However, the programs save prices, spreads, and yields, plus all intermediate results of calculations,using up to 16 digits (16 digits total, on both sides of the decimal point).
For this reason, the answers you get using UniVu sometimes differ slightly from what you'd get if you calculated the displayed numbers with a hand-held calculator:
Hint:
The programs display 7 decimal places for factors and 4 places for nominal and option-adjusted DV01.
Most--but not all--price, yield, and spread calculations work out the same in either direction. In other words, calculating an option-adjusted spread (OAS) from a price normally gives you the same answer as calculating a price from an OAS. (Or a similar answer--rounding may change the price or yield by a few tenths of a penny or of a basis point.)
However, if the security has options, the answer you get using OAS to calculate price or yield is different from the answer you get using price or yield to find OAS.
OAS from price or yield: When you enter a price, the yield-to-worst-call algorithm, for example, finds the worst yield by computing the yield to each potential call date. When you enter a yield, the program computes the price, given that yield, at each potential call date, then picks the lowest price. In either case, it displays the OAS associated with the worst-call price or yield.
Price or yield from OAS: When you enter an OAS, the program could take either of two approaches:
Unfortunately, this spread-to-price algorithm doesn't always find the same workout date (and thus price) as the algorithm that finds OAS from the price.
In portfolios, print-outs, and reports, UniVu sums certain attributes and averages others.
The averages may be weighted by market value or current holdings.
Some columns do not lend themselves to either totals or weighted averages. A column of CUSIPs, for example, cannot be totaled or averaged. These columns show no aggregate numbers.
Note: If a value is missing (a security is unpriced, for example) or is incorrect (as indicated by NaN , meaning "not a number"), UniVu ignores the missing or incorrect numbers, sums the remaining numbers, and divides by the actual number of values summed.
It does not remove the entire security from all calculations. It does include the security in simple counts such as the number of securities in the portfolio.
To find an average Moody's or S&P rating, UniVu assigns a number value to each rating value (for example, 3 to Aaa, 4 to Aa1, and so on). It then sums and averages the ratings, including the market value weighting.
If the result is a decimal number and the decimal part is less than or equal to 0.25, the result is rounded up to the next highest rating. For example, a result of 3.25 is rounded up to Aaa. Results from 3.26-3.99 are rounded down to Aa1.
The program ignores N/A and N/R ratings.
In portfolios, cash is handled in analyses as follows:
Most windows show amounts, and let you enter amounts, as numbers of thousands. For example, "1" equals $1,000. Do not enter a dollar sign.
To enter amounts quickly, use these codes:
M or m
MM or mm
B or b (not available on all windows)
For example, to enter $10 million, type 10mm
.
To enter prices, use these conventions:
102.125
89-24 for 89 24/32.
The program accepts + for 1/64:
89-24+
for 89 24/32 plus 1/64.
Use the third place after the hyphen for 1/256 to 7/256 (8/256 is 1/32):
89-241
for 89 24/32 and 1/256.
You cannot search for a security using its local price. Local prices are saved only at your workstation, not in a firm-wide or system-wide database. Since UniVu can't search your local workstation, it can't find a local price.
To enter prices, use these conventions:
102.125
89-24
for 89 24/32
89'25
for 89 25/64
99"127
for 99 127/128
UniVu uses Sybase's "C double" for floating-point calculations. Exponent size is 11, number of significant bits is 53, and precision is actually 15-17 digits.
Use to define the holding period.
The input formats are:
3Y
Note:
Do not use decimals--for example, do not use
1.5Y
for one and a half years. Instead, use months:
18M.
- Number of months:
n
M--for example,
24M
- Actual
horizon date :
MM/DD/YY
--for example,
04/01/01
Note: On total return and other analysis windows, UniVu automatically uses the first horizon entry in the current scenario file as the default horizon. This entry can be a date, a number of years, or a number of months.
EJV's default horizon date is calculated as:
today's date + 1 year + settlement days
A day that falls on a weekend or holiday is set to the next work day.
