2. "The story of mortgage-backed securities begins when ordinary mortgages become securitized, or bundled into a pool and then sold. It's a bit ironic that some of the most sophisticated financial derivatives ultimately depend on a very common, even mundane, instrument the homeowner's mortgage. These mortgages provide the underlying collateral backing up the security. "The first type of mortgage-backed security, still quite common, is the pass-through. Investors get a pro rata share of payments -- some fraction of the monthly mortgage payments made by the myriad homeowners in the pool. Since each monthly payment includes both principle and interest, investors get a mixture of those elements passed through' from the homeowners. This presents a problem in that the security has a very long maturity -- it takes years until the last homeowner completely pays off the last mortgage and returns the full value of the principle. Since homeowners have the option to pre-pay their mortgages, pass-through securities also include the risk that payments may arrive on a different schedule than investors initially expected. "In the summer of 1983, an important financial derivative, the Collateralized Mortgage Obligation (CMO), was developed by the Federal Home Loan Mortgage Corporation (Freddie Mac) to solve these problems. CMOs break the mortgage-backed security into a series of bonds known as 'tranches.' Each tranche gets its share of interest payments, but the principal is repaid sequentially. That is, principal payments go exclusively to the first tranche until it is paid off, then to the second tranche until it is paid off, and so forth. This breaks the security into several shorter bonds. For example, an investor holding $10 million of a $100 million 'pass-through' would not get all of his principal back until every mortgage had been paid off. By contrast, the holder of a $10 million first tranche CMO would get his principal back from the first $10 million paid. "The standard CMO still exhibits two types of risk. Interest-rate risk exists because market rates can change, making the present value of the payment stream worth different amounts. Pre-payment risk still exists, and it continues to make the maturity of the bond uncertain. For example, as interest rates fall, more people refinance and pre-pay their mortgages, so each tranche has a shorter maturity. As interest rates rise, fewer people pre-pay their mortgages, so each tranche has a longer maturity." (a) Why does an investor in CMOs care whether the underlying mortgages are being prepaid, and how does it affect the value of the bond (tranche)? How would an increase in interest rates affect the price of a CMO bond (be sure to explain how a rise in rates would lengthen the pay-off period for CMO bond holders)? (b) Normally, bond holders benefit if interest rates drop because it gives them a capital gain; but, the pre-payment effect makes CMOs behave somewhat differently. The bond holder receives more principal today, when interest rates are low, and consequently must sacrifice the high interest on the original CMO for lower interest on another security. Explain how this "reinvestment risk" may offset the capital gain resulting from the lower interest rates. 2. "The story of mortgage-backed securities begins when ordinary mortgages become securitized, or bundled into a pool and then sold. It's a bit ironic that some of the most sophisticated financial derivatives ultimately depend on a very common, even mundane, instrument the homeowner's mortgage. These mortgages provide the underlying collateral backing up the security. "The first type of mortgage-backed security, still quite common, is the pass-through. Investors get a pro rata share of payments -- some fraction of the monthly mortgage payments made by the myriad homeowners in the pool. Since each monthly payment includes both principle and interest, investors get a mixture of those elements passed through' from the homeowners. This presents a problem in that the security has a very long maturity -- it takes years until the last homeowner completely pays off the last mortgage and returns the full value of the principle. Since homeowners have the option to pre-pay their mortgages, pass-through securities also include the risk that payments may arrive on a different schedule than investors initially expected. "In the summer of 1983, an important financial derivative, the Collateralized Mortgage Obligation (CMO), was developed by the Federal Home Loan Mortgage Corporation (Freddie Mac) to solve these problems. CMOs break the mortgage-backed security into a series of bonds known as 'tranches.' Each tranche gets its share of interest payments, but the principal is repaid sequentially. That is, principal payments go exclusively to the first tranche until it is paid off, then to the second tranche until it is paid off, and so forth. This breaks the security into several shorter bonds. For example, an investor holding $10 million of a $100 million 'pass-through' would not get all of his principal back until every mortgage had been paid off. By contrast, the holder of a $10 million first tranche CMO would get his principal back from the first $10 million paid. "The standard CMO still exhibits two types of risk. Interest-rate risk exists because market rates can change, making the present value of the payment stream worth different amounts. Pre-payment risk still exists, and it continues to make the maturity of the bond uncertain. For example, as interest rates fall, more people refinance and pre-pay their mortgages, so each tranche has a shorter maturity. As interest rates rise, fewer people pre-pay their mortgages, so each tranche has a longer maturity." (a) Why does an investor in CMOs care whether the underlying mortgages are being prepaid, and how does it affect the value of the bond (tranche)? How would an increase in interest rates affect the price of a CMO bond (be sure to explain how a rise in rates would lengthen the pay-off period for CMO bond holders)? (b) Normally, bond holders benefit if interest rates drop because it gives them a capital gain; but, the pre-payment effect makes CMOs behave somewhat differently. The bond holder receives more principal today, when interest rates are low, and consequently must sacrifice the high interest on the original CMO for lower interest on another security. Explain how this "reinvestment risk" may offset the capital gain resulting from the lower interest rates