hedging strategies using futures

1. 3.1
Hedging Strategies Using
Futures
Chapter 3

2. 3.2
Long & Short Hedges: Anticipatory
Hedging Rule
 Do now in the futures market what you
expect to do in the future spot market
 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 & want to lock in the price

3. Examples of Anticipatory Hedging
 Airline goes long gasoline futures to hedge
a future purchase of jet fuel.
 Firm that will issue 20-year bonds a year
from now hedges by shorting T-bond
futures.
 Farmer shorts wheat futures to hedge his
sale of wheat in the future.

4. Opposites Hedging Rule
 Your position in the futures market should
the opposite of your position in the spot
market: if long one, short the other.
 A portfolio manager hedges via a short
position in stock index futures: spot long,
futures short.
 Company with outstanding floating-rate
debt hedges via long position in T-bill
futures: spot short, futures long.

5. 3.5
Argument in Favor of Corporate
Hedging
Companies should focus on the parts of
their business in which they possess
expertise. They should take steps to
minimize risks arising from interest
rates, exchange rates, and other market
variables as they lack expertise in
predicting these variables.

6. Another Argument in Favor of
Corporate Hedging
Better (cheaper, more accurate) for
company to hedge rather than the
individual investors (shareholders) to
hedge. The latter do not know the firm’s
precise exposure.

7. 3.7
Arguments against Corporate
Hedging
 Shareholders are usually well diversified
and can make their own hedging
decisions; stockholder in an airline also
owns share in an oil firm.
 Explaining ex-post a situation where there
is a loss on the hedge and a gain on the
underlying can be difficult, i.e. risk of
treasurer being fired.

8. Another Argument against
Corporate Hedging
It may increase risk to hedge when competitors
do not. Firms in the industry may have the
ability to pass on cost increases to customers,
i.e. complete pass-thru of cost changes. The
variables p (sales price) and c (cost per unit)
may be highly positively correlated; a natural
hedge exists.
E.g. jewelry manufacturer goes long gold futures.
What if gold price subsequently drops?!

9. Examples of natural hedges
(complete pass-through of cost)
 When p and c are highly positively
correlated. Thus, hedging with
futures/forward is not warranted.
 Gasoline refiner/retailer: retail price vs.
crude oil price.
 Meat packer (slaughters, processes,
distributes meat to retailers): wholesale
price vs. live cattle price.

10. 3.10
Convergence of Futures to Spot
(Hedge initiated at time t1 and closed out at time t2)
Time
Spot
Price
Futures
Price
t1 t2

11. 3.11
Basis Risk
 Basis is the difference between
spot & futures: B = S - F
 Basis risk arises because of
the uncertainty about the basis
when the hedge is closed out
 Hedging involves the
substitution of basis risk for
spot price risk.

12. 3.12
Long Hedge
 Suppose that
F1 : Initial Futures Price
F2 : Final Futures Price
S2 : Final Asset Price
 Hedge via a long futures contract the
future purchase of an asset, risk of S2
 Cost of Asset=S2 +(F1–F2) = F1 + Basis2

13. 3.13
Short Hedge
 Suppose that
F1 : Initial Futures Price
F2 : Final Futures Price
S2 : Final Asset Price
 Hedge via a short futures the future sale of
an asset, risk of S2
 Price Realized=S2+ (F1 – F2) = F1 + Basis2

14. 3.14
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, aka Cross-
hedging. There are then 2 components to
the basis.

15. 3.15
Optimal Hedge Ratio
Proportion of the exposure (a percent) that should
optimally be hedged is
where
σS is the standard deviation of ∆S, the change in the
spot price during the hedging period,
σF is the standard deviation of ∆F, the change in the
futures price during the hedging period
ρ is the coefficient of correlation between ∆S and ∆F
Measure of hedging effectiveness is square of ρ .
F
S
h
σ
σ
ρ=

16. Analogy: Simple Regression &
Optimal Hedge Ratio
A Variation to be
explained
Risk to be
hedged
B Explained
variation
Hedged risk
C Unexplained
variation
Unhedged risk
R^2 = B/A % Explained % Hedged

17. Perfect hedge iff no basis risk
 Perfect hedge: R^2 =1. Implies that
correlation between S and F = 1.
 R^2 is measure of hedging effectiveness.
What proportion of variance in spot price
is removed by hedging?
 No basis risk: variance of (S-F) = 0.
 Occurs when the correlation between S
and F = 1.

