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Derivatives

Derivatives. Lecture 5. Hedge Ratios. The art in hedging is finding the exact number of contracts to make the net gain/loss = $ 0. This is called the Hedge Ratio. Value Asset Value of Contract. # of Ks = ---------------------------------- X Hedge Ratio.

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Derivatives

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  1. Derivatives Lecture 5

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

  3. Hedge Ratios • 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. 20,000 5,000 4 contracts = ------------------------ X 1.0

  4. Cross Hedging • 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. Cross Hedging (example continued) Profit Loss Short S&P 500 Contract Long Stock Mutual Fund +2 -2 Asset Price 8 10

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

  7. Cross Hedging (example continued) • 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. 725,000 362,500 2 contracts = ------------------------ X 1.0

  8. Cross Hedging (example continued) • 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 Position Futures Position Starts Long $725,000 Short 2 contracts 362,500 x 2 = 725,000 Long 2 contracts to close position Price drop 20% Price drops 10% Finish 725,000 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. Beta Covariance between the stock market index and an asset Variance of the stock market index

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

  11. Cross Hedging (example continued) • 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. 725,000 362,500 4 contracts = ------------------------ X 2.0

  12. Cross Hedging (example continued) • 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 Position Futures Position Starts Long $725,000 Short 4 contracts 362,500 x 4 = 1,450,000 Long 4 contracts to close position Price drop 20% Price drops 10% Finish 725,000 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. Index Arbitrage • 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. Index Arbitrage --- S&P 500 Index ---S&P 500 Futures Contract Price 0 30 60 90 Time (days)

  15. Index Arbitrage • --- 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 Price 0 30 60 90 Time (days)

  16. Index Arbitrage (another example) • --- 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 Price 0 30 60 90 Time (days)

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