Chapter 30
Risk
Management
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
Chapter Outline
30.1 Insurance
30.2 Commodity Price Risk
30.3 Exchange Rate Risk
30.4 Interest Rate Risk
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-2
Learning Objectives
1. Explain what is meant by the statement that, in
a perfect market, insurance is actuarially fair.
2. Compute the value of an actuarially fair
insurance premium.
3. Explain why insurance for large risks that are
difficult to diversify has a negative beta;
evaluate the impact of that beta on price.
4. Discuss five market imperfections that are
sources of value for insurance.
5. List and define three costs of insurance.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-3
Learning Objectives (cont'd)
6.
Describe three risk management strategies firms use to
hedge their exposure to commodity price movements.
7.
Discuss the use of currency forwards and options contracts
to hedge exchange rate risk.
8.
Discuss the use of the cash-and-carry strategy in currency
hedging.
9.
Describe situations in which a firm would prefer currency
options to futures for hedging.
10. Use the Black-Scholes formula to compute the value of a
currency option.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-4
Learning Objectives (cont'd)
11. Define interest rate risk and discuss tools to
manage that risk.
12. Define and compute duration of a single asset
and of a portfolio.
13. Use duration to measure the change in value
attributable to a change in yields.
14. Explain the use of equity duration to manage
interest rate risk.
15. Describe the use of swaps in managing interest
rate risk; explain how the use of swaps
separates the risk of interest changes from the
risk of changes in the firm’s credit quality.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-5
30.1 Insurance
• Insurance is the most common method
firms use to reduce risk.
• Property Insurance
– A type of insurance companies purchase to
compensate them for losses to their assets due
to fire, storm damage, vandalism, earthquakes,
and other natural and environmental risks
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-6
30.1 Insurance (cont'd)
• Business Liability Insurance
– A type of insurance that covers the costs that
result if some aspect of a business causes
harm to a third party or someone else’s
property
• Business Interruption Insurance
– A type of insurance that protects a firm against
the loss of earnings if the business is
interrupted due to fire, accident, or some other
insured peril
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-7
30.1 Insurance (cont'd)
• Key Personnel Insurance
– A type of insurance that compensates a firm for
the loss or unavoidable absence of crucial
employees in the firm
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-8
The Role of Insurance: An Example
• Consider an oil refinery with a 0.02%
chance of being destroyed by a fire in the
next year.
– If it is destroyed, the firm estimates that it will
lose $150 million in rebuilding costs and lost
business.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-9
The Role of Insurance:
An Example (cont'd)
• The risk from fire can be summarized with
a probability distribution:
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-10
The Role of Insurance:
An Example (cont'd)
• Given this probability distribution, the firm’s
expected loss from fire each year is $30,000.
– 99.98% × ($0) + 0.02% × ($150 million) = $30,000
– While the expected loss is relatively small, the firm
faces a large downside risk if a fire does occur.
• The firm can manage the risk purchasing insurance to
compensate its loss of $150 million.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-11
The Role of Insurance:
An Example (cont'd)
• Insurance Premium
– The fee a firm pays to an insurance company for the
purchase of an insurance policy
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-12
Insurance Pricing in a Perfect
Market
• Actuarially Fair
– When the NPV from selling insurance is zero
because the price of insurance equals the
present value of the expected payment
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-13
Insurance Pricing
in a Perfect Market (cont'd)
• If rL is the appropriate cost of capital given
the risk of the loss, the actuarially fair
premium
is calculated as follows:
– Actuarially Fair Insurance Premium
Insurance Premium 
Pr(Loss)  E[Payment in the Event of Loss]
1  rL
• rL depends on the risk being insured.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-14
Insurance Pricing
in a Perfect Market (cont'd)
• Consider again the oil refinery. The risk of
fire is specific to this firm and, therefore,
diversifiable.
– By pooling together the risks from many
policies, insurance companies can create verylow-risk portfolios whose annual claims are
relatively predictable. In other words, the risk
of fire has a beta of zero, so it will not
command a risk premium. In this case, rL
equals the risk-free interest rate.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-15
Insurance Pricing
in a Perfect Market (cont'd)
• Not all insurable risks have a beta of zero.
– Some risks, such as hurricanes and
earthquakes may be difficult to diversify
completely.
– For risks that cannot be fully diversified, the
cost of capital rL will include a risk premium.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-16
Insurance Pricing
in a Perfect Market (cont'd)
• By its very nature, insurance for nondiversifiable hazards is generally a
negative beta asset (it pays off in bad
times).
– Thus, the risk-adjusted rate rL for losses is less
than the risk-free rate rf, leading to a higher
insurance premium in the actuarially fair
insurance premium equation.
• While firms that purchase insurance earn a return rL<
rf on their investment, because of the negative beta
of the insurance payoff, it is still a zero-NPV
transaction.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-17
Textbook Example 30.1
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-18
Textbook Example 30.1 (cont'd)
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-19
Alternative Example 30.1
• Problem
– As the owner of a concession booth in a major
airport, you decide to purchase insurance that
will pay $2 million in the event the airport
terminal is destroyed by terrorists. Suppose the
likelihood of such a loss is 0.05%, the risk-free
interest rate is 3%, and the expected return of
the market is 8%. If the risk has a beta of
zero, what is the actuarially fair insurance
premium? What is the premium if the beta of
terrorism insurance is −3?
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-20
Alternative Example 30.1 (cont’d)
• Solution
– The expected loss is 0.05% × $2 million =
$1,000. If the risk has a beta of zero, we
compute the insurance premium using the riskfree interest rate: ($1,000)/1.03 = $970.87. If
the beta of the risk is not zero, we can use the
CAPM to estimate the appropriate cost of
capital.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-21
Alternative Example 30.1 (cont’d)
• Solution (cont’d)
– Given a beta for the loss, βL, of −3, and an
expected market return, rmkt, of 8%:
– rL = rf + βL (rmkt − rf ) = 3% − 3 (8% − 3%) =
−12%
– In this case, the actuarially fair premium is
($1,000)/(1 − 0.12) = $1,136.36. Although
this premium exceeds the expected loss, it is a
fair price given the negative beta of the risk.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-22
The Value of Insurance
• In a perfect capital market, there is no
benefit to the firm from any financial
transaction, including insurance.
– Insurance is a zero-NPV transaction that has no
effect on value.
– The value of insurance comes from reducing
the cost of market imperfections.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-23
The Value of Insurance (cont'd)
• Consider the potential benefits of
insurance with respect to the following
market imperfections:
• Bankruptcy and Financial Distress Costs
– By insuring risks that could lead to distress, the
firm can reduce the likelihood that it will incur
these costs.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-24
The Value of Insurance (cont'd)
• Issuance Costs
– When a firm experiences losses, it may need to
raise cash from outside investors by issuing
securities.
– Insurance provides cash to the firm to offset
losses, reducing the firm’s need for external
capital thus reducing issuance costs.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-25
Textbook Example 30.2
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-26
Textbook Example 30.2 (cont'd)
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-27
Alternative Example 30.2
• Problem
– Suppose the risk of a railroad accident for a
major railroad is 1.2% per year, with a beta of
zero.
– If the risk-free rate is 6%, what is the
actuarially fair premium for a policy that
pays $100 million in the event of a loss?
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-28
Alternative Example 30.2
• Problem (continued)
– What is the NPV of purchasing insurance
for an airline that would experience $25
million in financial distress costs and $15
million in issuance costs in the event of a
loss if it were uninsured?
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-29
Alternative Example 30.2
• Solution
– The expected loss is:
• 1.2% × $100 million = $1,200,000
– The actuarially fair premium is:
• $1,200,000 ÷ 1.06 = $1,132,075
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-30
Alternative Example 30.2
• Solution (continued)
– The total benefit of the insurance to the
railroad is $100 million plus an additional $40
million in distress and issuance costs that it can
avoid if it has insurance.
– The NPV from purchasing the insurance is:
$1132 075 1.2% 
($100 million + $40 million)
 $566, 038
1.06
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-31
The Value of Insurance (cont'd)
• Tax Rate Fluctuations
– When a firm is subject to graduated income tax
rates, insurance can produce a tax savings if
the firm is in a higher tax bracket when it pays
the premium than the tax bracket it is in when
it receives the insurance payment in the event
of a loss.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-32
The Value of Insurance (cont'd)
• Debt Capacity
– Because insurance reduces the risk of financial
distress, it can relax the tradeoff between
leverage & financial distress costs and allow the
firm to increase its use of debt financing.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-33
The Value of Insurance (cont'd)
• Managerial Incentives
– By eliminating the volatility that results from
perils outside management’s control, insurance
turns the firm’s earnings and share price into
informative indicators of management’s
performance.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-34
The Value of Insurance (cont'd)
• Risk Assessment
– Insurance companies specialize in assessing
risk and will often be better informed about the
extent of certain risks faced by the firm than
the firm’s own managers.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-35
The Costs of Insurance
• Market imperfections can raise the cost of
insurance above the actuarially fair price.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-36
The Costs of Insurance (cont'd)
• Insurance Market Imperfections
– Three main frictions may arise between the firm and
its insurer.
• Transferring the risk to an insurance company entails
administrative and overhead costs.
• Adverse selection: A firm’s desire to buy insurance may signal
that it has above-average risk.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-37
The Costs of Insurance (cont'd)
• Insurance Market Imperfections
– Three main frictions may arise between the firm and
its insurer.
