Question

A 5 year bond that has the same feature as one of your 30 years bonds ie, same rating and same coupon rate of 4.5% and YTM of 6%. Calculate the new price of bond at the new YTM of 2%,4%, 8%, and 10% for both 5-years bond and 30-years bond. Plot the graph of the relationship between the price and YTM for each bond on the same graph. What did you find regarding the relationship between price and YTM for shorter and longer maturity bond? Which bond has a higher sensitive to the change in the price when the yield change?

	Price at 2%	Price at 4%	Price at 6%	Price at 8%	Price at 10%
5 year bond
30 year bond

Fill in graph and answer questions. Thank you!

Answer 1

Suppose the face value (par value) is $1000.

	price at 2%	price at 4%	price at 6%	price at 8%	price at 10%
5 years bond	1117.84	1022.26	936.81	860.26	791.51
30 years bond	1559.91	1086.46	793.53	605.98	481.52

1800 1600 1400 1200 1000 5 years 800 +30 years 600 400 200 0 2% 4% 6% 8% 10%

It can be found that as the YTM rises,the bond price falls.A general conclusion from the graph can be that the bond price decreases with a rise in YTM.WE can say that there is an inverse relationship between bond price and YTM.

The longer maturity bonds will be priced higher than shorter maturity bonds.Here bond having 30 years maturity prices bond than the bond with % years of maturity.

The 30-year bond is sensitive to change in the price than a 5-year bond.