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Topics Covered

• Why Manage Risk
• Insurance
• Payoff Profiles concerning Forwards, Futures
  and Options
• Spot-Future-Parity and the Relations Between Spot
  and Futures Markets
• An Example

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Key Elements of Risk - Management
Financial risks are market related price risks
concerning financial instruments.
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Hedging with Forwards and Futures

• Ex - Kellogg produces cereal. A major component
  and cost factor is sugar.
• Forecasted income sales volume is set by using
  a fixed selling price.
• Changes in cost can impact these forecasts.
• To fix your sugar costs, you would ideally like
  to purchase all your sugar today, since you like
  todays price, and made your forecasts based on
  it. But, you can not.
• You can, however, sign a contract to purchase
  sugar at various points in the future for a price
  negotiated today.
• This contract is called a Futures Contract.
• This technique of managing your sugar costs is
  called Hedging.

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Hedging with Forwards and Futures
1- Spot Contract - A contract for immediate sale
delivery of an asset. 2- Forward Contract - A
contract between two people for the delivery of
an asset at a negotiated price on a set date in
the future. 3- Futures Contract - A contract
similar to a forward contract, except there is an
intermediary that creates a standardized
contract. Thus, the two parties do not have to
negotiate the terms of the contract. The
intermediary is the Commodity Clearing Corp
(CCC). The CCC guarantees all trades provides
a secondary market for the speculation of
Futures.
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Futures Contract Concepts

• Not an actual sale of the underlying
• Always a winner a loser (unlike stocks)
• K (Contracts) are settled every day. (Marked
  to Market)
• Hedge - K used to eliminate risk by locking in
  prices
• Speculation - K used to gamble
• Margin - not a sale - post partial amount

Hog K 30,000 lbs Tbill K 1.0
mil Bundfuture K 100.000
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Types of Futures
Commodity Futures -Sugar -Corn -Orange
Juice -Crude Oil -Soy beans -Pork
bellies Financial Futures -Tbills -Yen -Eurobun
dfutures -Stocks -Eurodollars Index Futures
-SP 500 - Dax Future -REX-Future
SUGAR
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DerivativesProfit Loss - Characteristics
Long Future (Un)limited Risk
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DerivativesProfit Loss - Characteristics
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Derivative Instrumentsand Markets
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Futures and Spot Contracts
The Futures-Spot-Parity-Theorem shows the basic
relationship between futures prices and spot
prices for equity securities.
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Futures and Spot Contracts

• Example
• The DAX spot price is 5,450. The current 6-M
  interest rate is 2.5 and the dividend yield on
  the DAX index is 2.0. What is the expected price
  of the 6 -M DAX futures contract ?

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Futures and Spot Contracts
The basic relationship between futures prices and
spot prices for commodities.
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Futures and Spot Contracts

• Example
• In July the spot price for coffee was .7310 per
  pound. The interest rate was 1.5 per year. The
  net convenience yield was 12.2. What was the
  price of the 10 month futures contract ?

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Ex. - Settlement Speculation

• Example - You are speculating in Hog Futures.
  You think that the Spot Price of hogs will rise
  in the future. Thus, you go Long (buy) on 10
  Hog Futures (each 30,000 lbs.) at a price of
  50.80 cts./lbs. If the price drops .17 cents
  per pound (.0017) what is total change in your
  position?

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Ex - Settlement Speculate
30,000 lbs x .0017 loss x 10 Ks
510.00 loss
50.63
cents per lbs
50.80
-510
Since you must settle your account every day, you
must give your broker 510.00. If you do not, the
contract will be closed automatically, leaving
you with an open account of 510.00.
This has then been your last deal for years !!!!!!
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Commodity Hedge

• In June, farmer Fritz Schmidt expects to harvest
  10,000 bushels of corn during the month of
  August. In June, the September corn futures are
  selling for 2.94 per bushel (1K 5,000
  bushels). (1 bushel 1 Scheffel 6 Metzen 12
  Viertel 222,3 l)
• Fritz Schmidt wishes to lock in this price.
• Show the transactions if the September spot price
  drops to 2.80.

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Commodity Hedge

• In June, farmer Fritz Schmidt expects to harvest
  10,000 bushels of corn during the month of
  August. In June, the September corn futures are
  selling for 2.94 per bushel (1K 5,000
  bushels). Farmer Schmidt wishes to lock in this
  price.
• Show the transactions if the Sept spot price
  drops to 2.80.

