Subject: Financial Derivatives
Course Code: FM-407
Author: Dr. Sanjay Tiwari
Lesson No.: 3
Vetter: Prof. M.S. Turan
USE OF FUTURES FOR HEDGING
Concept and Types of Hedging
Basis Risk and Price Risk
Operational hedging: According to this approach, future markets are
supposed to be more liquid and investors (hedger) use futures as a substitute
for cash market.
Selection or discretionary hedging: This hedging is done only on
selected occasions or when
Supposing an oil producer made a contract on 10 Oct, 2006 to sell 1 million
barrel crude oil on a market price as on 10 Jan 2007. The oil producer
supposing that spot price on 10 Oct, 2006 is $ 50 per barrel and Jan crude
future price on NYMEX is $ 48.50
Hedging strategies using futures
When is a short futures position appropriate? When is a long futures
position appropriate? Which futures contract should be used? What is the
optimal size of the futures position for reducing risk? At this stage, we re
Apte, Prakash, G., International Financial Management, 3rd
edition, Tata McGraw Hill Publishing Company Ltd., New Delhi,
Bhalla, V.K., International Financial Management, 2nd edition,
Anmol Publishing House, New Del
3.6.1 Monitoring of hedge
To monitor the hedge on a continuous basis the following information
should be looked for:
Cash/spot position: The hedger should have an idea of the current
position in cash/spot and the relevant changes in the same. The gains/lo
uncertainty elements. To avoid the risk arising out of price fluctuations in
future, various strategies are devised keeping in view the timing and pricing
dimensions of the instruments. Suppose a farmer anticipates fall in prices of
his crop three months
How do you determine futures prices? Explain by giving suitable
Describe the relationship between the expected futures spot
price and futures prices with suitable examples.
Explain various theories of determining the prices of futures.
S2 and the loss on the hedge is F1 F2. The effective price is paid with
hedging will be:
S2 + F1 F2 = F1 + b2
In both the cases, the value is same.
Choice of asset underlying the futures contract and the choice of the
delivery month affect the basis risk.
Consider that a hedger takes a short futures position at time k1 and
knows that the asset will be sold at time t2. The price for the asset will be F1
The effective price will be:
S2 + (F1 F2) = F2 + b1
Basic risk = Spot price of asset to be hedged Fut
52.00 1.20 = 50.80
This can also be calculated as the initial futures price plus the final
50.00 + 0.80 = 50.80
The total price received is 50.80 30000 = $ 1,52,4000
Proof of the minimum variance hedge ratio formula
Hedging is basically a tool
Change in risk exposure: Frequent changes in risk exposure invite
changes in cash position which thereby initiate changes in volume of futures
Rolling the hedge: Due to changes in market development,
sometimes it becomes necessary to change hedg
The effective price obtained in cents per yen is the final spot price plus
the gain on the futures.
0.7500 + 0.005 = 0.7550.
This can also be written as the initial futures price plus the final basis
0.8000 0.0050 = 0.7950
The total amount received by the
TABLE 4.2: CALCULATION OF FORWARD RATES
Zero rate for an n-year Forward
investment (% p.a.)
year (% p.a.)
Thus a 10% p.a. rate for one year means that in return for an
in ABCL Ltd. Share price for every Rs. 20 change in SRKL Ltd.
Determine the amount of contract required to minimise risk.
3.10 References/suggested readings
Apte, Prakash, G., International Financial Management, 3rd
edition, Tata McGraw Hill Publishing Co
brokerage, fees, translation and management costs etc. For this purpose expost measure of effectiveness should be calculated with the help of deviation
or significant difference between the anticipated and ex-post hedged strategy.
Hedging is a
which the short (seller) intentions to deliver bonds. The first day is called
intention day or position day. On this day the short can notify the exchange
for his intention to deliver until 8.00 p.m. Central time on the position day to
declare an intentio
aspect too, copper may be traded in different multiples than required
actually. These are examples of cross hedging.
Basis and price risk
The difference between the spot price and future price is known as
basis. Basis is said to be positive if the spo
F. The hedge effectiveness can be defined as the proportion of the variance
that is eliminated by hedging. This is 2, or
The parameters ro, sigmaF, and sigmas in equation (4.1) are usually
estimated from historical data on S and F. (The impli
Self assessment questions
What do you understand by hedging? Explain the concept with
Discuss various concepts of hedging with suitable illustrations.
Hedging prevents the investor from future price fluctuations? Do
Understand the concept of interest rate futures.
Describe the functioning of short-term and long term interest
rate futures market.
Know the types of interest rate futures like T-bills, T-bonds,
municipal bonds and euro-dollar futures.
for each unit of the asset held. For a long hedge the change is
In either case the variance, r, of the change in value of the hedged
position is given by
v = s2 + h 2 2F 2h s F
= 2h 2F 2 s F
Setting this equal to zero, and noting that 2v/h
4.3.5 Euro Dollar Futures
Dollars deposited in foreign banks are known as Eurodollars. This
practice was started in Europe to gain higher yield available on other
instruments in US money market. The foreign banks offer attractive interest
on deposits beca
price sensitivity w.r.t. interest rate changes. In other words, a high duration
bonds price is more sensitive to interest rate changes than the low duration
bond. It is also defined as the weighted average as the maturities of the
bonds coupon and the pri
Suppose an FRA in which a financial institution agrees to earn an
interest rate of Rk for the period of time between T1 and T2 on a principal
amount of L.
Let RF is the forward LIBOR interest rate for the period between T1
and T2. R is the actual LIBOR in
Hedging with T-bond futures
Fixed interest bearing securities have risks associated with the volatile
interest rate markets. Unfavourable interest rate change may lead to
potential capital loss to the investors. Interest rate futures have been devised
4.2.4 Zero rate
An n-year zero interest rate is the interest rate on an investment which
starts on todays date and last for n-years. In this time period no intermediate
payment is made. All the interest and principal payment is realized at the
end of n-ye