Energy & Finance – Summary – Chapter 3, 5, 10, 13, 33
Based on Options, Futures and Other Derivatives by John Hull, 8th edition.
Chapter 3 Hedging Strategies Using Futures
Perfect hedge = completely eliminates the risk, they are rare.
3.1 Basic principles
Future: If the price of the commodity goes down, the gain on the futures position offsets the loss on
the rest of the company business and vice versa.
- Short hedge = short position in futures contracts. Offsetting the risk (selling asset)
o Appropriate when the hedge already owns an asset and expects to sell it at some
time in the future. Or is not owned right, but will be owned in the future
o Example:
Spot price $80, expected future price $79. Future contract.
Price is $75. So gain is of future contract is $79-75=$4. Total gain selling +
future contract is $75 + $4 = $79.
Price is $85. Loss of future contract is $85-79= $6. Total gain selling + future
contract is $85-6= $79.
Both cases close to expected future price. Offset part of the price risk.
- Long hedge = Long position in future contracts. Offsetting the risk (buying asset)
o Appropriate when a company knows it will have to purchase a certain asset in future
an wants to lock and wants to lock in a price now (close to expected future price)
3.2 Arguments for and against hedging
Pro:
- Companies have no particular skills or expertise in predicting variables. Better focus on main
activities.
- Avoid unpleasant surprises (sharp decreases or rise in prices)
Con’s
- Fluctuation in profits when operating in a market with high competition.
- Possible to have negative result of hedging. Everyone need to fully understand what is done
(treasure).
3.3 Basic risk
- The asset whose price is to be hedged may not be exactly the same as the asset underlying
the futures contract
- The hedger may be uncertain as the exact date when the asset will be bought or sold
- The hedge may require the future contract to be closed out before its delivery month
Basis = Spot price of asset to be hedge – future prices of contract used.
o =0 when the asset to be hedge and asset underlying the futures contract are the same.
o Prior to expiration, it can be positive or negative
Strengthen of the basis = increase in the basis Company position improves when short hedge,
worsens when long hedge.
Weakening of the basis = decrease in the basis Company position worsens when short hedge
,improves when long hedge.
* Financial asset Basis = futures price - Spot price
, Key factor affecting basic risk is the choice of the futures contracts
1. The choice of the asset underlying the future contract
a. Careful analysis, if assets are not the same
2. The choice of the delivery month
Basis risk increases as the time differences between the hedge expiration and the delivery month
increases. (choose a delivery month that is close as possible, but later, the expiration of the month).
Assumes sufficient liquidity in all contract’s to meet the hedger’s requirement. Liquidity is highest in
in short term futures contract.
- Final spot price – gain of future contract = The effective price paid
- Initial futures price + the final basis = The effective price paid
3.4 Cross hedging
Cross hedging = Assets of underlying futures are different than the asses whose price is being
hedged. Need to have hedge ratio different from 1.
Minimum Variance Hedge Ratio =
ρ = correlation between the two standard deviations of spot price and future price.
= slope of best-fit line from a linear regression of ΔS against ΔF.
o If ρ = 1 and σs = σf Hedge ratio is 1
Hedge effectives = the proportion of the variance that is eliminated by hedging = R² from regression
of ΔS against ΔF and equals ρ²
Optimal Number of contracts:
QA = size of position being hedged (what the firm wants to purchase)
QF = size of on futures contract (what the futures contract covers)
3.5 Stock index futures
Stock index = changes in value of a hypothetical portfolio of stocks. When the price of one particular
stock in the portfolio rises, there is automatically given more weight to this stock.
Can be used to hedge systematic risk in an equity portfolio.
Future contracts on stock indices are settled by cash (not by delivery).
VA = current value of portfolio. VF = current value of futures contract (price x size)
when β = 1 the portfolio mirrors the index. When β = 2 the excess return on the portfolio
tends to be twice as great as the excess return on the index. Assumes that maturity of the futures is
close to the maturity of the hedge. Stock indexes are used to change the beta of a portfolio without
changing the stocks that make up the portfolio.
Expected return on asset = RF +β(Rm – RF)
3.6 Stack and Roll
When the expiration date of the hedge is later than the delivery dates close out and enter in a
hedge position with later delivery dates. Results in creation of a long-dated futures contract by
trading series of short-dated contracts. Consider always the potential liquidity problems when
considering a hedging .
