Page 62 - DMGT513_DERIVATIVES_AND_RISK_MANAGEMENT

Unit 5: Pricing of Future Contracts

Methods of Calculating Hedge Ratio Notes

It is important to know that no one is certain about the relationship in future between the cash
and future prices of the underlying asset being hedged. One can simply make a study of the past
price behaviour and its relationship of these prices with an expectation that the same trend will
continue in future. A proper study of the concept of hedge ratio and its calculation is essential
for effective hedging purpose. Now, we discuss two methods for estimating hedge ratio.
1. The Naive Method: This method is based on two types of information, which are:
(a) Current market condition and forecast of futures market scenario.

(b) Relation between spot and futures prices, as evidenced from past data.
Under this approach, we assume that the minimum variance hedge ratio is equal to 1,
which is not always possible.

2. Regression Method: Another important method that may be used to determine the minimum
variance hedge ratio is regression analysis. This method is specifically designed to provide
the best linear relationship between two prices i.e., futures price and the price to be
hedged. The following linear equation can be used to find out the relationship.
DS = a + bDF + e ... (5.10)
t t t
where DS is the change in spot price, DF is change in future price, e is standard error form
t t t
with zero mean, a and b are estimated co-efficients.

Example: Let us consider the hedging of a long cash position of 5,000 tones of rice by
selling wheat futures. Assume that for `100 change in wheat futures price, the Re is ` 80. change
in rice cash prices. In order to establish the minimum variance hedge ratio, we need to calculate
the number of futures contract to sell.

Given, Q = 80, and Q = 100; Q = 1000 (1 ton = 1000 kgs.)
F S FC
So, Hedge Ratio HR = Q /Q = 80/100= 0.8
F S
The number of futures contract (NFC) that minimizes risk is given by
NFC = (Q /Q ) * HR … (5.11)
C FC
= ( 5000 / 1000) *0.8 = 4 contracts

Tasks NSE Nifty is currently trading in spot market at 3200. The cost of financing is 12%
per annum. Calculate the fair value of 3-month futures of Nifty, when the dividend yield
is 3% per annum.

Self Assessment

State the following are true or false:

14. The hedge ratio (HR) is the number of futures contacts one should use to hedge a particular
exposure in the spot market.
15. Generally the hedge ratio is 0.5.

LOVELY PROFESSIONAL UNIVERSITY 57