Chapter 21
Risk Management and Financial
Engineering
Professor XXX
Course Name & Number
Date
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
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
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 well-functioning
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  S 0 (1  r f ) 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 ) t
FBP 
or
t
Q$ (1  r$ )
(1  rBP ) t
FBP  S 0
(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
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 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. 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)
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.
Advantages: one-sided payoffs, short term (exchange-traded
options), liquid (exchange-traded options)
Disadvantages: premium (cost of option contracts)
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.
Structure of a Typical Interest Rate Swap
8%
Fixed-Rate Payer
(Company A)
6-month
LIBOR
7.85%
Intermediary
6-month
LIBOR
Floating-Rate Payer
(Company X)
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.
Using Swaps to Hedge
Advantages: long term, periodic cash flows, flexible contract
terms
Disadvantages: moderate credit risk
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.
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 underdeveloped countries will be developed.