ILB Example

This section uses a Treasury Inflation-Protected Security (TIPSs) as an example, but it can be extrapolated to any ILB that follows a similar convention (Canadian Real Return Bonds, post-2005 UK Treasury GILTs, etc.). The general practice of dividing a current day’s reference index value by a base index value applies to all ILBs.

TIPS use the Consumer Price Index for All Urban Consumers (CPI-U) with a 3-month lag (trailing-three-month index). For example, the CPIs used for February 1 and March 1 2013 are the CPIs from November 1 and December 1 2012.

Fig. 1

Every TIPS security has a reference CPI on dated date, also referred to as the Base CPI. This is the initial value against which all future index calculations will be made, and remains constant throughout the life of the security. Since CPIs are published monthly, supplying a base CPI requires the calculation of daily CPIs. These values are interpolated from the calculation CPIs of the current month and the next month. The difference between the two values is then spread evenly across the number of days in the current month. For example, November 20012’s CPI was 230.221 and December 2012’s was 229.601; these are the Calculation CPIs for February 2013 and March 2013 respectively.

Fig. 2

The Calculation CPI is 230.221 on February 1 and will decrease by 0.02214 each day until reaching 229.601 on March 1.

Fig. 3

The final step is calculating daily CPI ratios. This is done simply by dividing the daily Calculation CPI by the Base CPI on dated date. For example, the dated date CPI could be 164 and the daily reference CPI on February 15, 2013 was 229.911.

Fig. 4

The daily CPI ratio is the inflation multiplier used to calculate interest and principal payments on that date.

With daily CPI ratios in hand (and knowing that TIPS pay semiannual coupons and follow the ACT/ACT day count basis) traded interest, coupon payments, and principal payments can be calculated. Industry standard ACT/ACT day counts INCLUDE last payment or dated date and EXCLUDE settlement date. For Example, the ACT/ACT day count used in the scenario described below includes August 15, 2012and exclude February 1, 2013 (settlement date of buy trade) or February 15, 2013 (maturity date).

Fig. 5

Traded interest is equal to face value * daily CPI ratio on settlement date * interest rate / 2 / actual number of days in coupon period * actual number of days from last coupon or dated date to settlement date. TIPS start accruing on dated date, and each new accrual period starts on coupon date. Coupon payments are equal to face value * daily CPI ratio on coupon date * interest rate / 2. The principal payment at maturity is simply face value * daily CPI ratio on maturity date. For example, $1,000,000 face value is purchased with a settlement date of January 1, 2013, an interest rate of 3.875%, and daily CPI ratios of 1.40378659 on February 1, 2013 and 1.40189634 on February 15, 2013.

Fig. 6

Traded interest due on February 1, 2013 was $25,128.92. In addition, there was a coupon payment of $27,161.74 and a principal payment of $1,401,896.34 on the maturity date of February 15, 2013.

Accounting

Accounting requires that index (CPI) values be loaded monthly (or the appropriate frequency for the type of ILB) so the system can interpolate daily values. These daily reference index values are translated into daily ratios using each security’s base index (CPI) value. Accounting stores face value, the base index value, and the daily reference index value, which it uses to calculate current quantity on the fly when earnings or reports are run. The inflation-adjusted quantity is stored in Data Management.

Example (used throughout): TIPS pays semiannual coupons, follows the ACT/ACT day count basis, has a face value of $1,000,000, and an interest rate of 3.875%.

There are two components of ILB accrual processing in Eagle: inflation and interest. Inflation accruals capture the adjustments to a bond’s face value based on changes in the underlying index, and this inflation-adjusted face value is then used to calculate interest accruals.

Valuation & Inflation Accruals

Clean real prices must be used to value ILBs to take advantage of Eagle’s robust inflation and interest accrual processing functionality (clean meaning exclusive of interest and real meaning exclusive of inflation adjustments). Unless accrual processing is disabled, a dirty price will double count interest and a nominal price will double count inflation adjustments.

Early releases of Accounting used the current day’s index ratio to calculate the inflation-adjusted quantity (par value * index ratio). This resulted in zero inflation accrual recognized on settlement date of an open trade because the same inflation-adjusted quantity was used for both trading and daily processing, as illustrated in Fig. 7 below.

Fig. 7

Modern versions prior to V17 exclusively use next-day ratios to calculate valuation. This can result in reconciliation breaks if the system being reconciled against uses same-day ratios for valuation, such as Bloomberg. The difference is equal to one day's change in inflation, which is typically immaterial. If the price from February 2 was loaded in Eagle for February 1, for example, Eagle's end-of-day valuation for February 1 would exactly match Bloomberg’s valuation for February 2.