Revenue from Crop 10,000 x 2.80 28,000 June
Short 2K _at_ 2.94 29,400 Sept Long 2K _at_ 2.80
28,000 . Gain on
Position-------------------------------
1,400 Total Revenue
29,400
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Commodity Hedge

• In June, farmer John Smith expects to harvest
  10,000 bushels of corn during the month of
  August. In June, the September corn futures are
  selling for 2.94 per bushel (1K 5,000
  bushels). Farmer Smith wishes to lock in this
  price.
• Show the transactions if the Sept spot price
  rises to 3.05.

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Commodity Hedge

• In June, farmer John Smith expects to harvest
  10,000 bushels of corn during the month of
  August. In June, the September corn futures are
  selling for 2.94 per bushel (1K 5,000
  bushels). Farmer Smith wishes to lock in this
  price.
• Show the transactions if the Sept spot price
  rises to 3.05.

Revenue from Crop 10,000 x 3.05 30,500 June
Short 2K _at_ 2.94 29,400 Sept Long 2K _at_ 3.05
30,500 . Loss on
Position------------------------------- ( 1,100
) Total Revenue
29,400
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Commodity Speculation
You have lived in NYC your whole life and feel
independently wealthy. You think you know
everything there is to know about pork bellies
(uncurred bacon) because your butler fixes it for
you every morning. Because you have decided to go
on a diet, you think the price will drop over the
next few months. On the CME, each PB K is 38,000
lbs. Today, you decide to short three May Ks _at_
44.00 cents per lbs. In Feb, the price rises to
48.5 cents and you decide to close your position.
What is your gain/loss ?
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Commodity Speculation
You have lived in NYC your whole life and are
independently wealthy. You think you know
everything that is to know about pork bellies
(uncurred bacon) because your butler fixes it for
you every morning. Because you have decided to
go on a diet, you think the price will drop over
the next few months. On the CME, each PB K is
38,000 lbs. Today, you decide to short three May
Ks _at_ 44.00 cents per lbs. In Feb, the price
rises to 48.5 cents and you decide to close your
position. What is your gain/loss?
Nov Short 3 May K (.4400 x 38,000 x 3 )
50,160 Feb Long 3 May K (.4850 x 38,000 x 3 )
- 55,290 Loss of 10.23 -
5,130
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Margin

• The amount (percentage) of a Futures Contract
  Value that must be on deposit with a broker.
• Since a Futures Contract is not an actual sale,
  you need only pay a fraction of the asset value
  to open a position margin.
• CME margin requirements are between 5 and 15
• Thus, you can control 100,000 of assets with
  only 15,000.

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Spot Future - Parity
Today, one (theoretical) Index-Future is sold at
4.090 (1 per Index-point). Long and
Short-positions can be described by a profit and
loss diagram
If you are Long-Future, then you may claim for
delivery of one index at a price of 4090 at
the maturity of the index-future. That means, if
the index at delivery is quoted at more than
4090, you will win from your futures position.
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Spot Future - Parity
You hold an Index-Portfolio, currently valued at
5,500 (1 Index-point 1 ). If the annual risk
free rate rf is at 3.5 and the expected
dividends on your Index portfolio are at 100 (d
100/5,500) , an Index Future with one year to
maturity has a fair price of
To prevent our Index-Portfolio from losses, we
could hedge the price risk by taking a short
future position (selling a future at 5,592.40).
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Spot Future - Parity
The total expected payoffs from your portfolio
will depend on the fu-ture state of the
environment (see below payoffs 1-5). A decreasing
stock market will be compensated by profits from
the short future po-sition, increasing stock
prices will be outbalanced by losses due to
pay-ment obligations from the future.
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Spot Future - Parity
Initially you have paid 5,500 for your stock
portfolio. Taking the short future position, the
final outcome of your portfolio will be 5,692,40
, whatever the stock price will be, i.e. you
will earn 192,40 which equals 3.5. Obviously,
this profit is riskless
Spot-Future- Parity
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Spot Future - Parity
Rising future prices will due to arbitrage
trading - induce rising spot prices. For example,
a future traded at 6,000 is clearly overpriced,
when the stock portfolio remains unchanged at
5,500 . In this case, smart traders will make
arbitrage profits of 407,50 per contract and
bring back the market to equilibrium
Note, that the arbitrage profit equals the
difference between a fair- and mispriced future
(6,000 5,592,40) plus Dividends. Higher Future
prices will lead to massivly increased demand at
spot markets until spot prices and futures are
back to equilibrium.
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Spot Future ParityFinancial Market Stability

• Spot Markets and Future (Forward) Markets are
  interlinked.
• Mispriced spot or future market instruments will
  affect both markets
• Future market speculations that drive futures
  prices will also drive spot market prices due to
  arbitrage trading (et vice versa)
• Speculation on futures markets, resulting in
  higher future prices will induce higher spot
  market prices due to arbitrage trading. Finally
  this may result in spot market bubbles that
  jeopardizes the allocation mechanism of real
  goods markets.

