Question

Suppose three Treasury zero-coupon bonds with one, two and three years to maturity are trading for $989, $972 and $960 respectively. All three bonds have $1,000 par value (value paid at maturity). Construct and draw segment of the Treasury yield curve corresponding to 1-3 years to maturity. Please provide all necessary computations and indicate all relevant values on the graph.

Answer 1

YTM of Zero Coupon Bond = [ Maturity Price / Current Price ] ^ ( 1 / n ) - 1

n is Time Period.

Maturity 1 Year:

Particulars	Amount
Maturity price	$ 1,000.00
Current Price	$    989.00
Maturity period	1

YTM = [ Maturity Value / Current Price ] ^ ( 1 / n ) - 1
= [ $ 1000 / $ 989 ] ^ ( 1 / 1) - 1
= [ 1.0111 ] ^ ( 1 / 1) - 1
= 1.0111 - 1
= 0.0111
I.e 1.11 %
Maturity 2 Year:

Particulars	Amount
Maturity price	$ 1,000.00
Current Price	$    972.00
Maturity period	2

YTM = [ Maturity Value / Current Price ] ^ ( 1 / n ) - 1
= [ $ 1000 / $ 972 ] ^ ( 1 / 2) - 1
= [ 1.0288 ] ^ ( 1 / 2) - 1
= 1.0143 - 1
= 0.0143
I.e 1.43 %
  Maturity 3 Year:

Particulars	Amount
Maturity price	$ 1,000.00
Current Price	$    960.00
Maturity period	3

YTM = [ Maturity Value / Current Price ] ^ ( 1 / n ) - 1
= [ $ 1000 / $ 960 ] ^ ( 1 / 3) - 1
= [ 1.0417 ] ^ ( 1 / 3) - 1
= 1.0137 - 1
= 0.0137
I.e 1.37 %
Yield Curve:

X -Axis = Years

Y - Axis = YTM