Cash flow

**Order Instructions:**

15 Points

3.1. Mortgage markets have developed significantly since the early 1970s through the creation of secondary market instruments in the form of mortgage pass-throughs, collateralized mortgage obligations (CMOs), and REMICs. These collectively have been generally referred to as mortgage backed securities (MBS). In many ways, these instruments carry the characteristics of their underlying assets — individual mortgages.

a. Why is the cash flow of a mortgage, or a MBS, uncertain in the sense that the investor in the mortgage has granted the borrower a call option to prepay the mortgage? Compare a mortgage cash flow with a Treasury coupon bearing bond paying interest semi-annually and a payment of principal at maturity.

b. What does this call option depend upon and why?

c. The cash flow for a mortgage pass-through typically is based on some prepayment speed benchmark. Why is the assumed prepayment speed necessary to price the MBS?

d. Suppose a bank has decided to invest in a MBS and is considering the following two securities: a Freddie Mac pass-through with a WAM of 340 months and an average life of 7 years or a PAC tranche of a Freddie Mac CMO issue with an average life of 2 years. In terms of prepayment risk, contraction risk and extension risk, which MBS would probably be best for the bank’s asset/liability management perspective when it is known that liabilities generally have a duration less than 1 year and that assets have durations in the 2-year to 7-year range?

Average life is:

e. Compare the interest rate risk of a noncallable 10-year Treasury coupon bearing bond with a mortgage-backed pass-through security with prepayments related to the level of interest rates – lower market interest rates raise the rate of prepayments. Discuss how the changes in cash flows from a mortgage-backed security affect the duration of such securities. HINT: consider the coupon effect on duration.

Macaulay Duration Measure:

A more complete approximation to the proportional change in price of a bond with respect to a change in yield to maturity takes into account the convexity of the price-yield relationship for the bond:

where P = Price, C = coupon, F = Face value, y = Yield to maturity, M = maturity (years), t = time (year), dP is the total change in price, and is the partial change in price with respect to a change in yield to maturity. The second term, excluding the dy2, is the convexity effect.

**SAMPLE ANSWER**

**A). Cash flow uncertainty of a MBS and comparison with Treasury coupon bearing bond**

Mortgage based securities have cash flows that are uncertain due to several factors. A MBS is a bond which is created by redistribution of cash flows to the tranches based on payment rules thus the borrower has been granted by the mortgage a call option to repay. A MBS offers an opportunity to create separate rules that stipulate payment of regular scheduled principal payment, any prepayment and coupon interest. The nature of the bond at times contributes to the uncertainty of cash flows (Milne, 2013; Sinnock, 2014). When the bond is a pay-through structure in which there is only one class of bondholders at a given level of credit priority the prepayment risk is high leading to cash flow uncertainty. In a sequential-pay tranche bond each tranche cannot receive principal payment until the preceding tranche has been paid off causing cash flow uncertainty. At times the average life of the tranches is unevenly matched with the collateral. This implies that there might be cash flow constraints if the underlying security life is shorter than the MBS life (Milne, 2013).

A MBS faces both contraction and extension risk even though other tranches might protect it. Even if it is a Partially Amortized Class (PAC) bond prepayment risk is only mitigated for some class of investors but exposed to others. Furthermore it depends on the availability of supporting bonds to take bullets for PAC bonds. In the event that the supporting bonds are less than the PAC bonds then the PAC bonds are said to have no bodyguards and are hence exposed. Cash flows are thus uncertain because it depends on the expected future prepayment behavior of the collateral and the actual prepayment experience as it determines the level of prepayment protection (Milne, 2013). Cash flows from a Treasury coupon bearing bond paying interest semi-annually and a payment of principal at maturity has assured cash flows as opposed to MBS bonds. The repayment of MBS depends on the future repayment behavior of collateral and actual prepayment experience whereas a Treasury coupon bearing bond is guaranteed by the government and its coupon payments are actually considered to be risk free and assured. Treasury coupon bearing bond rate is used as the standard for risk free investment rate in capital asset pricing model because investment is such bonds is considered risk free(Milne, 2013).

