Gadah interpretation

There is an interest rate risk with bonds because the prices of bonds change inversely with interest rates. This implies that an increase in interest rate results in a decrease in the bond price while a decrease in interest rate results in a rise in bond prices. Duration and uncertainty helps investors in quantifying the level of uncertainty to the fixed-income investing.

The current price of the bond is $1162.2179. However, taking the potential change in the bond’s value in case the YTM rises by 2 percent using duration, modified duration and convexity implies that the new price will be $1069.47, $1073.0335 and $1077.80 respectively.  Therefore, an increase in the YTM results in the increase of the bond’s value. Larger changes in the interest rates often yield larger discrepancies between the bond’s actual price and the new price calculated using duration and convexity.

Since the bond price is equal to the total present value of all the bond payment, therefore the price of the bond will change inversely to the changes in the yield. This implies that the price of the bond will increase in case the yield to maturity decreased by 2 percent instead of increase. The current price of the bond is $1162.2179. However, the new price becomes $1254.97, $1251.40 and $1256.17 with regards to duration, modified duration and convexity. Modified duration is often relatively less than duration because it is the duration divided by one added to the yield per payment period. There is an increase in the bond’s value due to negative convexity because the changes in bond price are in the same direction as changes in the yield.

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