Answer: Portfolio ASD decreases by USD 110,000; portfolio BTE decreases by USD 70,000

## Explanation **Step 1 - Calculate the values of the two portfolios before increases in yield:** **Portfolio ASD** $P_A =$ Value before yield increase: $1,000,000 \times e^{(-0.1 \times 3)} + 1,000,000 \times e^{(-0.1 \times 9)}$ = USD 740,818.22 + USD 406,569.66 = USD 1,147,387.88 **Portfolio BTE** $P_B =$ Value before yield increase: $1,000,000 \times e^{(-0.08 \times 6)} = 618,783.39$ **Step 2 - Calculate the duration of the two portfolios before increases in yield:** **Portfolio ASD** $D_A =$ weighted-average durations of the two zero-coupon bonds = $(3 \times 740,818.22 + 9 \times 406,569.66) / 1,147,387.88 = 5.00$ **Portfolio BTE** $D_B = 6$ (since it's a single zero-coupon bond with 6-year maturity) **Step 3 - Calculate the percentage change in portfolio values using duration and convexity:** For continuous compounding, the percentage change formula is: $\Delta P/P = -D \times \Delta y + \frac{1}{2} \times C \times (\Delta y)^2$ Where: - $\Delta y = 0.02$ (200 bps increase) - $D$ = duration - $C$ = convexity **Portfolio ASD:** $\Delta P/P = -5.00 \times 0.02 + \frac{1}{2} \times 34.51 \times (0.02)^2$ = $-0.10 + 0.5 \times 34.51 \times 0.0004$ = $-0.10 + 0.006902$ = $-0.093098$ **Portfolio BTE:** $\Delta P/P = -6 \times 0.02 + \frac{1}{2} \times 36.00 \times (0.02)^2$ = $-0.12 + 0.5 \times 36.00 \times 0.0004$ = $-0.12 + 0.0072$ = $-0.1128$ **Step 4 - Calculate the dollar amount decrease:** **Portfolio ASD:** $\Delta P = 1,147,387.88 \times 0.093098 = USD 106,800$ (approximately USD 110,000) **Portfolio BTE:** $\Delta P = 618,783.39 \times 0.1128 = USD 69,800$ (approximately USD 70,000) Therefore, the best estimates are Portfolio ASD decreases by USD 110,000 and Portfolio BTE decreases by USD 70,000, which corresponds to option B.

Author: LeetQuiz .