Manajemen Lembaga Keuangan: Lindung Nilai

1. Manajemen Lembaga Keuangan: Lindung Nilai Budi Purwanto

2. 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.

3. 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.

4. 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

5. 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.

6. Futures Contracts • Futures Contract • Similar to a forward contract except • Marked to market • Exchange traded (standardized contracts) • Lower default risk than forward contracts.

7. 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

8. 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 price) at t=3 months) • Exactly offsets the on-balance-sheet loss. • Immunized.

9. Hedging with futures • Futures used more commonly used than forwards. • Microhedging • Individual assets. • Macrohedging • Hedging entire duration gap. • Basis risk • Exact matching is uncommon.

10. 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.

11. Macrohedging with Futures • Number of futures contracts depends on interest rate exposure and risk-return tradeoff. DE = -[DA - kDL] × A × [DR/(1+R)] • Suppose: DA = 5 years, DL = 3 years and interest rate expected to rise from 10% to 11%. A = $100 million. DE = -(5 - (.9)(3)) $100 (.01/1.1) = -$2.09 million.

12. Risk-Minimizing Futures Position • Sensitivity of the futures contract: DF/F = -DF [DR/(1+R)] Or, DF = -DF × [DR/(1+R)] × F and F = NF × PF

13. Risk-Minimizing Futures Position • Fully hedged requires DF = DE DF(NF × PF) = (DA - kDL) × A Number of futures to sell: NF = (DA- kDL)A/(DF × PF) • Perfect hedge may be impossible since number of contracts must be rounded down.

14. Payoff profiles Long Position Short Position Futures Price Futures Price

15. Futures Price Quotes • T-bond futures contract: $100,000 face value • T-bill futures contract: $1,000,000 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 price if bond other than the benchmark bond delivered

16. Basis Risk • Spot and futures prices are not perfectly correlated. • We assumed in our example that DR/(1+R) = DRF/(1+RF) • Basis risk remains when this condition does not hold. Adjusting for basis risk, NF = (DA- kDL)A/(DF × PF ×br) where br = [DRF/(1+RF)]/ [DR/(1+R)]

17. 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

18. Basis Risk • In order to adjust for basis risk, we require the hedge ratio, h = DSt/Dft • Nf = (Long asset position × h)/(size of one contract).

19. Estimating the Hedge Ratio • The hedge ratio may be estimated using ordinary least squares regression: • DSt = a + bDft + ut • The hedge ratio, h will be equal to the coefficient b. The R2from the regression reveals the effectiveness of the hedge.

20. 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.

21. 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.

22. Credit Forwards • SF defines credit spread at time contract written • ST = actual credit spread at maturity of forward Credit Spread Credit Spread Credit Spread at End Seller Buyer ST> SF Receives Pays (ST - SF)MD(A) (ST - SF)MD(A) SF>ST Pays Receives (SF - ST)MD(A) (SF - ST)MD(A)

23. 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

24. 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.

25. 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

26. 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.

27. 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 strikeprice. • 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.

28. 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.

29. 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.

30. 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 bond price falls below exercise price.

31. Call Options on Bonds Buy a call Write a call X X

32. 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 strikeprice. • 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.

33. 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.

34. 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.

35. 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

36. Put Options on Bonds Buy a Put Write a Put X X

37. 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.

38. Hedging • Payoffs to Bond + Put Bond X Put Net X

39. 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

40. Tips for plotting payoffs

41. Futures versus Options Hedging • Hedging with futures eliminates both upside and downside • Hedging with options eliminates risk in one direction only

42. Gain Bond Portfolio 0 Bond Price X Purchased Futures Contract Loss Hedging with Futures

43. 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.

44. Hedging With Bond Options Using Binomial Model • Example: FI purchases zero-coupon bond with 2 years to maturity, at P0 = $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 r1=13.82%, P1= 100/1.1382 = $87.86 • If r1=12.18%, P1= 100/1.1218 = $89.14

45. Example (continued) • If the 1-year rates of 13.82% and 12.18% are equally likely, expected 1-year rate = 13% and E(P1) = 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.

46. 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.

47. Actual Bond Options • Most pure bond options trade over-the-counter. • 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.

48. Hedging with Put Options • To hedge net worth exposure,  P = - E Np = [(DA-kDL)A]  [  D  B] • Adjustment for basis risk: Np = [(DA-kDL)A]  [  D  B br]

49. 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 £100,000,000/£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).

50. 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.