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Chapter 11
Hedging, Insuring, Diversifying
1
Contents
1.
2.
3.
4.
5.
6.
Forward and Futures
to Hedge Risk
Swap Contracts
Hedging, Matching
Assets to Liabilities
Minimizing the Cost
of Hedging
Insuring v. Hedging
Insurance Contracts
7.
8.
9.
10.
11.
Financial
Guarantees
Caps and Floors on
Interest Rates
Options as
Insurance
The Diversification
Principle
Diversification and
the Cost of
Insurance
2
Forward Contracts
Two Parties agree to exchange some
item in the future at a prearranged
price
3
Forward Contracts,Terminology




Forward price: The specified price of the
item
Spot price: The price for immediate
delivery of the item
Face value: quantity of item times the
forward price
Long/Short position: The position of the
party who agrees to buy/sell the item
4
Forward Contract, Example
Farmer, Baker
Uncertain about the future price of
wheat one month from now
Natural match
Forward contract: One month from
now, the farmer will deliver 100,000
bushels of wheat to the baker and
receive the face value $200,000 in
return
5
Futures Contracts
A standardized forward contract that
is traded on some organized
exchange
6
Futures Contract, Example
The farmer in Kansas, the baker in New York
They enter a wheat futures contract with the
future exchange at a price of $2 per bushel
farmer: short position
baker: long position
The exchange matches them
Futures Contract: Paying to (receiving from) the
exchange
($2-spot price)  100,000
7
Futures Contract, Example cont.
At due date
Wheat $1.5 per bu. $2 per bu. $2.5 per bu.
Farmer from distributor
$150,000
$200,000 $250,000
Farmer from\to exchange
$50,000
0
($50,000)
Total
$200,000
$200,000 $200,000
8
Swap Contracts
Consists of two parties exchanging
(swapping) a series of cash flows at
specified intervals over a specified
period of time
9
Swap Contracts, Example
Computer software business in US,
German company pays DM100,000 each year for a
period of 10 years for the right to produce and
market the software
The dollar/mark exchange rate risk
Currency swap: on an exchange rate of $0.5 per
mark. Each year the US party receives from\pays
to the counterparty DM100,000($0.5-spot rate)
10
Insuring versus Hedging


Hedging: Eliminating the risk of loss
by giving up the potential for gain
Insuring: Paying a premium to
eliminate the risk of loss and retain
the potential for gain
12
Insuring v. Hedging, Example
The farmer:
1. Takes no measures to reduce risk
2. Hedges with a forward contract,
100,000 bushels, $2 per bushel
3. Buys an Insurance for a premium
of $20,000, which guarantees a
minimum price of $2 per bushel
for her 100,000 bushels
13
Hedging v. Insuring
450000
400000
Revenue from Wheat
350000
Hedged
Insured
300000
250000
200000
150000
100000
50000
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Price of Wheat
14
Options
The right to either purchase or sell
something at a fixed price in the
future
19
Options, Terminology



Call/Put: An option to buy/sell a
specified item at a fixed price
Strike price or Exercise price: The
fixed price specified in the option
Expiration date or Maturity date:
The date after which an option can
no longer be exercised
20
Options


European Option: Can only be
exercised on the expiration date
American Option: Can be exercised
at any time up to and including the
expiration date
21
Diversifying
Splitting an investment among many
risky assets instead of concentrating
it all in only one
22
The Diversification Principle
By diversifying across risky assets
sometimes it is possible to reduce the
overall risk with no reduction in
expected return
23
Review
Y : a random variable
Var(X) :E[(X - E[X]) 2 ]  E[X 2 ] - E[X] 2
Y : another random variable
Cov(X, Y)  E[(X - E[X]) (Y - E[Y])]  E[XY] - E[X]E[Y]
Corr(X, Y)  Cov(X, Y)/ Var(X)Var( Y)
24
Review
ai  0, i  1,  , n
n
n
i 1
i 1
E[ ai X i ]   ai E[ X i ]
n
n
i 1
i 1
Var ( ai X i )   ai2Var ( X i )   ai a j Cov ( X i , X j )
i j
 i , j : Corr ( X i , X j ),  i2  Var ( X i )
n
n
i 1
i 1
Var ( ai X i )   ai2 i2   ai a j  i , j i j
i j
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Review
1
ai  , i  1,  , n
n
E[ X 1 ]  E[ X 2 ]    E[ X n ]  
n
E[ ai X i ]  
i 1
n
n
1
1 2
Var ( ai X i )  2  i   2  i , j i j
i j n
i 1 n
i 1
n
 1   2     n   ,   Var ( ai X i )
2
p
i 1
1 2
  2  (n    i , j )
n
i j
2
p
26
Uncorrelated Risks
 i , j  0, i, j  1,  , n, i  j
p 
i, j

,
n
  , i, j  1,  , n, i  j
2
n 1 2
 

 
n
n
2
P
27
Nondiversifiable Risk



In a randomly selected equally
weighted portfolio, with possible
positive correlation between stocks,
by adding more stocks the standard
deviation reduces just to a point
Diversifiable risk: The part of the
volatility that can be eliminated
Nondiversifiable risk: The part that
remains
28
Standare Deviation
Standard Deviations of Portfolios,
rho = 0.2, sig = 0.2
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
5
10
15
20
25
30
35
40
45
50
Portfolio Size
29
Standare Deviation
Standard Deviations of Portfolios,
rho = 0.8, sig = 0.2
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
5
10
15
20
25
30
35
40
45
50
Portfolio Size
30
Standare Deviation
Standard Deviations of Portfolios,
rho = 0.5, sig = 0.2
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
5
10
15
20
25
30
35
40
45
50
Portfolio Size
31
Standare Deviation
Standard Deviations of Portfolios,
rho = 0.2, sig = 0.2
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
Diversifiable Security Risk
Nondiversifiable Security Risk
0
5
10
15
20
25
30
Portfolio Size
32
35
40
45
50
Standare Deviation
Standard Deviations of Portfolios,
rho = 0.0, sig = 0.2
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
All risk is diversifiable
0
5
10
15
20
25
30
35
40
45
50
Portfolio Size
33
Standare Deviation
Standard Deviations of Portfolios,
rho = 1/(1-50) = -0.0204, sig = 0.2
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
5
10
15
20
25
30
35
40
45
50
Portfolio Size
34