3.2.1.4. Hedge Ratio
Now that we have some understanding of what beta is and how it works, we can calculate the hedge ratio for index futures. Remember that the hedge ratio is the number of futures contracts required to maximize a hedge. The hedge ratio is determined by the following formula:
Since the index reflects the market as a whole, the beta of the index is always equal to one. To find the hedge ratio then, you simply need to multiply the portfolio’s beta by the quotient of the value of your portfolio and the value of the index.
Sample Question 1
An investor buys 5 S&P 500 futures contracts, currently trading at 2,040 and deposits $21,000 per contract in her margin account. When the contracts rise to 2,050, the investor closes her position. The contract multiplier for the S&P 500 is $250. What is her profit or loss?
Answer: $12,500. Each contract rises in price by ten index points. Five contracts times 10 points times a contract multiplier of $250 yields a profit of $12,500. The margin percentage is irrelevant in calculating the dollar profit, but the $12,500 represents a profit margin of almost 12% on the $105,000 deposited ($21,000 x 5 contracts).
Sample Question 2
You have a stock portfolio valued at $928,000. The portfolio contains mostly small-cap securities that have a weighted average beta of 0.748, compared to its benchmark Russell 2000 Index, currently trading at 1,160. The contract multiplier for the Russell 2000 is 100. Fearing a market downturn, you decide to hedge your portfolio with Russell 2000 futures. How many contracts must you short to hedge your entire portfolio?
Answer: 6. To find the appropriate hedg