1. Agricultural Marketing
ECON 337:
Agricultural Marketing
Lee Schulz
Assistant Professor 1

2. Optimal Hedging
Depending on how well futures prices move with cash prices, it may not be optimal to hedge a cash position with a futures position 1 for 1.
Spot
Futures
Quantity
500,000 bushels
350,000 bushels

3. Optimal Hedging
Hedge Ratio: Ratio of the size of the futures and spot positions

4. Optimal Hedging Naïve hedge ratio: h =1
Hedge in the futures market exactly the same quantity that you have in the spot market

5. Optimal Hedging Optimal Hedge Ratio:
You want to choose the number of contracts so that the value of your hedged position has as small a variance as possible.

6. Optimal Hedging
Optimal Hedge Ratio:
Divide all terms by

7. Optimal Hedging
Optimal Hedge Ratio:
Divide all terms by

8. Optimal Hedging Optimal Hedge Ratio:
You want the variance of your hedged position to be as small as possible
Minimum of happens when

9. Optimal Hedging Optimal Hedge Ratio: Minimum of happens when
If the covariance of spot and futures price changes in the soybean market is 0.009
And the variance of futures price changes is
Then

10. Optimal Hedging Optimal Hedge Ratio:
Means that the soybean farmer should have only hedged in the futures market with 83.3% of the bushels he intended to sell in the cash market.
500,000 bu in spot
500,000* = 416,650 bu (83 contracts instead of 100)

11. Optimal Hedging Optimal Hedge Ratio:
Hedging is all about reducing the variance of the value of your total position
When there is uncertainty in the basis hedging 1 for 1 in the futures market is not optimal
Optimal hedge ratio:

12. Hedging Effectiveness
Definition
Percentage reduction in risk from total un-hedged position to total hedged position
i.e., how much hedging can reduce your risk
Risk in hedged position
change in value of combined spot and futures position
Risk involved in un-hedged position:
change in value of spot position

13. Hedging Effectiveness
Calculating hedging effectiveness

14. Class web site: