1. Lecture 5

2. The art in hedging is finding the exact number of contracts to make the net gain/loss = $ 0. This is called the Hedge Ratio # of Ks = ---------------------------------- X Hedge Ratio Value Asset Value of Contract HR Goal - Find the # of contracts that will perfectly offset asset position.

3.  Previous example: An Illinois farmer planted 100 acres of wheat this week, and plans on harvesting 20,000 bushels in March. If today’s futures wheat price is $1.56 per bushel and since the farmer is long in wheat, the farmer will need to go short on March wheat contracts. Since1 contract= 5,000 bushels, the farmer will short four contracts today and close the position in March. 4 contracts = ------------------------ X 1.0 20,000 5,000

4.  Hedging the risk of one asset with a contract on another asset.  Example You manage a stock mutual fund and wish to hedge against a drop in the stock prices. Since there is no contract on your specific mutual fund, you must use a different asset. You decide to use the S&P 500 Index K

5. Asset Price Profit Loss Short S&P 500 Contract Long Stock Mutual Fund 8 10 +2 -2

6. Asset Price Profit Loss Short S&P 500 Contract Long Stock Mutual Fund Risk: Contract price behavior is different than the price behavior of the mutual fund 8 10 +2 +1 -2

7. Assume the mutual fund has a total value of $725,000. One S&P 500 index futures contract has a price of 1,450. S&P Contract Value = (price) x 250 S&P Contract Value = (1450) x 250 = 362,500 Using a hedge ratio of 1.0, the # of contracts is as follows. 2 contracts = ------------------------ X 1.0 725,000 362,500

8. Profit / loss is as follows Recall…Mutual Fund price dropped from 10 to 8….a 20% decline Recall…Index futures price dropped from 10 to 9….a 10% decline Asset PositionFutures Position StartsLong $725,000Short 2 contracts 362,500 x 2 = 725,000 Long 2 contracts to close position Price drop 20% Price drops 10% Finish725,000 x.8 = 580,000 1450 x.9 x 2 x 250 = 652,500 loss $145,000 gain $ 72,500 Net position LOSS = $ 72,500 BAD HEDGE

9. Covariance between the stock market index and an asset Variance of the stock market index

10. Asset Price Profit Loss Short S&P 500 Contract Long Stock Mutual Fund Beta of Mutual Fund = 2.0 8 10 +2 +1 -2

11. Assume the mutual fund has a total value of $725,000. One S&P 500 index futures contract has a price of 1,450. S&P Contract Value = (price) x 250 S&P Contract Value = (1450) x 250 = 362,500 Using a hedge ratio of 2.0, the # of contracts is as follows. 4 contracts = ------------------------ X 2.0 725,000 362,500

12. Profit / loss is as follows Recall…Mutual Fund price dropped from 10 to 8….a 20% decline Recall…Index futures price dropped from 10 to 9….a 10% decline Asset PositionFutures Position StartsLong $725,000Short 4 contracts 362,500 x 4 = 1,450,000 Long 4 contracts to close position Price drop 20% Price drops 10% Finish725,000 x.8 = 580,000 1450 x.9 x 4 x 250 = 1,305,000 loss $145,000 gain $ 145,000 Net position Gain / Loss = $ 0 PERFECT HEDGE

13.  A profit opportunity from change in the traditional basis spread between index prices and index futures prices  The basis spread between the index and index futures contract should be constant.  Spreads which are larger or smaller than normal will result in arbitrage opportunities.

14. Price 0 30 60 90 Time (days) --- S&P 500 Index --- S&P 500 Futures Contract

15. Price 0 30 60 90 Time (days) --- S&P 500 Index --- S&P 500 Futures Contract To return to the proper basis spread, the contract will have to drop RELATIVE TO the index. Strategy: Short the contract Long the index

16. Price 0 30 60 90 Time (days) --- S&P 500 Index --- S&P 500 Futures Contract To return to the proper basis spread, the contract will have to rise RELATIVE TO the index. Strategy: Long the contract Short the index