• Agency costs
– Moral Hazard: When purchasing insurance reduces a firm’s
incentive to avoid risk.
» For example, after purchasing fire insurance, a firm
may decide to cut costs by reducing expenditures on
fire prevention.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-38
The Costs of Insurance (cont'd)
• Addressing Market Imperfections
– Insurance companies try to mitigate adverse selection
and moral hazard costs in a number of ways.
– For example, they may
• Screen applicants to assess their risk as accurately
as possible
• Investigate losses to look for evidence of fraud or
deliberate intent
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-39
The Costs of Insurance (cont'd)
• Addressing Market Imperfections
– Deductible
• A provision of an insurance policy in which an initial
amount of loss is not covered by the policy and must be paid
by the insured
– Policy Limits
• The provisions of an insurance policy that limit the amount of
loss that the policy covers regardless of the extent of
the damage
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-40
Textbook Example 30.3
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-41
Textbook Example 30.3
(cont'd)
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-42
The Insurance Decision
• For insurance to be attractive, the benefit
to the firm must exceed the additional
premium charged by the insurer.
– Insurance is most likely to be attractive to
firms that are currently financially healthy, do
not need external capital, and are paying high
current tax rates.
• They will benefit most from insuring risks that can
lead to cash shortfalls or financial distress, and that
insurers can accurately assess and monitor to prevent
moral hazard.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-43
30.2 Commodity Price Risk
• Many risks that firms face arise naturally
as part of their business operations.
– For example, the risk from increases in the
price of oil is one of the most important risks
that faces an airline.
• Firms can reduce, or hedge, their exposure to
commodity price movements.
– Like insurance, hedging involves contracts or
transactions that provide the firm with cash flows that
offset its losses from price changes.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-44
Hedging with Vertical Integration
and Storage
• Vertical Integration
– Refers to the merger of a firm and its supplier
or a firm and its customer.
• Because an increase in the price of the commodity
raises the firm’s costs and the supplier’s revenues,
these firms can offset their risks by merging.
• Vertical integration can add value if combining the
firms results in important synergies.
• Vertical integration is not a perfect hedge.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-45
Hedging with Vertical Integration
and Storage (cont'd)
• Long-term storage of inventory is another
strategy for offsetting commodity price
risk.
– For example, an airline concerned about rising
fuel costs could purchase a large quantity of
fuel today and store the fuel until it is needed.
By doing so, the firm locks in its cost for fuel at
today’s price plus storage costs.
• However, storage costs may be too high for this
strategy to be attractive.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-46
Hedging with Vertical Integration
and Storage (cont'd)
• Long-term storage of inventory also
requires a substantial cash outlay upfront.
– If the firm does not have the required cash, it
would need to raise external capital and would
suffer issuance and adverse selection costs.
• Maintaining large amounts of inventory
would dramatically increase working
capital requirements for the firm.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-47
Hedging with Long-Term Contracts
• Consider Southwest Airlines.
– In early 2000, when oil prices were close to
$20 per barrel, the CFO developed a hedging
strategy to protect the airline from a surge in
oil prices. By the time oil prices soared above
$30 per barrel later that year Southwest had
signed contracts guaranteeing a price for its
fuel equivalent to $23 per barrel.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-48
Hedging with Long-Term
Contracts (cont'd)
• However, had oil prices fallen below $23
per barrel in the fall of 2000, Southwest’s
hedging policy would have obligated it to
pay $23 per barrel for its oil.
– Southwest accomplished it’s objective by
locking in its cost of oil at $23 per barrel,
regardless of what the price of oil did on the
open market.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-49
Figure 30.1 Commodity Hedging
Smoothes Earnings
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-50
Textbook Example 30.4
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-51
Textbook Example 30.4 (cont'd)
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-52
Alternative Example 30.4
• Problem
– Consider a cereal manufacturer that will need
20 million bushels of corn next year.
– The current market price of corn is $3 per
bushel.
– At $3 per bushel, the firm expects earnings
before interest and taxes of $50 million next
year.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-53
Alternative Example 30.4
• Problem (continued)
– What will the firm’s EBIT be if the price of
corn rises to $3.50 per bushel?
– What will EBIT be if the price of corn falls
to $2.25 per bushel?
– What will EBIT be in each scenario if the
firm enters into a supply contract for corn
for a fixed price of $3.25 per bushel?
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-54
Alternative Example 30.4
• Solution
– At $3.50 per bushel:
• EBIT = $50,000,000 − [($3.50 − $3.00) × 20,000,000]
= $40,000,000
– At $2.25 per bushel:
• EBIT = $50,000,000 − [($2.25 − $3.00) × 20,000,000]
= $65,000,000
– At $3.25 per bushel:
• EBIT = $50,000,000 − [($3.25 − $3.00) × 20,000,000]
= $45,000,000
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-55
Hedging with Long-Term
Contracts (cont'd)
• Long-term supply contracts have several
potential disadvantages.
