assumes constant variance of returns on underlying asset. § Behavior of bond prices between issuance and maturity § Pull-to-par.
Hedging With Bond Options Using Binomial Model § Example: FI purchases zero-coupon bond with 2 years to maturity, at P 0 = $80. 45. This means YTM = 11. 5%. § Assume FI may have to sell at t=1. Current yield on 1 -year bonds is 10% and forecast for next year’s 1 -year rate is that rates will rise to either 13. 82% or 12. 18%. § If r 1=13. 82%, P 1= 100/1. 1382 = $87. 86 § If r 1=12. 18%, P 1= 100/1. 1218 = $89. 14
Example (continued) § If the 1 -year rates of 13. 82% and 12. 18% are equally likely, expected 1 -year rate = 13% and E(P 1) = 100/1. 13 = $88. 50. § To ensure that the FI receives at least $88. 50 at end of 1 year, buy put with X = $88. 50.
Value of the Put § At t = 1, equally likely outcomes that bond with 1 year to maturity trading at $87. 86 or $89. 14. § Value of put at t=1: Max[88. 5 -87. 86, 0] =. 64 Or, Max[88. 5 -89. 14, 0] = 0. § Value at t=0: P = [. 5(. 64) +. 5(0)]/1. 10 = $0. 29.
Actual Bond Options § Most pure bond options trade over-thecounter. § Open interest on CBOE relatively small § Preferred method of hedging is an option on an interest rate futures contract. § Combines best features of futures contracts with asymmetric payoff features of options.
Hedging with Put Options § To hedge net worth exposure, P = - E Np = [(DA-k. DL) A] [ D B] § Adjustment for basis risk: Np = [(DA-k. DL) A] [ D B br]
Using Options to Hedge FX Risk § Example: FI is long in 1 -month T-bill paying £ 100 million. FIs liabilities are in dollars. Suppose they hedge with put options, with X=$1. 60 /£ 1. Contract size = £ 31, 250. § FI needs to buy £ 100, 000/£ 31, 250 = 3, 200 contracts. If cost of put = 0. 20 cents per £, then each contract costs $62. 50. Total cost = $200, 000 = (62. 50 × 3, 200).
Hedging Credit Risk With Options § Credit spread call option § Payoff increases as (default) yield spread on a specified benchmark bond on the borrower increases above some exercise spread S. § Digital default option § Pays a stated amount in the event of a loan default.
Hedging Catastrophe Risk § Catastrophe (CAT) call spread options to hedge unexpectedly high loss events such as hurricanes, faced by PC insurers. § Provides coverage within a bracket of loss-ratios. Example: Increasing payoff if loss-ratio between 50% and 80%. No payoff if below 50%. Capped at 80%.
Caps, Floors, Collars § Cap: buy call (or succession of calls) on interest rates. § Floor: buy a put on interest rates. § Collar: Cap + Floor. § Caps, Floors and Collars create exposure to counterparty credit risk since they involve multiple exercise over-the-counter contracts.
Fair Cap Premium § Two period cap: Fair premium = PV of year 1 option + PV of year 2 option § Cost of a cap (C) Cost = Notional Value of cap × fair cap premium (as percent of notional face value) C = NVc pc
Buy a Cap and Sell a Floor § Net cost of long cap and short floor: Cost = (NVc × pc) - (NVf × pf ) = Cost of cap - Revenue from floor
SWAP The market for swaps has grown enormously and this has raised serious regulatory concerns regarding credit risk exposures. Such concerns motivated the BIS risk-based capital reforms. At the same time, the growth in exotic swaps such as inverse floater have also generated controversy (e. g. , Orange County, CA). Generic swaps in order of quantitative importance: interest rate, currency, credit, commodity and equity
Interest Rate Swaps § Interest rate swap as succession of forwards. § Swap buyer agrees to pay fixed-rate § Swap seller agrees to pay floating-rate. § Purpose of swap § Allows FIs to economically convert variablerate instruments into fixed-rate (or vice versa) in order to better match the duration of assets and liabilities. § Off-balance-sheet transaction.
Plain Vanilla Interest Rate Swap Example § Consider money center bank that has raised $100 million by issuing 4 -year notes with 10% fixed coupons. On asset side: C&I loans linked to LIBOR. Duration gap is negative. DA - k. DL < 0 § Second party is savings bank with $100 million in fixed-rate mortgages of long duration funded with CDs having duration of 1 year. DA - k. DL > 0
Example (continued) § Savings bank can reduce duration gap by buying a swap (taking fixed-payment side). § Notional value of the swap is $100 million. § Maturity is 4 years with 10% fixed-payments. § Suppose that LIBOR currently equals 8% and bank agrees to pay LIBOR + 2%.
Realized Cash Flows on Swap § Suppose realized rates are as follows End of Year LIBOR 1 9% 2 9% 3 7% 4 6%
Swap Payments End of Year 1 2 3 4 Total LIBOR + 2% 11 9 8 MCB Payment $11 11 9 8 39 Savings Bank $10 10 40 Net +1 +1 -1 -2 -1
Off-market Swaps § Swaps can be molded to suit needs § Special interest terms § Varying notional value § Increasing or decreasing over life of swap. § Structured-note inverse floater § Example: Government agency issues note with coupon equal to 7 percent minus LIBOR and converts it into a LIBOR liability through a swap.