18. Derive number of contracts, N, from h
 N = h (QA / QF )
 QA is size of exposure
 QF is size of futures contract
 Example 3.5 p. 60 : Airline wants to hedge
purchase 2 months from now of 2M gallons of jet
fuel via long position in oil futures contract.
Formula, h = .928 (.0263 / .0313 ) = .78, i.e.
hedge 78% of 2M gallons or 1.56M gallons. How
many contracts is that?
 Hedging effectiveness=.928^2 or 86%

19. How many contracts, N, is h=78%?
 Oil futures contract involves 42,000
gallons i.e., QF= .042M
 N = .78 (2M / .042M) = 37.14 or 37
contracts
 Take long position in 37 oil contracts.
 Will remove 86% of uncertainty via this
hedge.

20. Tailing the Futures Hedge
 Adjustment for the fact that the futures
hedge generates immediate cash flows
(marking to market) whereas the risk
being hedged pertain to some time in the
future.
 NTH= h (VA/VF) = h (QA S/QF F) = N (S/F)
 Back to Example 3.5 p. 60 with S =
1.94/gallon F = 1.99/gallon
 NTH= 37.14 (1.94/1.99) = 36.22 or 36
 Effect of tailing the hedge adjustment is to
reduce slightly the number of contracts

21. Should you tail the hedge?
 Hedge now receipt/payment in the future
with a futures contract? Yes!
 Why? Futures hedge cash flows start
occurring now & continue daily;
receipt/payment occurs at future date
 Hedge now receipt/payment a month from
now with 1-month forward contract? No!
 Hedge now receipt/payment a year from
now with 1-year forward contract? No!

22. 3.22
Rolling The Hedge Forward: Hedge a
long-term exposure with a time
sequence of short-term futures hedges
 We can use a series of futures
contracts to increase the life of a
hedge
 Each time we switch from 1 futures
contract to another we incur a type of
basis risk
 Metallgesellschaft debacle: p.69

23. 3.23
Hedging Using Index Futures
To hedge the risk (reduce to zero the
β ) of an investment portfolio the
number of contracts that should be
shorted is
where P is the value of the portfolio,
β is its beta, and F is the current
value of one futures (=futures price
times contract size)
F
P
β

24. 3.24
Reasons for Hedging an Equity
Portfolio
 Desire to be out of the market for a short
period of time. (Hedging may be cheaper
than selling the portfolio and buying it
back.)
 Desire to hedge systematic risk
(Appropriate when you feel that you have
picked stocks that will outperform the
market.)

25. 3.25
Example
Futures price of S&P 500 is 1,000
Size of portfolio is $5 million
Beta of portfolio is 1.5
One contract is on $250 times the index
What position in futures contracts on the
S&P 500 is necessary to hedge the
portfolio? N=1.5(5M/.25M)=30. If short 30
contracts, beta is reduced to zero.

26. More general stock index futures formula
 N*= number of contracts that must be held
long to change beta of portfolio to beta*
 N*= (beta* – beta) (P/F)
 Current portfolio exhibits beta
 If bullish, may want to raise beta
 P=market value of the managed portfolio
 F=value of the asset that underlies futures

27. 3.27
Changing Beta of Managed Portfolio
 What position is necessary to reduce the beta of
the portfolio to 0.75? N=(.75-1.5)(5M/.25M)=-15;
short 15 S&P 500 contracts. What if using Mini
S&P 500 contracts, F=0.05M? Short 75 Mini
S&P 500 contracts.
 What position is necessary to increase the beta
of the portfolio to 2.0? N=(2-1.5) (5M/.25M)=10;
take a long position in 10 S&P500 contracts.