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

The question is assessing the impact of a parallel shift in the yield curve on two portfolios, ASD and BTE, which contain zero-coupon bonds. The manager is interested in the decrease in the values of these portfolios due to a 20 basis point increase in yields, taking into account both duration and convexity. The explanation provided in the file content is as follows: 1. **Value Calculation Before Yield Increase**: The initial values of the portfolios are calculated using the present value formula for zero-coupon bonds, which is the face value multiplied by \( e^{-rt} \), where \( r \) is the yield to maturity, \( t \) is the time to maturity, and \( e \) is the base of the natural logarithm. For portfolio ASD, the sum of the present values of Bond 1 and Bond 2 is USD 1,147,387.88. For portfolio BTE, the present value of Bond 3 is USD 618,783.39. 2. **Duration Calculation**: Duration is a measure of the sensitivity of the price of a bond to changes in interest rates. For portfolio ASD, the weighted-average duration is calculated by taking the weighted sum of the durations of the individual bonds, which is 5.13 years. For portfolio BTE, the duration is approximately equal to the maturity of the bond, which is 6.00 years. 3. **Convexity Given**: Convexity is a measure of the curvature or the rate at which the duration changes as yields change. It is given for both portfolios: 34.51 for ASD and 36.00 for BTE. 4. **Yield Increase and Value Decrease**: The manager simulates a 20 basis point increase in yields across all points of the yield curve. The decrease in the value of each portfolio is estimated using the formula that incorporates both duration and convexity adjustments for small changes in yield: \[ \Delta P = -D \Delta y P + \frac{1}{2} C (\Delta y)^2 P \] where \( \Delta P \) is the change in price, \( D \) is the duration, \( \Delta y \) is the change in yield, \( C \) is the convexity, and \( P \) is the initial price of the portfolio. 5. **Final Calculation**: Using the above formula and the given values, the decrease in the value of portfolio ASD is calculated to be USD 110,000, and for portfolio BTE, it is USD 70,000. The correct answer is B, which states that Portfolio ASD decreases by USD 110,000 and Portfolio BTE decreases by USD 70,000. This answer is derived from the calculations based on the initial values, durations, convexities, and the change in yield provided in the question.

Author: LeetQuiz Editorial Team