- The document analyzes investment opportunities in tranches of Freddie Mac Multi Class Certificate Offering 2884. - Two cash flow models are constructed to value the tranches, with the second utilizing a more sophisticated prepayment model. - Based on 100 simulations, tranche ST was found to have the lowest standard deviation and risk relative to par value, making it the most suitable investment for the fund.

1. MUSTANG FUTURE ENDOWMENT
INVESTMENT RECOMMENDATION
Analysis By: Ben Katz, Arvin Khorram & Oleksandr Firsov
MARCH 10, 2016
CAL POLY
BUS 435

2. 1
Abstract
MUSTANG Future Endowment seeks an investment comparable to treasuries in its risk
profile, but producing higher returns. Thus, we turn to Freddie Mac’s mortgage backed
securities, Gold PCs, as a solution. We construct a model to value the tranches of Freddie Mac
Multi Class Offering Series 2884, and conduct sensitivity analysis in order to make a
recommendation in accordance with our client’s goals. Based on the Goldman Sachs prepayment
model, and utilizing the Cox-Ingersoll-Ross interest rate simulation process, we show that
tranche ST of this offering is the most logical investment for the endowment.
Contents
Abstract........................................................................................................................................... 1
1. Executive Summary.................................................................................................................... 2
2. Security Overview ...................................................................................................................... 3
3. Methodology............................................................................................................................... 6
4. Results....................................................................................................................................... 10
5. Recommendation ...................................................................................................................... 12
Appendix 1.................................................................................................................................... 14
Appendix 2.................................................................................................................................... 15
Appendix 3.................................................................................................................................... 16
Appendix 4.................................................................................................................................... 16

3. 2
1. Executive Summary
The investments in Freddie Mac Multi Class Certificates Offering 2884 are tranches of a
mortgage backed security. This means that they are slices of the collateral pool of mortgages
which generate the investments’ income. The separation into tranches allows for the creation of a
variety of risk profiles, one of which we deem well suited for MUSTANG Future Endowment.
We begin by explaining the security being examined, such that the client may understand the
investment. The concepts of what a security is and that of tranches are explained. We then
further explain the floating tranches FT, ST, FV, and SV, which stand out from the rest due to
their variable coupons. A discussion of the guarantees, limits, and structure associated with the
distribution of cash flows among the tranches follows. The introduction made, we proceed to
explain our analysis methodology. We construct two similar models in this process, differing in
their risk framework, but utilizing the same cash flow distribution structure. The first is used to
match values found in the prospectus, ensuring the validity of the portion which is constant
between the two models. This model utilizes PSA, a linear prepayment model which gives a
simple forecast of prepayment amounts based on an eventual constant monthly prepayment
reached after 30 months, and on various ramp-up speeds to it. The second model substitutes the
PSA model for the Goldman Sachs prepayment model, which is much more nuanced, and as a
result nonlinear. This model incorporates refinance incentive, seasoning, monthly factors, and
burnout. Among a variety of constant factors, refinance incentive is based on variable LIBOR
rates, which we forecast using the Cox-Ingersoll-Ross process. Once our model is confirmed, we
use it to calculate average value, standard deviation, option-adjusted spread, and duration of each
tranche. Our analysis discovered that tranche ST provides the best investment opportunity for the
MUSTANG Future Endowment, satisfying the low-risk preferences of the fund.

4. 3
2. Security Overview
Given the risk averse profile of the MUSTANG Future Endowment, it is recommended
than an investment be made into a mortgage backed security (MBS). The MBS market offers
large a wide array of high value investments, some of which make perfect matches to the
endowment’s risk-return profile. Freddie Mac Multiclass Certificate Offering Series 2884 (which
we henceforth denote as “the security”) offers such investments, one of which stands out
especially among others.
The offering is for tranches, or “slices,” of a mortgage pass-through security. This entails
a specific process in which the ownership of the original mortgages is sold by the originator
down a chain of entities. A special purpose entity (SPE) is created to handle to handle the pool,
while the originator remains with a small stake to ensure integrity in the sold assets and their
servicing--repossessions, payment collection, and other maintenance tasks as they may arise. The
SPE then hires structuring agents, underwriters, lawyers, and other participants, all of which
work to restructure the pool into the aforementioned tranches, enabling the creation of the
investment opportunities we are examining. The creation of these tranches effectively generates
a certain amount of individual investment opportunities, each with its own risk profile. The
tranches and their basic descriptions are listed in the prospectus, an image of which is included
below in Figure 1.

