Transcript Derivatives
Lecture 23 Valued similar to bonds (fixed incomes) Factors Prepayment Weighted average coupon (WAC) ◦ The monthly payment derived from the interest rate charged on the loans. Weighted average maturity (WAM) Required yield (YTM) Default (similar to prepayment) Cash Flow Pattern for Bonds Bonds Loan Payment 12 10 8 Interest Principal 6 4 2 0 1 2 3 4 5 6 Years 7 8 9 10 Cash Flow Pattern for MORTGAGES Reflecting PREPAYMENT Mortgages Loan Payment 12 10 8 Interest Principal 6 4 2 0 1 2 3 4 5 6 Years 7 8 9 10 MBS Valuation MBA Value = PV of cash flows Steps 1. Determine the monthly payment 2. Use prepayment assumption to derive maturity 3. Calculate the PV of the monthly payment at the YTM. MBS Valuation Using present value terminology PV = Price of MBS Pmt = monthly coupon payment from MBS i = Yield to Maturity n = t = Prepayment year assumption FV = Balance of mortgage at prepayment Example A mortgage pool contains $13,000,000 in loans made to homeowners. The weighted average maturity of these mortgages is 22 years. The weighted average interest rate charged on the loans is 6.5%. If the mortgage pool requires a risk adjusted yield to maturity of 7.4%, what is the value of the mortgage pool? Example A mortgage pool contains $13,000,000 in loans made to homeowners. The weighted average maturity of these mortgages is 22 years. The weighted average interest rate charged on the loans is 6.5%. If the mortgage pool requires a risk adjusted yield to maturity of 7.4%, what is the value of the mortgage pool? Assume NO prepayment. Step 1 – Find the monthly payment PV = $ 13,000,000 FV = 0 n = 264 (22 x 12) i = 0.54 % ( .065 / 12 ) solving for the PMT PMT = - 92,682 Example A mortgage pool contains $13,000,000 in loans made to homeowners. The weighted average maturity of these mortgages is 22 years. The weighted average interest rate charged on the loans is 6.5%. If the mortgage pool requires a risk adjusted yield to maturity of 7.4%, what is the value of the mortgage pool? Assume NO prepayment. Step 2 – Find Present Value of the monthly payments at the YTM PMT = - 92,682 FV = 0 n = 264 (22 x 12) i = 0.6167 % ( .074 / 12 ) solving for the PV PV = $ 12,061,114 Example A mortgage pool contains $13,000,000 in loans made to homeowners. The weighted average maturity of these mortgages is 22 years. The weighted average interest rate charged on the loans is 6.5%. If the mortgage pool requires a risk adjusted yield to maturity of 7.4%, what is the value of the mortgage pool? Instead, assume the loans are completely prepaid at the end of year 15. Example A mortgage pool contains $13,000,000 in loans made to homeowners. The weighted average maturity of these mortgages is 22 years. The weighted average interest rate charged on the loans is 6.5%. If the mortgage pool requires a risk adjusted yield to maturity of 7.4%, what is the value of the mortgage pool? Instead, assume the loans are completely prepaid at the end of year 15. Step 1 – Same as before. Calculate the monthly payment PMT = 92,682 Example A mortgage pool contains $13,000,000 in loans made to homeowners. The weighted average maturity of these mortgages is 22 years. The weighted average interest rate charged on the loans is 6.5%. If the mortgage pool requires a risk adjusted yield to maturity of 7.4%, what is the value of the mortgage pool? Instead, assume the loans are completely prepaid at the end of year 15. Step 2 – NEW – Calculate the balance at the end of year 15. PMT = - 92,682 PV = 13,000,000 i = 0.54 % ( .065 / 12 ) n = 180 (15 x 12) solving for the FV FV = - 6,241,454 Example A mortgage pool contains $13,000,000 in loans made to homeowners. The weighted average maturity of these mortgages is 22 years. The weighted average interest rate charged on the loans is 6.5%. If the mortgage pool requires a risk adjusted yield to maturity of 7.4%, what is the value of the mortgage pool? Instead, assume the loans are completely prepaid at the end of year 15. Step 3 – NEW – Calculate the PV of the new cash flows. PMT = - 92,682 FV = - 6,241,454 i = 0.6167 % ( .074 / 12 ) n = 180 (15 x 12) solving for the PV PV = $ 12,123,449 Example - Analysis Notice the MBS value drops from $ 12,061,114 to $ 12,123,449 when the prepayment assumption is added. Why? The MBS selling at a discount because the YTM was higher than the coupon. By getting the money sooner, the discount is reduced. REMIC - real estate mortgage investment conduits Variable maturity tranche Variable/Fixed rate tranche IO PO