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NISM-Series-XV: Research Analyst · Terminology in Equity and Debt Markets

Bond Features, Yields and Pricing Terms for NISM Series XV

Updated 11 October 2026 · Fact-checked

A bond pays a fixed coupon on its face value until maturity. Its price is the present value of those cash flows discounted at the yield to maturity. Price and yield move in opposite directions. Current yield is annual coupon ÷ market price. Duration measures price sensitivity to yield changes.

Understand Bond Features, Yields and Pricing Terms

A bond is a loan you give to an issuer. The issuer promises to pay interest and return the principal. The face value (par value) is the amount repaid at maturity. The coupon rate is the annual interest as a percentage of face value. A ₹1,000 bond with an 8% coupon pays ₹80 a year. The coupon rate is fixed when the bond is issued. It does not change with the market price.

The market price can differ from face value. A bond trades at a premium when price is above face value. It trades at a discount when price is below face value. It trades at par when the two are equal. Price moves because market interest rates move. If new bonds pay more than your bond, buyers pay less for yours.

This gives the inverse price-yield relationship. When yields rise, bond prices fall. When yields fall, bond prices rise. The current yield is annual coupon ÷ current market price. It ignores the gain or loss at maturity. Yield to maturity (YTM) is the single discount rate that makes the present value of all remaining cash flows equal to the price. It assumes you hold to maturity and reinvest coupons at the same YTM.

For a discount bond: coupon rate < current yield < YTM. For a premium bond: coupon rate > current yield > YTM. At par all three are equal.

Macaulay duration is the weighted average time, in years, to receive the bond's cash flows. Modified duration converts this into price sensitivity: it is the approximate percentage change in price for a 1% change in yield. Convexity captures the curve in the price-yield relationship. For a normal bond, it means the price rises more for a yield fall than it drops for an equal yield rise.

Key formulas to remember

Bond price
Price = Σ [C ÷ (1 + y)^t] + F ÷ (1 + y)^n
C = coupon per period, y = yield per period, F = face value, n = number of periods. Price is the present value of all cash flows.
Coupon
Annual coupon = Coupon rate × Face value
Always calculated on face value, never on market price.
Current yield
Current yield = Annual coupon ÷ Current market price
Ignores capital gain or loss and time value of money.
Approximate YTM
YTM ≈ [C + (F − P) ÷ n] ÷ [(F + P) ÷ 2]
A shortcut estimate only. The exact YTM needs trial and error or a calculator.
Modified duration
Modified duration = Macaulay duration ÷ (1 + YTM ÷ k)
k = coupon payments per year. Use YTM as a decimal.
Price change from duration
% change in price ≈ − Modified duration × change in yield (in %)
Good for small yield changes. Convexity corrects the error for large changes.
Duration rules
Zero-coupon bond: Macaulay duration = maturity
For coupon bonds, Macaulay duration is less than maturity. Higher coupon or higher yield usually means lower duration. Longer maturity usually means higher duration.
Yield ranking
Discount bond: coupon rate < current yield < YTM. Premium bond: coupon rate > current yield > YTM
At par, all three are equal.

How to solve Bond Features, Yields and Pricing Terms questions

Use this order for any question on bond terms, yields or pricing. Most questions test one relationship, not heavy calculation.

  1. 1Identify what is asked: price, current yield, YTM ranking, duration or price change.
  2. 2Write down face value, coupon rate, market price, maturity and yield. Convert the coupon rate into a rupee coupon on face value.
  3. 3Compare price with face value. Decide whether the bond is at a discount, par or premium.
  4. 4Apply the yield ranking for that case. This often answers the question without any calculation.
  5. 5If a yield is needed, use current yield = annual coupon ÷ price. Use the approximate YTM formula only if asked for an estimate.
  6. 6For rate-sensitivity questions, find modified duration. Then multiply by the yield change and attach a sign: yield up means price down.
  7. 7Check the direction and the units. Convert basis points to percent: 100 bps = 1%.
  8. 8Eliminate options that break the inverse relationship or use the wrong base for the coupon.

Quickest way: Discount, par or premium shortcut

When to use it: Use it when options compare coupon rate, current yield and YTM, or when the question asks about price direction.

