1Odds and Ends

1
1Odds and Ends

• This sub-section deals with three concepts.
• The temporal evolution of basis Definitions and
  theories.
• Hedge ratios, cross hedging and the concept of a
  minimum variance hedge ratio.
• Rollover hedging when contracts of sufficiently
  long maturity are either non-existent or do not
  function well.

2
2Basis Issues

• Basis is given by BT,t Pt - FT,t , and basis
  at maturity is BT,T PT - FT,T .
• Ignoring transportation costs, we should have PT
  FT,T . Why? The reasoning relies on the
  notion of arbitrage.
• Suppose that PT lt FT,T . Then an arbitrageur
  should
• ?short futures at time T (or just before T), then
• ?buy the asset at the delivery point, then
• ?deliver on the contract, then
• ?put the difference, FT,T - PT , into the bank.

3
3Basis and Arbitrage

• Alternatively, suppose that PT gt FT,T . Then an
  arbitrageur should reverse the above algorithm,
  i.e.,
• ? go long futures at time T (or just before T),
  then
• ?take delivery of the asset at the delivery
  point, then
• ?sell the delivered assets on the local spot
  market, then
• ?put the difference, PT gt FT,T , into the bank.
• Conclusion Supply and demand (market) forces
  should cause BT,T to converge towards 0 at the
  delivery point or when transportation costs are
  low or when there are not significant quality
  differences between a load and the contract
  specifications.

4
4Basis before Maturity, Contango

• Concerning BT,t, there are two situations
  Contango and Normal Backwardation.
• Defn Contango is where BT,t lt 0, i.e., Pt lt FT,t
  .

FT,t
Pt
FT,t
Pt
t
T
5
5Basis before Maturity, Normal Backwardation

• Defn Normal Backwardation is where BT,t gt 0,
  i.e., Pt gt FT,t .

Pt
Pt
FT,t
FT,t
FT,t
t
T
6
6Other uses of Contango and Normal Backwardation
Terms

• Sometimes these terms are used when considering
  the time t expected value of PT, i.e., EtPT.
• In this context,
• contango means EtPT lt FT,t , and
• normal backwardation means EtPT gt FT,t .
• But these versions of the concept are difficult
  to apply in practice because everyone has a
  different opinion about the value of EtPT.

7
7Example

• In November, May wheat futures might be in
  contango because the post-harvest spot price is
  low but people will likely expect the May spot
  price to be higher. They will bid the May
  maturity futures price up accordingly.
• In May, November wheat futures might display
  normal backwardation because the pre-harvest spot
  price is high but people will likely expect the
  November spot price to be lower. They will bid
  the November maturity futures price down
  accordingly.

8
8Relation between Futures Price and Expected
Future Spot Price

• What might the relationship between EtPT and
  FT,t be? Keynes and also Hicks suggested that
  one should look to where the demand for hedging
  services comes from.
• Often the demand is for net short positions.
  This is quite likely for agricultural
  commodities. This producer-level demand for
  hedging services must be met by speculator supply
  of long positions.
• As with any other good/service, speculator
  services come at a price. To the extent that
  being net long increases the systematic risk (as
  distinct from idiosyncratic risk) of the
  speculator, the speculator will demand a risk
  premium.

9
9Hicks and Keynes

• Thus, we are back into the world of CAPM.
  Assuming zero basis at maturity, the speculator
  will sell the long position at price FT,T PT .
  
• Therefore, the speculator will expect to profit
  by Et PT -FT,t per unit that
  she is net long. The requirement of a positive
  premium for the risk assumed requires that Et
  PT gt FT,t .
• In contrast, suppose that hedgers tended to be
  net long, e.g., ADM and other processors tended
  to be the principal hedgers. Then speculators
  will likely demand a positive risk premium for
  being net short. And so Et PT lt FT,t .
• (To be continued).

10
10Minimum Variance Hedge Ratio

• See the Hedge Ratio Handout.

V(?)
Minimum Variance Hedge
Minimum Variance Hedge Ratio
h
h
11
11Rollover Hedging

• Sometimes one may wish to hedge a risky position
  with maturity longer than the most distant liquid
  traded futures contract.
• Examples A company that uses large volumes of
  petroleum may want to lock in to prices up to
  five years out. As part of an international
  lending agreement, a bank may want to lock in on
  quarterly currency exchange rates for up to ten
  years out. A lumber company may wish to hedge on
  lumber forward contracts it has signed to be
  delivered in 30 months.

12
12Rolling Over

• Suppose a firm wishing to hedge X contacts short
  for delivering in 36 months. The furthest
  maturity contract may be 12 months out.
• Let Fi,i-12 be the maturity date i futures price
  at time i-12. The firm could
• ?short X contracts at time 0 with maturity month
  12
• ?close out at month 12 and simultaneously go
  short X contracts with with maturity month 24
• ?close out at month 24 and simultaneously go
  short X contracts with with maturity month 36
• ? close out at month 36.

13
13Rolling Over Diagram

• a

Month 0
Month 12
Month 24
Month 36
F36,24
F12,0
F24,12
F12,12
F24,24
F36,36
14
14Rolling Over Effectiveness

• For the strategy to be effective over the
  duration, F24,12 must covary strongly with
  F12,12, and F36,24 with F24,24 and P36 with
  F36,36 .
• Further, over this very long period margin calls
  may be very expensive. Eventually, such losses
  will likely be made up by gains in the actuals
  position (for a hedger). But the wait may be too
  long.
• Circa 1991 Metallgesellschaft, a German energy
  company, shorted large numbers of forward
  contracts (up to 10 years) to customers. It
  hedged by rollovers. Oil prices fell, and it had
  to pay margin calls. It baulked at financing
  through to the delivery dates. It closed out
  hedge positions and agreed with customers to
  abandon the forwards.