1. 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 Economics University of Maryland

2. 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

3. 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 NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 3

4. 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 NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 4

5. Introduction to LGM- Livestock Gross Margin - Dairy Crop Insurance (3) 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 NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 5

6. Introduction to LGM- Livestock Gross Margin -Dairy Crop Insurance (4) 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 NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 6

7. 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 NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 7

8. 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 NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 8

9. 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 NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 9

10. 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 NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 10

11. 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 NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 11

12. 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) NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 12

13. Indemnities: one month contracts Sales MonthMean Indemnity ($)Mean Net Return ($) January168-5 February559-17 March185-6 April479-14 May473-14 June95-3 July339-10 August185-6 September514-15 October214-6 November229-7 December354-11 NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 13

14. 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 NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 14

15. Indemnities: one month contracts (counts) Sales MonthNumber of Indemnities Percent years with indemnities January330% February440% March440% April330% May440% June220% July330% August330% September440% October218% November327% December545% NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 15

16. 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 NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 16

17. Indemnities: ten month contracts Sales MonthMean Indemnity ($)Mean Net Return ($) January00 February00 March10 April164-5 May319-10 June364-11 July463-14 August241-7 September30 October00 November00 December00 NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 17

18. 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) NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 18

19. Indemnities: ten month contracts (counts) Sales MonthNumber of Indemnities Percent years with indemnities January110% February00% March110% April330% May330% June330% July550% August440% September110% October00% November218% December19% NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 19

20. 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 contracts NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 20

21. 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?? NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 21

22. Thank you! Questions? NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 22

23. Appendix NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 23

24. Table 1. Expected Quantities of Milk Sold, Corn & Soybean Meal Purchased Table 1. Expected Quantities of Milk Sold, Corn Purchased, and Soybean Meal Purchased. MonthExpected milk sold (cwt)Expected corn fed (tons)Expected soybean meal fed (tons) January1794452.5 February1678422.5 March1877482.5 April1864482.5 May1952502.5 June1871482.5 July1842472.5 August1796402.5 September1717382.5 October1756402.5 November1694432.5 December1776452.5 Annual21620.453430 NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 24

25. Results 1-month contracts Table 2. Indemnities from One Month Contracts Sales MonthMean Indemnity Mean Return (after premium is subtracted) Number of Returns (out of 10- 11 years of historical data)Percent Returns January168.35-5.0505330.00% February559.1779-16.7753440.00% March184.542-5.536267440.00% April478.5453-14.35635330.00% May473.4582-14.20375440.00% June94.9502-2.848511220.00% July338.915-10.16743330.00% August184.9527-5.548541330.00% September514.4738-15.43419440.00% October214.1809-6.425393218.18% November229.1808-6.875479327.27% December354.2186-10.62661545.45% NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 25

26. Results 2-month contracts Table 3. Indemnities from Two Month Contracts Sales MonthMean Indemnity Mean Return (after premium is subtracted) Number of Returns (out of 10-11 years of historical data)Percent Returns January34.0491-1.021476110.00% February330.3836-9.911517550.00% March475.4044-14.26214220.00% April508.7007-15.26109330.00% May1414.411-42.43276440.00% June1091.659-32.75014330.00% July550.3084-16.50921440.00% August731.6905-21.95071330.00% September0000.00% October0000.00% November62.53711-1.876112218.18% December31.41885-0.9425686218.18% NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 26

27. Results 10-month contracts Table 11. Indemnities from Ten Month Contracts Sales MonthMean Indemnity Mean Return (after premium is subtracted) Number of Returns (out of 10- 11 years of historical data)Percent Returns January00110.00% February0000.00% March0.54375-0.0163125110.00% April163.7522-4.912584330.00% May318.5724-9.557218330.00% June364.0397-10.92117330.00% July463.0606-13.8918550.00% August240.8835-7.226471440.00% September3.240767-0.097223110.00% October0000.00% November00218.18% December0019.09% NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 27

