1 Chapter 11 Hedging, Insuring, Diversifying. 2 Contents 1. Forward and Futures to Hedge Risk 2. Swap Contracts 3. Hedging, Matching Assets to Liabilities.

1

Chapter 11

Hedging, Insuring, Diversifying

2

Contents

1. Forward and Futures to Hedge Risk

2. Swap Contracts3. Hedging, Matching

Assets to Liabilities4. Minimizing the Cost

of Hedging5. Insuring v. Hedging6. Insurance Contracts

7. Financial Guarantees8. Caps and Floors on

Interest Rates 9. Options as Insurance10. The Diversification

Principle11. Diversification and

the Cost of Insurance

3

Forward Contracts

Two Parties agree to exchange some item in the future at a prearranged price

4

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

5

Forward Contract, Example

Farmer, Baker Uncertain about the future price of

wheat one month from nowNatural matchForward 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

6

Futures Contracts

A standardized forward contract that is traded on some organized exchange

7

Futures Contract, Example

The farmer in Kansas, the baker in New YorkThey 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) theexchange ($2-spot price) 100,000

8

Futures Contract, Example cont.

At due dateWheat $1.5 per bu. $2 per bu. $2.5 per bu.Farmer from distributor $150,000 $200,000 $250,000Farmer from\to exchange $50,000 0 ($50,000)Total $200,000 $200,000 $200,000

9

Swap Contracts

Consists of two parties exchanging (swapping) a series of cash flows at specified intervals over a specified period of time

10

Swap Contracts, ExampleComputer software business in US, German company pays DM100,000 each year for aperiod of 10 years for the right to produce andmarket 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)

12

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

13

Insuring v. Hedging, Example

The farmer:1. Takes no measures to reduce risk2. Hedges with a forward contract,

100,000 bushels, $2 per bushel3. Buys an Insurance for a premium

of $20,000, which guarantees a minimum price of $2 per bushel for her 100,000 bushels

14

Hedging v. Insuring

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

0 0.5 1 1.5 2 2.5 3 3.5 4

Price of Wheat

Revenue from Wheat Hedged Insured

19

Options

The right to either purchase or sell something at a fixed price in the future

20

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

21

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

22

Diversifying

Splitting an investment among many risky assets instead of concentrating it all in only one

23

The Diversification Principle

By diversifying across risky assets sometimes it is possible to reduce the overall risk with no reduction in expected return

24

Review

Y)Var(X)Var(Y)/Cov(X, Y)Corr(X,

E[X]E[Y]-E[XY] E[Y])]-(Y E[X])-E[(X Y)Cov(X,

variable random another :Y

E[X]-]E[X]E[X])-E[(X:Var(X)

variablerandom a :Y222

25

Review

n

i

n

i jijijijiiiii

iijiji

n

i

n

i jijijiiiii

n

i

n

iiiii

i

aaaXaVar

XVarXXCorr

XXCovaaXVaraXaVar

XEaXaE

nia

1 1,

22

2,

1 1

2

1 1

)(

)(),,(:

),()()(

][][

,,1,0

26

Review

jijip

n

iiipn

jiji

n

i jii

n

iii

n

iii

n

i

nn

XaVar

nnXaVar

XaE

XEXEXE

nin

a

)(1

)(,

11)(

][

][][][

,,1,1

,2

22

1

221

,1

22

21

1

21

27

Uncorrelated Risks

22

2

,

,

1

,,,1,,

,

,,,1,,0

n

n

n

jinjin

jinji

P

ji

p

ji

28

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

29

Standard Deviations of Portfolios, rho = 0.2, sig = 0.2

0.000.020.040.060.080.100.120.140.160.180.20

0 5 10 15 20 25 30 35 40 45 50

Portfolio Size

Sta

nd

are

Dev

iati

on

30

Standard Deviations of Portfolios, rho = 0.8, sig = 0.2

0.000.020.040.060.080.100.120.140.160.180.20

0 5 10 15 20 25 30 35 40 45 50

Portfolio Size

Sta

nd

are

Dev

iati

on

31

Standard Deviations of Portfolios, rho = 0.5, sig = 0.2

0.000.020.040.060.080.100.120.140.160.180.20

0 5 10 15 20 25 30 35 40 45 50

Portfolio Size

Sta

nd

are

Dev

iati

on

32

Standard Deviations of Portfolios, rho = 0.2, sig = 0.2

0.000.020.040.060.080.100.120.140.160.180.20

0 5 10 15 20 25 30 35 40 45 50

Portfolio Size

Sta

nd

are

Dev

iati

on

Diversifiable Security Risk

Nondiversifiable Security Risk

33

Standard Deviations of Portfolios, rho = 0.0, sig = 0.2

0.000.020.040.060.080.100.120.140.160.180.20

0 5 10 15 20 25 30 35 40 45 50

Portfolio Size

Sta

nd

are

Dev

iati

on

All risk is diversifiable All risk is diversifiable

34

Standard Deviations of Portfolios, rho = 1/(1-50) = -0.0204, sig = 0.2

0.000.020.040.060.080.100.120.140.160.180.20

0 5 10 15 20 25 30 35 40 45 50

Portfolio Size

Sta

nd

are

Dev

iati

on