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Forward Rate Agreements
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Forward Rate Contracts
Rates
A financial contract that does not start
immediately but at a specified date in the future
is called a Foward Contract. Example Due to an
expected future business development your
corporate needs a 1-year loan of 10 Mio . The
loan should be available 1 year from now.
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Spot Rates and)
Forward Rate Contracts- Basic Concept -
To solve the problem you can fix a rate using a
Forward Contract. The rate, that can be locked in
today, results from a simple model The cost of
borrowing now for two years must equal the cost
of borrowing now for one year with an obligation
to extend the loan for a second year.
Using 1- and 2-year spot rates and solving the
equation for rf,1,1 results in
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Homemade ForwardRate Contracts
Forwards simply consist of borrowing and lending
at different maturities. Referring to our time
struc-ture, the cash flow of a forward contract
that starts in one year for one year can be
duplicated as follows
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Term Structure of Interest Rates and related
Spot Rates (Calculation)
Example
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Spot Rates and related Forward Rates (Calculation
Scheme)
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Forward Rates(F.R.A. - Application)
To contract a Forward-Rate means to lock in an
interest rate concerning a future period. Your
corporation might use an F.R.A. ( Forward Rate
Agreement) to make sure, that her future costs of
financing a 1-year 10 Mio loan will not exceed
3,30 .
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Forward Rates(F.R.A. - Application)
Scenario 1Short rate in t1 is at 5. Financing
costs will be 500 T. Compensations on F.R.A.
will be (5-3,3)x10 Mio 170 T. Total costs
(500-170)330 T ( 3,3)
Scenario 2Short rate in t1 is at 2. Financing
costs will be 200 T. Payments on F.R.A. will be
(2-3,3)x10 Mio -130 T. Total costs (200
130)330 T ( 3,3)
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EURO BUND FUTURES
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Euro-Bund-FutureCharacteristics
Contract Size 100.000 Settlement 6 German
Federal Bonds with 8,5 to 10,5 years remaining
term upon delivery Delivery day 10th of March,
June, September, December Quotation percentage
at a minimum price movement of 0,01 (10 ).
Seller (short) mustdeliver
Buyer (long) has to buy
Clearing Eurex
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Euro-Bund-FuturesDelivery Day/Months
Purchaseat 10th March
Delivery latestat 10th Dec.
10. March
10. June
10. Sept.
10. Dec.
Time to maturity max. 9 month
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Euro-Bund-FutureMechanisms
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Euro-Bund-Futures Pricing
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Short Future - Position Margin - Account
Futures
-1
-1
-1
-1
0
Interest Rate
8,00
8,50
7,50
7,00
7,00
Future
86,58
83,60
89,70
92,98
92,98
Change
0,00
-2,98
6,10
3,28
0,00
Value
0,00
2.980,00
-6.100,00
-3.280,00
0,00
Margin
2.500,00
2.500,00
5.480,00
2.500,00
2.500,00
Credits/Debits
2.980,00
-6.100,00
-3.280,00
-6.400,00
Current Balance
2.500,00
5.480,00
-620,00
-780,00
0,00
Maintenance
0,00
0,00
3.120,00
3.280,00
Taking a short position would only make sense, if
the future interest rate is expected to rise (see
the profit of 2,980 due to a rise of 50 BP). Only
in that case the Future, contracted at 86,58
could be delivered at lower prices. As this is
not the case, after 4 days the game ends with a
total loss of 6,400 Euro.
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How to Hedge a BondPortfolio with Bund Futures
Assume a small bond portfolio, that contains
following positions. Current prices are
calculated at an 8 flat rate
Now you expect the term structure to rise to
10 flat. Due to the rising rates your
devaluation risk is as follows
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How to Hedge a BondPortfolio with Bund Futures
Due to the expected future interest rate
scenario, you are exposed to the risk of
devaluation. According to Internationalo
Financial Reporting Standards you will have to
depreciate your bond portfolio. The
depreciation of 2,215 mio is going to worsen
your profit and loss account.
To compensate for this risk, you decide to hedge
using an instrument, that will profit from rising
rates. A short position in Bund Futures, where
the seller has to deliver 100.000 nominal per
contract, will gain from rising rates. A
declining Bund Future price allows for a cheap
delivery.
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How to Hedge a BondPortfolio with Bund Futures
Today (flat rate at 8) you may take a short
Bund-Future position at a Future-price of 86.56.
If the interest rates rise to a level of 10, the
Bund Future will be quoted at 78.66.
The short position will gain 7.900 (86,560
78,660) per contract, thus you need to short 280
contracts ( 2,215 mio / 7,900 T), to hedge the
risk of a portfolio devaluation at 2,215 mio .
(In this Ex. 156 K to hedge A and 124 K to hedge
B.)
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How to Hedge a BondPortfolio with Bund Futures
After the interest rate has risen to 10, the
total account of your bond and your hedge
(Bund-Future) portfolio looks as follows
The total loss in your bond portfolio (- 2,215
Mio ) is compensated by profits from your hedge
portfolio ( 2,212 Mio ).
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Interest RateSwaps
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Basic ConceptInterest Rate Swap

