Answer: 46.68 million, 39.1%

To construct a hedged butterfly position with a notional amount of EUR 100 million in the 5-year swap, the manager wants to neutralize the exposures to the level and slope principal components (PCs). The analyst has provided the current swap rates and Dv01s for the 2-year, 5-year, and 10-year swaps. The goal is to find the appropriate notional amounts for the 2-year and 10-year swaps and their risk weights relative to the Dv01 of the 5-year swap. The principal components analysis (PCA) results show the impact of each PC on the swap rates. The level PC has the greatest impact, followed by the slope PC, and the short rate PC has the least impact on the swap rates. The 5-year swap is the payer swap, and the 2-year and 10-year swaps are receiver swaps. To neutralize the exposures to the level and slope PCs, we need to find the notional amounts for the 2-year and 10-year swaps that will offset the exposures of the 5-year swap. We can use the PCA results and the Dv01s to calculate the risk weights. Let's denote the notional amount of the 2-year swap as \( N_2 \) and the notional amount of the 10-year swap as \( N_{10} \). The risk weights for the 2-year and 10-year swaps relative to the Dv01 of the 5-year swap can be calculated as follows: Risk weight of 2-year swap = \( \frac{N_2 \times DV01_{2-year}}{DV01_{5-year}} \) Risk weight of 10-year swap = \( \frac{N_{10} \times DV01_{10-year}}{DV01_{5-year}} \) We want the exposures to the level and slope PCs to be neutralized, which means the sum of the exposures for the 2-year and 10-year swaps should be equal and opposite to the exposure of the 5-year swap. Using the PCA results, we can set up the following equations: For the level PC: \( 5.06 \times N_2 + 5.43 \times N_{10} = -5.97 \times 100 \) (since the 5-year swap is the payer swap) For the slope PC: \( -2.93 \times N_2 + 0.02 \times N_{10} = 1.28 \times 100 \) (again, the 5-year swap is the payer swap) Solving these equations will give us the notional amounts \( N_2 \) and \( N_{10} \) that will neutralize the exposures to the level and slope PCs. Once we have \( N_2 \) and \( N_{10} \), we can calculate the risk weights using the formula mentioned earlier. The correct choice will be the one that satisfies the conditions of neutralizing the exposures to the level and slope PCs and has the appropriate risk weights relative to the Dv01 of the 5-year swap.

Author: LeetQuiz Editorial Team