In duration-based hedging, how is the number of contracts calculated?

In duration-based hedging, the calculation of the number of contracts needed is grounded in the relationship between the duration of the portfolio and the duration of the hedging instrument, typically futures contracts. The correct formula is derived from the goal of matching the interest rate sensitivity of the portfolio with that of the futures contracts, thereby minimizing interest rate risk exposure.

The formula involves several components: the value of the portfolio, the duration of the portfolio (often represented as Dp), the value of the futures contract, and the duration of the futures contract (Df). The negative sign in front of the formula reflects that a short position in futures is typically initiated to hedge against a decrease in interest rates, which would negatively impact the value of a bond portfolio.

The correct choice shows the appropriate relationship between these elements:

• The portfolio value is multiplied by the change in duration (Dp) to estimate the overall interest rate risk of the portfolio.

• This value is then divided by the product of the futures value and its duration (Df), allowing for the value of the futures contracts to counterbalance the risk from the portfolio.

This calculation effectively allows the hedger to determine the necessary number of futures contracts to maintain a neutral duration stance, ensuring that any adverse movement in interest rates