2011 CFA Program Curriculum: Level 2, Volume 5

CFA Institute

Chapter 57 MORTGAGE-BACKED SECTOR OF THE BOND MARKET - all with Video Answers

Educators

Chapter Questions

Problem 1

A. Complete the following schedule for a 30-year fully amortizing mortgage loan with a mortgage rate of $7.25 \%$ where the amount borrowed is $$\$ 150,000$$. The monthly mortgage payment is $$\$ 1,023.26$$.
B. Complete the following schedule for the mortgage loan in part A given the following information:

Charles Carter

Numerade Educator

04:34

Problem 2

A. Suppose that the servicing fee for a mortgage loan is $0.5 \%$. Complete the following schedule for the mortgage loan in the previous question. The column labeled "Servicing Fee" is the dollar amount of the servicing fee for the month. The column labeled "Net Interest" is the monthly interest after the servicing fee for the month.
B. Determine for the first six months the cash flow for an investor who purchases this mortgage loan after the servicing fee is paid.

Harmender Singh Yadav

Numerade Educator

Problem 3

Explain why you agree or disagree with the following statement: "Since mortgage passthrough securities issued by Ginnie Mae are guaranted by the full faith and credit of the U.S. government, there is no uncertainty about the cash flow for the security."

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Problem 4

Consider the following mortgage pool.
A. What is the weighted average coupon rate for this mortgage pool?
B. What is the weighted average maturity for this mortgage pool?

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Problem 5

Mr. Jamison is looking at the historical prepayment for a passthrough security. He finds the following:
mortgage balance in month $$42=\$ 260,000,000$$
scheduled principal payment in month $$42=\$ 1,000,000$$
prepayment in month $$42=\$ 2,450,000$$
A. What is the SMM for month 42 ?
B. How should Mr: Jamison interpret the SMM computed?
C. What is the CPR for month 42 ?
D. How should $\mathrm{Mr}$. Jamison interpret the CPR computed?

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Problem 6

Using the Public Securities Association Prepayment benchmark, complete the following table:
$$
\begin{array}{rrrr}
\hline \text { Month } & \text { PSA } & \text { CPR } & \text { SMM } \\
\hline 5 & 100 & & \\
15 & 80 & & \\
20 & 175 & & \\
27 & 50 & & \\
88 & 200 & & \\
136 & 75 & & \\
220 & 225 & & \\
\hline
\end{array}
$$

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Problem 7

Explain why 30 months after the origination of a mortgage pool, discussing prepayments in terms of one CPR and a PSA are identical.

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Problem 8

Suppose that in month 140 the mortgage balance for a mortgage pool underlying a passthrough security is $$\$ 537$$ million and that the scheduled principal repayment for month 140 is $$\$ 440,000$$. Assuming $175 \mathrm{PSA}$, what is the amount of the prepayment for month 140 ?

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Problem 9

Comment on the following statement: "The PSA model is a prepayment model."

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06:06

Problem 10

Robert Reed is an assistant portfolio manager who has been recently given the responsibility of assisting Joan Soprano, the portfolio manager for the mortgage-backed securities portfolio. Ms. Soprano gave Mr. Reed a copy of the Prudential Securities publication for November 1999 entitled Mortgage and Asse-Backed Prepayment and Issuance. An excerpt from the publication is given below:
The mortgage rate at the time of the report was $8.13 \%$.
$\mathrm{Mr}$. Reed asks the following questions about the information in the above excerpt. Respond to each question.
A. What does "GNMA 30 YEAR" mean?
B. What does "8.5 1994 " mean?
C. What do the numbers under "PROJECTED" mean?
D. Do the prepayment rates for "7.5 $1993^"$ apply to all GNMA issues in the market?
E. Why are the projected prepayments for "one year" and "long term" such that they increase with the coupon rate?

Sophie Knight

Numerade Educator

Problem 11

Suppose that you are analyzing prepayments of a passthrough security that was issued more than 15 years ago. The weighted average coupon (WAC) for the underlying mortgage pool was $13 \%$. Suppose that the mortgage rate over the year of the analysis declined from $8 \%$ to $7 \%$ but prepayments for this mortgage pool you are analyzing did not increase. Explain why there is no increase in prepayments despite the lower mortgage rate relative to $13 \%$ being paid by borrowers and the decline in the mortgage rates over the year.

