risk in real world for the best organization.ppt

Copyright © 2011 Pearson Prentice Hall. All rights reserved.
Chapter 30
Risk
Management

30-2
Chapter Outline
30.1 Insurance
30.2 Commodity Price Risk
30.3 Exchange Rate Risk
30.4 Interest Rate Risk

30-3
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.

30-4
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.

30-5
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.

30-6
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

30-7
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

30-8
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

30-9
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.

30-10
The Role of Insurance:
An Example (cont'd)
• The risk from fire can be summarized with
a probability distribution:

30-11
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.

30-12
An Example (cont'd)
• Insurance Premium
– The fee a firm pays to an insurance company for
the purchase of an insurance policy

30-13
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

30-14
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
• rL depends on the risk being insured.
Pr(Loss) [Payment in the Event of Loss]
Insurance Premium
1 L
E
r
×
=
+

30-15
Insurance Pricing
• 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 very-
low-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.

30-16
Insurance Pricing
• 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.

30-17
Insurance Pricing
• By its very nature, insurance for non-
diversifiable 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.

30-18
Textbook Example 30.1

30-19
Textbook Example 30.1 (cont'd)

30-20
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?

30-21
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 risk-
free 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.

30-22
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.

30-23
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.

30-24
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.

30-25
• 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.

30-26

30-27

30-28
• 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?

30-29
• 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?

30-30
• 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

30-31
• 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:
($100 million + $40 million)
$1 132 075 1.2% $566,038
1.06
− , , + × =

30-32
• 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.

30-33
• 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.

30-34
• 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.

30-35
• 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.

30-36
The Costs of Insurance
• Market imperfections can raise the cost of
insurance above the actuarially fair price.

30-37
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.

30-38
• 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.

30-39
• 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

30-40
• 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

30-41

30-42
(cont'd)

30-43
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.

30-44
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.

30-45
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.

30-46
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.

30-47
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.

30-48
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.

30-49
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.

30-50
Figure 30.1 Commodity Hedging
Smoothes Earnings

30-51

30-52

30-53
• 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.

30-54
• 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?

30-55
• Solution
– At $3.50 per bushel:
• EBIT = $50,000,000 − [($3.50 − $3.00) × 20,000,000]
= $40,000,000
• EBIT = $50,000,000 − [($2.25 − $3.00) × 20,000,000]
= $65,000,000
• EBIT = $50,000,000 − [($3.25 − $3.00) × 20,000,000]
= $45,000,000

30-56
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.

30-57
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.

30-58
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.

30-59
Figure 30.2 Futures Prices for Light,
Sweet Crude Oil, July 2009

30-60
• 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.

30-61
(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

30-62
(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

30-63
(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.

30-64
(cont'd)
– 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.

30-65
(cont'd)
– 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.

30-66
Table 30.1 Example of Marking to Market
and Daily Settlement for the July 2012 Light,
Sweet Crude Oil Futures Contract ($/bbl)

30-67
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.

30-68
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.

30-69
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.

30-70
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.

30-71
Figure 30.3 Dollars per Euro ($/€),
1999-2009

30-72

30-73

30-74
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.

30-75
(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

30-76
• Forward Exchange Rate
– The exchange rate set in a currency forward
contract: it applies to an exchange that will
occur in the future.

30-77

30-78

30-79
Figure 30.4 The Use of Currency
Forwards to Eliminate Exchange Rate
Risk

30-80
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.

30-81
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.

30-82
– 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

30-83
Figure 30.5 Currency Timeline Showing
Forward Contract and Cash-and-Carry
Strategy

30-84
• 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€.

30-85
• 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 $/€
– Invest the dollars today for one year at the
interest rate r$

30-86
• 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 cash-
and-carry strategy accomplish the same
conversion, by the Law of One Price they must
do so at the same rate.

30-87
• Combining the rates used in the cash-and-
carry strategy leads to the following no-
arbitrage formula for the forward exchange
rate:
– Covered Interest Parity
{ {
$
€
$ in one year $ today $ in one year / $ today
€ in one year € today € in one year / € today
1
1
r
F S
r
= ×
+
= ×
+
14 2 43

30-88
• 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 )
(1 )
T
T T
r
F S
r
+
= ×
+

30-89
• 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

30-90

30-91

30-92
• 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.