5. 4
Figure 1 – Tranche details, as provided by the prospectus
This process of securitization results in a number of numerical implications, the most
evident of which is the change in the interest amount paid from the original pool to the holders of
each tranche. While the original interest rate on the mortgages is 5.99% (from here on denoted as
the weighted average cost of capital, or the WAC), Figure 1 clearly indicated a smaller amount.
This is because 0.49% of the interest is allocated as fees to the originator and servicer FHLMC
Trust and to underwriter JPMorgan, leaving the coupon payments of most tranches at 5.5%. A
notable exception in this can be seen in the FT, FV, ST, and SV tranches, which are categorized
as “FLT” and “INV” in the prospectus. These stand for “floater” and “Inverse floater,”
respectively. The coupons on these depend on the London Interbank Offered Rate, or LIBOR,
the rate at which banks lend to each other, and thus serves as a benchmark of global interest
rates. The floaters more in the same direction of the LIBOR, while the inverse floaters more in

6. 5
the opposite direction. The specific coupons of these tranches, as they are linked to LIBOR, are
provided in Figure 2. Additionally, the tranches are structured in such a way that the floaters and
inverse floaters may be combined to form single merged tranches with coupons of 5.5%. The
merged pairs with this coupon are FT and ST, and FV and SV.
Figure 2 – Coupon rate details for floaters and inverse floaters, as provided by the prospectus
The other notable, and the most important, implication of the securitization process is the
structure of the security, which assigns a particular order in which tranches receive their shares
of the payments made to the collective pool (shares of the collateral cash flows), and imposes
guarantees and limits on the amount of interest and principal paid at each step. The limits and
guarantees are provided directly by Freddie Mac, which thus serves as a credit enhancer--an
entity which reduces the risk associated with the investments. The interest is guaranteed by the
agency, with each investment classified as a Gold Participation Certificate, and is paid out to all
tranches before any principal payments are made. The interest amount is directly based on the
coupon of each tranche and its balance at any given period. The structure of payments to the
tranches’ principals is more complex, and is given in Figure 3. To better illustrate the flows to
principle, we provide a simple example in Appendix X. This structuring has a direct effect on the
cash flows to each tranche, and thus alters the date at which the final payments to them are made,
the associated volatilities, and the return on each of the investments.

7. 6
Figure 3 – Order of recoupment of principle, as provided by the prospectus
3. Methodology
A standard in the valuation of every investment is the creation of a model for its cash
flows. The model for this offering depends on variable and fixed components. The variable
component, which is subject to a degree of uncertainty, is the vector of prepayment amounts,
which in themselves capture refinancing risk and the risk of early sale (which can be interpreted
as a form of refinancing, even though the real asset changes hands). The fixed components are
ones which are locked in through the use of constant inputs and structure. Specifically, they
include the balances, maturities, coupons, costs of capital, and target balances of each tranche at
every period, as well as the order in which the tranches receive payments. Based on this
categorization, the model can be viewed as being made up of two parts—a variable and a fixed

