HEDGING
Offsetting the future risk (Defensive ).
How hedging works
Core Principle: Taking an equal and opposite position in futures market against
position being held in the cash market
e.g. A enters in an agreement on May 20 to supply B 10 MTs of maize on August
20 at a price of 2160 Rs./q (price on may 20). A plans to buy maize for delivery on
august 20. On august 20, spot price rises to 2507 Rs./ q
On the other hand he buys August maize futures @2186 Rs./q. In august, the
futures price rises to 2533 Rs./q
Date Spot Market Futures Market
May 20 Price= Rs. 2160 /q Buy August futures @
2185 Rs./q
August 20 Buy physical stock @ 2507 Sell futures @ 2533 Rs./q
Rs./q
Impact Loss= 2507-2160=347 Gain= 2533-2185= 347
Rs./q Rs/q
Types of hedge
Short Hedge: Adopted when you are holding a commodity and want to
achieve protection against falling prices.
Consider a farmer entering into a contract to sell 1000 q of maize on 20th of may.
The price applying to that contract is market price on September 20th.
Spot price on may 20 = 1140Rs/q.
September future price= 1160 Rs./q.
Trading unit is 10 MT
Long Hedge: When you want to buy a commodity after some time and
want to protect yourself against rising prices
On oct. 20 a jeweller realizes that he requires 10 kg of gold on Jan 20th.
Spot price 29890 Rs/10g.
Future price is 29910 Rs/10g.
Trading unit is 1 kg
Benefits of Hedging
Stretching the Market Period
Protection of Inventory values
Forward Pricing
Limitations
Minimization of Risk
Perfect Hedge: one that completely eliminates the risk.
Basis Risk
Asset to be hedged is different from asset underlying future
contract.
Uncertainty about buying and selling date of asset
Closing out of hedge before delivery date
Basis Risk
Basis= (Spot price of the asset to be hedged)-(futures price of
contracts used)
Basis=0
If Asset to be hedged and asset underlying future contract are same
At expiration of contract
Increase in basis= Strengthening of basis- favourable for short
hedgers
Decrease in basis= Weakening of basis- favourable for long hedgers
S1= Spot price at time t1
S2= Spot Price at time t2
F1= Future Price at time t1
F2= Future Price at time t2
Basis at t1 = b1= S1- F1
Basis at t2= b2 = S2- F2
For short position
Price realized=S2+ F1-F2=F1+b2
For long position
Price paid=S2+ F1-F2=F1+b2
Example: on Jan 1, spot price = Rs. 2.5/kg, futures price= Rs 2.00/kg
On march 11, spot price= Rs. 2.2/kg, futures price = Rs. 1.9/kg
What affects Basis Risk?-Choice of Contract:
Choice of underlying asset
If asset being hedged and asset underlying future contract is exactly same, basis risk
is low
If they are different, careful analysis needed (the concept of Hedge Ratio)
Choice of delivery month
If hedge expiration and delivery month are same basis risk is low.
But generally
Contract with later delivery month is chosen
To ensure liquidity during delivery period
Close out before the delivery period
As the gap between hedge expiration and delivery month increases, basis risk
increases
Hence, Nearest delivery month is chosen.
It is March 1. A US company expects to receive 50 million Japanese yen at the
end of July. Yen futures contracts on the CME Group have delivery months of
March, June, September, and December. One contract is for the delivery of 12.5
million yen. When the yen are received at the end of July, the company closes
out its position. We suppose that the futures price on March 1 in cents per yen is
0.9800 and that the spot and futures prices when the contract is closed out are
0.9200 and 0.9250, respectively.
It is June 8 and a company knows that it will need to purchase 20,000 barrels of
crude oil at some time in October or November. Oil futures contracts are
currently traded for delivery every month on the NYMEX division of the CME
Group and the contract size is 1,000 barrels. The company therefore decides to
use the December contract for hedging. The futures price on June 8 is $88.00 per
barrel. The company finds that it is ready to purchase the crude oil on November
10. It therefore closes out its futures contract on that date. The spot price and
futures price on November 10 are $90.00 per barrel and $89.10 per barrel.
Hedge Ratio
Often, Asset transacted in spot market is different from the asset underlying the
futures contract. – Cross Hedging
Hedge ratio= Ratio of quantity of position taken in future market to exposure in
physical market
𝑄𝐹
ℎ=
𝑄𝑆
where,
QF= Quantity of position taken in futures market
QS= Quantity transacted in spot market
Relationship between hedge ratio and
variance
Minimum Variance Hedge
A company wants to buy
𝜎𝑆 22000 bales of cotton after
ℎ=𝜌 three months. One future
𝜎𝐹
contract = 100 bales
Where , Case 1: standard deviation of
h= hedge ratio changes in spot as well as
future price is same. and both
𝜎𝑠 = Standard deviation of ΔS
the spot and futures markets
𝜎𝐹 = Standard deviation of ΔF are perfectly correlated.
𝜌 = Correlation coefficient between ΔS and Case 2: standard deviation of
ΔF spot price change is .030 and
that of future price is .040. and
correlation coefficient between
future and spot price is .80
Hedge effectiveness
proportion of the variance that is eliminated by hedging.
𝜎𝐹2
ℎ𝑒 = ℎ∗ 2
𝜎𝑠2
Optimal number of contracts
∗
∗
ℎ 𝑄𝑠 QF = Size of one future contract
𝑁 = QS = Position to be hedged
𝑄𝐹
Example:
Change in Heating oil Change in jet fuel An airline expects to purchase 2 million gallons of
Month futures price per gallon price per gallon jet fuel in 1 month and decides to use heating oil
i ΔF ΔS futures for hedging. For 15 successive months, it
1 0.021 0.029
collects data on the change, S, in the jet fuel price
2 0.035 0.02
per gallon and the corresponding change, F, in the
3 -0.046 -0.044
4 0.001 0.008
futures price for the contract on heating oil that
5 0.044 0.026 would be used for hedging price changes during
6 -0.029 -0.019 the month.
7 -0.026 -0.01 It wants to know:
8 -0.029 -0.007
9 0.048 0.043 a. Minimum variance hedge ratio
10 -0.006 0.011 b. Optimal number of contracts it shall purchase
11 -0.036 -0.036
12 -0.011 -0.018
13 0.019 0.009
14 -0.027 -0.032
15 0.029 0.023
Tailing the Hedge
In case of futures- daily settlement- thus one day hedges
analysts sometimes calculate the correlation between percentage one-day changes in the futures and spot
prices.
One day Hedge Ratio =
Optimal number of contracts This is called tailing the hedge .
Also written as
where VA is the dollar value of the position being hedged (¼ SQA), VF is the dollar value of one futures
contract (¼ FQF) and h^ is defined similarly to h* as
