You manage a share portfolio currently worth $25m 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 $25m 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 31.25m.
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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 31.25m / $10 = 3,125,000 units.
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Calculate the number of options: This is done by dividing the beta-adjusted portfolio value (in units) by the strike price of the options. In this case, it would be 3,125,000 / 6900 = approximately 453 options.
So, to fully hedge this share portfolio, you would need to buy approximately 453 index put options. Please note that in practice, you can only buy a whole number of options, so you would need to round this number to the nearest whole number.
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