– They expose each party to the risk that the
other party may default and fail to live up to
the terms of the contract.
• Thus, while they insulate the firms from commodity
price risk, they expose them to credit risk.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-56
Hedging with Long-Term
Contracts (cont'd)
– Long-term supply contracts cannot be entered
into anonymously; the buyer and seller know
each other’s identity.
• This lack of anonymity may have strategic
disadvantages.
– The market value of the contract at any point
in time may not be easy to determine, making
it difficult to track gains and losses, and it may
be difficult or even impossible to cancel the
contract if necessary.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-57
Hedging with Futures Contracts
• Futures Contract
– An agreement to trade an asset on some future
date, at a price that is locked in today
• Futures contracts are traded anonymously on an
exchange at a publicly observed market price and
are generally very liquid.
• Both the buyer and the seller can get out of the
contract at any time by selling it to a third party at
the current market price.
• Futures contracts eliminate credit risk.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-58
Figure 30.2 Futures Prices for Light,
Sweet Crude Oil, July 2009
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-59
Hedging with Futures Contracts
• Futures prices are not prices that are paid
today.
– Rather, they are prices agreed to today, to be
paid in the future.
• The futures prices are based on the supply and
demand for each delivery date.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-60
Hedging with Futures Contracts
(cont'd)
• Eliminating Credit Risk
– Futures exchanges use two mechanisms to
prevent buyers or sellers from defaulting.
• Traders are required to post collateral when buying or
selling commodities using futures contracts.
– This collateral serves as a guarantee that traders will
meet their obligations.
– Margin
• Collateral that investors are required to post when
buying or selling futures contracts
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-61
Hedging with Futures Contracts
(cont'd)
• Eliminating Credit Risk
– Marking to Market
• Computing gain and losses each day based on the
change in the market price of a futures contract
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-62
Hedging with Futures Contracts
(cont'd)
• Marking to Market: An Example
– Suppose a buyer who enters into the contract
has committed to pay the futures price of $81
per barrel for oil.
• If the next day the futures price is only $79 per
barrel, the buyer has a loss of $2 per barrel on her
position.
– This loss is settled immediately by deducting $2 from
the buyer’s margin account.
• If the price rises to $80 per barrel on the following
day, the gain of $1 is added to the buyer’s margin
account.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-63
Hedging with Futures Contracts
(cont'd)
• Marking to Market: An Example
– The buyer’s cumulative loss is the sum of these
daily amounts and always equals the difference
between the original contract price of $81 per
barrel and the current contract price.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-64
Hedging with Futures Contracts
(cont'd)
• Marking to Market: An Example
– If the price of oil is ultimately $59 per barrel,
the buyer will have lost $22 per barrel in her
margin account.
• Thus her total cost is $59 + $22 = $81 per barrel, the
price for oil she originally committed to.
– Through this daily marking to market, buyers and
sellers pay for any losses as they occur, rather than
waiting until the final delivery date. In this way, the firm
avoids the risk of default.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-65
Table 30.1 Example of Marking to Market
and Daily Settlement for the July 2012 Light,
Sweet Crude Oil Futures Contract ($/bbl)
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-66
Deciding to Hedge Commodity Price
Risk
• The potential benefits of hedging
commodity price risk include reduced
financial distress and issuance costs, tax
savings, increased debt capacity, and
improved managerial incentives and risk
assessment.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-67
Deciding to Hedge Commodity Price
Risk
• Speculate
– When investors use futures to place a bet on
the direction in which they believe the market
is likely to move
• A firm speculates when it enters into contracts that do
not offset its actual risks.
• Speculating increases the firm’s risk rather than
reducing it.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-68
30.3 Exchange Rate Risk
• Floating Rate
– An exchange rate that changes depending on
supply and demand in the market
• The supply and demand for each currency is driven by
– Firms trading goods
– Investors trading securities
– The actions of central banks in each country
– Most foreign exchange rates are floating rates.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-69
30.3 Exchange Rate Risk (cont'd)
• Fluctuating exchanges rates cause a
problem known as the importer–exporter
dilemma.
– Consider a U.S. firm that imports parts from
Italy.
• If the supplier sets the price of its parts in euros, then
the U.S. firm faces the risk that the dollar may fall,
making euros, and therefore the parts, more
expensive.
• If the supplier sets its prices in dollars, then the
supplier faces the risk that the dollar may fall and it
will receive fewer euros for the parts it sells to the
U.S. firm.
