the optimal contract duration and portfolio effects for maryland dairy farmers’ participation in...

The Optimal Contract Duration and Portfolio Effects for Maryland Dairy Farmers’ Participation in Livestock

Gross Margin -Dairy Crop Insurance Laoura Maratou,

Wesley Musser, and Howard Leathers

Department of Agricultural and Resource EconomicsUniversity of Maryland

Outline

• Introduction to LGM- Livestock Gross Margin -Dairy Crop Insurance

• Conceptual Framework- quadratic risk program

• Data and Methods• Results• Conclusions

NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 2

Introduction to LGM- Livestock Gross Margin -Dairy Crop Insurance

• Price insurance for livestock • Contract Length between one and ten months• Sold with one month lag to begin• Insures the gross margin of milk sales minus

corn and soybean meal purchases• Available throughout NE• Sales begin in August, 2008


Introduction to LGM- Livestock Gross Margin -Dairy Crop Insurance (2)

• Gross margins are calculated with futures market prices for milk, corn and soybean meal

• Prices adjusted with the state basis for milk and for corn

• Margin calculated each month with futures prices for that month

• Multi-month contracts add monthly margins



• Insurance contract for planned milk production and feed use on the farm

• Guaranteed margin calculated with futures prices for different months at time of sale

• Actual gross margins are calculated with current closing futures prices for each month

• Indemnity paid if guaranteed (expected) margin greater than actual margin



• Advantages over options– can be written for the exact farm production

situation – Farmer doesn’t have to choose strike price and

other features of options

• Length combinations can vary• Different combinations may have portfolio

effects that could reduce risk more than single contract


Conceptual Framework

Quadratic risk program:• The objective function for the quadratic risk

program can be specified as follows (Musser, Mapp, and Barry, 1984):

• Maximize EU = c’x – x’Vx subject to• Ax ≤ b• and x≥ 0


2

a

Conceptual Framework (2)

• E-V framework consistent with quadratic utility function or normal returns

• E-V framework approximates other utility and probability distributions quite well

• Problem has large number of combinations so a programming framework is approriate


Data and Methods

• Representative MD 120 cow dairy– Annual milk production per cow of 18,107 lbs– State average for 2007– Monthly production with US monthly production

level percents of annual production– Feed use from coefficients used to calculate milk-

feed price ratios– Mean monthly gross margin for sales is $20,804


Data and Methods (2)

• Cash prices for actual gross margins from NASS• Risk aversion coefficients of .05, .10, & .15• Futures market data from exchanges– Averages of last three days: actual prices– Averages of last third, fourth, and fifth days for

guarantees: expected prices– Time series from October 1997 to December 2007– Length of milk contract


Data and Methods (3)

• Observations on different contracts for each year used to calculate c and V

• Premiums approximated with 1.03 times expected indemnities for a particular contract

• Expected returns negative• Purchase to reduce variations in gross margins


Results

• Quadratic programming not completed yet• So far, research has focused on indemnities

from alternative contracts• Calculation of means • Calculation of number of indemnities• Present here results for one and ten month

policies (see appendix for full results)


Indemnities: one month contractsSales Month Mean Indemnity ($) Mean Net Return ($)January 168 -5February 559 -17March 185 -6April 479 -14May 473 -14June 95 -3July 339 -10August 185 -6September 514 -15October 214 -6November 229 -7December 354 -11


Indemnities: one month contracts

• Indemnities in every month• Mean indemnities less than $1,000• June lowest mean---less than $100• Febr and Sept highest means---greater than

$500• Net returns (cost) negative but small absolute

value (cheap monthly cost) -$3 to -$17/month• Limited returns from one month contract


Indemnities: one month contracts (counts)

Sales Month Number of IndemnitiesPercent years

with indemnities January 3 30%February 4 40%March 4 40%April 3 30%May 4 40%June 2 20%July 3 30%August 3 30%September 4 40%October 2 18%November 3 27%December 5 45%

NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance

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Indemnities: one month contracts (counts)

• Number of years with indemnities out of ten to eleven years

• Ranges from two to five years• Lowest number of indemnities in June


Indemnities: ten month contractsSales Month Mean Indemnity ($) Mean Net Return ($)January 0 0February 0 0March 1 0April 164 -5May 319 -10June 364 -11July 463 -14August 241 -7September 3 0October 0 0November 0 0December 0 0


