Question

Suppose you have $100 million mortgage-backed security with a 4.5% coupon, with annual cash flows, annual interest payments, and the same prepayment amount each year over the life of the loan. Assume a maturity of 3 years and no amortization. Suppose you use this $100 million to create a fixed-rate sequential CMO with the following balances and coupons: Bond Balance Coupon

A. 30 2.5
B. 40 3.5
C. 30 4.5
Assuming $30 million prepays each year, what is the weighted average

Answer 1

To calculate the weighted average coupon of the fixed-rate sequential CMO, consider the balance and coupon rate of each bond tranche. Multiply the balance of each tranche by its corresponding coupon rate, summing up these values, and divide by the total balance across all tranches.

Step-by-step explanation:

In order to calculate the weighted average coupon of the fixed-rate sequential CMO, you need to consider the balance and coupon rate of each bond tranche. The weighted average coupon is determined by multiplying the balance of each tranche by its corresponding coupon rate, summing up these values, and dividing by the total balance across all tranches.

For example, for Tranche A with a balance of $30 million and a coupon rate of 2.5%, the contribution to the weighted average coupon would be 0.025 * 30 = $0.75 million. Likewise, for Tranche B with a balance of $40 million and a coupon rate of 3.5%, the contribution would be 0.035 * 40 = $1.4 million. Finally, for Tranche C with a balance of $30 million and a coupon rate of 4.5%, the contribution would be 0.045 * 30 = $1.35 million.

To calculate the weighted average coupon, add up the contributions from each tranche: $0.75 million + $1.4 million + $1.35 million = $3.5 million. Then divide this sum by the total balance across all tranches of $100 million: $3.5 million / $100 million = 0.035 or 3.5%.