Download Hedging Strategies Using Futures

Hedging Strategies Using
Futures
Chapter 3
Options, Futures, and Other Derivatives, 7th International Edition,
Copyright © John C. Hull 2008
1
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
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
2
Example 3.1: Long Hedges
It is Jan 15. A copper fabricator knows it will
require 100,000 pounds of copper on May 15
to meet a certain contract. The spot price of
copper is 340 cents per pound. May futures
price is 320 cents per pound.
Jan 15: Take a long position in four May
futures contracts on copper (each contract is
for the delivery of 25,000 pounds).
May 15: Close out the position.
After gains and looses on the futures are
taken into account, the price paid by the
company is close to 320 cents per pound.
Suppose spot price on May 15 is 325 cents
per pound.
Gain= 100,000 x (3.25-3.20) =$5,000
Suppose spot price is 305 cents per pound.
Loss= 100,000 x (3.20 -3.05) = $15,000
Example 3.2: Short Hedges
It s May 15. An oil producer has negotiated a
contract to sell 1 million barrels of crude oil.
The price in the sales contract is the spot
price on Aug. 15. Spot price on May 15: $60
per barrel. Aug. Oil futures: $59 per barrel.
May 15: Short 1000 Aug. Futures contract
(each futures contract is for the delivery of
1000 barrels)
Aug 15: Close out futures position.
After gains and looses on the futures are taken
into account, the price received by the company
is close to $59 per barrel.
Suppose spot price on Aug. 15 is $55 per barrel.
Gain: $59-$55 = $4 per barrel ($4 million in total)
Suppose the price of oil on Aug 15 is $65 per
barrel.
Loss: $65-$59 = $6 per barrel.
In all cases, the company ends up with app. $59
million.
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
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
7
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
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
8
Convergence of Futures to Spot
(Hedge initiated at time t1 and closed out at time t2)
Futures
Price
Spot
Price
Time
t1
t2
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
9
Basis Risk
Basis is the difference between the
spot and futures price
As time passes, the spot and
futures price do not change by the
same amount, as a result basis
changes.
Basis risk arises because of the
uncertainty about the basis when
the hedge is closed out
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
10
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 Realized=S2+ (F1 – F2) = F1 + Basis
F1– F2 : Profit on futures position
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
11
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 Asset=S2 + (F1– F2) = F1 + Basis
F1– F2: Loss on futures position
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
12
Short Hedge: If the basis strengthens, the
hedger’s postion improves.
If the basis weakens, the hedger’s position
worsens.
Long Hedge. If the basis strengthens, the
hedger’s position worsens.
If the basis weakens, the hedger’s position
improves.
Choice of Contract
One key factor affecting basis risk is the
choice of futures contract. This choice has
two components:
The choice of the asset underlying the futures
contract
The choice of the delivery month.
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
14
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.
Example 3.3
It is March 1. A U.S company expects to receive 50
million yen at the end of July. Yen futures contracts
on CME have delivery months of March, June, Sep
and Dec. One contract is for the delivery of 12.5
million. Sep contract is chosen for hedging purposes.
The Sep Futures price for yen is 0.7800 cents.
1. Short four Sep futures contracts on March 1 at a
futures price of 0.7800.
2. Close out the position when the yen arrive at the
end of July.
Spot price at the end of July is 0.7200.
Sep futures price at the end of July is 0.7250
Basis at the end of July = -0.0050
Net exchange rate after hedging:
Spot price on July + Gain on futures = 0.72+
(0.78- 0.725)= 0.775
Futures price in March +Basis in July = 0.78 –
0.0050 =0.775
Example 3.4
It is June 8. A company knows that it will
need to purchase 20,000 barrels of crude oil
some time in Oct or Nov. The current Dec oil
futures price is $68 per barrel. Hedging
strategy:
1. Take a long position in 20 Dec oil futures
contracts on June 8 at a futures price of $68
2. Close out the contract when ready to
purchase the oil
Company is ready to purchase oil on Nov 10
Spot price on Nov 10 is $75
Dec futures price on Nov 10 is $72.
Basis on Nov 10 is $3
Net cost:
Spot price on Nov 10 + Gain on Futures =
$75 – ($68-$72) = $71
Futures price on June 8 + Basis on Nov 10 =
$68 +$3 = $71
Optimal Hedge Ratio (page 55)
Proportion of the exposure that should optimally be
hedged is
s
r S
sF
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.
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
20
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 times
size of futures contract
The second approach incorporates an
adjustment for the daily settlement of futures
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
21
Hedging Using Index Futures
(Page 61)
To hedge the risk in a portfolio the
number of contracts that should be
shorted is
P
b
F
where P is the value of the portfolio, b is
its beta, and F is the value of one futures
contract
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
22
Example 3.5
Portfolio worth $5.05 million mirrors the S&P
500. The index futures price is 1,010 and
each futures is on $250 x the index.
Value of the portfolio (P) = 5,050,000
Value of one futures contract (F) = 250 x 1,010
= 252,500
Optimal number of contract (N)
=5,050,000/252,500 = 20 contracts
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
23
If the portfolio does not exactly mirror the index, we use beta.
Suppose that a futures contract with 4 months to maturity is
used to hedge the value of a portfolio over the next 3 months.
S&P 500 index is 1,000
S&P 500 futures price is 1,010
Value of Portfolio is $5,050,000
Beta of portfolio is 1.5
Risk-free rate is 4% per annum
Div yield on index is 1% per annum
What position in futures contracts on the S&P 500 is necessary
to hedge the portfolio?
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
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
25
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 riskfree return plus the excess return of your
portfolio over the market.
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
26
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
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
27