30-70
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
Figure 30.3 Dollars per Euro ($/€),
1999-2009
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-71
Textbook Example 30.5
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-72
Textbook Example 30.5 (cont'd)
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-73
Hedging with Forward Contracts
• By entering into a currency forward
contract, a firm can lock in an exchange
rate in advance and reduce or eliminate its
exposure to fluctuations in a currency’s
value.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-74
Hedging with Forward Contracts
(cont'd)
• A currency forward contract specifies
– An exchange rate
– An amount of currency to exchange
– A delivery date on which the exchange will take
place
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-75
Hedging with Forward Contracts
• Forward Exchange Rate
– The exchange rate set in a currency forward
contract: it applies to an exchange that will
occur in the future.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-76
Textbook Example 30.6
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-77
Textbook Example 30.6 (cont'd)
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-78
Figure 30.4 The Use of Currency
Forwards to Eliminate Exchange Rate
Risk
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-79
Cash-and-Carry and the Pricing of
Currency Forwards
• Cash-and-Carry Strategy
– A strategy used to lock in the future cost of an
asset by buying the asset for cash today and
“carrying” it until a future date
• The cash-and-carry strategy also enables a
firm to eliminate exchange rate risk.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-80
Cash-and-Carry and the Pricing of
Currency Forwards (cont'd)
• The Law of One Price and the Forward
Exchange Rate
– Currency forward contracts allow investors to
exchange a foreign currency in the future for
dollars in the future at the forward exchange
rate.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-81
Cash-and-Carry and the Pricing of
Currency Forwards (cont'd)
– Currency Timeline
• Indicates time horizontally by dates and currencies
vertically
– Note: An example of a currency timeline is on the
following slide.
– Spot Exchange Rate
• The current foreign exchange rate
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-82
Figure 30.5 Currency Timeline Showing
Forward Contract and Cash-and-Carry
Strategy
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-83
Cash-and-Carry and the Pricing of
Currency Forwards (cont'd)
• An investor can convert euros to dollars
today at the spot exchange rate, S $/€.
• By borrowing or lending at the dollar
interest rate r$, an investor can exchange
dollars today for dollars in one year.
• An investor can convert euros today for
euros in one year at the euro interest rate
r€.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-84
Cash-and-Carry and the Pricing of
Currency Forwards (cont'd)
• The cash-and-carry strategy consists of
the following simultaneous trades
– Borrow euros today using a one-year loan with
the interest rate r€
– Exchange the euros for dollars today at the
spot exchange rate S $/€
– Invest the dollars today for one year at the
interest rate r$
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-85
Cash-and-Carry and the Pricing of
Currency Forwards (cont'd)
• In one year’s time, an investor will owe
euros and receive dollars. That is, they
have converted euros in one year to
dollars in one year, just as with the
forward contract.
– Because the forward contract and the cashand-carry strategy accomplish the same
conversion, by the Law of One Price they must
do so at the same rate.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-86
Cash-and-Carry and the Pricing of
Currency Forwards (cont'd)
• Combining the rates used in the cash-andcarry strategy leads to the following noarbitrage formula for the forward exchange
rate:
– Covered Interest Parity
F

$ in one year
€ in one year

S
$ today
€ today
Copyright © 2011 Pearson Prentice Hall. All rights reserved.


1  r$
1  r€
$ in one year / $ today
€ in one year / € today
30-87
Cash-and-Carry and the Pricing of
Currency Forwards (cont'd)
• Letting T equal the number of years, the
no-arbitrage forward rate for an exchange
that will occur T years in the future is
(1  r$ )
FT  S 
T
(1  r€ )
T
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-88
Cash-and-Carry and the Pricing of
Currency Forwards (cont'd)
• Covered Interest Parity Equation
– States that the difference between the forward
and spot exchange rates is related to the
interest rate differential between the currencies
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-89
Textbook Example 30.7
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-90
Textbook Example 30.7 (cont'd)
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-91
Cash-and-Carry and the Pricing of
Currency Forwards (cont'd)
• Advantages of Forward Contracts
– A forward contract is simpler, requiring one
transaction rather than three.
– Many firms are not able to borrow easily in
different currencies and may pay a higher
interest rate if their credit quality is poor.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-92
Textbook Example 30.8
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-93
Textbook Example 30.8 (cont'd)
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-94
Hedging with Options
• Currency options are another method to
manage exchange rate risk.
– Assume that in December 2005, the one-year
forward exchange rate was $1.20 per euro. A
firm that will need euros in one year can buy a
call option on the euro, giving it the right to
buy euros at a maximum price.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-95
Hedging with Options (cont'd)
• Suppose a one-year European call option
on the euro with a strike price of $1.20 per
euro trades for $0.05 per euro.
