Question

A 10-year maturity zero-coupon bond selling at a yield to maturity of 7.25% (effective annual yield) has convexity of 157.5 and modified duration of 9.06 years. A 30-year maturity 7.5% coupon bond making annual coupon payments also selling at a yield to maturity of 7.25% has nearly identical duration—9.04 years—but considerably higher convexity of 251.6.

Answer 1

Answer:

For Zero coupon: 545.52

Explanation:

Check attachment

Answer 2

Answer:

Check the explanation

Explanation:

Zero coupon

                 K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

                  k=1

                 K =10

Bond Price =∑ [(0*1000/100)/(1 + 7.25/100)^k]     +   1000/(1 + 7.25/100)^10

                  k=1

Bond Price = 496.62

Coupon bond

                 K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

                  k=1

                 K =30

Bond Price =∑ [(7.5*1000/100)/(1 + 7.25/100)^k]     +   1000/(1 + 7.25/100)^30

                  k=1

Bond Price = 1030.26

a

Zero coupon bond

New bond price at YTM =8.25

                 K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

                  k=1

                 K =10

Bond Price =∑ [(0*1000/100)/(1 + 8.25/100)^k]     +   1000/(1 + 8.25/100)^10

                  k=1

Bond Price = 452.61

Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price

=-9.06*-0.01*496.62

=44.993772

Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price

=-9.06*0.01*496.62

=-44.993772

New bond price at YTM =8.25 using duration and convexity

Convexity adjustment = 0.5*convexity*Yield_Change^2*Bond_Price

=0.5*157.5*0.01^2*496.62

=3.9108825

New bond price = bond price+Mod.duration pred.+convex. Adj.

=496.62+-44.99+3.91

=455.54

Coupon bond

New bond price at YTM =8.25

                 K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

                  k=1

                 K =30

Bond Price =∑ [(7.5*1000/100)/(1 + 8.25/100)^k]     +   1000/(1 + 8.25/100)^30

                  k=1

Bond Price = 917.52

Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price

=-9.04*0.01*1030.26

=-93.135504

New bond price at YTM =8.25 using duration and convexity

Convexity adjustment = 0.5*convexity*Yield_Change^2*Bond_Price

=0.5*251.6*0.01^2*1030.26

=12.9606708

New bond price = bond price+Mod.duration pred.+convex. Adj.

=1030.26+-93.14+12.96

=950.08

b

Zero coupon bond

New bond price at YTM =6.25

                 K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

                  k=1

                 K =10

Bond Price =∑ [(0*1000/100)/(1 + 6.25/100)^k]     +   1000/(1 + 6.25/100)^10

                  k=1

Bond Price = 545.39

New bond price at YTM =6.25 using duration

Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price

=-9.06*-0.01*496.62

=44.993772

New bond price at YTM =6.25 using duration and convexity

Convexity adjustment = 0.5*convexity*Yield_Change^2*Bond_Price

=0.5*157.5*-0.01^2*496.62

=3.9108825

New bond price = bond price+Mod.duration pred.+convex. Adj.

=496.62+44.99+-3.91

=545.52

Coupon bond

New bond price at YTM =6.25

                 K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

                  k=1

                 K =30

Bond Price =∑ [(7.5*1000/100)/(1 + 6.25/100)^k]     +   1000/(1 + 6.25/100)^30

                  k=1

Bond Price = 1167.55

Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price

=-9.04*-0.01*1030.26

=93.135504

New bond price at YTM =6.25 using duration and convexity

Convexity adjustment = 0.5*convexity*Yield_Change^2*Bond_Price

=0.5*251.6*-0.01^2*1030.26

=12.9606708

New bond price = bond price+Mod.duration pred.+convex. Adj.

=1030.26+93.14+-12.96

=1136.36