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Problem 12

What type of prepayment risk is an investor interested in a short-term security concerned with when purchasing a mortgage-backed security?

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04:56

Problem 13

Suppose that a portfolio manager is considering a collateralized mortgage obligation structure KMF-01. This structure has three tranches. The deal is a simple sequential pay and was issued several years ago. The tranches are $A, B$, and $C$ with a coupon rate paid to each tranche each month and principal payments are made first to tranche $A$, then to tranche $B$, and finally to tranche G. Here is the status of the deal as of the time of the analysis:
A. Compute the principal, interest, and cash flow for tranche A for the 48 months.
B. Compute the principal, interest, and cash flow for tranche B for the 48 months.
C. Compute the principal, interest, and cash flow for tranche $\mathrm{C}$ for the 48 months.
D. Compute the average life for tranche $A$.

Julie Silva

Numerade Educator

Problem 14

Suppose that in the previous $\mathrm{CMO}$ structure, $\mathrm{KMF}-01$, that tranche $\mathrm{C}$ is an accrual tranche that accrues coupon interest monthly. We will refer to this new CMO structure as KMF-02.
A. What is the principal repayment, interest, and cash flow for tranche A in $\mathrm{KMF}-02$ ?
B. What is the principal balance for tranche $\mathrm{C}$ for the first five months?
C. What is the average life for tranche $\mathrm{A}$ in $\mathrm{KMF}-02$ and contrast this with the average life for tranche $\mathrm{A}$ in $\mathrm{KMF}=01$ ?

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Problem 15

Explain why it is necessary to have a cap for the floater when a fixed-rate tranche is split into a floater and an inverse floater.

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01:34

Problem 16

Suppose that a tranche from which a floater and an inverse floater are created has an average life of six years. What will be the average life of the floater and the inverse floater?

Wendi Zhao

Numerade Educator

Problem 17

How does a $\mathrm{CMO}$ alter the cash flow from mortgages so as to redistribute the prepayment risk across various tranches in a deal?

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Problem 18

"By creating a $\mathrm{CMO}$, an issuer eliminates the prepayment risk associated with the underlying mortgages loans." Explain why you agree or disagree with this statement.

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Problem 19

Ellen Morgan received a phone call from the trustee of a pension fund. Ms. Morgan is the portfolio manager for the pension fund's bond portfolio. The trustee expressed concerns abont the inclusion of CMOs in the portfolio. The trustee's concern arose after reading several articles in the popular press where the CMO market was characterized as the sector of the mortgage-backed securities market with the greatest prepayment risk and the passthrough sector as the safest sector in terms of prepayment risk. What should Ms. Morgan say to this trustee regarding such statements made in the popular press?

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Problem 20

What is the role of a support tranche in a CMO structure?

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Problem 21

Suppose that the manager of a savings \& loan association portfolio has decided to invest in mortgage-backed securities and is considering the following two securities: i) a Fannie Mae passthrough security with a WAM of 310 months or ii) a PAC tranche of a Fannie Mae CMO issue with an average life of 2 years. Which mortgage-backed security would probably be better from an asset/liability perspective?

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Problem 22

Suppose that a PAC bond is created using prepayment speeds of $90 \mathrm{PSA}$ and $240 \mathrm{PSA}$ and the average life is 5 years. Will the average life for this PAC tranche be shorter than, longer than, or equal to 5 years if the collateral pays at 140 PSA over its life? Explain your answer.

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Problem 23

Suppose that $$\$ 1$$ billion of passthroughs are used to create a CMO structure, $\mathrm{KMF}-05$. This structure includes a PAC tranche with a par value of $$\$ 650$$ million and a support tranche with a par value of $$\$ 350$$ million.
A. Which of the following will have the least average life variability: i) the collateral, ii) the PAC tranche, or iii) the support tranche? Why?
B. Which of the following will have the greatest average life variability: i) the collateral, ii) the PAC tranche, or iii) the support tranche? Why?