– The table on the following slide shows the
outcome from hedging with a call option.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-96
Table 30.2 Cost of Euros ($/€) When
Hedging with a Currency Option with a Strike
Price of $1.20/€ and an Initial Premium of
$0.05/€
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-97
Hedging with Options (cont'd)
• If the spot exchange rate is less than the
$1.20 per euro strike price of the option,
then the firm will not exercise the option
and will convert dollars to euros at the
spot exchange rate.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-98
Hedging with Options (cont'd)
• If the spot exchange rate is more than
$1.20 per euro, the firm will exercise the
option and convert dollars to euros at the
rate of $1.20 per euro. Adding in the initial
cost of the option gives the total dollar
cost per euro paid by the firm.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-99
Hedging with Options (cont'd)
• The following slide compares hedging with
options to the alternative of hedging with a
forward contract or not hedging at all.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-100
Figure 30.6 Comparison of Hedging the
Exchange Rate Using a Forward Contract,
an Option, or No Hedge
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-101
Hedging with Options (cont'd)
• If the firm does not hedge at all, its cost
for euros is simply the spot exchange rate.
• If the firm hedges with a forward contract,
it locks in the cost of euros at the forward
exchange rate and the firm’s cost is fixed.
• If the firm hedges with options, it puts a
cap on its potential cost, but will benefit if
the euro depreciates in value.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-102
Hedging with Options (cont'd)
• Options Versus Forward Contracts
– A firm may use options instead of forward
contract:
• So the firm can benefit if the exchange rate moves in
their favor and not be stuck paying an above-market
rate
• If the transaction they are hedging might not take
place
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-103
Textbook Example 30.9
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-104
Textbook Example 30.9 (cont'd)
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-105
Textbook Example 30.9 (cont'd)
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-106
Hedging with Options (cont'd)
• Currency Option Pricing
– If the current spot exchange rate is S dollars
per euro and the dollar and euro interest rates
are r$ and r€, respectively, then the price of a
European call option on the euro that expires in
T years with a strike price of K dollars per euro
is:
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-107
Hedging with Options (cont'd)
• Price of a Call Option on a Currency
S
K
C 
N (d1 ) 
N (d 2 )
T
T
(1  r€ )
(1  r$ )
– Where
ln( FT / K )
 T
d1 

2
 T
and d 2  d1   T
– FT is the forward exchange rate from Eq. 30.3
and F
Sx
T
K

PV ( K )
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-108
Textbook Example 30.10
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-109
Textbook Example 30.10 (cont'd)
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-110
30.4 Interest Rate Risk
• Interest Rate Risk Measurement: Duration
– A security’s duration is computed as:
PV (Ct )
Duration   t
 t
P
• Where Ct is the cash flow on date t, PV(Ct ) is its
present value (evaluated at the bond’s yield), and
P=ΣtPV(Ct ) is the total present value of the cash flows
– Therefore, the duration weights each maturity t by the
percentage contribution of its cash flow to the total
present value, PV(Ct ) ∕ P.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-111
Textbook Example 30.11
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-112
Textbook Example 30.11 (cont'd)
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-113
Table 30.3 Computing the Duration of
a Coupon Bond
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-114
30.4 Interest Rate Risk (cont'd)
• Interest Rate Risk Measurement: Duration
– Duration and Interest Rate Sensitivity: If r, the
APR used to discount a stream of cash flows,
increases to r + e, where e is a small change,
then the present value of the cash flows
changes by approximately:
Percent Change in Value   Duration 
e
1  r /k
• Where k is the number of compounding periods per
year of the APR
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-115
Textbook Example 30.12
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-116
Textbook Example 30.12 (cont'd)
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-117
Duration-Based Hedging
• If the market value of a firm’s assets and
liabilities are affected by changes in
interest rates, the firm’s equity value will
also be affected.
– The firm’s sensitivity to changes in interest
rates can be measured by computing the
duration of its assets and liabilities.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-118
Duration-Based Hedging
• Savings and Loans: An Example
– Consider a typical S&L.
• These institutions hold short-term deposits (checking
and savings accounts, certificates of deposit, etc.).
They also make long-term loans (car loans, home
mortgages, etc.).
– Most S&Ls face a problem because the duration of the
loans they make is generally longer than the duration of
their deposits.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-119
Duration-Based Hedging (cont'd)
• Savings and Loans: An Example
– When the durations of a firm’s assets and
liabilities are significantly different, the firm has
a duration mismatch.
• This mismatch puts the S&L at risk if interest rates
change significantly.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-120
Duration-Based Hedging (cont'd)
• Savings and Loans: An Example
– The following slide shows the market-value
balance sheet for Acorn Savings and Loan:
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-121
Table 30.4 Market-Value Balance Sheet
for Acorn Savings and Loan
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-122
Duration-Based Hedging (cont'd)
• Savings and Loans: An Example
– The duration of a portfolio of investments is the
value-weighted average of the durations of
each investment in the portfolio.
