The number of futures contracts to fully hedge the portfolio is given by:

N = -(P × DP) / (FC × DF)

Where:

• P = forward value of the fixed-income portfolio being hedged = $20,000,000
• DP = duration of the portfolio at the maturity date of the hedge = 5
• FC = futures contract price = $200,000
• DF = duration of the asset underlying the futures = 3

Thus: N = -($20,000,000 × 5) / ($200,000 × 3) N = -$100,000,000 / $600,000 N = -166.6667 ≈ -166

The negative sign implies that the number of contracts taken up must be the opposite of the original position. If the investor is long a portfolio, they must short N contracts to produce a position with zero duration. Therefore, 166 contracts should be shorted.