You can set your own default horizons in the scenario file or change them as needed on the analysis windows.
For each security, the program lets you access Bridge valuations, local prices, and proprietary prices.
Note: You cannot search for a security using its local price. Local prices are saved only at your workstation, not in a firm-wide or system-wide database. Since UniVu can't search your local workstation, it can't find a local price.
A portfolio supervisor at your firm can create sets of firm-wide prices, each set with its own name. These files appear throughout UniVu as "pricing environments" or "pricing contexts."
Creating price files is not done in UniVu. It is a separate batch process. The portfolio supervisor must:
Once the environments are created, the prices in the various environments are saved in an on-site database. All UniVu users at your firm can then switch among files and, therefore, among prices.
The portfolio supervisor can upload changes and additions to pricing files throughout the day. However, he or she may find it quicker to update prices with the User Pricing window. The changes are saved in the on-site database where they are available to all members of your firm.
UniVu computes option-adjusted values (spread, duration, convexity, etc.) for corporate bonds using a single-factor binomial model. The binomial lattice is constructed so as to price Treasury securities exactly. This produces a set of possible forward rates for Treasuries.
A corporate bond price is computed from the OAS by examining the cash flow of the bond at maturity and working backward in time until the settlement date is reached. At each period in the analysis, the model determines whether it is economic for the bond investor to exercise any existing put option, or for the bond issuer to exercise any call option. Cash flows are discounted at the appropriate forward Treasury rates, plus the OAS.
By default, the binomial lattice in UniVu uses approximately 60 evenly spaced periods (depending on the bond maturity) with 50/50 transition probabilities for rates moving up or down at any point in time. Arbitrage is removed from lattices by adjusting all of the interest rates in future periods to reproduce coupon Treasury prices, while maintaining the ratio between up and down rate moves (to be consistent with the specified volatility).
Option-adjusted analysis expands upon traditional cash-flow analysis in that the security's cash flows are not assumed to be fixed and known when the program is calculating yields and price sensitivities.
Instead, option-adjusted analysis simulates the performance of a mortgage pool (including ARM pools) or tranche over a number of randomly generated interest-rate paths that are centered on implied forward rates from the Treasury term structure.
UniVu generates cash flows along each of these paths using the Bridge prepayment model (at a user-defined speed or amplitude). The OAS is then calculated as the incremental spread, added to all of the Treasury spot rates, that results in the average present value from all randomly generated paths equaling the security's market value.
The simulation incorporates the mortgage holder's option to prepay and other factors, and therefore provides a much more realistic measure of the likely performance of the mortgage-backed securities or CMO tranches than cash-flow analysis alone.
The Bridge OAS simulation uses a model to calculate interest-rate paths. The program computes a minimum of 50 paths and a maximum of 250 paths. The model has a stopping criterion of 5 basis points accuracy in calculating OAS (unless all 250 paths have been used). If OAS with rate values is selected, the stopping criterion is 1.5 basis points. Therefore, calculating OAS with rate values will generally result in longer computing times.
The Bridge OAS model will re-use interest-rate paths, provided that the initial yield curve remains unchanged. Re-using interest-rate paths from the same initial yield curve tends to bias all securities' OAS estimation errors in the same direction. Consequently, when using the initial yield curve, the difference in OAS values between two securities is a useful indicator of their relative value.
Model assumptions:
In the generic sense, OAS analysis attempts to determine what effect future interest-rate volatility will have on the expected cash flows of a bond that has an optionality component to its cash flows. Optionality components are evident in both the corporate and mortgage bond markets. The call option of the issuer of certain corporate debt provides the optionality component of the cash flow of a corporate bond, whereas with mortgage-backed securities (MBS), cash-flow optionality or uncertainty is evident in the form of prepayment risk.
In this situation, option-adjusted spread is defined as the cost of the implied call embedded in the MBS, shown as an additional basis-yield spread. When this additional spread is added to the base-yield spread of an MBS without an operative call, it produces the option-adjusted spread.