28. Results 3-month contracts Table 4. Indemnities from Three Month Contracts Sales MonthMean Indemnity Mean Return (after premium is subtracted) Number of Returns (out of 10-11 years of historical data)Percent Returns January33.31842-0.9995554110.00% February269.6338-8.089025440.00% March384.2351-11.52707220.00% April515.8375-15.47509330.00% May1224.802-36.74363440.00% June1063.299-31.89902220.00% July718.3058-21.54918440.00% August793.8483-23.81545550.00% September122.4456-3.673361440.00% October0000.00% November202.0726-6.062225218.18% December0019.09% NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 28

29. Results 4-month contracts Table 5. Indemnities from Four Month Contracts Sales MonthMean Indemnity Mean Return (after premium is subtracted) Number of Returns (out of 10-11 years of historical data)Percent Returns January0000.00% February202.2253-6.066711330.00% March365.3974-10.96191220.00% April458.8793-13.7664330.00% May1127.329-33.8196440.00% June967.3331-29.01994330.00% July915.1498-27.45452440.00% August953.1484-28.59453550.00% September206.621-6.198661220.00% October0000.00% November293.3127-8.799411218.18% December23.59146-0.7077494218.18% NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 29

30. Results 5-month contracts Table 6. Indemnities from Five Month Contracts Sales MonthMean Indemnity Mean Return (after premium is subtracted) Number of Returns (out of 10-11 years of historical data)Percent Returns January0000.00% February132.1534-3.964557220.00% March318.4871-9.554651220.00% April521.3122-15.63937330.00% May997.1764-29.91528440.00% June801.0978-24.03293220.00% July897.3834-26.9216440.00% August833.4165-25.00247550.00% September291.0132-8.73038330.00% October0000.00% November00218.18% December0019.09% NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 30

31. Results 6-month contracts Table 7. Indemnities from Six Month Contracts Sales MonthMean Indemnity Mean Return (after premium is subtracted) Number of Returns (out of 10- 11 years of historical data)Percent Returns January00110.00% February52.75667-1.582698110.00% March255.8119-7.674383220.00% April476.7894-14.30366440.00% May884.9196-26.54759440.00% June702.5997-21.07794330.00% July845.2469-25.35737440.00% August648.0739-19.44223550.00% September275.1549-8.254627330.00% October0000.00% November00218.18% December0019.09% NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 31

32. Results 7-month contracts Table 8. Indemnities from Seven Month Contracts Sales MonthMean Indemnity Mean Return (after premium is subtracted) Number of Returns (out of 10- 11 years of historical data)Percent Returns January00110.00% February0000.00% March137.3464-4.120361220.00% April231.0654-6.931915440.00% May691.3473-20.74043550.00% June623.2374-18.69708330.00% July804.6215-24.1387440.00% August585.4318-17.56291440.00% September167.098-5.01291330.00% October0000.00% November00218.18% December0019.09% NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 32

33. Results 8-month contracts Table 9. Indemnities from Eight Month Contracts Sales MonthMean Indemnity Mean Return (after premium is subtracted) Number of Returns (out of 10- 11 years of historical data)Percent Returns January00110.00% February0000.00% March60.5127-1.815382220.00% April146.1254-4.383778220.00% May588.2812-17.64848440.00% June473.4616-14.20387330.00% July686.312-20.58945550.00% August539.7396-16.19222550.00% September130.6179-3.91854440.00% October0000.00% November00218.18% December0019.09% NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 33

34. Results 9-month contracts Table 10. Indemnities from Nine Month Contracts Sales MonthMean Indemnity Mean Return (after premium is subtracted) Number of Returns (out of 10- 11 years of historical data)Percent Returns January00110.00% February0000.00% March7.953914-0.2386172220.00% April124.9506-3.74851330.00% May421.6576-12.6498330.00% June405.8753-12.17625330.00% July605.1028-18.15303550.00% August363.0219-10.89068550.00% September53.26036-1.597812330.00% October0000.00% November00218.18% December0019.09% NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 34

35. 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 NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 35

36. 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 NAREA meeting July 1, 2008 - Maratou, Musser, Leathers U. Maryland: LGM Milk insurance 36