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

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?

Quizplus · Accepted Answer

Allright Insurance wants to hedge the balance sheet with T-bond option contracts, which means it wants to protect itself from interest rate risk. Since the underlying bonds have a duration of 8.82 years, it is suitable to use put options to hedge against rising interest rates. Additionally, since the delta of the options is 0.5, each option contract will protect half of the value of the underlying bonds.

To calculate the number of contracts, we need to determine the value of the bonds that need to be hedged. The market value of the $90 million in Baa bonds is:

$90,000,000 x $97,000/$100,000 = $87,300,000

Therefore, the value of the bonds that need to be hedged is $87,300,000. Each put option contract covers $100,000 in face value, so the number of contracts required is:

$87,300,000 / ($100,000 x 0.5) = 625 contracts

Hence, the best choice for Allright Insurance is to use put options and purchase 625 contracts to hedge its balance sheet.

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