Transcript Hedging Strategy

Hedging Strategies Using
Derivatives
1. Basic Principles
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Goal: to neutralize the risk as far as
possible.
I. Derivatives
A. Option: contract that gives its holder the
right to buy (or sell) an asset at a
predetermined price within a specified
period of time.
• A-1) Call option: option to buy an
underlying asset at a certain price within a
specific period
• A-2) Put option: option to sell an
underlying asset at a certain price within a
specific period
• Call  PN (d1 )  Xe rt N (d 2 )
Put   PN (d1 )  Xe rt N (d 2 )
d1  (ln(P / X )  (r   2 / 2)  t ) /(  t )
d 2  d1  
t
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call
Underlying asset
+
Exercise price
Time to expiration +
Risk free rate
+
Variance of return +
put
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• B. Forward Contracts:
- agreements where one party agree to
buy a commodity at a specific price on a
specific future date and other party agrees
to sell.
- Physical delivery occurs
• C. Future contracts:
• - similar to forward contracts
• - marked to market on a daily basis
• (margin account with minimum requirement,
reducing default risk)
• - settled with cash
• - standardized
• Ex) marking to market
• Setting up a margin account for futures
contract with initial margin – e.g)$4000
• Rebalanced daily to reflect investors’ gains
or losses, using daily futures prices.
• If the balance below maintenance margin,
there will be a margin call.
• The investor is entitled to withdraw any
balance in the margin account in excess of
the initial margin.
• D. Swap: two parties agree to exchange
obligations to make specified payment
streams.
• Ex) Floating rate bond & Fixed rate bond
• E. Structured notes: a debt obligation
derived from another debt obligation
• Ex) Stripping long term debts (30 years) to
create a series of zero coupon bonds
• Ex) CMO with mortgages loans
F. Inverse Floaters
• A note in which the interest paid moves
counter to market rates
Ex) note at prime plus 1%
II. Hedging with futures
• Short hedge: a hedge that involves a short
position in futures contract. Here the
hedger owns an asset and expects to sell
it in the future.
• Ex-1) suppose that an oil producer sell a
August 15 futures contract at $18.75 per
barrel. Now it is April.
• Suppose that the spot price on August 15
prove to be $17.50. And August 15 futures
price will be close to $17.50.
• gain = Sales of oil + difference of futures
price = 17.50+(18.75-17.50) = 18.75
• If the spot price goes up to $19, gain =
19+ (18.75 -19) =18.75
• Long hedges: hedges taking a long
position in a futures contract. Here
hedgers want to purchase a certain assets
• Ex) A copper fabricator buys a May futures
contract at 120 cents per pound. He or she
needs 10,000 pound in May. Now, It is January.
• If spot price goes up to 125 cents, costs =
10000*1.25- (1.25-1.20)*10000=120000
• If spot price goes down to 105 cents, costs =
10000*1.05+(1.20-1.05)*10000=120000
1) Basis Risk
As shown in the previous examples, to
achieve hedging, spot price and future
contract prices should converge around
the expiration date. If not,……
• Basis = spot price of asset to be hedged
– futures price of contract used.
• Reasons of basis:
- the asset for hedging is not the same as the
asset underlying the futures contract
- uncertain date when the asset will be
bought or sold
- closed out before its expiration date
• Strengthening of the basis: increasing
basis
• Weakening of the basis: decreasing basis
• 2) Minimum variance hedge ratio
• Ratio that minimize the variance of the
hedger’s position
h*  
s
F
S : changein spot price during the life of hedge
F : changein futures price during the life of hedge
 s : S t an dard deviationof S
 F : S t an dard deviationof F
 : correlation betweenS and F
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3) Optimal Number of Contracts
N: optimal number of contracts
NA: Size of position hedged
QF: Size of one contract
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h NA
N 
QF