Indemnities: ten month contracts

• Mean indemnities zero for Jan, Febr, and Oct-Dec

• Mean indemnities close to zero for March and Sept

• Mean indemnities less than $500 for other months

• Mean net returns greater than -$15/month for 10 months (quite cheap)


Indemnities: ten month contracts (counts)

Sales Month Number of IndemnitiesPercent years

with indemnities January 1 10%February 0 0%March 1 10%April 3 30%May 3 30%June 3 30%July 5 50%August 4 40%September 1 10%October 0 0%November 2 18%December 1 9%

NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance

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Indemnities: ten month contracts (counts)

• Three or more indemnities only for April-Aug• Zero indemnities for Febr and Oct• One or two indemnities for other months• Fewer indemnities and lower means for longer

contracts• More likely to average out positive monthly

indemnities over longer contracts• Higher premiums for multiple one month

contractsNAREA meeting July 1, 2008 - Maratou, Musser, Leathers

U. Maryland: LGM Milk insurance 20

Conclusions

• Large number of choices for farmers—120 different contracts per year

• Multiple possible contracts in each month result in very large number of possible combinations of contracts

• Limited mean indemnities—more for shorter contracts

• Will farmers use the contracts??


Thank you!

Questions?


Appendix


Table 1. Expected Quantities of Milk Sold, Corn & Soybean Meal Purchased

Table 1. Expected Quantities of Milk Sold, Corn Purchased, and Soybean Meal Purchased.Month Expected milk sold (cwt) Expected corn fed (tons) Expected soybean meal fed (tons)

January 1794 45 2.5

February 1678 42 2.5

March 1877 48 2.5

April 1864 48 2.5

May 1952 50 2.5

June 1871 48 2.5

July 1842 47 2.5

August 1796 40 2.5

September 1717 38 2.5

October 1756 40 2.5

November 1694 43 2.5

December 1776 45 2.5

Annual 21620.4 534 30


Results 1-month contracts Table 2. Indemnities from One Month Contracts

Sales Month Mean IndemnityMean Return

(after premium is subtracted)Number of Returns (out of 10-11 years of historical data) Percent Returns

January 168.35 -5.0505 3 30.00%

February 559.1779 -16.7753 4 40.00%

March 184.542 -5.536267 4 40.00%

April 478.5453 -14.35635 3 30.00%

May 473.4582 -14.20375 4 40.00%

June 94.9502 -2.848511 2 20.00%July 338.915 -10.16743 3 30.00%

August 184.9527 -5.548541 3 30.00%

September 514.4738 -15.43419 4 40.00%

October 214.1809 -6.425393 2 18.18%

November 229.1808 -6.875479 3 27.27%

December 354.2186 -10.62661 5 45.45%


Results 2-month contracts Table 3. Indemnities from Two Month Contracts

Sales Month Mean IndemnityMean Return (after premium is subtracted)

