Final Milk Presentation

Hedging the volatility of milk

Richard Strauss, Franco Levis, Benjamin Dionne

Agenda

1 Executive Summary

2 Recommendation

3 Supporting Analysis

4 Future Considerations

2

Meet Gerard: a third-generation owner of a California dairy farm.

Family-run business Rising Grain Costs

2,500 cows Volatile Milk Prices

200,000 pounds of milk
Blood is milk
produced per day

Gerard is dedicated to his farm but is suffering from increased costs and volatile
revenues, making it difficult to ensure he breaks-even.

Executive Summary Recommendation Supporting Analysis Future Considerations
3

The dairy farm industry has consolidated over the last 40 years.

648,000

Total Number of U.S. Dairy Farms
12,000,000
140

Number of Dairy Cows
120
120 9,100,000
Average Herd Size

100
80
60
40
19 75,000
20
0
1970 2006 1970 2006 1970 2006

Year Year Year

Even though the total number of dairy farms and cows has fallen, total milk
production has doubled due to advance in technology and animal health.

4

The dairy farm industry exhibits economies of scale.
Average Variable Costs Average Fixed Costs Average Total Costs
23%
30

% of Total Milk Production
25
ATC, AVC, AFC ($/cwt)

15%
20 14% 14% 14%
13%

15

10
5%
5
1%
0
0 50000 100000 150000 200000 250000 300000 350000 400000 15 45 75 150 350 750 1500 2000

Quantity of Milk Produced (cwt) Herd Size

Average costs fall as more milk is produced. Farmers have expanded their herd sizes
as a result.

5

The Milk Value Chain: A typical month for Gerard

Milk is processed into
Milk is bundled and Processors pass on
Cows are milked. different value-added
shipped to processors. proceeds to producers
products.

Gerard is a price taker. He cannot control the price he receives for his milk. He can
only control what quantity he sells (up to his quota.)

6

The Milk Value Chain: A typical month for Gerard

Milk is processed into
Processors pass on
. different value-added
proceeds to producers
products.

Gerard is a price taker. He cannot control the price he receives for his milk. He can
only control what quantity he sells (up to his quota.)

7

There are 5 different groups of value-added products made from milk.

Milk

Class 1 Class 2 Class 3 Class 4a Class 4b

Cream, Cottage
Ice Cream and Cheese other
Cheese, Yogurt, Butter and Dry
Fluid Milk Frozen than cottage
Sterilized Milk Products
Products cheese
Products

Mailbox price ($/cwt)

Gerard receives a mailbox price for his milk from processors based on a
complicated blend of prices for each value-added class.

8

Gerard’s payment schedule follows a one month delay.
Receives payment for Feb 1st- Feb
15th milk shipment based on the Receives credit/debit for both
January mailbox price Feb 28th and Mar 15th
payments based on available
Milk is produced and shipped January mailbox price

Feb 1st Feb 15th Feb 28th Mar 15th Mar 31st

Milk is produced and shipped Receives payment for Feb 15th
-28th milk shipment based on
January mailbox price

Gerard is subjected to debits/credit at each month end due to delayed mailbox
pricing.

9

Gerard, as a California farmer, operates under the Young Act.

California State’s Young Act

Established Producers and North and South Federal milk
minimum prices processors apart California have policies do not
processors must of California distinct apply to
pay for each Milk Pooling marketing and California
milk class Branch price areas producers

Gerard operates in a regulated environment protected from extreme price drops.

10

Historically mailbox prices have ranged from $10 to $17.

$18.00

$17.00

$16.00
Mailbox Prices ($/cwt)

$15.00

$14.00

$13.00

$12.00

$11.00

$10.00

$9.00

Date

Standard Deviation is 1.78. Mean-scaled standard deviation is 13.56%.
Mailbox prices are volatile.

11

The key question is:

How can Gerard hedge against the volatility of mailbox
milk prices and maintain positive cash flows?

12

Our recommendation is:

Purchase a put option to limit the downside potential on
mailbox prices but allow for upward gains.

13

Put options are financial instruments that protect against downside risk.
Right but not obligation to sell an underlying security at a specified price.

Value of At the money
option In the money Out of the money

4 5 6 7 8 9 10 11 12 13 14

Strike Price

A put option will only be valuable (in the money) when the underlying asset price is
below the strike price.

14

Holders of put options must pay premiums and transaction fees.

Gross value of
Value of the option
option

4 5 6 7 8 9 10 11 12 13 14

Premium and transaction
fees paid for the option

There are associated premiums and transaction costs associated with options that
will lower an option’s value to the holder.

15

Put options are financial instruments that protect against downside risk.
Right but not obligation to sell an underlying security at a specified price.

Net value of the option

Value of
option

4 5 6 7 8 9 10 11 12 13 14

Strike price – (Premium + Transaction Costs)

The point where the value of the option is $0 will be below the strike price.

16

Unfortunately there is not an option available for mailbox prices.

Gerard must find another put option to hedge his risk.


Which option should we choose?

Class III Class IV

Butter NFDM

We want the price of the chosen product to follow the mailbox price closely.

18

Class III and Class IV prices seem to have similar behaviours.
$22.00

$20.00

$18.00

$16.00
Mailbox
$14.00 Class III
Class IV
$12.00

$10.00
September-04

September-05

September-06
March-04

November-04

March-05

November-05

March-06

November-06

March-07
July-04

July-05

July-06
May-04

May-05

May-06

May-07
January-04

January-05

January-06

January-07
Testing the correlations would provide us with more evidence.

