Mortgage markets
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?
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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.
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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
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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).
b. 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).
c. 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
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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).
d. 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
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Fredie Mac CMO issue of a PAC tranche if its liabilities are closer to 340 months.
e. 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
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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).
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References
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.