8. 7
one, accordingly. We utilize two similar models which merge both of them. The first model is
similar to the one used in the prospectus, and we use it to ensure the validity of our interpretation
of the security’s structure, which makes up the fixed portion of both models. We do this by
approximately matching the values presented in the prospectus. With the validity of the fixed
portion of the model established, we swap out the variable model for a different, more precise
one, which provides a much more realistic view of prepayment. This is the final model with
which we conduct all further analysis of the security.
The fixed portion of the model follows calculations on a per-period basis. At each period,
it utilizes the inputs of the conditional prepayment rate (CPR), the weighted average cost of
capital (WAC), the coupon amount, the weighted average maturity (WAM), and the current
period. The CPR is the proportion of the total outstanding balance of the pool which is prepaid in
the given period. The WAM is the average length of the maturities of the mortgages in the pool.
These are used to calculated the mortgage payment, the interest, and the fees at each period.
Using these, we calculated the scheduled principal amount. We then combine the scheduled
principal with the scheduled prepayment amount, which we derive from the period’s outstanding
balance and the single month mortality, the percentage of the principal that is prepaid in the
current month, and is itself derived from the CPR. This gives us total principle, which we use to
find both the period’s collateral cash flow and the next period’s outstanding balance. Having
obtained the collateral cash flow, we proceed to allocate the cash to tranches, following the
structure in Figure 3. This process is a one-for-one mathematical representation of the process
outlined in the prospectus.
To verify the integrity of the fixed portion of the model, we replicate a table found in the
prospectus. We utilize the Public Securities Association Standard Prepayment model (PSA), the

9. 8
same type of model as is used in the prospectus, in order to find CPR values for each period, and
to approximately match the weighted average life (WAL) table found constructed by Freddie
Mac. The WALs are the numbers of years which will be required to pay off half the principle of
each tranche, and we use this as a bridging point between our interpretation of the security’s
structure, and that of the structurer. The PSA model gives CPR values at every period with an
assumption of a linear “ramp-up” period. This period accounts for the fact that the prepayment
amount gradually increases in the first 30 months after the initiation of the mortgage, until it
tapers off to a constant rate. This behavior can be attributed to reduced financial stability
associated with moving costs, such as the need to pay the down payment on the mortgage, and is
corroborated with empirical evidence. The linear increase also implicitly captures risk associated
with refinancing and moving. This model is able to account for variations in the ramp-up period,
adjusting for the maximum prepayment amount by altering the ramp-up speed, which is
interpreted as a percentage and called the PSA value.
In Figure 4, we approximately match the WAL values of the prospectus, utilizing the
stated PSA inputs. It should be noted that some variability is present between the two tables. This
occurs because significant information is not available on the structure of the model used in the
prospectus. One such discrepancy is its failure to consistently state the PSA used for each
tranche. Though the table gives definite values, the prospectus later states that tranche-specific
ranges were used. The methodology behind this procedure is not known. Nevertheless, our
model’s results match those of the prospectus closely. The only major deviations are found at 0
PSA, and can be disregarded because of this—a PSA value of zero implies that no prepayments
at all are ever made, resulting in entirely unrealistic results.

10. 9
Figure 4 – Weighted average life table as calculated by our cash flow model, at varying PSAs
With the fixed portion of the model verified, we swap the PSA model for a more
powerful one. We utilize the Goldman Sachs 1989 prepayment model, which gives a nonlinear
prediction of CPR. This model incorporates several concepts in a nonlinear fashion. The
refinance incentive, the seasoning factor, the monthly prepayment factor, and the burnout factor
parameters at each period are all multiplied together to produce the CPR for that period. The
refinance incentive parameter accounts for the changing incentives stemming from the mortgage
rate exceeding the refinancing rate. The burnout factor accounts for actual execution of this
refinancing, in that some individuals may act of the present incentives in a timely manner, and
others may not. This is dependent on the proportion of the principal outstanding during the
period to its initial balance. The seasoning factor accounts for prepayment changes based on the
mortgages’ ages, and the monthly prepayment factor includes the empirical variations present in
prepayment amounts based on the calendar months.
Special attention is paid to the refinance incentive component of the model, which is
based not only on calibrated constants, but also on the variable LIBOR rates. To obtain these
rates, we employ the Cox-Ingersoll-Ross (CIR) process. This method utilizes an initial rate, the
short rate, in a model with fixed parameters and a variable error term, taken randomly from a
normal distribution with a mean of 0 and a standard deviation of 1. The process also relies on
several constants: alpha, beta, and sigma. These represent the speed with which one approaches
Tranche 0 100 270 300 600
FT and ST 29.4 27.8 3.4 1.7 0.5
FV and SV 27.5 19.3 2.5 2.4 1.4
GN 24.3 11.0 6.6 4.9 2.2
GP 24.8 18.7 15.0 6.1 2.3
GT 25.5 11.0 3.4 3.1 1.9
GX 14.9 6.9 6.9 6.9 4.0
PSA

