The formula to calculate the Bond Convexity is:
\[ \text{Bond Convexity} = \frac{BP_{\text{up}} + BP_{\text{down}} - 2 \times BP}{BP \times (YD)^2} \]
Where:
Bond Convexity measures the sensitivity of the duration of a bond to changes in interest rates. It helps assess the risk and potential price changes of a bond when interest rates fluctuate.
Let's assume the following for Bond Alpha:
Step 1: Calculate the coupon per period:
\[ \text{Coupon per period} = \frac{1,000 \times 5\%}{1} = $50 \]
Step 2: Calculate the bond price:
\[ \text{Bond Price} = \sum_{k=1}^{10} \frac{50}{(1 + 8\%)^k} + \frac{1,050}{(1 + 8\%)^{10}} = $798.70 \]
Step 3: Calculate the bond price after shifting the bond yield:
For an upward shift (7% YTM):
\[ \text{Upwards Bond Price} = \sum_{k=1}^{10} \frac{50}{(1 + 7\%)^k} + \frac{1,050}{(1 + 7\%)^{10}} = $859.53 \]
For a downward shift (9% YTM):
\[ \text{Downwards Bond Price} = \sum_{k=1}^{10} \frac{50}{(1 + 9\%)^k} + \frac{1,050}{(1 + 9\%)^{10}} = $743.29 \]
Step 4: Calculate the bond convexity:
\[ \text{Bond Convexity} = \frac{859.53 + 743.29 - 2 \times 798.70}{798.70 \times (1\%)^2} = 67.95 \]
