Question

The following data shows the current prices of four default free zero coupon bonds. The redemption price in each case is 100Euro.

Maturity from now (in years) 1 2 3 4

Price now 98.12 95.46 92.39 88.72

Calculate the yield to maturity and explain the zero coupon yield curve using your answer from yield calculation

Answer 1

YTM is the rate of return from a bond till its maturity period.

YTM of 1 year Zero coupon bond = [ Maturity after a year / Current price ] - 1

= [100 / 98.12 ] - 1

= 1.0192 - 1

= 0.0192 i.e 1.92%

YTM of 2 year Zero coupon bond = [ Maturity after a year / Current price ]^1/2 - 1

= [100 / 95.46 ]^1/2 - 1

= [1.0476]^1/2 - 1

= 1.0235 - 1

= 0.0235 i.e 2.35%

YTM of 3 year Zero coupon bond = [ Maturity after a year / Current price ]^1/3 - 1

=[100 / 92.39 ]^1/3 - 1

= [1.0824]^1/3 - 1

= 1.0267 - 1

= 0.0267 i.e 2.67%

YTM of 4 year Zero coupon bond = [ Maturity after a year / Current price ]^1/4 - 1

=[100 / 88.72 ]^1/4 - 1

= [1.1271]^1/4 - 1

= 1.0304 - 1

= 0.0304 i.e 3.04%

Yield curve is graph on which Yield is plotted on one axis and time is plotted on another axis.

Year1 - 1.92%

Year2 - 2.35%

Year3 - 2.67%

Year4 - 3.04%