11. 10
the long term interest rate, how high the long term rate can be, and the volatility of the time
series, respectively. Initially, we set alpha to 0.1, beta to 0.0775, and sigma to 0.0225. The
formula outputs the short rate at the next period, which is cycled back into the formula to
produce the one after, and so forth. Graphs of one of these rate paths and the resulting CPR path
are provided in Appendix 1.
4. Results
After running one hundred simulations of each tranche’s cash flows, we determined
average both average present values and standard deviations of each tranche, discounting by the
simulated spot rates. These values, as well as the 5% and 95% quantile values, can be seen in
Figure 5. All tranches are valued at higher amount than their par value, with tranche GX’s
average value deviating from par the most by $10,936,681, or 5.59%. Standard deviations of
each tranche vary from $2,366 to $3,244,874, of tranche FT and GX respectively. It is important
to note that when comparing standard deviations to par value tranche FT, FV, and ST have the
lowest values at .02%, .04%, and .30% respectively. Tranche GX has the highest standard
deviation to par value ratio, at 1.66%. The 5% and 95% quantile values further show the effect of
tranche standard deviation on possible value.
Figure 5 – Average value, standard deviation, and 5%/95% quantile values
Tranche Average Value Average Std. Deviation 5% Quantile Value 95% Quantile Value
Tranche FT $11,597,851 $2,366.16 $11,593,469 $11,601,062
Tranche FV $39,492,480 $15,379.46 $39,474,293 $39,518,633
Tranche GN $7,631,782 $40,291.67 $7,563,977 $7,692,302
Tranche GP $11,245,483 $69,242.63 $11,124,852 $11,349,530
Tranche GT $9,465,074 $40,638.96 $9,397,713 $9,530,561
Tranche GX $206,612,681 $3,244,874.82 $200,573,917 $211,876,472
Tranche ST $3,223,075 $9,569.97 $3,207,239 $3,238,493
Tranche SV $24,318,974 $171,861.72 $24,025,593 $24,552,574

12. 11
Further analysis of average value allowed for the solving of each tranche’s option-
adjusted spread, or OAS. OAS, in this context, is the discount rate spread above the spot rates
that makes the present value of each tranche’s cash flows equal to its par value. A tranche with a
high OAS is desired, as a higher OAS indicates a larger risk premium, which in turn indicates a
more favorable investment. The tranche OAS values can be seen in Figure 6. Also, in Figure 7
the effect of a one percent shift in OAS on average value is shown. This could be seen as a
measure of risk, and tranche GX has the highest change in value, dropping in value by over $7.5
million for a 1% rise in OAS. Tranche ST has the lowest change in value, dropping by only
$11,786 for the same rise in OAS.
Figure 6 – Average option-adjusted spread
From the changes in value, we were able to calculate key-rate duration of each tranche.
Key-rate duration is a measure of sensitivity of the value of each tranche to a change in yield. In
laymen terms, it is a measure of the approximate price change of a tranche if the OAS shifts. A
tranche with a low key-rate duration is desired, as a lower duration indicates less sensitivity to
OAS shifts, which implies less risk to the investor. These duration values are shown in Figure 8,
with tranche ST having the lowest duration of 0.375.
Tranche -1% Change in OAS +1% Change in OAS
GX $8,024,513 -$7,520,644
FV $438,940 -$433,134
SV $258,762 -$255,367
GP $216,884 -$212,288
GT $141,730 -$139,316
GN $132,574 -$130,045
FT $44,044 -$43,813
ST $11,848 -$11,786
Change in Value
Figure 7 – Change in tranche values due to a 1% change in OAS
Tranche Average OAS
FT 1.25%
FV 1.27%
GX 1.35%
GP 2.00%
GN 2.04%
GT 2.08%
SV 3.64%
ST 6.25%