  1. Compare price with face value first.
  2. Price below face value: YTM is the highest of the three, coupon rate the lowest.
  3. Price above face value: YTM is the lowest of the three, coupon rate the highest.
  4. Yield up, price down. Yield down, price up.
  5. For duration, remember: longer maturity and lower coupon mean more sensitivity. A zero-coupon bond has the highest duration for its maturity.

Common mistakes in Bond Features, Yields and Pricing Terms

  • Calculating the coupon on market price instead of face value.

    Students mix up coupon rate with current yield.

    Fix: Coupon = coupon rate × face value. Only current yield uses market price, as the denominator.

  • Thinking a bond's coupon rate changes when its price changes.

    Yield and coupon are treated as the same thing.

    Fix: The coupon is fixed in rupees. Price changes, so the yield earned by a new buyer changes.

  • Saying current yield equals YTM.

    Both are called yields.

    Fix: Current yield ignores the gain or loss at maturity. They are equal only for a bond at par.

  • Confusing Macaulay duration with modified duration.

    Both are measured in numbers close to each other.

    Fix: Macaulay duration is in years. Modified duration = Macaulay ÷ (1 + YTM ÷ k) gives percentage price sensitivity.

  • Forgetting the negative sign in the duration price estimate.

    Focus stays on the multiplication.

    Fix: A rise in yield lowers the price. Write the sign before you compute.

  • Treating basis points as percent.

    Rushing through the question stem.

    Fix: 100 basis points = 1%. So 50 bps = 0.50%.

Worked examples

Example 1

A bond has face value ₹1,000 and a 8% annual coupon. It trades at ₹950. What is its current yield, and where does the YTM stand? Options: (a) 7.60% (b) 8.00% (c) 8.42% (d) 9.50%. Choose the current yield.

Show the solution
  1. Annual coupon = 8% × ₹1,000 = ₹80.
  2. Current yield = ₹80 ÷ ₹950 = 0.0842, or 8.42%.
  3. The price is below face value, so the bond is at a discount.
  4. For a discount bond, coupon rate (8%) < current yield (8.42%) < YTM.

Answer: Current yield is 8.42%, option (c). The YTM is higher than 8.42%.

Example 2

A bond has Macaulay duration of 5 years and YTM of 10% a year, with annual coupons. If the yield rises by 50 basis points, what is the approximate price change? Options: (a) fall of 2.27% (b) fall of 2.50% (c) fall of 4.55% (d) rise of 2.27%.

Show the solution
  1. Modified duration = 5 ÷ (1 + 0.10) = 5 ÷ 1.10 = 4.545, about 4.55.
  2. Yield change = 50 bps = 0.50%.
  3. Price change ≈ − 4.55 × 0.50 = − 2.27%.
  4. The sign is negative because yield rose. So the price falls.
  5. Option (b) uses Macaulay duration without adjusting. Option (c) forgets to convert bps correctly. Option (d) has the wrong direction.

Answer: The price falls by about 2.27%, option (a). Convexity would slightly reduce the size of this fall.

Exam tips

  • Expect direction questions: yield up or down, price up or down. Settle these with the inverse relationship before any arithmetic.
  • Memorise the discount and premium yield rankings. Many MCQs reduce to this.
  • Read whether the question asks for Macaulay or modified duration. Trap options use the wrong one.
  • A negative mark costs you, so skip a calculation-heavy question you cannot finish and return to it. Remember negative marking is 25% of the marks for the question.
  • Remember the convexity statement: for a standard bond, the duration estimate understates the price gain and overstates the price fall.

Practice questions from Terminology in Equity and Debt Markets

Bond Features, Yields and Pricing Terms in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Bond Features, Yields and Pricing Terms: frequently asked questions

What is the difference between coupon rate and YTM?

The coupon rate is the fixed interest on face value, set at issue. YTM is the return you earn if you buy at today's price and hold to maturity. It changes as the market price changes.

Why do bond prices fall when yields rise?

A bond's coupon is fixed. When market yields rise, new bonds pay more, so buyers pay less for your older bond. The price falls until its yield matches the market.

How is modified duration different from Macaulay duration?

Macaulay duration is the weighted average time to receive the cash flows, in years. Modified duration divides it by (1 + YTM ÷ k) and estimates the percentage price change for a 1% change in yield.

What does convexity tell me?

It describes the curvature of the price-yield relationship. For a standard bond, it means a yield fall raises the price by more than a yield rise of the same size lowers it. Duration alone misses this.