The Bridge prepayment model is an econometric, pool-specific, one-factor, path-dependent prepayment model based on historical and projected interest rates from current-coupon FNMA mortgages. These interest rates, in turn, are assumed to be equal to the yield on 10-year Treasury bonds plus a spread of 96 basis points. The 10-year yield is taken from the current scenario.
The Bridge prepayment model is more useful than the PSA model (and models dependent on the PSA) because it considers a wider variety of underlying factors. For example, UniVu looks at these attributes when making EJV-model forecasts:
To scale prepayment speeds up or down, change the percentages (like PSA):
The model makes prepayment projections for these mortgage pools and mortgage-backed securities:
The Bridge model does not make projections for tiered payment mortgages ( TPMs), project loans, convertible securities, or manufactured housing loans.
Note: The Bridge prepayment model is equivalent to the Lehman Brothers prepayment model for fixed-rate mortgages.
Valid prepayment speeds in UniVu are:
Note: When you switch from one prepayment model to another, the units are not converted.
Here are formulas for converting from PSA to CPR and from CPR to SMM. Note that PSA values are not readily converted to EJV, ABS, or vector prepayment model values. See How UniVu Calculates Equivalent PSA for more information.
On 12/16/93, the Public Securities Association released a new conversion formula that, unlike the old formula, specifies the treatment for months 0 and 30 and for CPRs greater than 100. It also specifies what the accrual period is between one month and the next.
The new formula is:
CPR = min {PSA%/100 * 0.2 * max [1, min(MONTH, 30)], 100}
where the commas indicate alternatives ("1 or MONTH or 30") and where
MONTH
is defined as the accrual period during which the loan age increases
from
MONTH -1 to MONTH
. In other words,
MONTH 5
is the period between 4 months and 5 months, not between 5 months
and 6 months.
The conversion formula is:
SMM = 1 - (1 - CPR) ^(1/12)
The Public Security Administration's new formula is:
CPR = min {PSA%/100 * 0.2 * max [1, min(MONTH, 30)], 100}
To work it out, note that it has two parts:
MONTH
is less than 1, use 1; if
MONTH
is less than 30, use
MONTH
; if
MONTH
is greater than or equal to 30, use 30.
100
. (CPR is capped at 100 percent.)All UniVu mortgage-backed security and CMO analysis applications offer equivalent PSAs.
Think of a prepayment model as a procedure for specifying a vector of monthly SMM rates, to be used to project cash flows for a mortgage-backed security. When you project cash flows with one of the available models (except for PSA, of course), the "equivalent PSA" value is the PSA that best approximates the prepayment speed that was forecast using the original model.
However, since each model starts with different assumptions and is calculated differently, the equivalent PSA results are different for each model. For example, the projections from nondeterministic models such as PSA and CPR don't change in response to pool characteristics or interest-rate scenarios. The EJV and vector models, on the other hand, do consider, and are affected by, various pool characteristics and scenarios.
There is no standard method for computing equivalent PSA, and different firms do it different ways. Four of the most common methods, however, are:
Bridge supports the first three methods, although UniVu windows that show equivalent PSAs use only the first method.
The results of the first three methods are usually not very different. For example, a typical range would be 285 PSA to 300 PSA, a difference of only 5 percent.
Many users like the idea of the equivalent-yield method , but it can be ambiguous:
Most analysts try to avoid this issue by setting the price at least 5 points higher or lower than the parity price.
Computing equivalent-yield PSAs for CMOs is, however, a problem, since collateral is often heterogeneous and just plain odd (balloons, projects, and so on). Of all the available prices, which one do you pick? (Note that the fourth method is the only one that requires a price.)
Calculating the equivalent PSA for a tranche is a two-step process. UniVu first forecasts a speed based on the tranche's average life. It then fits the result to what it knows of the underlying collateral's average life. In other words, the tranche's collateral equivalent PSA is calculated by targeting its collateral's weighted average life.
