Question

Assume that the yield curve is as given below. Assume semi-annual compounding. Compute the par rates out to two years at semiannual intervals.

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

Hint: Compute discount factors from the yield curve using the formula from class. Then, use the formula for par yields C(T) from part 1) above.

Note! The formula gives you a decimal number, i.e. a number like 0.031875. This number means 3.1875%.

1) 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)

2)  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)

3) 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)

4) 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)

Answer 1

Par yield is the coupon rate at which bond price equals the par value of the bond. If annual par yield is c, then

(c/2)*discount factor for period 1 + (c/2)*discount factor for period 2 + ...... (par value + c/2)*discount factor for period T = par value

Using this concept, we derive the par yield formula as

c = (1 -d)*m/A where d = present value of $1 received at maturity; A = present value of an annuity that gives $1 at each coupon date and m = the frequency of payments in a year

The par yields for each time period are calculated in the last column of the table above.