Question

Assume that the yield curve is as given below. Assume semi-annual compounding.

a- Calculate the 6-month par yield . Write your answer as a decimal with six digits after the decimal point (e.g. 3.1875% is to be entered as 0.031875)

b- Calculate the 1-year par yield . Write your answer as a decimal with six digits after the decimal point (e.g. 3.1875% is to be entered as 0.031875)

c- Calculate the 1.5-year par yield . Write your answer as a decimal with six digits after the decimal point (e.g. 3.1875% is to be entered as 0.031875)

d- Calculate the 2-year par yield . Write your answer as a decimal with six digits after the decimal point (e.g. 3.1875% is to be entered as 0.031875)

T (in years)	r(T)
0.50	0.047502
1.00	0.050016
1.50	0.052508
2.00	0.054751

Answer 1

The par yield is the coupon rate that causes the Bond price equal to the par value.

Considering the par value as $100

'c/2' is the semi-annual coupon and 'c' is the required par yield

Here, we find the value of c for which the bond value is at par ie. $100

Coupons are giving every 6 months, and the cash flow generated is discounted based on the yield curve rates given.

a.)

Solving this equation, we get c= 4.7502% = 0.047502

b.)

Solving this equation, we get c= 4.998493% = 0.049984

c.)

Solving this equation, we get c= 5.24211% = 0.052421

d.)

Solving this equation, we get c= 5.459252% = 0.054592