Answer: Portfolio ASD: USD 110,000 Portfolio BTE: USD 70,000

The correct answer to the question is option B, which estimates a decrease in value of USD 110,000 for portfolio ASD and USD 70,000 for portfolio BTE due to a parallel shift in the yield curve by 200 basis points (bps). The explanation is as follows: 1. **Value Calculation Before Yield Increase**: The initial step is to calculate the current value of each portfolio before the yield increase. This is done by discounting the future cash flows of each bond at their respective yields using the formula for the present value of a zero-coupon bond, which is \( P = \frac{FV}{e^{rt}} \), where \( P \) is the present value, \( FV \) is the face value, \( r \) is the yield, and \( t \) is the time to maturity. - For **Portfolio ASD**, the value is calculated by summing the present values of Bond 1 and Bond 2: \( Pa = 1,000,000 \cdot e^{-0.1 \cdot 3} + 1,000,000 \cdot e^{-0.1 \cdot 9} \) \( Pa = USD 740,818.22 + USD 406,569.66 = USD 1,147,387.88 \) - For **Portfolio BTE**, the value is calculated for Bond 3: \( PB = 1,000,000 \cdot e^{-0.08 \cdot 6} = USD 618,783.39 \) 2. **Duration Calculation**: Duration measures the sensitivity of a bond's price to changes in interest rates. The weighted-average duration is calculated for each portfolio by taking the weighted sum of the time to maturity for each bond, weighted by the present value of each bond's cash flow. - For **Portfolio ASD**, the duration \( Da \) is calculated as: \( Da = 3 \cdot \left(\frac{740,818.22}{1,147,387.88}\right) + 9 \cdot \left(\frac{406,569.66}{1,147,387.88}\right) = 5.13 \) years 3. **Convexity Calculation**: Convexity is a measure of the curvature or the rate at which the duration of a bond changes as interest rates change. It provides a more accurate measure of the price sensitivity of a bond to interest rate changes than duration alone. - The convexities given are 34.51 for portfolio ASD and 36.00 for portfolio BTE. 4. **Estimating the Decrease in Value**: The decrease in value due to a change in yield can be estimated using the first-order (duration) and second-order (convexity) approximations. The formula for the change in price due to a change in yield is: \( \Delta P = -P \cdot \Delta y \cdot D - \frac{1}{2} P \cdot (\Delta y)^2 \cdot C \) where \( \Delta P \) is the change in price, \( P \) is the initial price, \( \Delta y \) is the change in yield, \( D \) is the duration, and \( C \) is the convexity. - For **Portfolio ASD**, the decrease in value is: \( \Delta Pa = -1,147,387.88 \cdot 0.02 \cdot 5.13 - \frac{1}{2} \cdot 1,147,387.88 \cdot (0.02)^2 \cdot 34.51 \) - For **Portfolio BTE**, the decrease in value is: \( \Delta PB = -618,783.39 \cdot 0.02 \cdot 5.13 - \frac{1}{2} \cdot 618,783.39 \cdot (0.02)^2 \cdot 36.00 \) After calculating these values, the estimated decrease in value for portfolio ASD is USD 110,000, and for portfolio BTE, it is USD 70,000, which corresponds to option B. This analysis assumes continuous compounding and uses the approximation formulas for duration and convexity to estimate the impact of a parallel shift in the yield curve on the portfolio values.