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Problem 24

Suppose that the $$\$ 1$$ billion of collateral in the $\mathrm{CMO}$ structure $\mathrm{KMF}=05$ in the previous question was divided into a PAC tranche with a par value of $$\$ 800$$ million and a support tranche with a par value of $$\$ 200$$ million (instead of $$\$ 650$$ million and $$\$ 350$$ million). The new structure is KMF-06. Will the PAC tranche in KMF-06 have more or less protection than the PAC tranche in KMF-05?

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04:53

Problem 25

Suppose that $$\$ 500$$ million of passthroughs are used to create a CMO structure with a PAC tranche with a par value of $$\$ 350$$ million (PAC I), a support tranche with a schedule (PAC II) with a par value of $$\$ 100$$ million, and a support tranche without a schedule with a par value of $$\$ 200$$ million.
A. Will the PAC I or PAC II have less average life variability? Why?
B. Will the support tranche without a schedule or the PAC II have the greater average life variability? Why?

Karen Song

Numerade Educator

Problem 26

In a CMO structure with several PAC tranches that pay off sequentially, explain what the structure effectively becomes once all the support tranches are paid off.

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01:03

Problem 27

Suppose that for the first four years of a $\mathrm{CMO}$, prepayments are well below the initial upper PAC collar and within the initial lower PAC collar. What will happen to the effective upper collar?

Sheryl Ezze

Numerade Educator

Problem 28

Consider the following CMO structure backed by $8 \%$ collateral:
$$
\begin{array}{lcc}
\hline \hline \text { Tranche } & \text { Par Amount (\$) } & \text { Coupon Rate (\%) } \\
\hline \text { A } & 400,000,000 & 6.25 \\
\text { B } & 200,000,000 & 6.75 \\
\text { C } & 225,000,000 & 7.50 \\
\text { D } & 175,000,000 & 7.75 \\
\hline
\end{array}
$$
Suppose that the structurer of this CMO wants to create a notional IO tranche with a coupon rate of $8 \%$. Calculate the notional amount for this notional IO tranche.

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Problem 29

An issuer is considering the following two CMO structures:
Structure I:
$$
\begin{array}{lcc}
\hline \text { Tranche } & \text { Par Amount (5) } & \text { Coupon Rate (\%) } \\
\hline \text { A } & 150 \text { million } & 6.50 \\
\text { B } & 100 \text { million } & 6.75 \\
\text { C } & 200 \text { million } & 7.25 \\
\text { D } & 150 \text { million } & 7.75 \\
\text { E } & 100 \text { million } & 8.00 \\
\text { F } & 500 \text { million } & 8.50 \\
\hline
\end{array}
$$
Tranches A-E are a sequence of $\mathrm{PAC}$ Is, and $\mathrm{F}$ is the support tranche.
Structure II:
$$
\begin{array}{lcc}
\hline \text { Tranche } & \text { Par Amount (\$) } & \text { Coupon Rate (\%) } \\
\hline \text { A } & 150 \text { million } & 6.50 \\
\text { B } & 100 \text { million } & 6.75 \\
\text { C } & 200 \text { million } & 7.25 \\
\hline \text { D } & 150 \text { million } & 7.75 \\
\text { E } & 100 \text { million } & 8.00 \\
\text { F } & 200 \text { million } & 8.25 \\
\hline \text { G } & 300 \text { million } & \text { ???? } \\
\hline
\end{array}
$$
Tranches A-E are a sequence of PAC Is, F is a PAC II, and G is a support tranche without a schedule.
A. In Structure II tranche $\mathrm{G}$ is created from tranche $\mathrm{F}$ in Structure I. What is the coupon rate for tranche $\mathrm{G}$ assuming that the combined coupon rate for tranches $\mathrm{F}$ and $\mathrm{G}$ in Structure II should be $8.5 \%$ ?
B. What is the effect on the value and average life of tranches $\mathrm{A}-\mathrm{E}$ by including the PAC II in Structure II?
C. What is the difference in the average life variability of tranche $G$ in Structure II and tranche F in Structure I?

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Problem 30

What is a broken or busted PAC?

