Question

the 6-month and 1-year zero rates are 3% and 4%

The 6-month and 1-year zero rates are 3% and 4% per annum with semi-annual compounding. Which of the following is the par yield for a bond that provides semi-annual coupons with a maturity of one year and a par value of 1007 *Do not convert to a continuous compounding version of par yield 04.03% 3.99% 3.89% 3.95%

Answer 1

Par yield is equals to coupon rate thus Bond price equals to par value of bond.

In given case,

Par value of bond = $100

Coupon amount(semi-annual) = C

6-month zero rate = 3% pa. = 1.5% semi-annual

1-year zero rate = 4% p.a = 2% semi-annual.

Putting the the values in Bond value formula.

$\frac{C}{(1+0.015)}+\frac{C}{(1+0.02)^2}+\frac{100}{(1+0.02)^2} = 100$

by solving,

thus,

Annual coupon rate or Par yield:

$\textup{Par yield} = \frac{2*1.995037}{100}$

$\large \textup{Par yield} = 3.99\%$

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.