Calculation of Indicators under the Three Classifications of Bond Trading Accounting

The following article aims to introduce the "three classifications" of bonds under accounting standards (typically IFRS 9 or similar standards)—namely, Fair Value Through Profit or Loss (FVTPL), Amortized Cost, and Fair Value Through Other Comprehensive Income (FVOCI)—and focuses on how these three categories perform core valuation and profit/loss calculations in practical business operations.

The article will expand on four aspects: classification background, classification criteria, specific calculation methods, and practical considerations.

---

I. Classification Background and Primary Motivations

Under the previous IAS 39 (or China’s old accounting standards), financial assets were often classified into:

• Trading Financial Assets
• Held-to-Maturity Investments (HTM)
• Available-for-Sale Financial Assets (AFS)
• Loans and Receivables

Since the implementation of IFRS 9 (Financial Instruments), the classification logic for financial assets such as bonds has been simplified to:

1. Amortized Cost
2. Fair Value Through Profit or Loss (FVTPL)
3. Fair Value Through Other Comprehensive Income (FVOCI)

The distinction between these three categories primarily depends on:

• Business Purpose ("Business Model"): whether the primary purpose is trading, collecting interest and principal, or a combination of both.

• Whether the bond itself meets the "Solely Payments of Principal and Interest (SPPI)" contractual cash flow characteristics.

• FVTPL (Fair Value Through Profit or Loss):
  Typically used for trading purposes or active management (where SPPI is not met), with daily fair value changes recorded in current profit and loss.

• Amortized Cost (Held-to-Maturity):
  The business model aims to "collect contractual cash flows," and the bond’s cash flows meet SPPI. Daily fair value fluctuations are not reflected; only the effective interest rate method is used to amortize costs.

• FVOCI (Fair Value Through Other Comprehensive Income):
  The business model involves both collecting interest and potentially selling (similar to the old "available-for-sale" standard). Interest is recorded in current profit and loss, but unrealized fair value changes are recorded in OCI (Other Comprehensive Income) and only transferred to P&L upon sale or impairment.

---

II. Classification Criteria and Brief Definitions

1. FVTPL (Fair Value Through Profit or Loss)

• Business Model: Active trading; or the financial instrument has complex features that do not meet SPPI; or the entity voluntarily designates FVTPL to reduce accounting mismatches.
• Accounting Treatment:
  • Year-end valuation: Assessed at fair value.
  • Current profit and loss: Includes all fair value changes (including unrealized gains/losses) and coupon income.

2. Amortized Cost

• Business Model: The goal is to hold the bond until maturity or for an extended period, essentially collecting contractual principal and interest.
• Accounting Treatment:
  • Year-end valuation: Amortized cost (not fair value).
  • Current profit and loss: Primarily interest income (calculated using the effective interest rate method) and impairment losses. Fair value changes generally do not enter current profit and loss or OCI; realized gains or losses are only recognized upon sale or impairment.

3. FVOCI (Fair Value Through Other Comprehensive Income)

• Business Model: The entity aims to collect interest but may also sell based on market conditions.
• Accounting Treatment:
  • Year-end valuation: Assessed at fair value.
  • Current period:
    • Coupon income and premium/discount amortization are recorded in current profit and loss.
    • Unrealized fair value changes are recorded in OCI (equity account) and only transferred to P&L upon sale or impairment.

---

III. Core Calculations for the Three Bond Accounting Classifications

1. Common Indicators

Regardless of the bond classification, the following indicators are often calculated or disclosed (in financial reports, internal management, or risk monitoring):

1. Face Value: The nominal amount of the bond, the principal amount due at maturity.
2. Coupon: The agreed interest on the bond, typically calculated as "annual coupon rate × face value."
3. Accrued Interest: The interest accrued but not yet paid between the last coupon date and the current date.
4. Effective Interest Rate (EIR): Used to calculate interest and premium/discount amortization, especially under the amortized cost method.
5. Amortized Cost (Carrying Amount): The cumulative balance on the books, including purchase price, transaction costs, premium/discount amortization, and interest received/paid.
6. Fair Value: The fair price of the bond obtained through market quotes or valuation techniques. For FVTPL and FVOCI, fair value affects current profit and loss or OCI; for Amortized Cost, it may only be disclosed internally or in financial report notes.
7. Allowance for Expected Credit Losses (ECL): IFRS 9 requires an assessment of expected credit losses for bonds, applicable to Amortized Cost and FVOCI classifications. FVTPL also assesses credit risk but typically reflects it directly through fair value changes in P&L.

