Note that the futures contract involves the delivery of bonds with a face value of USD 100,000. Thus, the value of one futures contract is USD 104,000.

The number of contracts that should be traded (with a negative number indicating a short position) for a hedge should be:

$-\frac{E_V}{E_F}$

Where:

• $E_F$ is the increase in value of one futures contract for a 1-basis point downward parallel shift in the zero curve.
• $E_V$ is the increase in value of a trader's position for a 1-basis point downward parallel shift in the zero curve.

The increase in value of a trader's position for a 1-basis point downward parallel shift in the zero curve is:

$E_V = 1,000,000 \times 5 \times 0.0001 = 500$

The increase in value of one futures contract for a 1-basis point downward parallel shift in the zero curve is:

$E_F = 104,000 \times 5 \times 0.0001 = 52$

Thus, the number of contracts required is:

$= -\frac{500}{52} = -9.615 \approx -10$

The negative sign indicates a short position of approximately 10 contracts is required to fully hedge the portfolio.