MUSTANG FUTURE ENDOWMENT INVESTMENT RECOMMENDATION Analysis By: Ben Katz, Arvin Khorram & Oleksandr Firsov

MARCH 10, 2016 CAL POLY BUS 435

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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

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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.

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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.

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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

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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.

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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

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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

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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.

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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

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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

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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%

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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

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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.

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Appendix 1

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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

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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