2. Trading Securities (FVTPL) — Calculation Logic

Core: All fair value changes are recorded in current profit and loss.

1. Daily (or periodic) fair value changes:

   $$\text{Unrealized Gain/Loss} = \text{Current Market Value} - \text{Previous Market Value}$$

   • Fair value changes: Reflect only price fluctuations (excluding new accrued interest).

2. Realized gains (Realized PNL):
   When a trade occurs:

   $$\text{Trade PNL} = \text{Sale Proceeds} - \text{Purchase Cost}$$

   Directly recorded in P&L.

3. Coupon Income (Coupon Interest):
   Current or daily coupon income is recorded in P&L.

   • Interest income: Accrued daily (reflecting time value).

4. Total Profit/Loss (Total P&L):
   The sum of fair value changes + realized gains + interest income is fully reflected in the current income statement.

3. Held-to-Maturity Investments (Amortized Cost) — Calculation Logic

Core: The carrying amount is amortized cost, and daily fair value fluctuations are not recorded in profit and loss; gains or losses are only recognized upon actual sale or impairment.

1. Amortized Cost Update (Effective Interest Rate Method):
   The core formula for rolling amortized cost updates (using the effective interest rate method) is as follows:

   1. Interest Income:

   $$\text{InterestIncome}_t = \text{AmCost}_{t-1} \times \text{EIR} \times \Delta t$$

   2. Amortized Cost Update:

   $$\text{AmCost}_t = \text{AmCost}_{t-1} + \text{InterestIncome}_t - \text{CF}_t$$

   Where:

   • $\text{AmCost}_t$ / $\text{AmCost}_{t-1}$ are the amortized costs on day $t$ and the previous day, respectively.
   • $\text{EIR}$ is the annualized yield to maturity (effective interest rate).
   • $\Delta t$ is the annualized day count fraction ($\text{DC.yearFraction}(t-1,t)$).
   • $\text{CF}_t$ is the cash flow on day $t$: 0 on non-payment dates; $- \text{coupon}$ on coupon dates; $- (\text{coupon} + \text{principal})$ on maturity dates.

   Combined into a single formula:

   $$\boxed{ \text{AmCost}_t = \text{AmCost}_{t-1} + \bigl(\text{AmCost}_{t-1} \times \text{EIR} \times \Delta t\bigr) - \text{CF}_t }$$

   Here, "interest income" = "opening book balance × effective interest rate (EIR)." Any premium or discount is reflected in the current period's interest income.

2. Interest Income (Interest Income):
   Calculated using EIR (effective interest rate):

   $$\text{Interest Income} = \text{Opening Amortized Cost} \times \text{Effective Interest Rate (EIR)}$$

3. (If Applicable) Realized Gains/Losses:

   • Upon actual sale or early redemption:

     $$\text{Gain/Loss} = \text{Sale Price (Net)} - \text{Book Amortized Cost}$$

     This difference is then recorded in current P&L.

4. Impairment (Credit Losses):

   • IFRS 9 requires an expected credit loss (ECL) assessment for Amortized Cost bonds. If risk increases or actual default occurs, impairment must be increased accordingly and recorded in profit and loss.

4. Available-for-Sale Securities (FVOCI) — Calculation Logic

Core: Fair value changes are not directly recorded in current profit and loss but in Other Comprehensive Income (OCI); however, coupons and amortization are recorded in P&L.

1. Daily Fair Value Changes:

   $$\Delta \text{FV} = \text{Current Market Value} - \text{Previous Market Value}$$

   These unrealized changes are accumulated in the OCI account.

2. Interest and Premium/Discount Amortization:
   Similar to Amortized Cost, interest income and premium/discount amortization calculated using the EIR method are recorded in current P&L.

3. Realized Gains/Losses Upon Sale/Impairment:

   • Upon sale (or impairment), the cumulative unrealized portion in OCI is transferred to current P&L:

     $$\text{Realized PNL} = \text{Sale Price (Net)} - \text{(Original Amortized Cost)} + \text{(Prior OCI Accumulation)}$$

     In practice, it is common to transfer the entire fair value change from initial purchase to sale date to P&L on the sale date.

4. Impairment (Credit Losses):

   • An ECL assessment is also required. If credit risk increases or actual impairment occurs, impairment losses are reflected in P&L, and the fair value accumulation in OCI is adjusted accordingly.

---

IV. Practical Considerations and Summary

1. Management vs. Accounting Perspectives:

   • Financial institutions or investment departments often calculate so-called "management perspective" returns, such as daily fair value fluctuations (including HTM), to understand portfolio market value changes, risk exposure, and internal performance. However, the accounting perspective is constrained by standards: HTM (Amortized Cost) does not reflect unrealized price fluctuations in daily profit and loss, and FVOCI unrealized changes enter OCI rather than P&L.
   • Therefore, differences in "return" values between the two perspectives require consistent internal and external reconciliation management.

