Analysis of Price Risk in Bonds

Fill in the table below following Step $1$ and $2,$ and answer the following questions in Step $3$ and $4.$

Step $1.$ Calculate the bond price.

Bond price can be calculated from the following formula:

Bond Price $=$ Annual Coupon $(\frac{1-\frac{1}{(1+YTM{)}^t}}{YTM})+$ Face Value $\frac{1}{(1+YTM{)}^t}$

Step $2.$ Calculate the rate of change in bond price $(\%$Change in Bond Price$).$

$\%$ Change in bond price can be calculated from the following formula:

$\%$ Change $in$ Price $=\frac{\text{B}\text{o}\text{n}\text{d}\text{P}\text{r}\text{i}\text{c}\text{e}\text{a}\text{f}\text{t}\text{e}\text{r}YTM\text{c}\text{h}\text{a}\text{n}\text{g}\text{e}\text{s}}{\text{B}\text{o}\text{n}\text{d}\text{P}\text{r}\text{i}\text{c}\text{e}\text{b}\text{e}\text{f}\text{o}\text{r}\text{e}YTM\text{c}\text{h}\text{a}\text{n}\text{g}\text{e}\text{s}}-1$

Step $3.$ Analyze the Price Risk in Bonds

Which bond has a higher price risk, bond $W$ or bond $x?$ Why?

Which bond has a higher price risk, bond Y or bond Z$?$ Why?

Which bond has a higher price risk, bond W or bond Y$?$ Why?

Which bond has a higher price risk, bond X or bond Z$?$ Why?

Step $4.$ Do the findings in Step $3$ always hold? Why?