Part 4'1 Applications of Financial Futures And Forwards

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Part 4.1Applications of Financial Futures And
Forwards
Derivative Instruments Introduction To
Mechanisms, Applications and Valuation
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Topics Covered

• Spot Rates and Forward Rates
• Forward Rate Agreements
• Euro-Bund-Futures
• SWAPS
• How to Set Up A Hedge Using Swaps

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Long Short Hedges

• A long futures hedge is appropriate when you know
  you will purchase an asset in the future and want
  to lock in the price
• A short futures hedge is appropriate when you
  know you will sell an asset in the future and
  want to lock in the price

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Arguments in Favor of Hedging

• Companies should focus on the main business they
  are in and take steps to minimize risks arising
  from interest rates, exchange rates, and other
  market variables

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Arguments against Hedging

• Shareholders are usually well diversified and can
  make their own hedging decisions
• It may increase risk to hedge when competitors do
  not
• Explaining a situation where there is a loss on
  the hedge and a gain on the underlying can be
  difficult

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Convergence of Futures to Spot(Hedge initiated
at time t1 and closed out at time t2)

Futures Price
Spot Price
Time
t1
t2
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Basis Risk

• Basis is the difference between the spot and
  futures price
• Basis risk arises because of the uncertainty
  about the basis when the hedge is closed out

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Long Hedge

• We define
• F1 Initial Futures Price
• F2 Final Futures Price
• S2 Final Asset Price
• If you hedge the future purchase of an asset by
  entering into a long futures contract then
• Cost of AssetS2 (F2 F1) F1 Basis

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Short Hedge

• Again we define
• F1 Initial Futures Price
• F2 Final Futures Price
• S2 Final Asset Price
• If you hedge the future sale of an asset by
  entering into a short futures contract then
• Price RealizedS2 (F1 F2) F1 Basis

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Choice of Contract

• Choose a delivery month that is as close as
  possible to, but later than, the end of the life
  of the hedge
• When there is no futures contract on the asset
  being hedged, choose the contract whose futures
  price is most highly correlated with the asset
  price. This is known as cross hedging.

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Optimal Hedge Ratio (page 55)

• Proportion of the exposure that should optimally
  be hedged is
• where
• sS is the standard deviation of DS, the change
  in the spot price during the hedging period,
• sF is the standard deviation of DF, the change
  in the futures price during the hedging period
• r is the coefficient of correlation between DS
  and DF.

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Tailing the Hedge

• Two way of determining the number of contracts to
  use for hedging are
• Compare the exposure to be hedged with the value
  of the assets underlying one futures contract
• Compare the exposure to be hedged with the value
  of one futures contract (futures price time size
  of futures contract
• The second approach incorporates an adjustment
  for the daily settlement of futures

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Hedging Using Index Futures

• To hedge the risk in a portfolio the number of
  contracts that should be shorted is
• where P is the value of the portfolio, b is its
  beta, and F is the value of one futures contract

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Example

• SP 500 futures price is 1,000
• Value of Portfolio is 5 million
• Beta of portfolio is 1.5
• What position in futures contracts on the SP
  500 is necessary to hedge the portfolio?

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Changing Beta

• What position is necessary to reduce the beta of
  the portfolio to 0.75?
• What position is necessary to increase the beta
  of the portfolio to 2.0?

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Hedging Price of an Individual Stock

• Similar to hedging a portfolio
• Does not work as well because only the systematic
  risk is hedged
• The unsystematic risk that is unique to the stock
  is not hedged

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Why Hedge Equity Returns

• May want to be out of the market for a while.
  Hedging avoids the costs of selling and
  repurchasing the portfolio
• Suppose stocks in your portfolio have an average
  beta of 1.0, but you feel they have been chosen
  well and will outperform the market in both good
  and bad times. Hedging ensures that the return
  you earn is the risk-free return plus the excess
  return of your portfolio over the market.

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Rolling The Hedge Forward (page 64-65)

• We can use a series of futures contracts to
  increase the life of a hedge
• Each time we switch from one futures contract to
  another we incur a type of basis risk

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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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Homemade Forward Rate 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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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-Future Characteristics
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 ).
Buyer (long) has to bedelivered
Seller (short) mustdeliver
Clearing Eurex
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Euro-Bund-Futures Delivery 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-Future Mechanisms
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Euro-Bund-Futures Pricing
Pricing Euro - Bund Future at 18th June 2002
106,41 (Term-structure as of 17th June)
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Short-Future-Position and Margin - Account 5 Days
to Settlement
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, 4 days the game ends with a total
loss of 6,400 Euro.
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How to Hedge a Bond Portfolio UsingBund 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 Bond Portfolio UsingBund 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 Bond Portfolio UsingBund 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 Bond Portfolio UsingBund 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 ).