3.2

Terminology in Debt Market

This sub‑topic covers the essential terminology used in the Indian debt market. It explains how bonds are priced, the various yield calculations, and the risk measures that analysts must master for the NISM Series XV exam. Understanding these terms helps you answer questions on bond valuation, yield comparison and credit assessment accurately.

Learning Objectives

  • 1Identify and define core debt‑market terms such as face value, coupon, and maturity.
  • 2Explain clean price, dirty price and how accrued interest is calculated.
  • 3Compute common yield measures – current yield, yield to maturity and yield to call.
  • 4Recognise risk indicators like duration, convexity and credit rating and their exam relevance.

Key Debt Market Terms

A bond is a debt instrument issued by a corporation, government or other entity to raise capital. The issuer promises to pay a fixed coupon (interest) at regular intervals and to return the face value (also called par value) on the maturity date. In India, most bonds have a face value of INR 1,000, but the market price can be higher (premium) or lower (discount) depending on interest‑rate movements.

The coupon rate is expressed as a percentage of the face value and determines the periodic cash flow to the bondholder. For example, a 7% annual coupon on a INR 1,000 bond pays INR 70 per year, usually split into semi‑annual payments of INR 35 each. The maturity period can range from a few months (commercial paper) to 30 years (long‑term government bonds).

Exam candidates must differentiate between the face value (a contractual amount) and the market price (the price at which the bond trades). Many questions test whether you know that coupon calculations use the face value, while yield calculations use the market price. Remember: the coupon amount never changes after issuance, even if the bond trades at a discount or premium.

  • Face value – contractual repayment amount at maturity.
  • Coupon – periodic interest based on face value.
ℹ️Exam Trap – Face Value vs Market Price

Students often mistakenly use the market price when computing the coupon payment. The coupon is always a percentage of the face (par) value, not the current trading price.

Pricing Concepts

Bond prices are quoted in two ways: clean price and dirty price. The clean price excludes any interest that has accrued since the last coupon payment, while the dirty price adds this accrued interest. In Indian markets, the quoted price on exchanges is usually the clean price; the dirty price is what the buyer actually pays.

Accrued interest represents the interest earned by the seller for the period they held the bond after the last coupon date. It is calculated proportionally based on the number of days elapsed in the coupon period. The formula uses the coupon amount, days elapsed and total days in the period.

For the exam, you will be asked to convert between clean and dirty prices, or to compute accrued interest when given settlement dates. Pay attention to whether the question states “quoted price” (clean) or “settlement price” (dirty). Misreading this leads to incorrect yield calculations.

Formula: Accrued Interest
C×F×dD\frac{C \times F \times d}{D}

Where:

C= Annual coupon rate (in decimal, e.g., 0.07 for 7%)
F= Face value of the bond in rupees
d= Number of days elapsed since the last coupon date
D= Total number of days in the coupon period (e.g., 180 for semi‑annual)

Worked Example

Given a 7% annual coupon, face value INR 1,000, 60 days since last coupon, semi‑annual period of 180 days: Step 1: AI = (0.07 × 1000 × 60) / 180 Step 2: AI = (70 × 60) / 180 = 4200 / 180 = 23.33 Verification: (0.07 × 1000 × 60) / 180 = 23.33.

⚠️Dirty vs Clean Price Mistake

When a question asks for the amount payable on settlement, add accrued interest to the quoted clean price. Forgetting this step reduces the computed yield by the accrued amount.

Yield Measures

Yield measures help analysts compare bonds with different coupons, maturities and credit quality. The simplest is the Current Yield, which looks only at the annual coupon relative to the market price. It ignores capital gains or losses that occur if the bond is held to maturity.

The more comprehensive measure is Yield to Maturity (YTM). YTM assumes the bond is held until it matures and that all coupon payments are reinvested at the same rate. Because the exact YTM equation is iterative, the NISM syllabus provides an approximate formula that is sufficient for most exam calculations.

Other yields include Yield to Call (used for callable bonds) and Yield Spread (difference between a corporate bond’s yield and a risk‑free benchmark). Remember to identify which yield the question is targeting – the presence of call dates or embedded options signals YTM‑to‑Call.

Formula: Current Yield
CannualP×100\frac{C_{annual}}{P}\times 100

Where:

C_{annual}= Annual coupon payment in rupees
P= Current market price of the bond in rupees

Worked Example

Bond with annual coupon INR 70 and market price INR 950: Step 1: CY = (70 / 950) × 100 Step 2: CY = 0.07368 × 100 = 7.37% Verification: (70 / 950) × 100 = 7.37%.

Formula: Approximate Yield to Maturity (YTM)
Cannual+FPnF+P2\frac{C_{annual}+\frac{F-P}{n}}{\frac{F+P}{2}}

Where:

C_{annual}= Annual coupon payment in rupees
F= Face value of the bond in rupees
P= Current market price in rupees
n= Years to maturity

Worked Example

Bond: Face INR 1,000, coupon INR 70, market price INR 950, 10 years to maturity: Step 1: Numerator = 70 + (1000-950)/10 = 70 + 5 = 75 Step 2: Denominator = (1000 + 950)/2 = 975 Step 3: YTM ≈ 75 / 975 = 0.07692 = 7.69% Verification: (70 + (1000-950)/10) / ((1000+950)/2) = 0.07692.

