Presentation for Darden Business Publishing, University of Virginia research paper on Risk Exposure and Hedging, Bodily, Samuel E., Lee Fiedler, 2002

1. “Risk Exposure
and Hedging”
Bodily, Samuel E.,
Lee Fiedler, 2002
HIRAL JHAVERI HARSH
CHITRODA & AYUSHI DOSHI

2. Introduction
Out of various uncertainties around
a business, only a few
uncertainties matter to a business.
Let’s consider an example of a
farmer
People have exposure to risks; the
exposure then relates to
uncertainties that matter
Uncertainties
Uncertainties
that really matter
Future exchange
rates
Crop yields
Employment levels Commodity Prices
Crop yields
Commodity Prices

3. Two Key
Steps
Step 2:
After identification of variables
quantify the relationship between the
variable and the NPV or
anything else that you care about.
Step 1:
Change in a variable will make you
better or worse, if unaffected then
there is no exposure.

4. Airline
Example
price of jet fuel
increases by
10cents a gallon
Pass to the passenger
& Immediately recover
Cannot pass to the
passengers and recover
No exposure
No need to worry!
Exposure
How much exposure?

5. How much
exposure?
If the airline buys 2,000,000 gallons of jet fuel every
month, it is exposed to the extent of $ 20,000 per 1 cent
increase in jet fuel price per month.
Quantifying exposure is easy with one variable but gets
complicated if more than one variable is involved.

6. Hedging a
Single
Exposure
Hedging in most cases is taking a long position in one
asset that moves in the opposite direction to the exposure.
Mostly the quantity of the asset to be hedged is known and
the Value of the asset is unknown.
Forward Contracts can be used by the management.
Example: Farmer can enter forward contracts to sell a
known quantity of crop he will produce at a specified price
on a specified time.
If the manager wants to hedge for an unknown quantity of
an asset and enter into forward contracts, many a times
there are no forwards available for the relevant asset.

7. Cross
Hedging
Hedging instruments are not available for the specific
asset in concern, but there can be related assets.
Cross hedging comes in picture in such situations.
Use a forward contract based on one asset to hedge a
price of another asset.
Let's return to the above airline example for the need of
2,000,000 gallons of aviation fuel. There are no forward
contracts on aviation fuel, but we have observed the
prices of gasoline and aviation fuel as follows:

8. Average monthly price of aviation fuel and gasoline

9. Analysis of the
graph and
hedging
strategy
Price of aviation fuel and gasoline move closely
together, thus one can use forward contracts on
gasoline to hedge the cost of aviation fuel.
Focus: to achieve lowest standard deviation in the net
cost
How many gallons of gasoline should be bought to
hedge? ( hedge ratio “H”)
Net cost= Price per gallon of aviation fuel- H* Price per
gallon of finished gasoline

10. In this example, a hedge
ratio of 1 offers the lowest
standard deviation of net
cost for the four different
hedge ratios concerned,
however there may be a
better hedge amount.

11. Using
regression
analysis to
find the
optimal hedge
ratio
Finding the hedge ratio by plugging in different numbers
and calculating standard deviation is not very efficient
 Regression for hedging, regress the price of the
variable that is important to you (Y variable) against the
prices of the variable you are considering to use as a
hedge (X variable).
This coefficient between the two variables is the optimal
hedge ratio.
In our case the X and Y variable will the Average refiner
price of the finished gasoline and the Average price of
Aviation fuel as seen in the Table 1 below: Price history
for gasoline and aviation fuel.

12. Using
regression
analysis to
find the
optimal hedge
ratio
The best hedge will be forward
contract to buy 1,794,200
 By plotting the price of aviation fuel against the refiner price
of finished gasoline, you notice the following pattern:
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.98133
R Square 0.96301
Adjusted R Square 0.96117
Standard Error 3.27036
Observations 22.00000
ANOVA
df SS MS F Significance F
Regression 1 5569.617009 5569.617 520.7552 8.58459E-16
Residual 20 213.9053778 10.69527
Total 21 5783.522386
Coeffici
ents Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 36.099 3.770230179 9.574864 6.54E-09 28.23487985 43.96400453 28.2348798 43.96400453
59.20 0.8898 0.038990883 22.82006 8.58E-16 0.8084408 0.971107915 0.8084408 0.971107915
-10
-5
0
5
10
0 50 100 150
Residuals
59.20
Residual Plot
0
50
100
150
200
0 50 100 150
87
59.20
Line Fit Plot
Series1
Predicted 87
0
50
100
150
0 50 100 150
87
Sample Percentile
Normal
Probability Plot

13. Why is that
the regression
coefficient
works as the
optimal hedge
ratio?
It’s the regression
The regression coefficient will produce the lowest standard
deviation for Y – (H * X)
Formula Method:
H = Correlation X & Y *(Standard Deviation Y / Standard
Deviation X
H = .9841* (17.6671 / 19.3799) = .8971
The R-squared: The R-squared effectively tells you what
percentage of the variance in Y can be eliminated with the cross
hedge. In our example we can the R-squared is 0.9685
Assumptions for using regression for hedging assumes: Standard
deviation is appropriate measure of risk. In many cases this may
be acceptable, but if the risk profile is not normally distributed,
standard deviation is not synonymous with risk.

14. Hedging
multiple
uncertainties
In real life situation there are often multiple
uncertainties, for example a manager a manager
hedging revenue in a foreign currency may not know
today what those revenues will turn out to be.
Add another uncertainty and see what happens……
Example: the expected usage: 2000000 gallons next
month, but its uncertain, a normal distribution with
standard deviation of 100,000 gallons. What should be
done in such a case?

15. Independent
uncertainties
Basic assumption: quantity of fuel used is independent
of price.
Fuel usage is driven by factors like the number of
cancelled flights and wind speeds.
Price Quantity
Total Cost

16. Independent
uncertainties
Independent uncertainty about quantity means there
should be more total exposure for the manager.
If the exposure is greater, his interest in hedging should
be greater.
Most assumed: no quantity exposure, quantity risk can
make a real difference to your total exposure and your
strategy for hedging it.

17. Dependency
Basic assumption: Quantity of fuel used depends on Price.
The above line represents that price and quantity are not
independent.
Typical measure of dependency is correlation.
Price Quantity
Total Cost

18. Statistics Total costs with no
quantity uncertainty
Total costs with two
independent
uncertainties
Total costs with two
independent
uncertainties +.99
correlation
Total costs with two
independent
uncertainties
-.99 correlation
Mean 2712000 2709191 2715236 2708045
Standard Deviation 78000 157599 212449 61971
Variance 6084000000 24837311576 45134635795 3840443226
Percentage change in
Variance
0% 308% 642% -37%

19. Thank You