30-93

30-94

30-95
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.

30-96
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.

30-97
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/€

30-98
• 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.

30-99
• 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.

30-100
• The following slide compares hedging with
options to the alternative of hedging with a
forward contract or not hedging at all.

30-101
Figure 30.6 Comparison of Hedging the
Exchange Rate Using a Forward Contract,
an Option, or No Hedge

30-102
• 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.

30-103
• 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

30-104

30-105

30-106

30-107
• 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:

30-108
• Price of a Call Option on a Currency
– Where
– FT is the forward exchange rate from Eq. 30.3
and
1 2
€ $
( ) ( )
(1 ) (1 )
T T
S K
C N d N d
r r
= −
+ +
1 2 1
ln( / )
and
2
T
F K T
d d d T
T
σ
σ
σ
= + = −
( )
x
T
F S
K PV K
=

30-109

30-110

30-111
30.4 Interest Rate Risk
• Interest Rate Risk Measurement: Duration
– A security’s duration is computed as:
• 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.
( )
Duration t
t
PV C
t
P
= ×
∑

30-112

30-113

30-114
Table 30.3 Computing the Duration of
a Coupon Bond

30-115
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 + , where  is a small change,
then the present value of the cash flows
changes by approximately:
• Where k is the number of compounding periods per
year of the APR
Percent Change in Value Duration
1 /
r k
ε
≈ − ×
+

30-116

30-117

30-118
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.

30-119
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.

30-120
Duration-Based Hedging (cont'd)
– 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.

30-121
– The following slide shows the market-value
balance sheet for Acorn Savings and Loan:

30-122
Table 30.4 Market-Value Balance
Sheet for Acorn Savings and Loan

30-123
– 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:
A B A B
A B
D D D
A B A B
+ = +
+ +

30-124
– The duration of Acorn’s assets is:
– The duration of Acorn’s liabilities is:
10 120 170
0 2 8 5.33 years
300 300 300
A
D = × + × + × =
120 90 75
0 1 12 3.47 years
285 285 285
L
D = × + × + × =

30-125
– The duration of Acorn’s equity is calculated as:
300 285
5.33 3.47 40.67 years
15 15
E A L A L
A L
D D D D
A L A L
−
= = −
− −
= × − × ×

30-126
– 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%

30-127
– 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.

30-128
– 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
×
=

30-129
– 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

30-130
– If it Acorn does so, the duration of its assets
will
decline to:
– Thus the equity duration will fall to:
Decreased mortgage holdings
Increased cash balance
10 76.3 120 170 76.3
0 2 8 3.30 years
300 300 300
+ −
× + × + × =
6 4 7 48 6 4 7 4 8
300 285
3.30 3.47 0
15 15
× − × =

30-131
Table 30.5 Market-Value Balance Sheet for
Acorn Savings and Loan After Immunization

30-132
• 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.

30-133
• 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.

30-134
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.

30-135
Swap-Based Hedging (cont'd)
– 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.”

30-136
– 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

30-137
– 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.

30-138
– 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.

30-139
Table 30.6 Cash Flows ($ millions) for a
$100 million Fixed-for-Floating Interest Rate
Swap

30-140
– 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.

30-141
• 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.

30-142
– Consider Alloy Cutting Corporation (ACC).
• It needs to borrow $10 million to fund this expansion.
Currently, the six-month LIBOR is 4% and the ten-
year 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.

30-143
– 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.

30-144
– 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 + t where rt is
the new LIBOR and t 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, t should decline from its current 1%
level.

30-145
– 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.

30-146
– Combining the cash flows from the swap with
ACC’s short-term borrowing, ACC’s net
borrowing cost is computed as follows:
Floating Rate Net
Short-Term Fixed Rate
Received Borrowing
Loan Rate Due on Swap
from Swap Cost
6% 6%
t t t t
r r
δ δ
+ − =
+ + − = +
% %

30-147
– 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.

30-148
Table 30.7 Trade-Offs of Long-Term
Versus Short-Term Borrowing for ACC

30-149

30-150

30-151
• 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.

30-152

30-153

30-154
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?

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