1 Jan 2012 ... Maturity Spread Calculation Example – TRX.II.AAA.1.Mar.12 . ... Top and Tail
Process – Simple Average (TRX.II example).
TRX.NA & TRX.II Spread Aggregation Methodology
1/1/2012
Markit TRX.NA & TRX.II Spread Aggregation Methodology Strictly private and confidential
Contents Dealer Submissions ........................................................................................................................................................... 3 Maturity Spread Calculation .............................................................................................................................................. 3 Top and Tail Process Table ............................................................................................................................................. 3 Maturity Spread Calculation Example – TRX.II.AAA.1.Mar.12 ........................................................................................ 4 Aggregate Index Level Calculation ................................................................................................................................... 5 Calculation of Constituent Spreads and Prices .............................................................................................................. 5 Top and Tail Process – Simple Average (TRX.II example).............................................................................................. 5 Spread to Price Conversion ............................................................................................................................................. 5 **Trepp Cashflows ....................................................................................................................................................... 5 Aggregate Index Level Price ............................................................................................................................................ 8 Simple Average of Constituents ................................................................................................................................... 8 Aggregate Index Level Spread .......................................................................................................................................... 8 Aggregating Cashflows .................................................................................................................................................... 8 Weighting ..................................................................................................................................................................... 8 Normalization ............................................................................................................................................................... 8 Combination ................................................................................................................................................................. 8 Calculating the Spread ..................................................................................................................................................... 9
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Markit TRX.NA & TRX.II Spread Aggregation Methodology Strictly private and confidential
Dealer Submissions 11 Licensed TRX Dealers submit each business day for the below TRX products: 8 Maturity Spreads o TRX.NA.AAA.1.Mar12 o TRX.NA.AAA.1.Jun12 o TRX.NA.AAA.1.Sep12 o TRX.NA.AAA.1.Dec12
TRX.II.AAA.1.Mar12 TRX.II.AAA.1.Jun12 TRX.II.AAA.1.Sep12 TRX.II.AAA.1.Dec12
136 CMBS cash bond spreads o 118 bonds – TRX.NA o 25 Bonds – TRX.II
Maturity Spread Calculation At the maturity level a basic top and tail process is performed to remove the upper and lower quartiles of the submissions (as shown below in the table, this may vary depending on the amount of Dealers submissions received for any business day). Once this procedure is conducted, a simple average calculation using the remaining submissions is executed to arrive at the EOD Composite Spread for each maturity (Mar12, Jun12, Sep12, Dec12) Top and Tail Process Table Number of Upper Quartile Lower Quartile Number of Quotes used in Fixing Contributors Discards Discards 1 0 0 No fixing calculated 3 0 0 No fixing calculated 4 1 1 2 5 1 1 3 7 1 1 5 8 2 2 4 11 2 2 7 12 3 3 6 15 3 3 9 16 4 4 8 19 4 4 11 20 5 5 10
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Markit TRX.NA & TRX.II Spread Aggregation Methodology Strictly private and confidential
Maturity Spread Calculation Example – TRX.II.AAA.1.Mar.12
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Markit TRX.NA & TRX.II Spread Aggregation Methodology Strictly private and confidential
Aggregate Index Level Calculation
Calculation of Constituent Spreads and Prices Top and Tail Process – Simple Average (TRX.II example) Each Licensed Dealer submits a spread for each one of the CMBS cash constituents (18) that make up the TRX.II Index. As shown above in the Top and Tail Process Table, a top and tail process is performed to remove the top and bottom quartile of the submissions. Once this is complete, the process uses the remaining spreads to calculate a simple average composite spread for each of the 25 bonds. The next step involves spread to price conversion using Trepp cashflows and Markit’s proprietary yield curve. Spread to Price Conversion **Trepp Cashflows Please note all below references to cashflows require Markit to receive a projected cashflow file from Trepp every morning for each of the constituents in the TRX indices. The projected cashflows are based on a standardized scenario of 0% CPR, 0% CDR. As discussed below, Confidential. Copyright © 2011, Markit Group Limited. All rights reserved. www.markit.com
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Markit TRX.NA & TRX.II Spread Aggregation Methodology Strictly private and confidential
Markit’s end of day closing process uses the cashflows to determine the appropriate spread, price, and duration for the individual constituents and aggregate index level.
Once the constituent composite spreads have been calculated from the dealer submissions, we run a spread-to-price calculation for each constituent, as follows: 1. Calculate the weighted average life from the cashflows. Using a 30/360 US day count convention, we sum the principal payments from the cashflows, each weighted by a year fraction between the calculation date and the payment date from the cashflow, then divide by the outstanding balance (calculated from the current factor and the original balance):
Where:
2. Calculate the swap rate using a spot rate taken from Markit’s proprietary yield curves:
Where:
3. We use this to get the yield as the sum of the swap rate and input spread:
4. Each cashflow is discounted by multiplying the principal and interest payments by a discount factor. The factor is based on a discount rate:
5. We use this discount rate as the basis for calculating the discount factor that must be applied to each cashflow. We have a starting discount factor, which is multiplied by an increment for each successive cashflow:
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Markit TRX.NA & TRX.II Spread Aggregation Methodology Strictly private and confidential
Where:
6. The discounted cashflow payments are then aggregated to give the present value:
Where:
7. We then calculate how much has accrued so far this period by multiplying the fraction of a year that has elapsed since the last accrual period end date by the current balance, including interest rates and other modifiers:
Where:
8. Finally we can calculate the price as the present value (excluding how much has already accrued this period) divided by the notional amount:
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Markit TRX.NA & TRX.II Spread Aggregation Methodology Strictly private and confidential
Aggregate Index Level Price Simple Average of Constituents Process adds up the individual bond prices and divides by the number of actual constituents (18). The result of this calculation is the Aggregate Index Level Price for a specific day.
