Hedging
Hedging does not necessarily improve the
financial outcome; What it does however is,
that it makes the outcome more certain.
Hedgers could be government institutions,
private corporations like financial
institutions, trading companies and even
other participants in the value chain, for
instance farmers, millers, processors etc.,
who are influenced by the commodity prices.
The current interest rate is 8% & the interest
rate under a future contract for borrowing 3
months later is 9%.
Downside Risk:
• Definition: When the market conditions
move against the company (e.g., interest
rates increase), the company benefits from
hedging because it avoids the negative
impact of the unfavorable change.
Upside Risk:
• Definition: When the market conditions
move in favor of the company (e.g.,
interest rates decrease), hedging can
become costly because the company
misses out on the benefits of the
favorable change.
Basic Principles of Hedging
There are basically two kinds of hedges that can be
taken.
A company that wants to sell an asset at a particular
time in the future can hedge by taking short futures
position. This is called a short hedge.
Similarly, a company that knows that it is due to buy
an asset in the future can hedge by taking long
futures position. This is known as long hedge.
Short Hedge
A short hedge is a hedge that requires a
short position in futures contracts.
A short hedge is appropriate when the
hedger already owns the asset, or is likely
to own the asset and expects to sell it at
some time in the future.
Short Hedge
On 15th of January a refined soy oil producer has
negotiated a contract to sell 10,000 Kgs of soya oil. It has
been agreed that the price that will apply in the contract is
the market price on the 15th April.
Suppose the spot price for soya oil on January 15 is Rs.450
per 10 Kgs and the April soya oil futures price on the
NCDEX is Rs.465 per 10 Kgs.
The producer can hedge his exposure by selling 10,000
Kgs worth of April futures contracts (1 unit).
Short Hedge
Case 1: On 15th April, the spot price is Rs. 455 per 10 Kgs.
The company realizes Rs.4,55,000 under its sales contract.
On 15th April, the company closes its short futures position
at Rs. 455, making a gain of Rs.465 - Rs.455 = Rs.10 per 10
Kgs, or Rs. 10,000 on its short futures position.
The total amount realized from both the futures
position and the sales contract is therefore about Rs. 465
per 10 Kgs, Rs.4,65,000 in total
Short Hedge
Case 2: On April 15th the spot price is Rs.475 per 10 Kgs.
The company realizes Rs.4,75,000 under its sales
contract.
The company closes its short futures position at a spot of Rs.
475, making a loss of Rs.475 - Rs.465 = Rs.10 per 10 Kgs, or Rs.
10,000 on its short futures position.
The total amount realized from both the futures position and
the sales contract is therefore about Rs. 465 per 10 Kgs, Rs.
4,65,000 in total
Payoff for a short hedge
Long Hedge
Suppose that it is now January 15. A firm
involved in industrial fabrication knows
that it will
require 300 kgs of silver on April 15.
The spot price of silver is Rs.26800 per kg
and the April silver futures price is Rs.
27300 per kg.
A unit of trading is 300 kgs.
Long Hedge
Case 1: On April 15, the spot price is Rs. 27800 per kg.
The fabricator pays Rs. 83,40,000 to buy the silver
from the spot market.
The company closes its long futures position at Rs. 27800,
making a gain of Rs.27800 - Rs.27300 = Rs.500
per kg, or Rs. 1,50,000 on its long futures position.
The effective cost of silver purchased works out to be
about Rs. 27300 per Kg, or Rs.81,90,000 in total.
Long Hedge
Case 2: The spot price is Rs. 26900 per Kg.
The fabricator pays Rs.80,70,000 to buy the silver
from the spot market.
The company closes its long futures position at Rs. 26900 spot,
making a loss of Rs.27300 - Rs.26900 = Rs.400 per kg, or Rs.1,20,000
on its long futures position.
The effective cost of silver purchased works
out to be about Rs. 27300 per Kg, or Rs.81,90,000 in total
Payoff for buyer of a long hedge
Basis Risk
In the previous example of aluminium price b2 was 0, there is no risk, it’s a perfect hedge
If the contract is exited on expiry, b2 will be 0 only
Imperfect hedging & basis risk
Consider the case of SpiceJet. One of the major expenses for
SpiceJet is aviation fuel. The price of aviation fuel is highly
volatile and SpiceJet would like to hedge the price risk of
aviation fuel.
However, futures contracts are not available for aviation fuel.
SpiceJet can still hedge its exposure to some extent by entering
into futures contracts written on related assets.
A related asset is one whose price changes are highly correlated
with the price changes of the asset which is exposed to. For
example, the change in the price of aviation fuel is likely to be
highly correlated with the change in the price of crude oil, on
which futures are available.
Thus, SpiceJet will use crude oil futures to hedge against the risk
of price changes in aviation fuel.
