Question

2. A bond pays a 5% quarterly on a 30/360 basis.

(a) What yield on an actual/360 basis is equivalent to the 5% yield on a 30/360 basis when the coupon period is 89 days?

(b) What is the mortgage equivalent yield of a quarterly paying bond with a 5% yield?

can someone explain this in detail please, I am really confused on how to calculate interest using different day counts

Answer 1

Answer (a):

Quarterly payment on a 30/360 basis is payment for 90 days.

Actual coupon period is 89 days

The yield on an actual/360 basis which is equivalent to the 5% yield on a 30/360 basis = 90 /89 * 5% = 5.0562%

The yield on an actual/360 basis which is equivalent to the 5% yield on a 30/360 basis = 5.0562%

Answer (b):

Effective annual rate of quarterly paying bond with a 5% yield = (1 + 5% / 4) ⁴ - 1=5.09453%

Let us assume mortgage equivalent yield = r

Effective annual rate of mortgage with r yield = (1 + r / 12) ¹²- 1

Hence:

=> (1 + r / 12) ¹²- 1 = 5.09453%

=> (1 + r / 12) ¹²​​​​​​​ = 5.09453% + 1

=> 1 + r / 12 = (1.0509453) ^1/12 = 1.004149

> r / 12 = 1.004149 - 1 = 0.004149

=> r = 0.004149 * 12 = 4.98%

Mortgage equivalent yield = 4.98%