Based on Options, Futures and Other Derivatives by John Hull, 8th edition.
Chapter 3 Hedging Strategies Using Futures
Perfect hedge = completely eliminates the risk, they are rare.
3.1 Basic principles
Future: If the price of the commodity goes down, the gain on the futures position offsets the loss on
the rest of the company business and vice versa.
- Short hedge = short position in futures contracts. Offsetting the risk (selling asset)
o Appropriate when the hedge already owns an asset and expects to sell it at some
time in the future. Or is not owned right, but will be owned in the future
o Example:
Spot price $80, expected future price $79. Future contract.
Price is $75. So gain is of future contract is $79-75=$4. Total gain selling +
future contract is $75 + $4 = $79.
Price is $85. Loss of future contract is $85-79= $6. Total gain selling + future
contract is $85-6= $79.
Both cases close to expected future price. Offset part of the price risk.
- Long hedge = Long position in future contracts. Offsetting the risk (buying asset)
o Appropriate when a company knows it will have to purchase a certain asset in future
an wants to lock and wants to lock in a price now (close to expected future price)
3.2 Arguments for and against hedging
Pro:
- Companies have no particular skills or expertise in predicting variables. Better focus on main
activities.
- Avoid unpleasant surprises (sharp decreases or rise in prices)
Con’s
- Fluctuation in profits when operating in a market with high competition.
- Possible to have negative result of hedging. Everyone need to fully understand what is done
(treasure).
3.3 Basic risk
- The asset whose price is to be hedged may not be exactly the same as the asset underlying
the futures contract
- The hedger may be uncertain as the exact date when the asset will be bought or sold
- The hedge may require the future contract to be closed out before its delivery month
Basis = Spot price of asset to be hedge – future prices of contract used.
o =0 when the asset to be hedge and asset underlying the futures contract are the same.
o Prior to expiration, it can be positive or negative
Strengthen of the basis = increase in the basis Company position improves when short hedge,
worsens when long hedge.
Weakening of the basis = decrease in the basis Company position worsens when short hedge
,improves when long hedge.
* Financial asset Basis = futures price - Spot price
, Key factor affecting basic risk is the choice of the futures contracts
1. The choice of the asset underlying the future contract
a. Careful analysis, if assets are not the same
2. The choice of the delivery month
Basis risk increases as the time differences between the hedge expiration and the delivery month
increases. (choose a delivery month that is close as possible, but later, the expiration of the month).
Assumes sufficient liquidity in all contract’s to meet the hedger’s requirement. Liquidity is highest in
in short term futures contract.
- Final spot price – gain of future contract = The effective price paid
- Initial futures price + the final basis = The effective price paid
3.4 Cross hedging
Cross hedging = Assets of underlying futures are different than the asses whose price is being
hedged. Need to have hedge ratio different from 1.
Minimum Variance Hedge Ratio =
ρ = correlation between the two standard deviations of spot price and future price.
= slope of best-fit line from a linear regression of ΔS against ΔF.
o If ρ = 1 and σs = σf Hedge ratio is 1
Hedge effectives = the proportion of the variance that is eliminated by hedging = R² from regression
of ΔS against ΔF and equals ρ²
Optimal Number of contracts:
QA = size of position being hedged (what the firm wants to purchase)
QF = size of on futures contract (what the futures contract covers)
3.5 Stock index futures
Stock index = changes in value of a hypothetical portfolio of stocks. When the price of one particular
stock in the portfolio rises, there is automatically given more weight to this stock.
Can be used to hedge systematic risk in an equity portfolio.
Future contracts on stock indices are settled by cash (not by delivery).
VA = current value of portfolio. VF = current value of futures contract (price x size)
when β = 1 the portfolio mirrors the index. When β = 2 the excess return on the portfolio
tends to be twice as great as the excess return on the index. Assumes that maturity of the futures is
close to the maturity of the hedge. Stock indexes are used to change the beta of a portfolio without
changing the stocks that make up the portfolio.
Expected return on asset = RF +β(Rm – RF)
3.6 Stack and Roll
When the expiration date of the hedge is later than the delivery dates close out and enter in a
hedge position with later delivery dates. Results in creation of a long-dated futures contract by
trading series of short-dated contracts. Consider always the potential liquidity problems when
considering a hedging .