UniVu currently displays only the second result: the collateral equivalent PSA.
The number of mortgage pools underlying CMOs ranges from 1 to almost 3,000, with an average of about 300. Computing an OAS for a CMO involves calculating prepayments and cash flows for each piece of collateral along many different interest-rate paths. The speed of an OAS calculation is, therefore, directly related to the number of pieces of collateral.
Collateral aggregation refers to the compression of the pools underlying a CMO, known as the full collateral , into a number of "weighted average" aggregates. The rules used to perform this compression specify which pool characteristics are to be considered and when pools are deemed alike enough to be assigned to the same aggregate.
Collateral aggregation can be performed to varying degrees. However, there is a trade-off between speeding up calculations by high levels of compression and the accuracy of the results.
At one extreme, the rules can require that only pools alike in every respect are placed in the same aggregate. This type of compression is called non-destructive , since the prepayments and cash flows generated from the resulting aggregates are identical to the cash flows of the full collateral.
At the other extreme, the full collateral may be compressed into a single aggregate. This type of compression is called full compression . While full compression results in the fastest OAS calculations, it blurs the differences among heterogeneous collateral and may, therefore, produce dramatically different results than one would get from the full collateral.
For example, full compression would compress FNMA 9s and 7s into FNMA 8s. However, the average prepayments of 9s and 7s are not the same as FNMA 8 prepayments. The result is different cash flows and OAS results.
By default, UniVu uses non-destructive compression to calculate all nominal measures and cash flows. The results exactly match the results from full collateral, yet reduce calculation times (particularly for GNMA-backed deals).
The rules that UniVu follows fall between full and non-destructive compression. They are:
For many deals, these settings result in an average compression of about 95% and a reduction in the calculation time by a factor of 5 to 10. Although calculation speeds for deals with few pools in their full collateral do not improve noticeably, these deals run relatively quickly anyway.
The effect of aggregation on OAS varies with the CMO structure being analyzed. Uncomplicated deals with simple serial or parallel tranching are affected very little (a few basis points in OAS). On the other hand, deals with PACs close to breaking, jump tranches and so forth, may be off by 10 to 20 basis points. Nevertheless, the pros of aggregation greatly outweigh the cons, and if OAS measures are viewed only as approximate gauges of relative value (as they should be), the aggregated results are just as valuable as the full-collateral results.
A pool factor contains information about homeowners' scheduled payment and prepayment activity during a particular month. This activity determines the payments that are passed along to investors during the following month (or later, depending on the pool's stated delay days).
Bridge uses the first day of the month following the homeowners' payments as the effective date of the factor. In other words, an October 1 or October date on a UniVu window reflects the balance in the pool at the end of September, the prior month.
Payment and calculation activity for a GNMA I pool (stated delay of 45 days) is as follows:
All of these tapes contain October 1 factor data:
Bridge receives FNMA CMO factors on the first of each month, and FHMLC CMO factors on the 11th of each month.
Factors for private (non-agency) CMOs and asset-backed securities are delivered according to the deals' scheduled payment dates.
UniVu default benchmarks are based on the on-the-run Treasuries. The options, besides the standard Treasury maturities (3 months, 6 months, one year, and so on), are:
You can create your own at-horizon curve on the Scenario window and an at-settlement curve on the Financial Assumptions windows (available from the Assumptions menus).
The program calculates historical prepayment speeds for mortgage pools and CMOs as follows:
Using the amortization characteristics of the loans--WAC, WAM, amortization method, and so on--the prepayment speed is the speed that will, when applied to the unpaid principal balance at the beginning of the period, result in the unpaid principal balance reported at the end of the period.
Prepayments for aggregated mortgage pools and CMOs are calculated by applying the prepayment speed to each of the pools in the set.
In the case of CMOs, only the portion of the pool used as collateral for the deal is used to calculate the prepayments.