19

Scatterplots show the general degree of correlation.

We can expect Class III and Class IV classes to have a higher correlation coefficient.

20

The correlation matrix shows the numerical values of correlation.

Mailbox Class III Class IV Butter NFDM

Mailbox 1

Class III 0.9627 1

Class IV 0.8439 0.8155 1

Butter 0.786 0.7231 0.5513 1

NFDM 0.1721 0.2233 0.5608 -0.2902 1

Class III prices have the highest correlation with mailbox prices.

21

Class III products exhibit the best fit assuming a linear relation.

A Class III option is therefore the best possibility to hedge Gerard’s position.

22

The client has a break-even price to be taken into account.

Operation Costs Hedging Costs
$12/cwt ~$0.50/cwt

$12.50/cwt

He wants to ensure getting a payoff from the option if the price falls below $12.50

23

Conditional distribution of Class III on mailbox price is normally distributed.

Under certain assumptions, we will be able to determine the correct strike price.

24

To prove the assumptions, several tests must be undergone.

Our model Assumptions

Normality of errors

Homoscedasticity

We will assess normality both graphically and mathematically.

25

We generated the residuals and plotted their distribution.

e y ˆ
y

This is our first evidence of normality.

26

Another graphical way of assessing normality are probability plots.

P-P and Q-Q plots also support our assumption of normality.

27

Finally, we would like a mathematical result to confirm normality.

Shapiro – Wilk test

2 where
n
( i 1
ai x( i ) ) mTV 1
W (a1 ,..., an )
n 2 (mT V 1V 1m)1/2

i 1
( xi x) m (m1 ,..., mn ) T

Under the null hypothesis, our residuals follow a normal distribution.

28

The result doesn’t reject the null hypothesis, so we can assume normality.

W statistic Rule of
P-Value
value decision

0.98341 0.80217 Accept

Further tests showed some evidence of heteroscedasticity, but it’s effect on SE was
negligible, and didn’t affect the final values of the strike price.

29

Gerard had a specific request regarding a confidence level of the prediction.

How can he be 95% confident that he will be in the
money if the mailbox price falls under $12.50?

30

There are two options available for determining the interval.

A range of values so defined as, over multiple samples, what
Confidence
the range of mean values of the dependent variable will be
Interval when evaluated at a specified independent variable level.

A range of values so defined as, given only the current sample,
Prediction
what the range of values for the dependent variable will be
Interval when evaluated at a specified independent variable level.

Since we want to predict an actual class III price using our current sample at a specific
mailbox price, a prediction interval is more appropriate.

31

Class III price as a function of the mailbox price ($/cwt) at α = 0.05.

(12.5, 14.24)

Class III = -1.557 + 1.182×(Mailbox Price)

32

Class III price as a function of the mailbox price ($/cwt) at α = 0.01.

(12.5, 14.69)


33

Class III price in function of the mailbox price ($/cwt) at α = 0.10.

(12.5, 14.01)


34

The upper bound increases as the confidence level increases.

α = 0.01 α = 0.05 α = 0.10

Upper-bound of
the Prediction 14.69187 14.24446 14.01269
Interval ($/cwt)

Strike price
14.75 14.25 14.25
($/cwt)

The strike price remains the same for α = 0.05 and α = 0.10 because Class III options
are only sold by increments of $0.25.

35

The highest hedged profits are at a 99% confidence level

$6
$5
$4
$3 Hedged (α = 0.01)
Profits

$2
Hedged (α = 0.05 &
$1 0.10)
$- Unhedged
$(1)
$(2)
$(3)

Hedged Hedged Hedged
Unhedged
(α = 0.01) (α = 0.05) (α = 0.10)
Average profits ($/cwt) 1.13 1.95 1.60 1.60
Standard Deviation 1.78 0.88 1.01 1.01

36

As the mailbox price increases, Gerard will incur limited losses.

Difference of profits between an unhedged and hedged position
$4

$3

$2

α = 0.05 & 0.10
$1
α = 0.01

$0

-$1

37

Gerard should hedge against the volatility of the mailbox price.

By buying put options at a strike price of
$14.25/cwt, Gerard can be 95% confident that
he will be in the money if the mailbox price
drops under $12.50/cwt.

38

There are two future considerations for Gerard.

What if his operation costs change?

What if option costs change?

39

Changes in operation costs can change the upper-bound of the prediction interval.
$18
$17
$16
Strike Price

$15
$14
$13
$12
$11
$10 $11 $12 $13 $14 $15
Operation Costs

As operation costs increase, the necessary strike price for Gerard to be 95% confident
he will be in the money increases.

40

The cost of the option can also change the upper-bound of the prediction interval.
$15.00

$14.75
Strike Price

$14.50

$14.25

$14.00

$13.75
$- $0.20 $0.40 $0.60 $0.80 $1.00
Option Costs

Similarly, as option costs increase, the strike price at which Gerard is 95% confident
that he is going to be in the money increases.

41

Key Takeaways

Options can be Linearly correlated
used to hedge goods can be used as
against volatility. substitute options.

Normality assumptions In reality, put option
and Heteroscedasticity costs will increase as
must be addressed. the strike increases.

42

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