You manage a share portfolio currently worth $250m Australian dollars. The beta of this portfolio is 1.25. Index put options trade on the S&P/ASX200 index with a strike price of 6900. Calculate the number of index put options required to fully hedge this share portfolio. Note that S&P/ASX200 index options have a standard multiplier of $10. Round your answer to the nearest whole number.
Question
You manage a share portfolio currently worth $250m Australian dollars. The beta of this portfolio is 1.25.
Index put options trade on the S&P/ASX200 index with a strike price of 6900.
Calculate the number of index put options required to fully hedge this share portfolio.
Note that S&P/ASX200 index options have a standard multiplier of $10. Round your answer to the nearest whole number.
Solution
To calculate the number of index put options required to fully hedge the share portfolio, we need to follow these steps:
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Calculate the portfolio beta-adjusted value: This is done by multiplying the portfolio value by the beta. In this case, it would be 312.5m.
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Convert this value to the same units as the index options: The S&P/ASX200 index options have a standard multiplier of 10. This would be 10 = 31.25 million units.
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Calculate the number of options: This is done by dividing the beta-adjusted portfolio value (in units of $10) by the strike price of the options. In this case, it would be 31.25 million units / 6900 = approximately 4528.99 options.
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Round to the nearest whole number: Since we can't have a fraction of an option, we round this number to the nearest whole number. So, the number of index put options required to fully hedge this share portfolio is approximately 4529.
Similar Questions
You manage a share portfolio currently worth $250m Australian dollars. The beta of this portfolio is 1.25. Index put options trade on the S&P/ASX200 index with a strike price of 6900. Calculate the number of index put options required to fully hedge this share portfolio. Note that S&P/ASX200 index options have a standard multiplier of $10. Round your answer to the nearest whole number.
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