An FI has a $100 million portfolio of 6 year Eurodollar bonds with an 8% coupon. The bonds are trading at par and have a duration of 5 years. The FI wishes to hedge the portfolio with T-bond options, which have a delta of -0.625. The underlying bonds on the option have a duration of 10.1 years and trade at $96157 per $100000 face value. Each put option has a premium of 3.25 (% of $100000).
How many put options are needed to hedge the portfolio?
If interest rates increase by 1%, what’s the expected gain or loss on the puts?
If interest rates increase by 1%, what’s the expected change in market value?
How far must interest rates move before the gain on the bond portfolio offsets the cost of the hedge?