• A portfolio of securities with market values A and B
and durations DA and DB, respectively, has the
following duration:
DA  B
A
B

DA 
DB
A  B
A  B
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-123
Duration-Based Hedging (cont'd)
• Savings and Loans: An Example
– The duration of Acorn’s assets is:
DA
10
120
170

 0 
 2 
 8  5.33 years
300
300
300
– The duration of Acorn’s liabilities is:
DL
120
90
75

 0 
 1 
 12  3.47 years
285
285
285
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-124
Duration-Based Hedging (cont'd)
• Savings and Loans: An Example
– The duration of Acorn’s equity is calculated as:
A
L
DE  DA  L 
DA 
DL
A  L
A  L
300
285

 5.33 
 3.47  40.67 years
15
15
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-125
Duration-Based Hedging (cont'd)
• Savings and Loans: An Example
– Therefore, if interest rates rise by 1%, the
value of Acorn’s equity will fall by about 40%.
• This decline in the value of equity will occur as a
result of the value of Acorn’s assets decreasing by
approximately $16 million, while the value of its
liabilities decrease by only $9.9 million. Acorn’s
market value of equity therefore declines by $6.1
million or 40.67%.
– 5.33% × $300 million = $16 million
– 3.47% × $285 million = $9.9 million
» ($16 million – $9.9million) ∕ $15 million = 40.67%
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-126
Duration-Based Hedging (cont'd)
• Savings and Loans: An Example
– To fully protect its equity from an overall
increase or decrease in the level of interest
rates, Acorn needs an equity duration of zero.
• A portfolio with a zero duration is called a
duration-neutral portfolio or an immunized
portfolio, which means that for small interest rate
fluctuations, the value of equity should remain
unchanged.
• Adjusting a portfolio to make its duration zero is
referred to as immunizing the portfolio.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-127
Duration-Based Hedging (cont'd)
• Savings and Loans: An Example
– To make its equity duration neutral, Acorn must
reduce the duration of its assets or increase
the duration of its liabilities.
• The firm can lower the duration of its assets by selling
some of its mortgages in exchange for cash.
Change in Portfolio Duration  Portfolio Value
Amount to Exchange 
Change in Asset Duration
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-128
Duration-Based Hedging (cont'd)
• Savings and Loans: An Example
– Acorn would like to reduce the duration of its
equity from 40.7 to 0.
• Because the duration of the mortgages will change
from 8 to 0 if the S&L sells the mortgages for cash,
Acorn must sell $76.3 million worth of mortgages.
– (40.7 – 0) × 15 ∕ (8 – 0) = $76.3
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-129
Duration-Based Hedging (cont'd)
• Savings and Loans: An Example
– If it Acorn does so, the duration of its assets
will
decline to:
Decreased mortgage holdings
Increased cash balance
10  76.3
300
 0 
120
 2 
300
170  76.3
300
 8  3.30 years
– Thus the equity duration will fall to:
300
285
 3.30 
 3.47  0
15
15
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-130
Table 30.5 Market-Value Balance Sheet for
Acorn Savings and Loan After Immunization
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-131
Duration-Based Hedging (cont'd)
• A Cautionary Note
– Duration matching has some important
limitations.
• The duration of a portfolio depends on the current
interest rate.
– As interest rates change, the duration of the portfolio
changes.
» Maintaining a duration-neutral portfolio requires
constant adjusting as interest rates change.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-132
Duration-Based Hedging (cont'd)
• A Cautionary Note
– Duration matching has some important
limitations.
• A duration-neutral portfolio is only protected against
parallel shifts in the yield curve.
– If short-term interest rates were to rise while long-term
rates remained stable, then short-term securities would
fall in value relative to long-term securities, despite
their shorter duration.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-133
Swap-Based Hedging
• Interest Rate Swap
– A contract in which two parties agree to
exchange the coupons from two different types
of loans
• Interest rate swaps are an alternative way of
modifying the firm’s interest rate risk exposure.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-134
Swap-Based Hedging (cont'd)
• Interest Rate Swap
– In a standard interest rate swap, one party
agrees to pay coupons based on a fixed
interest rate in exchange for receiving coupons
based on the prevailing market interest rate
during each coupon period.
• An interest rate that adjusts to current market
conditions is called a floating rate. Thus the parties
exchange a fixed-rate coupon for a floating-rate
coupon, which explains why this swap is also called a
“fixed-for-floating interest rate swap.”
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-135
Swap-Based Hedging (cont'd)
• Interest Rate Swap
– Consider a five-year, $100 million interest rate
swap with a 7.8% fixed rate. Standard swaps
have semiannual coupons, so that the fixed
coupon amounts would be $3.9 million every
six months.
• ½ × 7.8% × $100 million = $3.9
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-136
Swap-Based Hedging (cont'd)
• Interest Rate Swap
– The floating-rate coupons are often based on
the six-month LIBOR.