Macrohedging with Swaps § Assume a thrift has positive gap such that E = -(DA - k. DL)A [ R/(1+R)] >0 if rates rise. Suppose choose to hedge with 10 -year swaps. Fixed-rate payments are equivalent to payments on a 10 -year T-bond. Floatingrate payments repriced to LIBOR every year. Changes in swap value DS, depend on duration difference (D 10 - D 1). S = -(DFixed - DFloat) × NS × [ R/(1+R)]
Macrohedging (continued) § Optimal notional value requires S = E -(DFixed - DFloat) × NS × [ R/(1+R)] = -(DA - k. DL) × A × [ R/(1+R)] NS = [(DA - k. DL) × A]/(DFixed - DFloat)
Pricing an Interest Rate Swap § Example: § Assume 4 -year swap with fixed payments at end of year. § We derive expected one-year rates from the on-the-run Treasury yield curve treating the individual payments as separate zerocoupon bonds and iterating forward.
Solving the Discount Yield Curve P 1= 108/(1+R 1) = 100 ==> R 1 = 8% ==> d 1 = 8% P 2 = 9/(1+R 2) + 109/(1+R 2)2 = 100 ==> R 2 = 9% 9/(1+d 1) + 109/(1+d 2)2 = 100 ==> d 2 = 9. 045% Similarly, d 3 = 9. 58% and d 4 = 10. 147%
Solving Implied Forward Rates d 1 = 8% ==> E(r 1) = 8% 1+ E(r 2) = (1+d 2)2/(1+d 1) ==> E(r 2) = 10. 1% 1+ E(r 3) = (1+d 3)3/(1+d 2)2 ==> E(r 3) = 10. 658% 1+ E(r 4) = (1+d 4)4/(1+d 3)3 ==> E(r 4) = 11. 866%
Currency Swaps § Fixed-Fixed § Example: U. S. bank with fixed-rate assets denominated in dollars, partly financed with £ 50 million in 4 -year 10 percent (fixed) notes. By comparison, U. K. bank has assets partly funded by $100 million 4 -year 10 percent notes. § Solution: Enter into currency swap.
Cash Flows from Swap
Fixed-Floating + Currency § Fixed-Floating currency swaps. § Allows hedging of interest rate and currency exposures simultaneously
Credit Swaps § Credit swaps designed to hedge credit risk. § Total return swap § Pure credit swap § Interest-rate sensitive element stripped out leaving only the credit risk.
Credit Risk Concerns § Credit risk concerns partly mitigated by netting of swap payments. § Netting by novation § When there are many contracts between parties. § Payment flows are interest and not principal. § Standby letters of credit may be required.
Securitization is another mechanism that may be employed by FIs to hedge their interest rate exposure. This chapter explores the role of securitization in improving the risk-return trade-off. The three major forms of asset securitization, and its mortgage lending origins are also explained.
Introduction § Securitization: Packaging and selling of loans and other assets backed by securities. § Many types of loans and assets are being repackaged in this fashion including royalties on recordings ( David Bowie, Rod Stewart). § Original use was to enhance the liquidity of the residential mortgage market.
The Pass-Through Security § Government National Mortgage Association (GNMA) § Sponsors MBS programs and acts as a guarantor. § Timing insurance. § FNMA actually creates MBSs by purchasing packages of mortgage loans.
Freddie Mac § Federal Home Loan Mortgage Corporation § Similar function to FNMA except major role has involved savings banks. § Stockholder owned with line of credit from the Treasury. § Sponsors conventional loan pools as well as FHA/VA mortgage pools.
Incentives and Mechanics of Pass-Through Security Creation § Example: § Create a mortgage pool from one-thousand, $100, 000 mortgages (Results in $100 million). § Each mortgage receives credit risk protection from FHA. § Capital requirement: $4 million. § Must issue more than $96 million in liabilities due to reserve requirements (+ FDIC premia).
Further Incentives § § § Gap exposure Illiquidity exposure Default risk by mortgagees § Phoenix, AZ in 1980 s. § Default risk by bank/trustee
Effects of prepayments § Good news effects § Lower market yields increase present value of cash flows. § Principal received sooner. § Bad news effects § Fewer interest payments in total. § Reinvestment at lower rates.
Prepayment effects § Prepayments result of § Refinancing § Housing Turnover § Most GNMA pools allow assumable mortgages § Not the case for FNMA nor FHLMC passthroughs
Prepayments § Since prepayment affects the cash flows to MBS, pricing models require estimates of the prepayment rates. § Weighted-average life WAL = [ Time × Expected Principal received] Total principal outstanding
Prepayment Models § Methods: § Public Securities Association approach. § Other empirical approaches. § Option pricing approach.
