1. Professor XXX Course Name & Number Date Risk Management and Financial Engineering Chapter 21

2. Risk Management Introduction Risk management –Identifies sources of risk –Chooses which risks to hedge –Chooses how to hedge Importance of risk management function grew in response to volatile financial markets starting in 1970s Increased use of derivative securities to manage risk exposures

3. Overview of Risk Management Risk Factors –Interest Rates –Exchange rates –Commodity prices Transaction exposure – change in risk factor(s) that negatively affect the value of specific transactions Economic exposure – change in risk factor(s) that has a broad impact on cash flows of firms

4. Motivations for Hedging Motivations for hedging –Buying insurance vs. hedging –Reducing expected costs of financial distress –Saving taxes –Reducing risk for owners of closely held firms –Improving the ability to evaluate manager’s performance Tools of the trade –Forward and futures contracts –Options –Swaps

5. Forward Contracts Agreements to buy/sell underlying asset at a fixed price on a future date –Buyer (long position) pays forward price and accepts delivery of underlying asset. –Seller (short position) receives forward price and delivers underlying asset

6. Forward Prices A forward price must satisfy a “no arbitrage” condition. –Forward prices create an alternative to the forward contract that has identical cash flows. –Arbitrage opportunities quickly disappear in well-functioning markets. Assumptions: –Risk free borrowing and lending –No transaction costs –Ability to use the proceeds from short sales

7. Forward Prices (Continued) The forward price, F, for an asset that pays no income and does not cost anything to store should be: Where S 0 = the spot price of the asset at time 0 r f = the risk-free rate of interest at time 0 t = number of years until settlement date of contract

8. Forward Prices (continued) For an asset that pays income (e.g., a coupon bond) or is costly to store (e.g., commodities): Where I = the present value of income to be paid by the asset E = the present value of the cost to store the asset for the life of the forward contract

9. Currency Forward Rates Currency forward contracts involve exchanging one currency for another at a fixed date in the future. Where: F BP = the forward price for British pounds, expressed as the number of pounds per dollar, for delivery in t years S 0 = the spot price for British pounds, expressed as the number of pounds per dollar, Q BP /Q $, at time 0 r $ = the risk-free rate of interest at time 0 for borrowing/lending in U.S. Dollars r BP = the risk-free rate of interest at time 0 for borrowing/lending in British pounds t = number of years until the settlement date of the contract

10. Interest Rate Forward Contracts (Forward Rate Agreements) An FRA is an agreement between two parties to exchange cash flows based on a reference interest rate and principal amount in the future. The size of the payment depends on –The notional principal –The difference between the market rate of interest and the forward rate.

11. Cash Flows in a FRA FRAs are standardized such that the cash flows are determined as where r S = the reference rate on the contract settlement date (e.g., the 3-month Treasury bill rate) r F = the forward rate established at contract origination. D= the number of days in the contract period

12. Hedging With FRAs, Forwards & Futures FRAs can be used to hedge against an increase or a decrease in interest rates. Hedging with forward contracts offer advantages & disadvantages. –Advantages: flexible contract terms (customizability). –Disadvantage: credit risk, illiquidity, transaction costs. Like a forward contract, a futures contract involves two parties agreeing today on a price at which the purchaser will buy a given amount of a commodity or financial instrument from the seller at a fixed date sometime in the future.

13. Futures vs. Forwards Futures are exchange traded; forwards are traded over the counter. Forwards are customized; futures are standardized Forwards are not liquid; futures are very liquid. Forwards involve credit risk, futures have virtually no credit risk. There are no interim cash flows in a forward contract; futures contracts are marked-to-market daily. Futures contracts feature daily cash settlement of all contracts.