Number of Returns (out of 10-11 years of historical data) Percent Returns

January 34.0491 -1.021476 1 10.00%

February 330.3836 -9.911517 5 50.00%

March 475.4044 -14.26214 2 20.00%

April 508.7007 -15.26109 3 30.00%

May 1414.411 -42.43276 4 40.00%

June 1091.659 -32.75014 3 30.00%

July 550.3084 -16.50921 4 40.00%

August 731.6905 -21.95071 3 30.00%

September 0 0 0 0.00%

October 0 0 0 0.00%

November 62.53711 -1.876112 2 18.18%

December 31.41885 -0.9425686 2 18.18%


Results 10-month contracts Table 11. Indemnities from Ten Month Contracts



January 0 0 1 10.00%

February 0 0 0 0.00%

March 0.54375 -0.0163125 1 10.00%

April 163.7522 -4.912584 3 30.00%

May 318.5724 -9.557218 3 30.00%

June 364.0397 -10.92117 3 30.00%

July 463.0606 -13.8918 5 50.00%

August 240.8835 -7.226471 4 40.00%

September 3.240767 -0.097223 1 10.00%

October 0 0 0 0.00%

November 0 0 2 18.18%

December 0 0 1 9.09%


Results 3-month contracts Table 4. Indemnities from Three Month Contracts



January 33.31842 -0.9995554 1 10.00%

February 269.6338 -8.089025 4 40.00%

March 384.2351 -11.52707 2 20.00%

April 515.8375 -15.47509 3 30.00%

May 1224.802 -36.74363 4 40.00%

June 1063.299 -31.89902 2 20.00%

July 718.3058 -21.54918 4 40.00%

August 793.8483 -23.81545 5 50.00%

September 122.4456 -3.673361 4 40.00%

October 0 0 0 0.00%

November 202.0726 -6.062225 2 18.18%



Results 4-month contracts Table 5. Indemnities from Four Month Contracts



January 0 0 0 0.00%

February 202.2253 -6.066711 3 30.00%

March 365.3974 -10.96191 2 20.00%

April 458.8793 -13.7664 3 30.00%

May 1127.329 -33.8196 4 40.00%

June 967.3331 -29.01994 3 30.00%

July 915.1498 -27.45452 4 40.00%

August 953.1484 -28.59453 5 50.00%

September 206.621 -6.198661 2 20.00%

October 0 0 0 0.00%

November 293.3127 -8.799411 2 18.18%

December 23.59146 -0.7077494 2 18.18%


Results 5-month contracts Table 6. Indemnities from Five Month Contracts



January 0 0 0 0.00%

February 132.1534 -3.964557 2 20.00%

March 318.4871 -9.554651 2 20.00%

April 521.3122 -15.63937 3 30.00%

May 997.1764 -29.91528 4 40.00%

June 801.0978 -24.03293 2 20.00%

July 897.3834 -26.9216 4 40.00%

August 833.4165 -25.00247 5 50.00%

September 291.0132 -8.73038 3 30.00%

October 0 0 0 0.00%

November 0 0 2 18.18%



Results 6-month contracts Table 7. Indemnities from Six Month Contracts



January 0 0 1 10.00%

February 52.75667 -1.582698 1 10.00%

March 255.8119 -7.674383 2 20.00%

April 476.7894 -14.30366 4 40.00%

May 884.9196 -26.54759 4 40.00%

June 702.5997 -21.07794 3 30.00%

July 845.2469 -25.35737 4 40.00%

August 648.0739 -19.44223 5 50.00%

September 275.1549 -8.254627 3 30.00%

October 0 0 0 0.00%

November 0 0 2 18.18%



Results 7-month contracts Table 8. Indemnities from Seven Month Contracts



January 0 0 1 10.00%


March 137.3464 -4.120361 2 20.00%

April 231.0654 -6.931915 4 40.00%

May 691.3473 -20.74043 5 50.00%

June 623.2374 -18.69708 3 30.00%

July 804.6215 -24.1387 4 40.00%

August 585.4318 -17.56291 4 40.00%

September 167.098 -5.01291 3 30.00%

October 0 0 0 0.00%

November 0 0 2 18.18%



Results 8-month contracts Table 9. Indemnities from Eight Month Contracts



January 0 0 1 10.00%


March 60.5127 -1.815382 2 20.00%

April 146.1254 -4.383778 2 20.00%

May 588.2812 -17.64848 4 40.00%

June 473.4616 -14.20387 3 30.00%

July 686.312 -20.58945 5 50.00%

August 539.7396 -16.19222 5 50.00%

September 130.6179 -3.91854 4 40.00%

October 0 0 0 0.00%

November 0 0 2 18.18%



Results 9-month contracts Table 10. Indemnities from Nine Month Contracts



January 0 0 1 10.00%


March 7.953914 -0.2386172 2 20.00%

April 124.9506 -3.74851 3 30.00%

May 421.6576 -12.6498 3 30.00%

June 405.8753 -12.17625 3 30.00%

July 605.1028 -18.15303 5 50.00%

August 363.0219 -10.89068 5 50.00%

September 53.26036 -1.597812 3 30.00%

October 0 0 0 0.00%

November 0 0 2 18.18%



Conceptual Framework (1b)

• EU is expected utility• c is expected returns from insurance• x is insurance contracts for different months

and lengths• a is a risk aversion coefficent • V is a variance-covariance matrix for the

insurance returns• Includes gross margins from actual production


Conceptual Framework (1c)

• A is the constraint matrix which links contracts to monthly milk production levels

• b is the maximum production levels for all months


the optimal contract duration and portfolio effects for maryland dairy farmers’ participation in...

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