**What this call option depends upon and why**

The call option depends on a number of issues. The call option determines the type of bond that is invested in. An MBS bond can be an Interest only bond or a principal only bond. In an interest only bond the bond faces contraction risk in that if interest is paid quite fast then the risk is high since the remaining principal will fall fast reducing the amount of interest payable. A bond can be a PAC bond which has few supporting bond (Sinnock, 2014). Supporting bonds are the body guards and if they are fewer in number than the PAC bonds even though PAC bonds are noted to have lesser prepayment risk in this case it will be higher. This is because supporting bonds ensure PAC bonds principal prepayment is made before they are prepaid. The repayment of MBS depends on the future repayment behavior of collateral and actual prepayment experience of the mortgage class. Bonds can be Z bonds, sequential-pay tranches etc depending on the call option rules (Sinnock, 2014).

**The influence of prepayment speed on pricing of MBS**

The prepayment speed of a bond is determined by the principal pay-down window. This represents the time taken to repay the principal from start of prepayment to the end of the principal repayment. Tranches can have average lives that could be shorter or longer than the underlying mortgage securities (Sinnock, 2014). Tranches have considerable variability in average lifespan. Each tranche faces separate prepayment risk due to its life span. Shorter term tranches face extension risk whereas longer term tranches face contraction risk. The level of risk determines the price of the MBS. The longer the duration that the principal of a MBS will take to be repaid the higher will be the price and vice versa. This is because if repayment is slower investors will be concerned with the reinvestment risk (Sinnock, 2014).

**A decision criteria by a bank to invest in a MBS**

The Freddie Mac pass-through MBS is a pass-through security whereby cash flow of depends on the cash flow of the underlying mortgages. A weighted average maturity (WAM) is found by weighting the amount of mortgage outstanding by the remaining number of months to maturity for each mortgage loan in the pool. Freddie Mac issues a pass-through guarantees both interest and principal payments. It however guarantees the timely payment of interest only. The MBS give a guarantee that scheduled payment will be made no later than a specified date even though the scheduled principal is passed through as it is collected. Freddie Mac pass-through MBS still entails prepayment risk and uncertainty in cash flows. A Freddie Mae CMO issue with an average of 2 years is a security backed by a pool of pass-throughs, whole loans, or stripped mortgage-backed securities that are structured so there are several classes of bondholders with varying stated maturity dates. Tranches is the name given to the different classes of bonds created. Principal payments are used to retire a class of bonds given in the prospectus provided. There is still considerable prepayment risk despite the redistribution of prepayment risk with sequential pay and accrual CMOs. This problem is mitigated by planned amortization class (PAC) tranche bonds as it reduces average life variability of bonds. With lock out and reverse structure arrangement PAC bonds offer less prepayment risk. The bank should focus on matching assets and liabilities since all option pose prepayment risk. The bank should choose Fredie Mac CMO issue of a PAC tranche if its liabilities are closer to 340 months.

**Comparison of the interest rate risk of a noncallable 10-year Treasury coupon bearing bond with a mortgage-backed pass-through security with prepayments related to the level of interest rates**

The interest rate risk is determined using Macaulay Duration Measure:

(http://www.investopedia.com/terms/m/macaulayduration.asp)

Macaulay duration is an equation that measures the volatility of bond price with respect to interest rates prevailing in an economy. A noncallable 10-year Treasury coupon bearing bond is subject to volatility of interest rates in the same way as a mortgage-backed pass-through security with prepayments related to the level of interest rates. A Treasury coupon bearing bond which is noncallable faces interest rate risk since as interest rates rise the coupon payments will also feature the interest rate which is fixed and will benefit the issuer (Kim, 2011). But if interest rates fall the issuer will continue to pay the high interest rates agreed at the issuance of the treasury bearing bond. Interest rates are thus fixed and cannot be changed for a noncallable 10-year Treasury coupon bearing bond. Whereas in a mortgage-backed pass-through security with prepayments related to the level of interest rates, the issuer will benefit if rates go down since principal prepayments will go up and vice versa (Kim, 2011).** **

**References**

http://www.investopedia.com/terms/m/macaulayduration.asp

Kim, D. H. (2011). *Essays in corporate finance and bond interest rate volatility. *(Order No. 3465651, The University of Oklahoma). *ProQuest Dissertations and Theses, *, 144-n/a. Retrieved from http://search.proquest.com/docview/884226076?accountid=45049. (884226076).

Milne, A. (2013). Register, cap and trade: A proposal for containing systemic liquid risk.* **Economics, 7*(7), 0_1,1-31A. Retrieved from http://search.proquest.com/docview/1329188224?accountid=45049

Sinnock, B. (2014). Toxic mortgage bonds perform A lot better now.* **National Mortgage **News, 38*(20), 1. Retrieved from http://search.proquest.com/docview/1496773233?accountid=45049

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