To completely hedge the fixed income portfolio's key rate exposures, the combined Key Rate '01s of the portfolio and the hedging bonds must equal zero for each tenor. Let $F_1, F_2, F_3$ be the face amounts (in hundreds of USD) of Bond 1, Bond 2, and Bond 3 needed.

1. 30-year exposure: Bond 3 is the only hedging instrument with a 30-year exposure. $300.0000 + F_3 \times 0.0487 = 0$$F_3 = -300.0000 / 0.0487 = -6160.16$Since$F_3$is in hundreds, the face value is$-6160.16 \times 100 = -616,016 \approx -616,000$. The negative sign implies selling USD 616,000 of Bond 3.

2. 10-year exposure: Both Bond 2 and Bond 3 have 10-year exposures. $193.4292 + F_2 \times 0.0250 + (-6160.16) \times 0.0314 = 0$`$193.42`92 + F_2 \times 0.0250 - 193.429 = 0$$F_2 \times 0.0250 \approx 0 \implies F_2 = 0$ No transaction is needed for Bond 2.

3. 5-year exposure: Bonds 1, 2, and 3 all have 5-year exposures. $80.4895 + F_1 \times 0.0175 + F_2 \times 0.0099 + F_3 \times 0.0232 = 0$`$80.4895 + F_1 \times 0.0175 + 0 + (-6160.16) \times 0.0232 = 0$ $80.48`95 + F_1 \times 0.0175 - 142.9157 = 0$ $F_1 \times 0.0175 = 62.4262$ $F_1 = 62.4262 / 0.0175 = 3567.21$ Since $F_1$ is in hundreds, the face value is $3567.21 \times 100 = 356,721 \approx 357,000$. The positive sign implies buying USD 357,000 of Bond 1.

The correct transaction is to buy USD 357,000 of Bond 1 and sell USD 616,000 of Bond 3.