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- 1. Hedging the volatility of milkRichard Strauss, Franco Levis, Benjamin Dionne
- 2. Agenda 1 Executive Summary 2 Recommendation 3 Supporting Analysis 4 Future Considerations 2
- 3. 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
- 4. 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 9,100,000Average 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. Executive Summary Recommendation Supporting Analysis Future Considerations 4
- 5. The dairy farm industry exhibits economies of scale. Average Variable Costs Average Fixed Costs Average Total Costs 23% 30 % of Total Milk Production 25ATC, AVC, AFC ($/cwt) 15% 20 14% 14% 14% 13% 15 10 5% 5 1% 0 0 50000 100000 150000 200000 250000 300000 350000 400000 15 45 75 150 350 750 1500 2000 Quantity of Milk Produced (cwt) Herd Size Average costs fall as more milk is produced. Farmers have expanded their herd sizes as a result. Executive Summary Recommendation Supporting Analysis Future Considerations 5
- 6. The Milk Value Chain: A typical month for Gerard Milk is processed into Milk is bundled and Processors pass onCows are milked. different value-added shipped to processors. proceeds to producers products. Gerard is a price taker. He cannot control the price he receives for his milk. He can only control what quantity he sells (up to his quota.) Executive Summary Recommendation Supporting Analysis Future Considerations 6
- 7. The Milk Value Chain: A typical month for Gerard Milk is processed into Processors pass on . different value-added proceeds to producers products.Gerard is a price taker. He cannot control the price he receives for his milk. He can only control what quantity he sells (up to his quota.)Executive Summary Recommendation Supporting Analysis Future Considerations 7
- 8. There are 5 different groups of value-added products made from milk. Milk Class 1 Class 2 Class 3 Class 4a Class 4b Cream, Cottage Ice Cream and Cheese other Cheese, Yogurt, Butter and Dry Fluid Milk Frozen than cottage Sterilized Milk Products Products cheese Products Mailbox price ($/cwt) Gerard receives a mailbox price for his milk from processors based on a complicated blend of prices for each value-added class. Executive Summary Recommendation Supporting Analysis Future Considerations 8
- 9. 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 availableMilk is produced and shipped January mailbox priceFeb 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. Executive Summary Recommendation Supporting Analysis Future Considerations 9
- 10. Gerard, as a California farmer, operates under the Young Act. California State’s Young Act Established Producers and North and South Federal milkminimum prices processors apart California have policies do notprocessors 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. Executive Summary Recommendation Supporting Analysis Future Considerations 10
- 11. Historically mailbox prices have ranged from $10 to $17. $18.00 $17.00 $16.00Mailbox Prices ($/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. Executive Summary Recommendation Supporting Analysis Future Considerations 11
- 12. The key question is:How can Gerard hedge against the volatility of mailbox milk prices and maintain positive cash flows?Executive Summary Recommendation Supporting Analysis Future Considerations 12
- 13. Our recommendation is:Purchase a put option to limit the downside potential on mailbox prices but allow for upward gains. Executive Summary Recommendation Supporting Analysis Future Considerations 13
- 14. 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. Executive Summary Recommendation Supporting Analysis Future Considerations 14
- 15. Holders of put options must pay premiums and transaction fees. Gross value ofValue of the optionoption 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. Executive Summary Recommendation Supporting Analysis Future Considerations 15
- 16. 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 optionValue ofoption 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. Executive Summary Recommendation Supporting Analysis Future Considerations 16
- 17. Unfortunately there is not an option available for mailbox prices.Gerard must find another put option to hedge his risk. Executive Summary Recommendation Supporting Analysis Future Considerations
- 18. 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.Executive Summary Recommendation Supporting Analysis Future Considerations 18
- 19. 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.Executive Summary Recommendation Supporting Analysis Future Considerations 19
- 20. Scatterplots show the general degree of correlation.We can expect Class III and Class IV classes to have a higher correlation coefficient.Executive Summary Recommendation Supporting Analysis Future Considerations 20
- 21. 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. Executive Summary Recommendation Supporting Analysis Future Considerations 21
- 22. 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. Executive Summary Recommendation Supporting Analysis Future Considerations 22
- 23. The client has a break-even price to be taken into account. Operation Costs Hedging Costs $12/cwt ~$0.50/cwt $12.50/cwtHe wants to ensure getting a payoff from the option if the price falls below $12.50Executive Summary Recommendation Supporting Analysis Future Considerations 23
- 24. Conditional distribution of Class III on mailbox price is normally distributed. Under certain assumptions, we will be able to determine the correct strike price. Executive Summary Recommendation Supporting Analysis Future Considerations 24
- 25. To prove the assumptions, several tests must be undergone. Our model Assumptions Normality of errors Homoscedasticity We will assess normality both graphically and mathematically.Executive Summary Recommendation Supporting Analysis Future Considerations 25
- 26. We generated the residuals and plotted their distribution. e y ˆ y This is our first evidence of normality.Executive Summary Recommendation Supporting Analysis Future Considerations 26
- 27. Another graphical way of assessing normality are probability plots. P-P and Q-Q plots also support our assumption of normality. Executive Summary Recommendation Supporting Analysis Future Considerations 27
- 28. Finally, we would like a mathematical result to confirm normality.Shapiro – Wilk test 2 where n ( i 1 ai x( i ) ) mTV 1W (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. Executive Summary Recommendation Supporting Analysis Future Considerations 28
- 29. 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. Executive Summary Recommendation Supporting Analysis Future Considerations 29
- 30. 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 $12.50? Executive Summary Recommendation Supporting Analysis Future Considerations 30
- 31. There are two options available for determining the interval. A range of values so defined as, over multiple samples, what Confidence the range of mean values of the dependent variable will be Interval when evaluated at a specified independent variable level. A range of values so defined as, given only the current sample, Prediction what the range of values for the dependent variable will be Interval when evaluated at a specified independent variable level.Since we want to predict an actual class III price using our current sample at a specific mailbox price, a prediction interval is more appropriate. Executive Summary Recommendation Supporting Analysis Future Considerations 31
- 32. Class III price as a function of the mailbox price ($/cwt) at α = 0.05. (12.5, 14.24) Class III = -1.557 + 1.182×(Mailbox Price) Executive Summary Recommendation Supporting Analysis Future Considerations 32
- 33. Class III price as a function of the mailbox price ($/cwt) at α = 0.01. (12.5, 14.69) Class III = -1.557 + 1.182×(Mailbox Price) Executive Summary Recommendation Supporting Analysis Future Considerations 33
- 34. Class III price in function of the mailbox price ($/cwt) at α = 0.10. (12.5, 14.01) Class III = -1.557 + 1.182×(Mailbox Price) Executive Summary Recommendation Supporting Analysis Future Considerations 34
- 35. 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. Executive Summary Recommendation Supporting Analysis Future Considerations 35
- 36. 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 Executive Summary Recommendation Supporting Analysis Future Considerations 36
- 37. 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 Executive Summary Recommendation Supporting Analysis Future Considerations 37
- 38. 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. Executive Summary Recommendation Supporting Analysis Future Considerations 38
- 39. There are two future considerations for Gerard. What if his operation costs change? What if option costs change?Executive Summary Recommendation Supporting Analysis Future Considerations 39
- 40. 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. Executive Summary Recommendation Supporting Analysis Future Considerations 40
- 41. 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. Executive Summary Recommendation Supporting Analysis Future Considerations 41
- 42. 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.Executive Summary Recommendation Supporting Analysis Future Considerations 42
- 43. Thank you.

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