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 Insurance holds fixed-rate bonds with a long duration of 8.82 years. Therefore, to hedge against interest rate risk, it should use put options as they provide protection against a fall in bond prices resulting from a rise in interest rates. The delta of 0.5 indicates that the value of the option will change by 0.5 for every 1% change in the price of the underlying bonds. 
To calculate the number of contracts needed, we use the following formula:
Number of contracts = (Dollar value of assets / 100) * (Duration of assets / Delta of options)
= ($140 million / 100) * (8.82 / 0.5)
= 625 contracts. 
Therefore, the best choice is option C, puts; 625 contracts.

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