13. 12
We supported our results with further sensitivity analysis on both the CIR and Goldman
Sachs models. Alpha, beta, and sigma of the CIR model were all changed, and the results of this
analysis can be seen in Appendix 2. As for the Goldman Sachs model, more weight was applied
to the refinancing incentive, and those results are shown in Appendix 3.
5. Recommendation
Taking into account the MUSTANG Future Endowment’s low risk preference, we
recommend that the fund invest in tranche ST of the Freddie Mac Multi Class Offering Series
2884 security. Having the lowest duration of 0.375 is an indicator that it is a safe tranche to own,
while the highest OAS of 6.25% indicates that tranche ST provides a significantly greater return
for greater risks when compared to other tranches, having the highest OAS by nearly 3
percentage points. The sensitivity analysis on both the CIR and Goldman Sachs models also
display the safety of the tranche, with average values of the tranche changing very insignificantly
to changes in parameters of the models. Another factor leading to our recommendation was how
short of an investment tranche ST is projected to be. Our model shows that tranche ST is
projected to pay back its entire principle within just seven months, leaving little time for the
rising of interest rates to negatively affect the coupon rate of tranche ST. The average interest
rates of this tranche can be seen in Appendix 4, which are significantly higher than that of a one-
Tranche Average Duration
GX 3.972
GP 1.985
GN 1.784
GT 1.533
FV 1.120
SV 1.100
FT 0.381
ST 0.375
Figure 6 – Average Duration of each tranche from 100 simulations

14. 13
year treasury (2.40% as of 12/1/2004), and those of each other tranche. It is clear that tranche ST
is the most logical tranche to invest in. Our recommendation may change if Mustang Future
Endowments would be willing to have higher risk tolerance, and wanted to invest more than the
$3.15 million possible.

15. 14
Appendix 1

16. 15
Appendix 2
Tranche Average Value (α=.5) Average Value (α=1)
Tranche FT $11,596,578 $11,588,782
Tranche FV $39,476,812 $39,349,556
Tranche GN $7,573,054 $7,318,650
Tranche GP $11,141,592 $10,713,939
Tranche GT $9,407,706 $9,146,235
Tranche GX $199,950,833 $185,961,372
Tranche ST $3,215,841 $3,165,539
Tranche SV $24,105,921 $23,076,375
Average Value of Tranche's with β = .0775 and σ = .0225
Tranche Average Value(β=.025) Average Value(β=.15)
Tranche FT $11,600,020 $11,595,516
Tranche FV $39,509,128 $39,463,928
Tranche GN $7,699,799 $7,531,676
Tranche GP $11,367,864 $11,066,067
Tranche GT $9,530,896 $9,368,292
Tranche GX $218,849,821 $191,942,055
Tranche ST $3,231,314 $3,211,691
Tranche SV $24,562,928 $23,968,329
Average Value of Tranche's with α = .1 and σ = .0225
Tranche Average Value(σ=.05) Average Value(σ=.075)
Tranche FT $11,597,925 $11,597,670
Tranche FV $39,487,331 $39,473,030
Tranche GN $7,626,390 $7,624,483
Tranche GP $11,236,913 $11,234,639
Tranche GT $9,459,380 $9,456,848
Tranche GX $206,461,464 $207,062,494
Tranche ST $3,222,471 $3,221,892
Tranche SV $24,299,117 $24,297,859
Average Value of Tranche's with α = .1 and β = .0775

17. 16
Appendix 3
Appendix 4
Tranche 150% Weight to RI 200% Weight to RI
Tranche FT $11,582,811 $11,574,704
Tranche FV $39,345,613 $39,260,947
Tranche GN $7,575,527 $7,540,567
Tranche GP $11,143,236 $11,095,819
Tranche GT $9,414,347 $9,375,080
Tranche GX $205,125,865 $204,201,662
Tranche ST $3,203,488 $3,192,731
Tranche SV $24,102,839 $23,970,259
Average Value of Tranche's with More Weight to Refinancing Incentive
Month Average Int Rate
1 9.78%
2 9.68%
3 9.51%
4 9.28%
5 9.05%
6 8.85%
7 8.76%
Tranche ST