1
UAE University                Spring 2017
Prof. Dr. Abdulnasser Hatemi-J
A Project in Derivative Securities
The main goal of this project is to make use of futures for hedging purposes. You need to estimate the optimal
hedge  ratio  (sometimes  called  the  minimum  variance  hedge  ratio).  Estimated  both  the  symmetric  and
asymmetric optimal hedge ratios. Interpret your results. You need to collect data for spot prices and futures
prices for a given asset and calculate the price changes first. Present your  results in form of a report and submit
it via e-mail  (AHatemi@uaeu.ac.ae  ).  You will be informed about the deadline for submitting your report later.
You need to perform the following:
  Define the optimal hedge ratio. Why is it important to make use of the optimal hedge ratio? When
should the hedger have a long position and when should he/she have a short position in the futures?
   Why is it important to allow for asymmetry in the optimal hedge ratio and how can this be achieved?
  Present your estimation results of you optimal hedge ratio in table format and describe the implication
  Structure  your report in terms of sections such as 1. Introduction, 2.  Background information for the
selected market, 3. Methods and data discerption, 4. Estimation results and analysis, 5. Conclusions.
References should be presented at the end of the report. Name and student ID number for each author
should be clearly indicated. Make sure that you select an appropriate title for your project. Be original
and use your  own words. If you use any other literature as a source, make sure that you reword the
content in addition to appropriate citation. Feel welcome to contact my any time you have questions.
Some useful equations:
The  symmetric  optimal  hedge  ratio  (OHR),  denoted  by  h*,  can  be  calculated  via  the  following  equation
according to Hull (2012):
F
S
h

 
*
2
Where
S

represents  the  standard  deviation  of  ∆S,
F

signifies  the  standard  deviation  of  ∆F,  and  the
correlation coefficient between  ∆S  and  ∆F  is denoted by

. Note that ∆S  represents the change in the spot
price and ∆F represents  the change in the future price.  This OHR can  also be obtained by  estimating the
following regression model:
t t t u F h S      
,
Where α is an intercept and ut is an error term.
The asymmetric optimal hedge ratio (AOHR) is introduced by El-Khatib and Hatemi-J (2012), denoted by h
+
or h
-. It can be calculated via the following equations:

 

F
S
h

or

 

F
S
h

.
Where

S

represents  the  standard  deviation  of  ∆S
+
,

F

signifies  the  standard  deviation  of  ∆F
+
,  and  the
correlation coefficient between ∆S
+
and ∆F
+
is denoted by

.  The  AOHR can also be obtained by estimating
the following regression equations:
    
    
t t t u F h S 
,   or
    
    
t t t u F h S 
Note that the following equation are used to transform the data into positive and negative components:
) 0 , (
 
  
t t
S MAX S
,
) 0 , (
 
  
t t F MAX F
,
) 0 , (
 
  
t t
S MAX S
and
) 0 , (
 
  
t t F MAX F
.
References
Hull. J.C. (2012) Options, Futures, and other Derivatives. Pearson Education.
Hatemi-J A. and El-Khatib Y. (2011) Asymmetric Optimal Hedge Ratio with an Application, IAENG
International Journal of Applied Mathematics, 41:4, IJAM_41_4.
Good Luck