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Yield, Coupon and Price Relationship

Introduction

The relationship between yield, coupon, and price is a fundamental concept in fixed income securities, especially bonds. This topic is frequently asked in banking exams like IBPS PO, SBI PO, and SSC CGL, as well as in insurance and other financial awareness sections. Understanding this relationship helps candidates analyze how bond prices fluctuate with changes in interest rates and yields.

Pattern: Yield, Coupon and Price Relationship

Pattern

This pattern tests the understanding of how bond price varies inversely with yield and the role of coupon rate in determining bond price relative to its face value.

Key Concept:

Bond Price and Yield have an inverse relationship; when yield rises, bond price falls and vice versa. The coupon rate determines if a bond sells at par, premium, or discount.

Important Points:

  • Coupon Rate = The fixed interest rate paid by the bond issuer on the face value.
  • Yield to Maturity (YTM) = The total return anticipated on a bond if held until maturity.
  • Price Relationship = If coupon rate = YTM, bond price = face value (par); if coupon rate > YTM, bond price > face value (premium); if coupon rate < YTM, bond price < face value (discount).

Related Topics:

  • Types of Bonds (Discount, Premium, Par)
  • Interest Rate Risk
  • Yield Curve

Step-by-Step Example

Question

In the context of bonds, if the coupon rate is higher than the yield to maturity, the bond will be priced at:

Options:

  • A. Par value
  • B. Discount
  • C. Premium
  • D. Face value

Solution

  1. Step 1: Understand coupon rate and yield

    The coupon rate is the fixed interest paid by the bond, while yield to maturity is the market rate of return expected.

  2. Step 2: Compare coupon rate and yield

    If the coupon rate is higher than the yield, investors are willing to pay more than the face value to get the higher coupon payments.

  3. Step 3: Determine bond price

    Since the coupon rate exceeds the yield, the bond price will be above its face value, i.e., at a premium.

  4. Final Answer:

    Premium → Option C

  5. Quick Check:

    Coupon rate > YTM = Bond price premium ✅

Quick Variations

This pattern may appear as questions on:

  • 1. Effect of rising interest rates on bond prices
  • 2. Identifying bond price when coupon rate equals yield
  • 3. Calculating yield to maturity given price and coupon

Trick to Always Use

  • Remember: "Coupon > Yield → Premium; Coupon = Yield → Par; Coupon < Yield → Discount"
  • Mnemonic: "CYP" (Coupon, Yield, Price) to recall the relationship quickly

Summary

Summary

  • Bond price moves inversely to yield changes.
  • Coupon rate determines if bond sells at premium, discount, or par.
  • Understanding this helps in evaluating fixed income investments.

Remember:
Coupon rate compared to yield decides bond price status

Practice

(1/5)
1. If a bond's coupon rate is equal to its yield to maturity (YTM), the bond will be priced at:
easy
A. Premium
B. Discount
C. Par value
D. Below face value

Solution

  1. Step 1: Identify the concept

    The question tests the fundamental relationship between coupon rate, yield to maturity, and bond price.

  2. Step 2: Apply the concept

    When the coupon rate equals the yield to maturity, the bond price equals its face value, also called par value.

  3. Final Answer:

    Par value → Option C

  4. Quick Check:

    Coupon rate = YTM = Par value ✅
Hint: Coupon rate equal to YTM means bond price equals face value.
Common Mistakes: Confusing par value with premium or discount when coupon equals yield.
2. When the market interest rates rise, the price of an existing bond will generally:
easy
A. Increase
B. Decrease
C. Remain unchanged
D. Become equal to face value

Solution

  1. Step 1: Understand the inverse relationship

    Bond prices and market interest rates (or yields) have an inverse relationship.

  2. Step 2: Apply the concept

    When market interest rates rise, existing bonds with lower coupon rates become less attractive, so their prices fall.

  3. Final Answer:

    Decrease → Option B

  4. Quick Check:

    Interest rates rise = Bond price decrease ✅
Hint: Remember: Interest rates up → bond prices down.
Common Mistakes: Assuming bond prices rise with interest rates or remain constant.
3. A bond with a coupon rate lower than the yield to maturity will be sold at:
easy
A. Discount
B. Premium
C. Par value
D. Face value

Solution

  1. Step 1: Identify the relationship

    The coupon rate compared to yield to maturity determines bond price status.

  2. Step 2: Analyze the comparison

    If the coupon rate is less than the yield, investors pay less than face value, so the bond sells at a discount.

  3. Final Answer:

    Discount → Option A

  4. Quick Check:

    Coupon rate < YTM = Discount price ✅
Hint: Coupon less than yield means bond price below face value.
Common Mistakes: Mixing discount with premium or par value in this context.
4. Which of the following statements is TRUE regarding bond price and yield relationship?
medium
A. Bond price and yield have an inverse relationship
B. Bond price remains constant irrespective of yield changes
C. Bond price and yield move in the same direction
D. Bond price is always equal to its face value

Solution

  1. Step 1: Understand bond price and yield dynamics

    Bond price and yield are inversely related due to fixed coupon payments.

  2. Step 2: Evaluate options

    Only the statement that bond price and yield have an inverse relationship is correct; others contradict basic bond principles.

  3. Final Answer:

    Bond price and yield have an inverse relationship → Option A

  4. Quick Check:

    Bond price vs yield = Inverse relationship ✅
Hint: Inverse relationship is key to bond pricing.
Common Mistakes: Assuming bond price moves with yield or stays constant.
5. If a bond is trading at a premium, which of the following must be TRUE?
medium
A. Coupon rate is less than the yield to maturity
B. Coupon rate is equal to the yield to maturity
C. Bond price is less than face value
D. Coupon rate is greater than the yield to maturity

Solution

  1. Step 1: Recall bond price classifications

    A bond trading at a premium means its price is above face value.

  2. Step 2: Link premium price to coupon and yield

    For a bond to trade above face value, the coupon rate must be higher than the yield to maturity.

  3. Final Answer:

    Coupon rate is greater than the yield to maturity → Option D

  4. Quick Check:

    Premium price = Coupon rate > YTM ✅
Hint: Premium means coupon rate exceeds yield to maturity.
Common Mistakes: Confusing premium with discount or equal coupon and yield.

Mock Test

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