CHAPTER II: INTEREST RATE — INTRODUCTION (PART 3 OF 3)

1. CONVERSION OF INTEREST RATES INTO CASH AMOUNTS

1.1 The Necessity of Standardisation

To convert a quoted percentage interest rate into an actual cash payment, market participants must agree on a set of core parameters. Without establishing these parameters beforehand, a single percentage rate could yield several different cash outcomes.

1.2 Four Key Parameters for Calculation

The conversion of an interest rate into a cash amount requires the explicit specification of the following four parameters:

• Payment Frequency: This parameter specifies when the cash interest is actually paid out to the investor. Standard payment frequencies include monthly, quarterly, semiannual, or annual payments, or a single payment at the very end of the investment term. In money market instruments, the standard market convention is to pay interest at the end of the term.
• Compounding Frequency: This parameter specifies whether the interest is simple or compounded. When compounding is applicable, a strict structural rule applies: the compounding frequency must be higher than, and an exact integral multiple of, the payment frequency.
• Day Count Fraction (Day Count Basis): This parameter specifies how a calendar payment period is converted into a mathematical year fraction (for example, converting a six-month period into 0.5 of a year). To perform this conversion, market participants must agree on a standard method for counting both the number of days in the specific interest accrual period and the number of days in a year. This metric is always expressed as a fraction.
• Payment Timing: This parameter specifies whether the cash interest is paid upfront or in arrears of the payment period. If paid upfront, it is referred to as a discount yield; if paid in arrears, it is known as an investment yield.

2. DAY COUNT BASIS AND INDIAN MARKET CONVENTIONS (FIMMDA RULES)

2.1 The Role of FIMMDA

The Fixed-income and Money Market Derivatives Association of India (FIMMDA) is the self-regulatory organisation (SRO) in India for the money, bond, and derivatives markets. FIMMDA establishes standard business practices and code of conduct rules to ensure order and consistency in how debt instruments are priced, traded, and settled.

2.2 Standard FIMMDA Market Conventions

According to FIMMDA rules, transactions in the Indian debt and money markets must adhere to the following strict conventions:

• Rounding of Interest Amounts: All final cash interest amounts must be rounded off to the nearest whole rupee.
• Rounding of Quotes: Price and yield quotes must be rounded to the nearest fourth decimal place when they are used directly in interest amount calculations.
• The Day Count Standard: For all standard money and bond transactions, the day count basis is Actual/365 Fixed.
• The Sovereign Bond Exception: There is one major exception to the Actual/365 Fixed rule. For the calculation of accrued interest in the secondary market for sovereign bonds, the day count basis must be 30E/360.
• Quoting Discount Instruments: The yield on money market discount instruments, such as Treasury Bills (T-Bills), Certificates of Deposit (CDs), and Commercial Paper (CP), must be quoted on a true yield (Y) basis and not on a discount yield basis.
• Bill Rediscounting Exception: For bill rediscounting transactions, yields must be quoted on a discount yield (DY) basis.

3. ACCRUED INTEREST AND SECONDARY MARKET BOND PRICING

3.1 Clean Price vs. Dirty Price

When a bond is traded in the secondary market between two coupon payment dates, its valuation is divided into two distinct prices:

• Clean Price: This is the price at which the bond is negotiated and agreed upon by the buyer and seller in the market. It represents the pure capital value of the bond, excluding any accumulated interest.
• Dirty Price: This is the actual cash price at which the bond transaction is settled on the settlement date. The dirty price is always higher than the clean price because it incorporates the value of the interest that has accumulated since the last coupon payment.

3.2 The Settlement Formula

The relationship between the two secondary market bond prices is expressed as follows:

Dirty Price = Clean Price + Accrued Interest

3.3 Accrued Interest Timeline and Ownership Rights

Accrued interest represents the interest that has accumulated at the bond's coupon rate from the previous coupon date up to the settlement date of the trade.

The settlement date of a secondary market trade falls directly between two coupon dates (the previous coupon date and the next coupon date). This timeline dictates who is contractually entitled to the interest cash flows:

• Seller Entitlement: Between the previous coupon date and the settlement date, the seller owns the bond. Therefore, the seller is legally entitled to receive the interest accrued during this specific period.
• Buyer Entitlement: Between the settlement date and the next coupon date, the buyer owns the bond. Consequently, the buyer is entitled to the interest accrued during this latter period.
• The Compensation Mechanism: When the next coupon date arrives, the issuer pays the entire coupon amount for the full period to the current holder of the bond (the buyer). Because the buyer receives the full coupon but did not own the bond for the first part of the period, the buyer must compensate the seller upfront at the time of settlement. This is done by adding the accrued interest to the negotiated clean price, forming the dirty price.

3.4 Why Market Participants Negotiate on Clean Prices

A logical question is why market participants do not negotiate directly on the dirty price (the settlement price).

If accrued interest were incorporated directly into the negotiated market price (clean price), it would create an artificial, daily "rise-and-fall" volatility pattern in the bond's price. Because daily interest accrual is constant, the bond's market price would rise smoothly and steadily every single day by the daily accrual amount, only to fall abruptly by the entire coupon amount on the coupon payment date.

To prevent this artificial price volatility and allow investors to track the actual market demand and credit quality of the bond, the negotiated price is kept "clean" of interest accruals.

4. KEY SUMMARY AND COMPARATIVE ANALYSIS

The table below synthesis the key conversion parameters, FIMMDA rules, and pricing dynamics covered in this part:

Important Terms for Exam Reference

• FIMMDA: Fixed-income and Money Market Derivatives Association of India, the self-regulatory organisation governing Indian debt markets.
• Arrears (Investment Yield): Interest payment timing where cash interest is paid at the end of the accrual period.
• Upfront (Discount Yield): Interest payment timing where cash interest is paid or deducted at the start of the accrual period.
• True Yield (Y): The standard quoting basis required by FIMMDA for money market instruments like T-Bills, CDs, and CPs.