Question

Suppose the zero rates are 5%, and 5.8% for 6-month and 1-year period respectively. What is the par yield for a bond that provide semi-annual coupons with a maturity of one-year? Choose from the following;

		5.87%
		5.47%
		6.57%
		6.87%

Answer 1

Let c be the par yield
Par yield is the coupon rate such that price is equal to par
Let par be 100

c/2*e^(-5%*0.5)+c/2*e^(-5.8%*1)+100*e^(-5.8%*1)=100
=>c=(100-100*e^(-5.8%*1))/(1/2*e^(-5%*0.5)+1/2*e^(-5.8%*1))
=>c=5.87298

So, par yield=5.87%