An investor owns a bond with a value of $980 that has a modified duration of 6.0. The investor expects interest rates to rise by 50 basis points. To hedge against this interest rate risk, the investor plans to use an interest rate future contract. Each futures contract has a price of $100,000 and a modified duration of 4.5. How many futures contracts should the investor sell to fully hedge the portfolio's interest rate risk?

Correct answer: C. 13 contracts

The number of futures contracts (Nf) needed to hedge a bond portfolio's interest rate risk is calculated as Nf = (Portfolio Value * Portfolio Modified Duration) / (Futures Price * Futures Modified Duration). Portfolio Value = $980,000 (assuming $980 is 980,000 for a realistic bond portfolio size), Portfolio Modified Duration = 6.0, Futures Price = $100,000, Futures Modified Duration = 4.5. Nf = ($980,000 * 6.0) / ($100,000 * 4.5) = $5,880,000 / $450,000 = 13.066. Therefore, the investor should sell approximately 13 futures contracts. If the portfolio value was literally $980, then the answer would be 0.013 contracts, which is not realistic. Assuming $980,000 for 'a bond with a value of $980' (which is a common way to phrase a bond price per $1000 par), then 13 contracts is correct.