2. Market Value Calculation and Valuation System Configuration in China:

   • Priority to ChinaBond Valuation: In the Chinese bond market, the fair value of bonds should primarily use the ChinaBond Yield Curve as the valuation benchmark.
   • Dual Validation Mechanism:
     • Primary valuation source: ChinaBond Valuation (CFETS).
     • Secondary valuation source: China Securities Valuation/Clearing House Valuation.
     • For bonds without active market quotes, the ChinaBond Yield Curve + Credit Spread Adjustment method should be used to determine fair value.

3. Correct Application of the Effective Interest Rate (EIR) Method:

   • For Amortized Cost and FVOCI, the EIR method must be used to amortize premiums/discounts and recognize interest income. The EIR method requires discounting future cash flows to the current book value, so transaction costs, premiums, and discounts at purchase must be included.

   • During the holding period, the EIR method slightly updates the amortized cost and calculates interest income each period.

   • Calculating the Annual Effective Interest Rate (EIR) for bond transactions is a core step in bond pricing, amortized cost methods, and investment return analysis.

   • Clarifying the Relationship Between EIR and YTM:

     • At initial recognition, the effective interest rate (EIR) and yield to maturity (YTM) are numerically equal, calculated as:

       $$\text{Purchase Price} = \sum \frac{\text{Cash Flows}}{(1+\text{EIR/YTM})^t}$$

     • Key Differences:

       Aspect	Effective Interest Rate (EIR)	Yield to Maturity (YTM)
       Calculation Time	Determined at purchase and unchanged	Changes with market prices
       Included Elements	Includes transaction costs, premiums/discounts	Typically based on clean price
       Accounting Use	Used for amortized cost interest calculation	Used for market pricing reference

   • For bonds with transaction costs, the EIR calculation formula is adjusted as follows:

     $$\text{Total Cost} = \text{Transaction Clean Price} + \text{Transaction Commission} + \text{Stamp Duty}$$

     Then, the total cost is used as the cash outflow to calculate EIR.

4. Other Amortization Calculation Methods:

In addition to the "daily rolling" EIR method, the following methods for "amortized cost" or premium/discount amortization may be encountered in practice or under different standards:

• Periodic EIR Amortization:

  • The logic is the same as daily rolling, except that amortized cost updates are only performed on coupon dates (or monthly/quarterly) rather than daily.
  • Example: For annual payments, only the following is needed:

    $$\Delta t = \text{YearFraction}(\text{prevCouponDate}, \text{thisCouponDate}) \text{InterestIncome} = \text{AmCost\_prev} \times \text{ytm} \times \Delta t \text{AmCost\_new} = \text{AmCost\_prev} + \text{InterestIncome} - \text{Coupon}$$

    On non-payment dates, the book value remains unchanged or is interpolated linearly.

• Straight-Line Amortization Method:

  • The "total premium or discount" (= present value of all future cash flows - initial cost) is allocated evenly across payment periods (or days).
  • Amortization per period = Total discount / Total number of periods;
    or daily amortization = Total discount / Total number of days.
  • Advantages: Simple calculation; disadvantages: Does not reflect actual EIR and is typically only permitted under certain tax or local GAAP rules.

• Intra-Period Linear Interpolation:

  • For periodic EIR, if reporting is needed for interim dates, first calculate the one-time EIR amortization amount $\Delta P$ for "start of period → end of period," then interpolate linearly (or by DayCount ratio) within the period.
  • This is a compromise—ensuring correct total EIR per period without daily recalculations.

• Continuous Compounding Method:

  • Treat the yield to maturity as a continuous compound rate $r$, using:

    $$\text{InterestIncome}_t = \text{AmCost}_{t-1} \times (e^{r \cdot \Delta t} - 1)$$

    to replace "ytm × Δt."
  • Mathematically more elegant but results in minor differences and is rarely used in bond markets.

Reminder:

• Under IFRS 9/US GAAP, held-to-maturity bonds must use the effective interest method (EIR) for amortized cost; other methods are only permitted under specific local GAAP or tax scenarios.
• Periodic EIR and daily EIR are theoretically consistent, differing only in "no interim updates" vs. "daily updates"; if reporting only requires coupon date or month-end balances, periodic EIR is sufficient.
• Straight-line amortization is simple but causes actual yields to deviate from the promised yield to maturity across periods.