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03:26

Problem 31

Assume that in FJF-01 (see Exhibit 5 in the reading), tranche $C$ had been split to create a floater with a principal of $$\$ 80,416,667$$ and an inverse floater with a principal of $$\$ 16,083,333$$.
A. What would be the cap rate for the inverse floater if the coupon rate for the floater is 1-month LIBOR plus $1 \%$ ?
B. Assuming that 1) the coupon formula for the floater is 1-month LIBOR plus $1 \%$ and 2 ) a floor is imposed on the inverse floater of zero, what would be the cap rate on the floater?

James Kiss

Numerade Educator

01:58

Problem 32

A. In assessing the prepayment protection offered by a seasoned PAC tranche, explain why the initial collars may provide limited insight?
B. What measure provides better information about the prepayment protection offered by a seasoned PAC tranche?

Anand Jangid

Numerade Educator

Problem 33

A. For a mortgage loan, is a higher or lower loan-to-value ratio an indication of greater credit risk? Explain why.
B. What is the empirical relationship between defaults and loan-to-value ratio observed by studies of residential mortgage loans?

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Problem 34

A. What is a principal-only mortgage strip and an interest-only mortgage strip?
B. How does an interest-only mortgage strip differ with respect to the certainty about the cash flow from a Treasury strip created from the coupon interest?
C. How is the price of an interest-only mortgage strip expected to change when interest rates change?

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02:34

Problem 35

A. An investor purchased $$\$ 10$$ million par value of a $7 \%$ Ginnie Mae passthrough security agreeing to pay 102 . The pool factor is 0.72 . How much does the investor pay to the seller?
B. Why would an investor who wants to purchase a principal-only mortgage strip not want to do so on a TBA basis?

Ayush Naidu

Numerade Educator

Problem 36

Why can't all residential mortgage loans be securitized by either Ginnie Mae, Fannie Mae, or Freddie Mac?

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Problem 37

Why is credit enhancement needed for a nonagency mortgage-backed security?

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04:55

Problem 38

With respect to a default by the borrower, how does a residential mortgage loan differ from a commercial mortgage loan?

Pragya Ahuja

Numerade Educator

Problem 39

Why is the debt-to-service coverage ratio used to assess the credit risk of a commercial mortgage loan?

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Problem 40

A. What types of provisions are usually included in a commercial loan to protect the lender against prepayment risk?
B. In a commercial mortgage-backed securities deal, explain why the investor in a security may be afforded prepayment protection at the deal level.

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Problem 41

What is balloon risk and how is it related to extension risk?

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Problem 42

In the prevailing economic envinonment, which of the following best describes the risk encountered by investors in mortgage passthrough securities?
A. Extension risk, because prepayments are most likely to increase.
B. Extension risk, because prepayments are most likely to decrease.
C. Cycle risk, because prepayments are most likely to increase.

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Problem 43

The WAC and WAM for Security A are closest to:
$$
\begin{array}{|c|c|c|}
\hline & \text { WAC } & \text { WAM } \\
\hline & 6.04 \% & 167 \text { months } \\
\hline & 6.07 \% & 165 \text { months } \\
\hline & 6.07 \% & 167 \text { months } \\
\hline
\end{array}
$$

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Problem 44

Which of the securities is most likely subject to higher interest-rate risk?
A. Security $A$, because it has a longer maturity.
B. Security B, because it has a higher coupon.
C. Security B, because it has a longer average life.

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Problem 45

Given $150 \mathrm{PSA}$, the CPR (conditional prepayment rate) and SMM (single monthly mortality rate) for Security B for month 140 are closest to:
A. $6.0 \% \quad 0.5143 \%$
B. $6.0 \% \quad 0.7828 \%$
C. $9.0 \% \quad 0.7828 \%$

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04:03

Problem 46

The monthly mortgage-servicing fee for Security $\bar{B}$ is closest to:
A. $0.05 \%$.
B. $0.50 \%$.
C. $0.60 \%$.

Narayan Hari

Numerade Educator

Problem 47

Which of the two securities is most likely to have the lower credit risk?
A. Security $A$ because it has the shortest average life.
B. Security B because it has an "agency" guarantee.
C. Security $\mathrm{B}$ because it has conventional mortgages.

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