However, it is to be noted that it will not be a perfect hedge
since the final basis will be the difference between the spot price
of aviation fuel and the price of crude oil futures, and there is no
need for these two prices to be the same; hence, the final basis
will not be zero, causing the hedge to be less than perfect.
Hedge Ratio
Hedge Ratio
Hedging effectiveness= h^2 * σ^2F/ σ^2S
Caselet
i. A long hedge involves purchasing futures contracts to protect against the risk of rising prices in the future. In
this case, SpiceJet is concerned that the price of crude oil (and consequently, aviation fuel) might increase.
By entering into a long hedge, they lock in the current price of crude oil through futures contracts. This ensures
that even if the price of crude oil increases in the future, they will pay the price agreed upon in the futures
contract rather than the higher market price.
ii. SpiceJet’s long hedge aims to mitigate the risk of rising fuel prices, which is a significant cost component for the
airline. By locking in the price of crude oil through futures contracts, SpiceJet can stabilize its fuel costs, protect its
profit margins, and plan its finances more effectively. This reduces the uncertainty associated with fuel costs and
shields the company from potential adverse movements in crude oil prices .
iii. Basis Risk: The futures contract for crude oil may not perfectly match the price movement of aviation
fuel. The difference between the spot price of aviation fuel and the futures price of crude oil could lead
to some residual risk.
Hedge Ineffectiveness: If the timing or volume of the hedge does not perfectly align with SpiceJet's
actual fuel consumption, there could be some exposure to price fluctuations.
Operational Risk: External factors, such as changes in regulations or unexpected disruptions in oil supply,
may still affect aviation fuel prices in ways that the hedge cannot fully cover.
Caselet
Thus, the optimal hedge ratio is 1.23. This hedge ratio suggests
that SpiceJet should hedge 123% of its exposure. In practical
terms, for every 1 unit of aviation fuel exposure, SpiceJet should
hedge 1.23 units using crude oil futures contracts. This will help
minimize the price risk effectively.
The hedging effectiveness can be calculated using the square of the correlation
coefficient (ρ2): Hedging Effectiveness=ρ2= the hedging effectiveness is 92.16%. This means
that the hedge using crude oil futures contracts will reduce the variability in the cost of
aviation fuel by 92.16%. In other words, the hedge will effectively mitigate the price risk.
Number of Contracts= Exposure × h*/ Contract Size
Number of Contracts=2,000,000×1.23/100 = 24,600
So, SpiceJet should enter into 24,600 crude oil futures contracts to hedge its exposure
optimally.
• A company will require 11,000 bales of cotton in
three months.
• Suppose the SD of the change in the price per
quintal of cotton over a three-month period is
calculated as 0.032.
• The SD of the change in the cotton futures price
over a three-month period is 0.040 and
• the coefficient of correlation between the change in
price of cotton and the change in the cotton futures
price is 0.8.
• The unit of trading and the delivery unit for cotton
on the NCDEX is 55 bales.
• What is the optimal hedge ratio? How many cotton
futures contracts should it buy?
Optimal hedge ratio = 0.8 x 0.032 / 0.040 = 0.64
If the hedge ratio were 1, that is if the cotton spot
and futures were perfectly correlated, the hedger
would have to buy
11,000 / 55 = 200 units
If the hedge ratio works out to be 0.64, the
company will hence require to take a long position in
0.64 x 200 units = 128 units of cotton futures to get
an
effective hedge
Hedge Ratio
HR= (Value of hedged portfolio / Price of
future contract) * Beta
HR = % change in weighted avg. portfolio
price/ % change in future index
Cross Hedging in an Airline Company
Hedging by closest alternative asset
available.
An airline might be forced to cross hedge its
exposure to jet fuel by buying crude oil
futures instead
Crude oil and jet fuel are highly correlated
and will therefore likely function adequately
as a hedge
Risk remains that if the price of these
commodities diverges significantly
Rolling the Hedge Forward
Rolling the Hedge Forward
Time horizon notthe
Rolling matching
Hedgethe hedger’s requirements.
Forward
If actual time horizon is shorter, no problem.
If the actual time horizon is longer, hedger has to go for a
Futures contract, close it out just before expiry and
simultaneously go in for the next Futures.
This procedure to be repeated till reaching desired tenure.
Transaction costs likely to be higher.
Basis risk.
Basis Risk
• In reality, hedging can only minimize the risk but cannot
fully eliminate it. The reasons are as follows:
• The asset whose price is to be hedged may not be exactly
the same as the asset underlying the futures contract.
For example, in India we have a large number of varieties of
cotton being cultivated. It is impractical for an Exchange to
have futures contracts with all these varieties of cotton as an
underlying.
Therefore the hedge would not be perfect.
The hedger may be uncertain as to the
exact date when the asset will be bought
or sold. The future contract expiry date
and delivery date in spot market might
not same. This could result in an
imperfect hedge.