• Each coupon is calculated based on the six-month
interest rate that prevailed in the market six months
prior to the coupon payment date.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-137
Swap-Based Hedging (cont'd)
• Interest Rate Swap
– The following slide shows the cash flows of the
swap under a hypothetical scenario for LIBOR
rates over the life of the swap.
• For example, at the first coupon date in six months,
the fixed coupon is $3.9 million and the floating-rate
coupon is $3.4 million (½ × 6.8% × $10 million =
$3.4 million), for a net payment of $0.5 million from
the fixed- to the floating-rate payer.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-138
Table 30.6 Cash Flows ($ millions) for a
$100 million Fixed-for-Floating Interest Rate
Swap
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-139
Swap-Based Hedging (cont'd)
• Interest Rate Swap
– Each payment of the swap is equal to the
difference between the fixed- and floating rate
coupons.
• Because the $100 million swap amount is used only
to calculate the coupons but is never actually paid, it
is referred to as the notional principal of the swap.
• The fixed rate of the swap contract is set based on
current market conditions so that the swap is a fair
deal (i.e., has an NPV of zero) for both sides.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-140
Swap-Based Hedging (cont'd)
• Combining Swaps with Standard Loans
– The interest rate a firm pays on its loans can
fluctuate for two reasons.
• The risk-free interest rate in the market may change.
• The firm’s credit quality can vary over time.
– By combining swaps with loans, firms can
choose which of these sources of interest rate
risk they will tolerate and which they will
eliminate.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-141
Swap-Based Hedging (cont'd)
• Combining Swaps with Standard Loans
– Consider Alloy Cutting Corporation (ACC).
• It needs to borrow $10 million to fund this expansion.
Currently, the six-month LIBOR is 4% and the tenyear interest rate for AA-rated firms is 6%. Given
ACC’s low current credit rating, the bank will charge
the firm a spread of 1% above these rates.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-142
Swap-Based Hedging (cont'd)
• Combining Swaps with Standard Loans
– ACC’s managers are considering whether they
should borrow on a short-term basis and then
refinance the loan every six months or whether
they should borrow using a long-term, ten-year
loan.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-143
Swap-Based Hedging (cont'd)
• Combining Swaps with Standard Loans
– ACC can use an interest rate swap to combine
the best of both strategies.
• First, ACC can borrow the $10 million it needs for
expansion using a short-term loan that is rolled over
every six months.
– The interest rate on each loan will be rt + dt where rt is
the new LIBOR and dt is the spread ACC must pay
based on its credit rating at the time.
» Given ACC’s belief that its credit quality will improve
over time, dt should decline from its current 1%
level.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-144
Swap-Based Hedging (cont'd)
• Combining Swaps with Standard Loans
– To eliminate the risk of an increase in rt in the
future, ACC can enter into a ten-year interest
rate swap in which it agrees to pay a fixed rate
of 6% per year in exchange for receiving the
floating rate.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-145
Swap-Based Hedging (cont'd)
• Combining Swaps with Standard Loans
– Combining the cash flows from the swap with
ACC’s short-term borrowing, ACC’s net
borrowing cost is computed as follows:
Short-Term
Loan Rate
rt  d t
Fixed Rate


Due on Swap

6%
Copyright © 2011 Pearson Prentice Hall. All rights reserved.

Floating Rate
Received
from Swap
rt
Net
 Borrowing
Cost

6%  d t
30-146
Swap-Based Hedging (cont'd)
• Combining Swaps with Standard Loans
– ACC will have an initial net borrowing cost of
7% but this cost will decline in the future as its
credit rating improves and the spread declines.
• At the same time, this strategy protects ACC from an
increase in interest rates.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-147
Table 30.7 Trade-Offs of Long-Term
Versus Short-Term Borrowing for ACC
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-148
Textbook Example 30.13
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-149
Textbook Example 30.13 (cont'd)
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-150
Swap-Based Hedging (cont'd)
• Using a Swap to Change Duration
– A swap contract will alter the duration of a
portfolio according to the difference in the
duration of the corresponding long-term and
short-term bonds.
• Swaps are a convenient way to alter the duration of a
portfolio without buying or selling assets.
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-151
Textbook Example 30.14
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-152
Textbook Example 30.14 (cont'd)
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-153
Chapter Quiz
1. How can insurance add value to a firm?
2. Identify the costs of insurance that arise due to
market imperfections.
3. Discuss risk management strategies that firms use to
hedge commodity price risk.
4. What are the potential risks associated with hedging
using futures contracts?
5. How can firms hedge exchange rate risk?
6. Why may a firm prefer to hedge exchange rate risk
with options rather than forward contracts?
7. How can firms hedge exchange rate risk?
8. Why may a firm prefer to hedge exchange rate risk
with options rather than forward contracts?
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
30-154