Risk Measures

Duration measures the weighted average time to receive the bond’s cash flows and indicates price sensitivity to interest‑rate changes. A higher duration means the bond’s price will move more for a given change in yields. The NISM syllabus often refers to Macaulay duration and Modified duration – the latter adjusts for the yield level.

Convexity captures the curvature of the price‑yield relationship. While duration provides a linear approximation, convexity improves accuracy for larger interest‑rate movements. In exam questions, convexity is rarely required to be calculated, but you should know its qualitative impact: higher convexity reduces price volatility.

Credit risk is reflected through credit ratings assigned by agencies such as CRISIL, ICRA, or Moody’s. A higher rating (AAA) indicates lower default risk and typically results in a lower yield spread over government securities. Remember that the rating hierarchy (AAA > AA > A > BBB > BB > B > CCC) is a frequent multiple‑choice theme.

Comparison of Duration Types

Duration TypeDefinitionTypical Use in Exam
Macaulay DurationWeighted average time until cash flows are received, expressed in years.Identify price sensitivity; convert to Modified Duration.
Modified DurationMacaulay Duration divided by (1 + YTM/k), where k is compounding frequency.Directly used for price change estimation.
Effective DurationUses price changes for bonds with embedded options.Relevant for callable/putable bonds.

Special Bond Features

Callable bonds give the issuer the right to redeem the bond before maturity, usually at a specified call price. This feature benefits the issuer when interest rates fall, but adds reinvestment risk for the investor. The presence of a call option reduces the bond’s price and increases its yield.

Putable bonds allow the investor to sell the bond back to the issuer at a predetermined price before maturity. This protects the holder if rates rise, leading to a higher price and lower yield compared with non‑putable bonds.

Convertible bonds can be exchanged for a predetermined number of equity shares. They combine debt and equity characteristics, offering upside potential while retaining fixed‑income features. The conversion premium and ratio are key exam parameters.

Zero‑coupon bonds do not pay periodic coupons. They are issued at a deep discount and mature at face value. Yield is derived entirely from the price appreciation, making the YTM calculation straightforward but requiring careful handling of compounding periods.

Typical Yields Across Bond Categories in India

Example: Calculating Accrued Interest, Dirty Price, Current Yield and Approximate YTM

Scenario

An investor purchases a 10‑year Indian government bond with a face value of INR 1,000 and an annual coupon rate of 7%. The bond pays coupons semi‑annually. On the settlement date, the market (clean) price is INR 950. The last coupon was paid 60 days ago and the next coupon is due in 120 days.

Solution

First compute accrued interest: AI = (0.07 × 1000 × 60) / 180 = 23.33 rupees. Dirty price = clean price + AI = 950 + 23.33 = 973.33 rupees. Current yield = (70 / 950) × 100 = 7.37%. Approximate YTM = [70 + (1000‑950)/10] / [(1000+950)/2] = 75 / 975 = 7.69%. All calculations use the standard formulas and round to two decimal places where appropriate.

Conclusion

The example demonstrates how to move from a quoted clean price to the amount actually paid (dirty price) and then to key yield metrics. Remember to adjust the coupon period when calculating accrued interest for semi‑annual bonds.

Exam Takeaways

  • Bond coupon payments are always based on the face (par) value, not the market price.
  • Clean price excludes accrued interest; dirty price = clean price + accrued interest.
  • Current Yield = (Annual Coupon ÷ Market Price) × 100 – useful for quick comparisons.
  • Approximate YTM formula: [C + (F‑P)/n] ÷ [(F+P)/2]; provides a close estimate for exam calculations.
  • Duration indicates price sensitivity; higher duration = higher interest‑rate risk.
  • Callable bonds lower price and raise yield; putable bonds do the opposite.
  • Zero‑coupon bonds trade at a discount; their yield comes entirely from price appreciation.
  • Always check whether a question refers to clean or dirty price before computing yields.

Practice Questions

8 questions on Terminology in Debt Market

1

What does the term "face value" refer to in the context of Indian bonds?

2

In Indian bond markets, the quoted price on exchanges is usually the ______, and the amount actually paid by the buyer is the ______.

3

A bond has an annual coupon rate of 7%, a face value of INR 1,000, and 60 days have elapsed since the last coupon. The coupon period is semi‑annual (180 days). What is the accrued interest?

4

A bond pays an annual coupon of INR 70 and is currently trading at INR 950. What is its current yield (to two decimal places)?

5

A bond has a clean price of INR 950, an annual coupon of INR 70, and 60 days of accrued interest (semi‑annual period of 180 days). What is the current yield based on the amount actually paid by the buyer?

6

Which of the following statements about duration is correct?

7

Compared with a regular coupon‑paying bond, a zero‑coupon bond's yield is derived ______.

8

Which sequence correctly represents the credit‑rating hierarchy used in the NISM syllabus?

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