• A swap is an agreement between two parties to
  exchange interest payments within a defined
  period of time, calculated of an agreed contract
  volume. Frequently swaps simply regulate to
  exchange floating rate payments against fixed
  rate payments et vice versa.
• The contract volume will not be exchanged. Also
  interest payments will not be fully exchanged,
  but only the saldo.
• Plain-Vanilla-Swaps are based upon David
  Ricardos Theory of Trade.

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Basic ConceptInterest Rate Swap
Fixed Rate
Floating Rate
The party paying the fixed rate is called to be
in a Payer-Swap-position, while the party
receiving fixed rates takes the
Receiver-Swap-position. When the contract is
signed, the N.P.V. of both cash flows, the
variable and the fixed equal zero.
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Basic ConceptInterest Rate Swap
Banks publish their swap-conditions. Usually the
fixed rates offered referring payer or
receiver-swaps are determined by the current term
structure of interest rates
Term structure (26th Dec. 2005)
WestLB (26th Dec. 2005)
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Basic ConceptInterest Rate Swap
Example Two corporations, A (Rating AAA) and B
(Rating A) are exposed to very different market
conditions
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Plain-VanillaInterest Rate Swap
1. Step A and B chose financing contracts at
their relatively best positions, i.e. A choses a
fixed rate while B enters a floating rate loan.
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Plain-VanillaInterest Rate Swap
2. Step A and B sign a swap-arrangement, with A
receiving a fixed rate of 5.5 from B and paying
Euribor to B.
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Plain-VanillaInterest Rate Swap
Balance of Payment A
Balance of Payment B
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Plain-VanillaInterest Rate Swap
More realistic A und B contract a Swap
agreement by a financial intermediator (JPSwap).
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Plain-VanillaInterest Rate Swap
Balance JPSwap
Balance B
Balance A
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Example Risk Managementwith Asset Swaps
Corporation A receives interest revenues
generated by a 100 Mio. bond investment (6y to
maturity, 8 coupon). The bonds have been put on
the assets side at their costs of purchase
(100). The financial management of A forcasts
the interest rates to rise by 1 over the next
year.
Rising rates will lead to declining prices
(deprecia-tions). Secondly, in case of rising
rates, A is not proper-ly invested which may
affect her competetive position.Risk management
may prevent from losses.
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Example Risk Managementwith Asset Swaps
To manage the forecasted interest rate related
risk, A enters a 6y Payer-Swap (paying a fixed
rate of 8, receiving a floating rate at
12-m-Euribor. The contract volume mirrors the
nominal value of the risky asset (100 Mio )
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Example Risk Managementwith Asset Swaps
If, one year later, the interest rates would have
risen by linearly 1.5, the future cash flows
referring the 100 Mio Swap (which now matures
in 5y !) could be valued using the new spot rates
Value of the swap contract is at 2,038,655 Mio .
To close out, A will be paid the swaps present
value.
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Example Risk Managementwith Asset Swaps
Theoretically, after one year A could enter a
second swap, where she becomes a fixed rate
receiver (5y at 8,5)
The advantage of 0.5 or 500 T over a period of
5 years has a present value of 2.038.655 . A
second swap could be reasonable to ensure the
advantage and to protect from tax payments.
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Example Risk Managementwith Asset Swaps
If interest rates rise as forcasted, the value of
the 100 Mio. bonds investment will decrease to
97,961 Mio
A necessary depreciation will affect the profit
and loss account by a loss of 2.038.655 (100
Mio purchase price minus 97,961,345 current
market price).
In our case, the swap based risk management has
shown a positive present value of 2,038,655 . A
close out and the close out payment at this
amount would perfectly compensate the loss from
the bonds investment.