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School of Management
Finance
Chapter 11: Hedging, Insuring
and Diversifying
Objective
•
To explain market mechanisms for
implementing hedges, insurance
and diversification
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The purpose of this chapter is to give more detailed
and concrete understanding of all the three methods of
transferring risk and how they are used in practice.
Hedging
Insuring
Diversifying
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Chapter 11 Contents
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Using Forward and Future Contracts to Hedge Risk
Hedging Foreign-Exchange Risk with Swap Contracts
Hedging Shortfall Risk by Matching Assets to Liabilities
Minimizing the Cost of Hedging
Insuring versus Hedging
Basic Features of Insurance Contracts
Financial Guarantees
Options as Insurance
The Diversification Principle
Diversification and the Cost of Insurance
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Hedging

The action taken to reduce exposure to a loss
but also give up the potential of a gain

Financial markets offer a variety of
mechanisms for hedging against the risks.
– Forward and futures contracts
– Swap contracts
– Matching assets to liabilities
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A Simple Example

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
You are planning a trip
from Boston to Tokyo a
year from now.
You make your flight
reservation now.
You can either lock in a
price of $1,000 by
committing now or wait to
do nothing.



In either case, payment will
not take place until the day
of flight.
In entering the forward
contract you eliminate the
risk of the airfare going
above $1,000.
However, you will have to pay
the $1,000 even if the price
turns out to be $500 on the
day of your flight.
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Forward Contracts
Any time two parties agree to exchange some
item in the future at a prearranged price, they
are entering into a forward contract.
 No money is paid in the present by either
party to the other.

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Terminology
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Forward price
Spot price
Face value
Long position
Short position
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Forward Contract vs. Spot Contract
Price
Delivery price (fixed)
To enter into the
contract
(quantity, price
and future date)
To exchange the
asset (delivery)
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T
Time
A spot contract is an agreement to buy
or sell an asset immediately.
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An Illustration: A Forward Contract

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A farmer has planted her fields
with wheat, and the size of her
crop is reasonably certain.
It is now a month before
harvest.
A large fraction of her wealth is
tied up in her wheat crop.
She want to eliminate the risk
associated with uncertainty
about its future price by selling
it now at a fixed price for
future delivery.

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A baker will need wheat a
month from now to produce
bread.
A large fraction of his wealth
is tied up in his bakery
business.
The way for him to reduce the
price risk is to buy wheat now
for future delivery.
The baker is a natural match
for the farmer to enter into a
forward contract.
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Suppose the size of the the farmer’s wheat crop is
100,000 bushels.
The forward price is $2 per bushel.
At the end of the month, the farmer will deliver
100,000 bushels wheat to the baker and receive
$200,000 from the baker in return.
Both parties eliminate the risk associated with the
uncertainty about the spot price of wheat at the
delivery date.
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Difficulties to Match a Forward Contract

The farmer and the baker may be separated by a
great distant.
– The farmer is located in Kansas, and usually sells her
wheat to a local distributor in Kansas.
– The baker is located in New York, and usually buys
wheat from a local supplier in New York.
The exactly matched quantity
 The credit risk

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Futures Contracts

A future contract is a standardized forward
contract that is traded on an organized
exchange.
– Standardization of the terms of the future contracts
(e.g., quantity, quality and delivery date ) ;
– The exchange interposes itself between the buyer
and the seller as an intermediary;
– The margin requirement and the mechanism of
‘mark-to-market’.
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Further Illustration: A Future Contract
Farmer ’s Transaction
Proceeds from sale of wheat to distributor
Cash flow from the futures contract
Total receipts
Spot Price of Wheat on Delivery Date
$1.50 per bu.
$2 per bu.
$2.50 per bu.
$150,000
$200,000
$250,000
$50,000
$50,000
0
Paid to farmer
Paid by farmer
$200,000
$200,000
$200,000
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Further Illustration: A Future Contract
Baker ’s Transaction
Cost of wheat bought from supplier
Cash flow from the futures contract
Total receipts
Spot Price of Wheat on Delivery Date
$1.50 per bu.
$2 per bu.
$2.50 per bu.
$150,000
$200,000
$250,000
$50,000
$50,000
0
Paid by baker
Paid to baker
$200,000
$200,000
$200,000
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Farmer’s Receipts (thousands)
$300
$250
$200
$150
$100
$50
$0
-$50
-$100
$1.00
$1.50
Sale of wheat
$2.00
Futures
$2.50
$3.00
Total
Price of Wheat at Delivery Date
Farmer’s Total Cash Flows from Hedging with Futures
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Whether a transaction reduces or increases risk
depends on the particular context in which it is
undertaken.
Both parties to a risk-reducing transaction can benefit
by it even though in retrospect it may seem as if one of
the parties has gained at the expense of the other.
Even with no change in total output or total risk,
redistributing the way the risk is borne can improve the
welfare of the individuals involved.
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Margin and Marking to Market
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Another Illustration: A Series of
Forward Contracts
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Suppose you own a
computer-software business
in the United States.
A Germany company wants
to acquire the right to
produce and market your
software in Germany.
The Germany company
agrees to pay your
company DM 100,000 each
year for the next ten years
for these rights.