PSA Model § Assumes 0. 2 percent per annum in first month, increasing by 0. 2 percent per month for first 30 months, until annualized prepayment rate equals 6 percent § Actual outcomes affected by relative coupon level, age of mortgage pool, amortization, assumability, size of pool, conventional/nonconventional, location, and demographics of mortgagees.
Other Empirical Models § Generally proprietary variants of PSA model § Incorporate § economic variables § burn-out factor variables § idiosyncratic factors
Option Model Approach § Use option pricing theory to figure fair yield spread of pass-throughs over Treasuries. § Fair price on pass-through decomposable into two parts § PGNMA = PTBOND - PPREPAYMENT OPTION § Option-adjusted spread between GNMAs and T-bonds reflects value of a call option.
Collateralized Mortgage Obligation (CMO) § CMO structure § Prepayment effects differ across tranches (classes) § Z-Class CMO § R Class § Improves marketability of the bonds
Mortgage-Backed Bonds (MBBs) § § § Normally remain on the balance sheet. Regulatory concerns. Other drawbacks to MBBs.
Innovations in Securitization § Pass-through strips § IO strips § Negative duration. § PO strips § Securitization of other assets § CARDs § Various receivables, loans, junk bonds, ARMs.
Other Credit Risks Management This chapter discusses the growing role of loan sales and other techniques that can be used to address the control of credit risk in FIs. The use of loan sales is not new and may even involve foreign loans. With development of secondary markets for many types of loans, and securitized variants, loan sales are employed even by relatively small FIs.
Loan Sales § Loan sales have taken place for over 100 years. § Correspondent banking § Small banks selling parts of loans to larger banks. § Participations. § Expansion of loan sales during 1980 s. § Due to expansion of HLT loans. § Early 1990 s decline in loan sales followed by recent expansion.
Bank Loan Sale Market § May be sold with or without recourse. § Types of loan sales § Emerging market § Domestic § Traditional short term § HLT Loan sales
Traditional Short Term § Key characteristics § Secured by assets of borrowing firm. § Loans to investment grade borrowers or higher. § Short term. § Yield closely tied to commercial paper. § Denominations of $1 million +.
HLT Loan Sales § Key characteristics § Term loans. § Usually senior secured. § Long maturity (often 3 - to 6 -year maturities). § Floating at rates tied to LIBOR, prime or a CD rate. § Strong covenant protection. § Usually distinguished as distressed / nondistressed.
Types of Loan Sales Contracts § Participations § Limited contractual control. § Assignments § Currently form bulk of the market (90% +). § All rights transferred on sale of loan. § Normally associated with Uniform Commercial Code filing. § Complexity associated with accrued interest
The Buyers § Often segmented. § Example: distressed HLT loan buyers generally investment banks, hedge funds, vulture funds. § Inter-bank loan sales in traditional market historically due to branching restrictions. § Foreign banks dominant buyer of domestic loans § Insurance companies and pension funds in long-term loans. § Mutual funds and nonfinancials
The Sellers § Major money center banks, U. S. government and its agencies. § Good Bank - Bad Bank: § Establishment of subsidiary banks specializing in handling nonperforming loans (NPLs). § Increases value of Good Bank. § Allows structuring of Bad Bank to improve management incentives and operating efficiency.
Other Sellers § Foreign banks § ING is a major market maker (HLTs). § Investment Banks § Bear Stearns. Generally large HLTs. § Government and agencies (HUD for example) § Increased due to Federal Debt Improvements Act, 1996. § Largest sales to date, RTC.
Why Banks and Other FIs Sell Loans § Credit risk management § Reserve requirements § If sold without recourse, removed from balance sheet. § Fee income § boosts reported earnings under current accounting rules.
Why FIs Sell Loans (continued) § Capital costs § Meet capital requirements by reducing assets. § Liquidity risk reduced by loan sales.
Factors Deterring Future Loan Sales Growth § Access to commercial paper market § Customer relationship effects § Customers may take negative view of having their loan sold to another party. § Legal concerns § Fraudulent conveyance.
Factors Encouraging Loan Sales Growth § BIS Capital Requirements § Market Value Accounting § Asset Brokerage and Loan Trading § Government loan sales § Credit rating of loans offered for sale § Purchase and sale of foreign bank loans
Kepustakaan § Siamat, Dahlan. 2004. Manajemen Lembaga Keuangan. Lembaga Penerbit Fakultas Ekonomi Universitas Indonesia. § Saunders, A. , Cornett M. M. 2006. Financial Institution Management. Mc. Graw-Hill International. § Kasmir. 2002. Manajemen Perbankan. Jakarta: Divisi Buku Perguruan Tinggi PT Raja. Grafindo Persada. § Kuncoro, M & Suhardjono. 2002. Manajemen Perbankan: Teori dan Aplikasi. BPFE Yogyakarta. § Riyadi, S. 2004. Banking Assets Liability Management. Penerbitan FE-UI § Gandapradja, P. 2004. Dasar dan Prinsip Pengawasan Bank. Penerbit PT Gramedia Utama.
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