Chapter 27
Risk Management and
Financial Engineering
Professor XXX
Course Name/Number
© 2007 Thomson South-Western
Overview of Risk Management
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 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 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
Probability Distribution of Possible Cash
Flows for a Corporation
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
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 wellfunctioning markets.
Assumptions:
Risk free borrowing and lending
No transaction costs
Ability to use the proceeds from short sales
Forward Prices (Continued)
The forward price, F, for an asset that pays no
income and does not cost anything to store
should be:
F  S0 (1  rf )
t
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
Forward Prices (continued)
For an asset that pays income (e.g., a coupon
bond) or is costly to store (e.g.,
commodities):
F  (S 0  I  E)(1  r f )
t
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
Currency Forward Rates
 Currency forward contracts involve exchanging one currency for
another at a fixed date in the future.
QBP (1  rBP )
FBP 
or
t
Q$ (1  r$ )
t
(1  rBP )
FBP  S 0
t
(1  r$ )
t
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
Payoff Diagram for a 1-Month
Forward Contract on the British Pound
Buyer
Seller
11
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 FRA
FRAs are standardized such that the cash flows
are determined as
notional principal  (rS  rF )  ( D / 360)
1  (rS  ( D / 360))
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
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 purchaser will
buy a given amount of a commodity or financial
instrument from seller at a fixed date sometime in the
future.
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-tomarket daily.
Futures contracts feature daily cash
settlement of all contracts.
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 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
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.
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.
Using Options to Hedge
Advantages: one-sided payoffs, short term
(exchange-traded options), liquid (exchangetraded options)
Disadvantages: premium (cost of option
contracts)
Swaps
 Swap contract: two parties agree to exchange
payment obligations on two underlying financial
liabilities equal in principal amount but different in
payment patterns
 Swaps are used to change characteristics of cash
flows:
 Interest Rate Swaps
 Currency Swaps
 Fixed-for-floating interest rate swap: one party makes
fixed-rate payments to another party in exchange for
floating-rate payments
 Size of the payments based on hypothetical principal amount
called “notional principal”
Typical Structure of a Fixed-for-Floating
Swap
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.
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.
Semiannual Net Cash Flow for the Fixed-Rate
Payer in a Fixed-for-Floating Swap with a Notional
Principal of$10 Million
Semiannual Net Cash Flow for the Floating-Rate
Payer in a Fixed-for-Floating Swap with a Notional
Principal of$10 Million
Currency Swaps
Using Swaps to Hedge
Advantages: long term, periodic cash
flows, flexible contract terms
Disadvantages: moderate credit risk
Financial Engineering
 For many firms, risk exposure is unique: based on an
asset whose value is not easily hedged.
 Financial engineering: can be defined as the process
of using the principles of financial economics to
design and price financial instruments.
 Firms can create a financial instrument that
 meets the needs of the corporation trying to hedge risk
exposure or
 offers the institutional investor an investment opportunity
with a unique payoff structure.
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.