If you want to hedge the risk of
fluctuation in the dollar value of
your expected stream of
revenues, what can you do?
– Enter into a series of forward
contracts.
– Enter a currency swap now to
exchange your future stream of
marks for a future stream of
dollars at a or a set of prespecified exchange rate(s).
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Hedging Foreign-Exchange Risk
with Swap Contracts
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A swap contract is an agreement between two parties
(counterparties) to exchange (or swap) a series of cash
flows at specified intervals over a specified period of
time.
No immediate payment of money to either party
Based on principal (notional) amount
The swap contract is equivalent to a series of forward
contracts.
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Hedging Foreign-Exchange Risk with
Swap Contracts: An Illustration

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Suppose that the
dollar/mark exchange
rate is currently $.50 per
mark.
It also applies to all
forward contracts
covering the next ten
years.
By entering the swap
contract, you lock in a
dollar revenue of $50,000
on the settlement date
each year.


Suppose one year from now on the
settlement date, the spot rate of
exchange is $.40 per mark.
– The counterparty is obliged to pay
you 100,000×($.50-.40)=$10,000.
If the spot rate of exchange in the
second year is $.70 per mark.
– You will be obliged to pay the
counterparty 100,000×($.70.50)=$20,000.
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Interest Rate Swap: An Illustration

The cost of financing of two corporations with different
credit ratings.

AAA corp. has relative advantage in fixed rate financing,
while BBB corp. has relative advantage in floating rate
financing.
BBB wants to have fixed rate liability, while AAA wants to
have floating rate liability.

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Hedging Shortfall-Risk by Matching
Assets to Liabilities

Financial intermediaries (such as insurance
companies) need to assure their customers that
the product they are buying is free of default
risk.

Hedge their liabilities by investing in assets that
match the characteristics of their liabilities.
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An Illustration
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An insurance company sells a customer a guaranteed
investment contract that promises to pay $1,000 five
years from now for a one-time premium today of $783.53
(interest rate=5%).
The insurance company can match its assets to this
liabilities by buying a five-year government zero-coupon
bond for less than $783.53.
However, if the insurance company invests the premium
in a portfolio of stocks, there will be a risk of shortfall.
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Other Hedging Instruments to Match
Assets to Liabilities
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A savings bank has customer liabilities that are shortterm deposits earning an interest rate that changes with
market conditions (floats).
Hedging instruments
– To buy a floating-rate bond
– A strategy of “rolling over” short-term bonds
– To invest in long-term fixed bonds and enter a swap contract to
swap the fixed rate for a floating rate
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Minimizing the Cost of Hedging

You live in Boston and are planning to move to Tokyo a
year from now.

An apartment you agreed to buy it for ¥10.3 million.

The dollar/yen exchange rate is currently $0.01 per yen.

You have just sold your condominium in Boston for
$100,000, and have invested the money in one-year U.S.
Treasury bills at an interest rate of 3%.

You plan to use the money to pay for the apartment in
Tokyo.
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The risk of exchange rate has been fluctuating, as low
as $.008 per yen and as high as $.011.
Two ways to eliminate your exposure to the risk of a
rise in the dollar price of the yen
– To enter a forward contract, the forward price is $.01 per yen;
– To get the owner of the Tokyo apartment to sell it to you for a
price fixed in U.S. dollars.

The mechanism chosen to implement the hedge should
be the one that minimizes the cost of achieving the
desired reduction of risk.
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Insuring versus Hedging

When you hedge, you eliminate the risk of loss
by giving up the potential for gain.

When you insure, you pay a premium to
eliminate the risk of loss and retain the
potential for gain.
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An Illustration
Insuring
Hedging

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A trip from Boston to Tokyo a
year from now.
You make your flight
reservation now and lock in a
price of $1,000.
By entering the forward
contract you eliminate the risk
of the price going above $1,000.
But …



Alternatively, the airline offer
you the possibility of paying $20
now for the right to purchase
your ticket a year from now at a
price of $1,000.
If the price turns out to be more
than $1,000, you will exercise the
right.
Otherwise you will let it expire.
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Farmer's Cash Receipts
The Farmer’s Wheat Crop
$500,000.00
$400,000.00
$300,000.00
$200,000.00
$100,000.00
$0.00
$0.00
$1.00
$2.00
$3.00
$4.00
Price of Wheat
Revenue from Wheat
Hedged
Insured
Hedging versus Insuring against Price Risk: The Farmer
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The Farmer’s Wheat Crop
By insuring, the farmer retains much of the
economic benefit of an increase in the price of
wheat while eliminating the downside risk.
 This benefit comes at the cost of paying a
premium for the insurance.

