Allright Insurance has total assets of $140 million consisting of $50 million in 2-year, 6 percent Treasury notes and $90 million in 10-year, 7.2 percent fixed-rate Baa bonds.These assets are funded by $100 million 5-year, 5 percent fixed rate GICs and equity. On the advice of its chief financial officer, Allright wants to hedge the balance sheet with T-bond option contracts.The underlying bonds currently have a duration of 8.82 years and a market value of $97,000 per $100,000 face value.Further, the delta of the options is 0.5.What type of contract, and how many contracts should Allright use to hedge this balance sheet?

Question

Quizplus · Accepted Answer

Allright wants to hedge against the potential decrease in the value of its bond portfolio due to rising interest rates. Therefore, it should use put options to protect against this risk. The delta of 0.5 indicates that the put options would provide effective coverage for approximately half of the portfolio. To calculate the number of contracts needed:
- Calculate the value of the bond portfolio: $90M * $97,000/$100,000 = $87,300,000
- Determine the notional amount of options needed to cover half of the bond portfolio: $87,300,000 / (2 * $100,000) = 437.5 contracts (rounded up to 438 contracts)
- Adjust for the delta of 0.5: 438 contracts / 0.5 = 876 contracts
Therefore, Allright should use 625 put option contracts to hedge its balance sheet.

Allright Insurance Has Total Assets of $140 Million Consisting of $50