Corporate finance chapter 011 hedzging and insuring
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Chapter 11: Hedging and
Insuring
Objective
Explain market mechanisms for
implementing hedges and insurance
1
Chapter 11 Contents
11.1 Using Forward & Futures
Contracts to Hedge Risks
11.6 Basic Features of
Insurance Contracts
11.2 Hedging ForeignExchange Risk with Swap
Contracts
11.7 Financial Guarantees
11.3 Hedging Shortfall-Risk by
Matching Assets to
Liabilities
11.4 Minimizing the Cost of
Hedging
11.5 Insuring versus Hedging
11.8 Caps & Floors on Interest
Rates
11.9 Options as Insurance
11.10 The Diversification
Principle
11.11 Insuring a Diversified
Portfolio
2
Value of 30-Year Mortgage 5-Years Out (6%)
16,000,000
Market Value of Mortgages
Market Value of Mortgage
14,000,000
12,000,000
10,000,000
8,000,000
6,000,000
4,000,000
Book Value of Mortgages
2,000,000
0
1%
3%
5%
7%
Market Interest Rate
3
9%
11%
Cash from Mortgages and Cash Needed for CDs
Cash Flows From Mortgages and to
CDs
1,200,000
CD Interest Payments
1,000,000
800,000
600,000
400,000
Mortgage Interest Payments
200,000
0
1%
2%
3%
4%
5%
6%
7%
8%
Current Interest Rate
4
9% 10% 11% 12%
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
Price of Wheat
5
3
3.5
4
Hedging with a Put
16000
14000
12000
10000
Share Holding
Value Puts
FV Premium
Total Wealth
8000
6000
4000
2000
0
50
60
70
80
90
100
110
-2000
Share Price
6
120
130
140
150
Standard deviation, 1 firm
State of the World Probability
One Failure
One Success
0.5
0.5
Payoff
0
400000
Mean
200000
200000
Deviation
Dev SQR
-200000
200000
4E+10
4E+10
<- * Prob
2E+10
2E+10
Sum =
4E+10
Sqrt ^|
200000
•The
•TheStandard
StandardDeviation
Deviationisis$200,000
$200,000
7
Standard deviation, 2 firms
State of the World Probability
One Failure
One Success
Two Successes
0.25
0.5
0.25
Payoff
0
200000
400000
Mean
Deviation
200000
200000
200000
Dev SQR
-200000
0
200000
4E+10
0
4E+10
<- * Prob
1E+10
0
1E+10
Sum =
2E+10
Sqrt ^|
141421.356
•The
•TheStandard
StandardDeviation
Deviationisis
about
about$141,000
$141,000(c.f.
(c.f.$200,000)
$200,000)
8
Standard deviation, equal
investment in “n” firms
• Generalizing the argument, it is easy to
prove that the standard deviation in this
case is just $200,000/SqrareRoot(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
9
Correlated Homogeneous
Securities
• Pharmaceutical projects do have positive
correlation (Why?)
• Loosen the assumptions made about the
correlation, and set it to ρ, and use the
generalization of
σ = w σ + w σ + 2w1w2σ 1σ 2 ρ 1, 2
2
p
2
1
2
1
2
2
2
2
10
Correlated Homogeneous
Securities
• We obtain the relationship
σport= σsec *QSRT(ρ + 1/n)
• In the case of n -> Infinity, there
remains the term
σport= σsec *QSRT(ρ)
• This risk is not diversifiable
11
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
Portfolio Size
12
35
40
45
50
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
Portfolio Size
13
35
40
45
50
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
Portfolio Size
14
35
40
45
50
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
15
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
Portfolio Size
16
35
40
45
50
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
Portfolio Size
17
35
40
45
50