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Basic Features of Insurance Contracts
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Exclusions are losses that might seem to meet the
conditions for coverage under the insurance contract but
are specifically excluded.
Caps are limits placed on compensation for particular
losses covered under an insurance contract.
A deductible is an amount of money that the insured
party must pay out of his or her own resources before
receiving any compensation from the insurer.
A copayment feature means that the insured party must
cover a fraction of the loss.
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Financial Guarantees
Financial guarantees are insurance against
credit risk, which is the risk to you that the
counterparty to your contract will default.
 Examples of guarantees

– Credit card: guarantees of banks to merchants;
– Residential mortgages: guarantees of payment
by government.
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Caps and Floors on Interest Rates
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You have $5,000 on
deposit in a bank
money-market account.
The interest rate you
earn is adjusted on a
daily basis.
The risk is that the
interest rate will fall.
Insurance policy:
interest-floor
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You took a $100,000
adjustable-rate mortgage
loan for a house.
The mortgage interest
rate is tied to the oneyear U.S.Treasury bill
rate.
Insurance policy:
interest-cap
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Options as Insurance

A option is the right (not the obligation) to
purchase or sell something at a specified price
(the exercise price) in the future.
– A call and a put
– Strike or exercise price
– Expiration or maturity date
– European- or American-type
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Put Options on Stocks

Lucy is a manager working for XYZ corporation.

She has received shares of XYZ stock as compensation in the
past and now owns 1,000 shares.

The current market price of XYZ is $100 per share.

She can buy XYZ puts at an exercise price of $100 per share
expiring in one year.

The current price of a one-year European put on a share of
XYZ with a $100 exercise price is $10.

By choosing a put with a lower exercise price (such as $95), she
will increase the ‘deductible’ but lower the cost of the
insurance.
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Put Options on Bonds
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We know that the prices of bonds will fluctuate
substantially because of changes in possible losses to
bondholders from default (the default risk) and
changes in the level of risk-free interest rates.
However, a put option on a bond can provide
insurance against losses stemming from either source
of risk, and thus the bondholders are guaranteed a
minimum price which is the exercise price of put
option on the bond.
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The Diversification Principle
Diversifying means splitting an investment
among many risky assets instead of
concentrating it all in only one.
 The diversification principle states that by
diversifying across risky assets people can
sometimes achieve a reduction in their overall
risk exposure with no reduction in their
expected return.

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Diversification with Uncorrelated Risks

Investing in a single drug.
– initial capital: $100,000
– probability of success: 50%
– uncertainty: $400,000 or nothing

Possible outcomes and payoffs:
– fail with probability 0.5 and with no
payoff
– succeed with probability 0.5 and
with $400,000
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Diversification with Uncorrelated Risks
Investing in two drugs
（diversifying by holding a portfolio）
– initial capital: $100,000（$50,000 per
drug）
– probability of success: 50%
– uncertainty: $200,000 or nothing
– independence of successes
 Possible outcomes and payoffs:

Expected Payoff
=$200,000
Standard Deviation
=$200,000
– No drugs succeed with probability 0.25 and
with no payoff;
– One drug succeeds with probability 0.5
and with $200,000;
– Both drugs succeed with probability 0.25
and with $400,000.
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Diversification with Uncorrelated Risks
Expected Payoff
=$200,000
Standard Deviation
=$200,000
Standard
Deviation falls
Expected Payoff
=$200,000
Standard Deviation
=$141,421
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Diversification with Uncorrelated Risks

Generalizing the argument, it is easy to prove that the
standard deviation in the case of N drugs is:
 portfolio  $200,000


N
Conclusion: Given the facts of this example, the risk
may be made as close to zero as we wish if there are
sufficient securities!
In reality, however, N is must be finite, and
pharmaceutical projects have a non-zero correlations.
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Nondiversifiable Risk
The part of the portfolio volatility that can be
eliminated by adding more stocks is the
diversifiable risk.
 The part that remains no matter how many
stocks are added is the nondiversifiable risk.

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Correlated Homogeneous Securities
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Pharmaceutical projects do have positive correlation.
(Why?)
Loosen the assumptions made about the correlation,
and set it to ρ, and use the generalization of
 2p  w1212  w22 22  2w1w21 2 1,2

With the homogeneous securities, we have
 p2 
1 2 N 1 2
 
 
N
N
nondiversifiable risk:
diversifiable
risk:
Perfect correlation
(ρ=1) does not
reducerisk
risk!
systematic
firm-specific risk
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0.20
Standard Deviation of
Portfolio Rate of Return
0.18
0.16
  0.2   0.2
Diversifiable
Security Risk
Diversifiable Security
Risk
0.14
0.12
0.10
0.08
0.06
Nondiversifiable Security Risk
Nondiversifiable Security Risk
0.04
0.02
0.00
0
5
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Portfolio Size
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Standard Deviation of
the Portfolio rate of return
Finance
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
  0.0   0.2
All risk is diversifiable!
All risk is diversifiable
0
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Portfolio Size
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Portfolio standard deviation
Diversification of Risk
The effect of increasing the
number of securities in a portfolio
Diversifiable (Unique) risk
Approx. 20%
Nondiversifiable (Market) risk
0
5
10
15
Number of Securities
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Diversification and the Cost of
Insurance

The more diversified are the risks in a portfolio of a
given size, the less it will cost to insure the portfolio
against a loss.
– Insuring each stock separately would cost twice as much as
insuring the portfolio of two stocks.
In chapter 12, you will learn how
to select an efficient portfolio.
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