Definition
Gross Redemption Yield (GRY), also known as Effective Yield or Yield to Maturity (YTM), is a measure of the total return an investor can expect to earn if a bond is held until it matures. GRY incorporates all income, including coupon payments, as well as all capital payments due at maturity. Importantly, the calculation does not take into account any taxes payable on the interest and capital repayments. This metric is critical in assessing the attractiveness of bond investments.
Examples
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Zero-Coupon Bond Example: Assume you purchase a zero-coupon bond with a face value of $1,000 for $700, and the bond matures in 10 years. The GRY would be calculated as the discount rate that equates the purchase price to the present value of the bond’s future payments.
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Coupon-Bearing Bond Example: If you buy a bond with a face value of $1,000, a coupon rate of 5%, annual coupon payments, and a purchase price of $950, the GRY would be the discount rate that makes the present value of all future coupon payments and the maturity value of the bond equal to $950.
Frequently Asked Questions
The GRY, or YTM, is found by solving the following equation for the discount rate \( r \):
\[ P = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^n} \]
where:
- \( P \) = Current bond price
- \( C \) = Annual coupon payment
- \( F \) = Face value of the bond
- \( n \) = Number of years to maturity
- \( r \) = Yield to Maturity (YTM)
Is GRY the same as interest rate?
No, GRY is not the same as the bond’s stated interest rate (coupon rate). GRY provides a comprehensive measure of return, incorporating the coupon payments, the capital gains or losses if the bond is bought at a price different from its face value, and the reinvestment of coupon payments.
How does the Gross Redemption Yield relate to bond pricing?
The GRY is inversely related to the bond price. When bond prices decrease, GRY increases, reflecting a higher rate of return, and vice versa.
Are taxes considered in the Gross Redemption Yield calculation?
No, GRY calculations do not consider taxes payable on the interest and capital repayments.
Can GRY change over the life of the bond?
While the GRY is calculated based on holding a bond to maturity, changes in market interest rates, bond price, and re-investment rates can affect the effective yield realized by the investor.
Coupon Rate
The stated annual interest rate paid on a bond, expressed as a percentage of the face value.
Current Yield
A bond’s annual coupon payment divided by its current price.
Yield Spread
The difference in yields between different debt instruments, often of different credit quality or maturity dates.
Online References
Suggested Books for Further Studies
- “Bond Markets, Analysis, and Strategies” by Frank J. Fabozzi
- “Fixed Income Analysis” by Frank J. Fabozzi, CFA
- “The Handbook of Fixed Income Securities” by Frank J. Fabozzi
Accounting Basics: Gross Redemption Yield Fundamentals Quiz
### What does the Gross Redemption Yield (GRY) measure?
- [ ] Annual coupon payments only.
- [ ] Capital repayments only.
- [x] Total return including all income and capital payments until maturity.
- [ ] The tax payable on the bond's interest and capital repayments.
> **Explanation:** GRY measures the total return an investor can expect to earn if a bond is held until maturity, excluding taxes on the interest and capital repayments.
### How is GRY different from the current yield?
- [ ] GRY considers only annual coupons, while current yield considers all payments.
- [x] GRY includes all future income and capital payments, while current yield only considers annual coupon payments.
- [ ] GRY includes taxes, while current yield does not.
- [ ] GRY is calculated annually, while current yield is a one-time calculation.
> **Explanation:** GRY includes all future income and capital payments, whereas current yield only considers the annual coupon payments divided by the bond's current price.
### What is an essential factor ignored in the GRY calculation?
- [ ] Coupon rate.
- [ ] Bond price.
- [ ] Maturity date.
- [x] Taxes payable on interest and capital repayments.
> **Explanation:** GRY calculations exclude taxes payable on the interest and capital repayments, focusing on the pre-tax return.
### If bond prices decrease, what happens to the GRY?
- [x] The GRY increases.
- [ ] The GRY decreases.
- [ ] The GRY remains unchanged.
- [ ] There is no consistent impact on GRY.
> **Explanation:** When bond prices decrease, the GRY increases, indicating a higher return due to the lower initial investment.
### What must you solve to calculate the GRY?
- [ ] Price of the bond formula.
- [ ] Coupon interest formula.
- [x] Present value of all future payments matching the purchase price.
- [ ] Annual coupon payment formula.
> **Explanation:** GRY is calculated by solving for the discount rate at which the present value of all future payments (coupons and face value) equals the purchase price.
### Considering a bond’s GRY, which of the following is NOT included in the calculation?
- [x] Realized taxes on interest.
- [ ] Annual coupon payments.
- [ ] Future capital repayments at maturity.
- [ ] Current bond purchase price.
> **Explanation:** GRY calculations do not include realized taxes on interest, focusing instead on gross returns.
### Why is GRY an important metric for investors?
- [ ] It measures the bond issuer's ratings.
- [ ] It helps predict future interest rates.
- [x] It provides a comprehensive return measure for bonds held to maturity.
- [ ] It helps in accounting for monthly bond payments.
> **Explanation:** GRY provides investors with a comprehensive measure of return for bonds held until maturity, integrating all coupon and capital payments.
### What happens when the coupon rate of a bond is higher than the GRY?
- [x] The bond is bought at a premium.
- [ ] The bond is bought at a discount.
- [ ] The coupon rate aligns with market interest rates.
- [ ] The bond price remains unaffected.
> **Explanation:** When the coupon rate is higher than the GRY, the bond is typically bought at a premium above its face value.
### Which key variable is essential in the GRY equation but not in current yield?
- [ ] Annual coupon payment.
- [ ] Bond price.
- [x] Reinvestment of coupon payments.
- [ ] Length of time to maturity.
> **Explanation:** The GRY considers the reinvestment of coupon payments till maturity, a factor not considered in the current yield calculation.
### What primarily causes a bond’s GRY to differ from its coupon rate?
- [ ] Changes in issuer's policies.
- [x] Market interest rate fluctuations.
- [ ] Issuer’s credit rating changes.
- [ ] Bond's listing status.
> **Explanation:** Market interest rate fluctuations are the primary cause of differences between a bond's GRY and its coupon rate, affecting the bond's price and resultant yield.
Thank you for exploring the concept of Gross Redemption Yield with us. We hope this comprehensive guide and quiz enhance your understanding and proficiency in bond investment metrics!
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