Aggregate Index Level Spread Aggregating Cashflows The calculation of an Index Level Spread (or portfolio spread) from an Index Price requires the combination, weighting, and normalization of all of the underlying constituent cashflows into one single index level cashflow. Weighting Using the individual bond cashflows, the calculation of the Index Spread begins with equally weighting the underlying constituent cashflows as equal percentages of the index notional. All forecasted principal and interest payments for a constituent are expressed as percentages of index notional, so that they properly incorporate their weighting and they can be easily adjusted for any notional. Normalization In the process of creating a single aggregate cashflow, the payment dates for each constituent are adjusted forward to the first calendar day of the month following their scheduled payment dates in order to be consistent with the accrual period for the TRX Index (1 st to 1st). It is important to note, even though the individual bonds pay through the middle of the month the aggregate cashflows are adjusted as described above. Most CMBS securities have payments with a 10-15 day delay from the end of their accrual period, and together with the forward adjustment to the 1st of the next month, this can result in a payment delay of up to one full accrual period for the cashflows of each TRX constituent in the aggregation process. Combination The Index Level Spread calculation will utilize this aggregated set of cashflows in the calculator and the end of day batch process. It is important to note that this aggregate set of cashflows is only generated once per month and it will not change throughout the month based on the payments associated with the underlying. Individual bond cashflows will always incorporate the most recent payments in the calculation of price, but the aggregate level index calculations will always look towards the next 1st of the month as the first projected payment date, even if the constituent payment dates have passed. The index accrual period (1st to 1st) is used for the purposes of accrual in this calculation as well.
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Markit TRX.NA & TRX.II Spread Aggregation Methodology Strictly private and confidential
Calculating the Spread The index level price is aggregated as an average from the constituent prices, and we use a numerical method (Secant) to calculate the spread from the aggregated price. An initial guess is made of the spread, and it is input into a spread-to-price calculation. This is the same methodology that is used to calculate the constituent level prices (see Spread to Price Conversion **Trepp Cashflows Please note all below references to cashflows require Markit to receive a projected cashflow file from Trepp every morning for each of the constituents in the TRX indices. The projected cashflows are based on a standardized scenario of 0% CPR, 0% CDR. As discussed below, Markit’s end of day closing process uses the cashflows to determine the appropriate spread, price, and duration for the individual constituents and aggregate index level. above), but using the aggregate set of cashflows. The result is checked, and the input iteratively adjusted and run again through the same calculation until the result is the same as the aggregated price, to within a specified degree of accuracy (10-10). This gives us the spread that results from the aggregate price.
The spread-to-price calculation is as follows: 1. Calculate the weighted average life from the aggregated cashflows. Using a 30/360 US day count convention, we sum the principal payments from the cashflows, each weighted by a year fraction between the calculation date and the payment date from the cashflow, then divide by the outstanding balance (calculated from the current factor and the original balance):
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Markit TRX.NA & TRX.II Spread Aggregation Methodology Strictly private and confidential
Where:
2. Calculate the swap rate using a spot rate taken from Markit’s proprietary yield curves:
Where:
3. We use this to get the yield as the sum of the swap rate and input (guessed) spread:
4. Each cashflow is discounted by multiplying the principal and interest payments by a discount factor. The factor is based on a discount rate:
5. We use this discount rate as the basis for calculating the discount factor that must be applied to each cashflow. We have a starting discount factor, which is multiplied by an increment for each successive cashflow:
Where:
6. The discounted cashflow payments are then aggregated to give the present value, from which we derive a price. Keep in mind the principal payment, interest payment, and PV are all “normalized” Confidential. Copyright © 2011, Markit Group Limited. All rights reserved. www.markit.com
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Markit TRX.NA & TRX.II Spread Aggregation Methodology Strictly private and confidential
values here, meaning they are expressed as percentages in decimal format so they can be easily adjusted based on a notional input (simply multiply these by any given notional)
Where:
7. We then calculate how much has accrued so far this period by multiplying the fraction of a year that has elapsed since the last reset date by the notional amount and the current factor, including interest rates and other modifiers:
Where:
8. Finally we can calculate the price as the present value (excluding how much has already accrued this period) divided by the notional amount. This step and the steps before it are run with different spreads until we tie out to an appropriate spread, as defined at the beginning of this section. Again the PV, accrued, and Price here are all expressed as decimals: -.
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