14. Futures vs. Forwards (Continued) Gains (losses) in a futures position are deposited in (withdrawn from) the investor’s margin account. –Initial margin varies by contract. –Maintenance margin issues arise when losses decrease margin below level needed to maintain an open position. –Margin calls take place when margin account falls below level needed to maintain an open position. Delivery rarely takes place in a futures contract; delivery usually takes place in a forward contract. Futures contracts usually have smaller denominations than forward contracts.

15. Closing out a Futures Position Futures traders usually “unwind” positions rather than taking delivery (or delivering) the underlying asset. The ability to close out a position by taking an offsetting position is referred to as fungibility. Computing profit or loss Long position: spot price at maturity - original futures price OR futures price when closed out - original futures price Short Position: original futures price - spot price at maturity OR original futures price - futures price when closed out

16. Hedging with Futures Contracts Concerns about hedging with futures: –Basis risk –Cross Hedging –Tailing the Hedge –Delivery Options Hedging with currency futures is similar to hedging with currency forwards. The differences are related to the differences in forwards are futures. Hedging with interest rate futures differs from FRAs because the underlying asset in most interest rate futures is a bond rather than a reference interest rate.

17. Using Options to Hedge Options protect against underlying change in risk factor while leaving open the possibility to gain from favorable moves. Call options on interest rates are called interest rate caps. A put option is called an interest rate floor. Buying an interest rate cap and simultaneously selling an interest rate floor is called an interest rate collar. Advantages: one-sided payoffs, short term (exchange-traded options), liquid (exchange-traded options) Disadvantages: premium (cost of option contracts)

18. Swaps In a swap contract, two parties agree to exchange payment obligations on two underlying financial liabilities that are equal in principal amount but differ in payment patterns. Swaps are used to change the characteristics of cash flows. We concentrate on two types: Interest Rate Swaps Currency Swaps In fixed-for-floating interest rate swap, one party will make fixed-rate payments to another party in exchange for floating-rate payments. The size of the payments are based on a hypothetical principal amount called the notional principal.

19. Structure of a Typical Interest Rate Swap Fixed-Rate Payer (Company A) Floating-Rate Payer (Company X) Intermediary 6-month LIBOR 8%7.85% 6-month LIBOR

20. Interest Rate Swaps Typically, interest rate swaps arise because one party would have liked to issue fixed-rate debt, but chose instead to issue floating-rate debt, either because the fixed rate market was closed to this issuer or it was more costly By entering a swap agreement, the floating rate issuer can effectively obtain a fixed rate payment obligation. By paying a fixed rate and receiving a floating rate, the cash inflows for this firm in the form of floating rate payments can be used to make the floating-rate payments on the debt that is outstanding. The fixed-rate payments being made on the swap are all that remain.

21. Currency Swaps In a currency swap, two parties exchange payment obligations denominated in different currencies. Another variant of the currency swap is the fixed-for-floating currency swap. Combination of a currency swap and an interest rate swap The first party pays a fixed rate of interest denominated in one currency to the second party in exchange for a floating rate of interest denominated in another currency. Using Swaps to Hedge Advantages: long term, periodic cash flows, flexible contract terms Disadvantages: moderate credit risk

22. Financial Engineering For many firms, their risk exposure is unique in the sense that the risk exposure is based on an asset whose value is not easily hedged. Financial engineering, at least for our purposes here, can be defined as the process of using the principles of financial economics to design and price financial instruments. By combining elements of forwards, futures, options, and swaps, firms can create a financial instrument that meets the needs of the corporation that is trying to hedge its risk exposure or one that offers the institutional investor an investment opportunity with a unique payoff structure.

23. Trends in Risk Management and Financial Engineering Longer-maturity risk management products will continue to be developed. Even more complex securities will be developed to hedge multiple interest rate, currency, and input/output pricing risks particularly in the international arena. New techniques for hedging, pricing, and underwriting risks in the issuance of new securities will continue to be developed as the securitization trend accelerates around the world. New methods of hedging the strategic and currency risks of investing in small, politically unstable, or financially under- developed countries will be developed.