In V17 and above, the entity-level election Ilb Valuation Method (18047) allows you to specify whether next-day or same-day ratios are used for valuation. System Default (T+1) produces the same results as modern versions prior to V17, while T+0 substitutes same-day ratios instead.

Interest Accruals & Coupon Payments

Accounting uses the standard Eagle accrual convention of creating coupon payments based on the prior day’s period-to-date (PTD) accrued interest. If an ILB is purchased off-market (during the period), traded interest is included when computing the first payment. Therefore the PTD accrual on coupon date minus one (plus any traded interest) will equal the coupon payment amount. Traded interest and principal payments are calculated at the time of the transaction.

Early releases of Accounting that used same-day ratios produced coupon payments that were missing one day of inflation accruals. The coupon was generated with the index ratio from coupon date minus one (last day of accruals) instead of coupon date.

All modern releases (including V17) exclusively use next-day ratios for interest accruals to align Accounting with actual coupon payments. Accrued interest on coupon date minus one is calculated using the index ratio from coupon date. At the end of each day the security is always fully accrued (including inflation) for the next day, producing a PTD accrual on coupon date minus one that is equal to the actual coupon payment. The examples below demonstrate this, as the expected coupon on January 15, 2013 is $27,161.74.

Same-Day Ratios

• PTD accrual 2/14/2013 = face value * current day’s daily index ratio * interest rate / 2 / actual number of days in coupon period * actual number of days in coupon period.
• Example: PTD accrual 8/15/2012 through 2/14/2013

Fig. 8

Next-Day Ratios (Current Process)

• PTD accrual 2/14/2013 = face value * next day’s daily index ratio * interest rate / 2 / actual number of days in coupon period * actual number of days in coupon period.
• Example: PTD accrual 8/15/2012 through 2/14/2013

Fig. 9

The PTD accrual on 2/14/2013 using same day ratios is $27,164.36 (Fig. 8), which would equal the coupon on 2/15/13. This is incorrect. The PTD accrual on 2/14/2013 must be $27,161.74 (Fig. 9) so that Accounting generates the correct coupon on 2/15/2013. This is achieved using next-day ratios.

When an ILB is purchased off-market, Accounting will present a PTD accrual during the first coupon period with traded interest backed out. (See Traded Interest section below for details.) The PTD accrual calculations are the same that would be done if the ILB had been held for the entire coupon period, minus traded interest. Therefore the first coupon that Accounting generates will reflect the PTD accrual from coupon date minus one plus traded interest. This equals the actual coupon payment (Fig. 10). All subsequent periods will be processed normally.

• Example: lot opened 2/1/2013

Fig. 10

Accounting’s PTD accrual on 2/14/2013 plus traded interest from 2/1/2013 equals the actual coupon payment of $27,161.74.

Inflation adjustments must be captured in the accrual process because coupon payments are generated based on PTD accruals. Since the accrual process for a given period stops on coupon date minus one, next-day ratios must be used in order to capture all of the inflation adjustments for the period. Traded interest and principal payment inflation adjustments are calculated when the transactions take place, so their inflation adjustments use same day ratios. This is why Eagle’s trade module matches Bloomberg’s BXT and YA screens, as they also represent a “trading view.”

Traded Interest

At the time of a trade Accounting calculates traded interest. The formula determines what the PTD accrual would be through settlement date minus one, using the daily index ratio from settlement date. This is the same formula used by Bloomberg for the BXT and YA screens, so these will always match Eagle’s trade panel. If an identical lot were already open, its PTD accrual from settlement date minus one would match the second lot’s traded interest on settlement date (see Fig. 11 below).

Traded Interest = face value * daily index ratio on settlement date * interest rate / actual number of days in coupon period * actual number of days from last coupon or dated date to settlement date minus one

• Example: lot 1 held for entire coupon period, lot 2 opened 2/1/2013

Fig. 11

• Traded interest on open transaction with settlement date of 2/1/2013 is $25,128.92, same as the PTD accrual from 1/31/2013 of a previously held lot

Principal Payments

At maturity Accounting multiplies face value by the daily index ratio on maturity date.

Principal Payment = face value * daily index ratio on maturity date

• Example: maturity date of 2/15/2013

Fig. 12

• Principal payment on 2/15/2013 is $1,401,896.34