Prepayments for sets of pools are saved in the Bridge databases.
Note: For pools, the start of a "from issuance" calculation is the pool issue date.
For CMOs, the start is the CMO issue date.
UniVu's total-return calculators display both annualized and nominal rates of return (ROR).
Bridge uses this formula to convert a nominal ROR value into an annualized ROR value:
AROR = [(1 + NROR)^1/n)-1] * (f * 100)
where:
AROR = annualized rate of return; NROR = nominal rate of return; n = number of coupon payments in the horizon period (set to 2 in Bridge applications); and f is the compounding frequency (also set to 2).
Note that Bridge assumes two coupon payments a year for all securities, including CMOs and mortgage pools which usually pay monthly, when annualizing RORs. Calculating interest payments on a semi-annual basis makes it easier to compare dissimilar securities.
Annualized ROR reflects semi-annual compounded interest, whereas nominal ROR reflects simple interest. The values for nominal and annualized RORs differ, therefore, whenever the horizon period is greater than one year. For nominal and annualized RORs to be equal:
Following are descriptions of the tranche and deal types used in Bridge applications.
A tranche that receives, as principal, specified principal payments on the underlying assets. It may also receive, as principal, the interest paid on the underlying assets to the extent that such interest exceeds certain required interest distributions, as described in the tranche's prospectus supplement.
A tranche that receives, as interest, certain payments on the underlying assets that, on a particular distribution date, may be insufficient to fully cover the accrued and unpaid interest at the rate specified for the accrual period.
When an insufficiency exists, the unpaid interest amount may be carried over to later distribution dates. This unpaid interest amount may itself accrue interest. The carried amount continues until payments are sufficient to cover all such unpaid interest amounts. However, if the insufficiencies remain unpaid, they will not be covered by the agency's guaranty. (From FNMA.)
Typical properties include multi-family dwellings such as apartment buildings, retail centers, hotals, restaurants, hospitals, warehouses, and office buildings. (From Fabozzi et al., Whole-Loan CMOs .)
An excess tranche sometimes has a specified principal amount but no specified tranche coupon.
The issuer of a Master Trust has a legal responsibility to the investors if there are payment defaults and delays. See also Owner Trust .
The issuer of an Owner Trust has no legal responsibility to the investors if there are payment defaults and delays. See also Master Trust.
There can be more than one PAC in a deal. The additional PACs will have different collars and different principal payment priorities. They are designated PAC 1, PAC 2, PAC 3, and so on. (From FNMA, FHLMC.)
For example, if the deal is worth $1 million and there are 10 investors, each investor ultimately gets $100,000. The first investor to receive his or her $100,000 is the first to win the redemption lottery.
The factor for a random-lot redemption tranche is always 1.
See also Owner's Request Redemption.
The funds in the reserve are reinvested in short-term high-quality securities, which--for the subordinate tranches--leads to a decline in yield without a corresponding decline in risk. See Shifting Interest for a different approach to the same problem. (From Fabozzi et al., Whole-Loan CMOs .)
(From Fabozzi et al., Whole-Loan CMOs .)
The tranche may also receive principal payments from principal paid on the underlying PCs or other REMIC pool assets. Also known as "Very Accurately Defined Maturity" (VADM) and "Accretion Directed" tranche.
The tranche jumps to its new priority on the first payment date when the trigger condition is met and it retains ("sticks to") that priority until retired.
When packaging deals from mortgages with interest rates higher than the desired remittance rate for the senior tranches, the issuer strips off all interest above that rate and assigns it to a separate tranche. This tranche is the WAC IO. (From Fabozzi, et al., Whole-Loan CMOs .)
When packaging deals from mortgages with interest rates below the desired remittance rate for the senior tranches, the issuer strips off enough principal so that the interest on the senior tranches, in relation to the remaining principal, equals the desired remittance rate. The principal is sold as a WAC PO. (From Fabozzi, et al., Whole-Loan CMOs .)