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Risk Management and Financial Engineering

Risk Management and Financial Engineering

Chapter 21Chapter 21

Risk Management IntroductionRisk 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

Overview of Risk ManagementOverview 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

Motivations for HedgingMotivations 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

Forward ContractsForward 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

Forward PricesForward 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

Forward Prices (Continued)Forward Prices (Continued)

The forward price, F, for an asset that pays no income and does not cost anything to store should be:

Where S0 = the spot price of the asset at time 0

rf = the risk-free rate of interest at time 0

t = number of years until settlement date of contract

tfrSF )1(0

Forward Prices (continued)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 assetE = the present value of the cost to store the asset for

the life of the forward contract

tfrEISF )1)(( 0

Currency Forward RatesCurrency Forward Rates

• Currency forward contracts involve exchanging one currency for another at a fixed date in the future.

Where:

FBP = the forward price for British pounds, expressed as the number of pounds per dollar, for delivery in t years

S0 = the spot price for British pounds, expressed as the number of pounds per dollar, QBP/Q$, at time 0

r$ = the risk-free rate of interest at time 0 for borrowing/lending in U.S. Dollars

rBP = 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

t

t

BP0BPt

t

BPBPBP r1

r1SFor

r1Q

r1QF

)(

)(

)(

)(

$$$

Interest Rate Forward Contracts(Forward Rate Agreements)

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.

Cash Flows in a FRACash Flows in a FRA

FRAs are standardized such that the cash flows are determined as

where

rS = the reference rate on the contract settlement date (e.g., the

3-month Treasury bill rate)

rF = the forward rate established at contract origination.

D = the number of days in the contract period

))360/((1

)360/()(

Dr

Drrprincipalnotional

S

FS

Hedging With FRAs, Forwards & Futures 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.

Futures vs. ForwardsFutures 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.

Futures vs. Forwards (Continued)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.

Closing out a Futures PositionClosing 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 priceOR

futures price when closed out - original futures priceShort Position:

original futures price - spot price at maturityOR

original futures price - futures price when closed out

Hedging with Futures ContractsHedging 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.

Using Options to HedgeUsing 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)

SwapsSwaps

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 SwapsCurrency 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.

Structure of a Typical Interest Rate SwapStructure of a Typical Interest Rate Swap

Fixed-Rate Payer(Company A)

Floating-Rate Payer(Company X)Intermediary

6-monthLIBOR

8% 7.85%

6-monthLIBOR

Interest Rate SwapsInterest 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.

Currency SwapsCurrency 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

Financial EngineeringFinancial 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.

Trends in Risk Management and Financial Engineering

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.