Bonds and debentures are core fixed-income securities that play a vital role in investment portfolios, banking systems, and capital markets, offering predictable returns, risk diversification, and long-term funding for governments and corporations. This comprehensive guide explains what a bond is, its key terminologies such as issuer, face value, coupon rate, coupon payment, bond price, yield to maturity (YTM), current yield, maturity, duration, convexity, credit rating, default risk, yield curve, spread, clean price and dirty price, and how bond prices fluctuate with changes in market interest rates. It also covers the classification of bonds, including government bonds, corporate bonds, municipal bonds, zero-coupon bonds, coupon-bearing bonds, callable bonds, puttable bonds, floating-rate bonds, Treasury Bills (T-Bills), certificates of deposit (CDs), fixed deposit receipts (FDRs), and preference shares, highlighting their features, risks, and returns. The article further explains the importance of fixed-income securities in banking for liquidity management, asset allocation, loan pricing benchmarks, and risk management, while clearly defining debentures as unsecured corporate debt instruments that rely on issuer creditworthiness rather than collateral. Finally, it provides a clear comparison between zero-coupon bonds and coupon-bearing bonds, helping investors, students, and finance professionals understand income generation, capital appreciation, interest-rate sensitivity, and investment suitability across different fixed-income instruments.
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আপনি যদি Bond Valuation, YTM (Yield to Maturity), Bond Price, Bond Calculator, Fixed Income Securities, Debenture, JAIBB, AIBB, Banking Diploma, BBA, MBA, MBM, CMA, CA, অথবা Corporate Finance-এর গাণিতিক সমস্যা ও তাত্ত্বিক ধারণা সহজে শিখতে চান, তাহলে নিচের Play বাটনে ক্লিক করে সম্পূর্ণ ভিডিওটি দেখুন। এই Master Class-এ আপনি বাস্তব উদাহরণ, পরীক্ষায় আসা প্রশ্নের সমাধান এবং গুরুত্বপূর্ণ শর্টকাট কৌশলের মাধ্যমে Bond Valuation ও YTM Calculation আয়ত্ত করতে পারবেন। ভিডিওটি শেষ করার পর নিচের Lecture Notes, Bond Calculator, Practice Problems এবং Online Quiz ব্যবহার করে নিজের প্রস্তুতিকে আরও শক্তিশালী করুন।
What is Bond?
A bond is a fixed-income financial instrument that represents a loan made by an investor to a borrower (typically a corporation, government, or financial institution). In essence, it is a debt security under which the issuer (borrower) is obliged to pay the bondholder (lender) periodic interest—known as the coupon rate—and to repay the principal amount (face value or par value) on a specified maturity date.
Key Features of Bond:
1. lssuer: The entity that borrows funds (e.g., Government, Bank, or Company).
2. Face Value (Par Value)
- Definition: The amount the bond issuer agrees to repay the bondholder at maturity. It is also the reference amount used to calculate coupon payments.
- Example: A bond with a face value of $1,000 means issuer will repay $1,000 at maturity to the bond holder.
3. Coupon Rate
- Definition: The annual interest rate paid by the bond issuer to the bondholder, expressed as a percentage of the face value.
- Example: A bond with a 5% coupon rate and a face value of $1,000 will pay $50 annually ($1,000 × 5%).
4. Coupon Payment
- Definition: The periodic interest payment made to bondholders, typically semiannually or annually.
- Example: A bond with a 5% coupon rate and a face value of $1,000 will pay $25 every 6 months ($1,000 × 5% / 2).
5. Yield to Maturity (YTM)
- Definition: The total return anticipated on a bond if it is held until maturity, considering the current market price, coupon payments, and face value.
Example: A bond with a face value of $1,000, coupon rate 5% paid semiannually and current market price is now $900 and years to maturity is ten years. If anyone buy this bond now at $900 now and keeps it until maturity then what return (rate in %) he/she will earn. That’s rate or return is called YTM. Here YTM of 6.37%.
6. Current Yield
- Definition: The annual coupon payment divided by the bond’s current market price.
- Example: A bond with a $50 annual coupon payment and a current market price of $900 has a current yield of 5.56% (50/900).
7. Bond Price
- Definition: The market price at which the bond is currently trading. It may be at a premium (above face value), at par (equal to face value), or at a discount (below face value).
- Example: A bond with a face value of $1,000 might trade at $1,050 (premium), $1,000 (par), or $950 (discount).
8. Maturity Date
- Definition: The date on which the bond issuer repays the face value to the bondholder and terminates the bond.
- Example: A bond issued on January 1, 2023, with a 10-year maturity will mature on January 1, 2033.
9. Duration
- Definition: A measure of the bond’s sensitivity to interest rate changes, expressed in years. It estimates the percentage change in bond price for a 1% change in yield.
- Macaulay Duration: Weighted average time to receive cash flows.
- Modified Duration: Adjusts Macaulay Duration for changes in yield.
- Example: A bond with a modified duration of 5 years will see its price change by approximately 5% for a 1% change in yield.
10. Convexity
- Definition: A measure of the curvature of the bond’s price-yield relationship. It provides a more accurate estimate of price changes for large yield changes.
- Example: A bond with high convexity will have a larger price increase when yields fall compared to a bond with low convexity.
Bond Valuation
The Standard Valuation Formula
A coupon-bearing bond pays a series of periodic interest payments (coupons) plus the face value at maturity. Its current market price is the sum of the present values of all future cash flows, discounted at the bond’s yield to maturity (YTM).
Where: P = price | C = periodic coupon payment | r = yield per period | F = face value | n = number of periods
⚡ The summation covers each coupon period from t = 1 to t = n.
Step-by-Step Example
Consider a corporate bond with the following terms:
Bond Terms
- Face Value (F): $1,000
- Coupon Rate: 6% per annum (paid semi-annually)
- Coupon Payment (C): $30 every 6 months
- Yield to Maturity (r): 5% per annum (semi-annual yield = 2.5%)
- Years to Maturity: 8 years → n = 16 semi-annual periods
16 coupon payments of $30 + final principal payment of $1,000 at period 16.
P = 30/(1.025)1 + 30/(1.025)2 + … + 30/(1.025)16 + 1,000/(1.025)16
PVcoupons = 30 × [ (1 − (1.025)−16) / 0.025 ] = 30 × 13.055 = $391.65
PVprincipal = 1,000 / (1.025)16 = 1,000 / 1.4845 = $673.62
Since the coupon rate (6%) exceeds the market yield (5%), the bond trades at a premium to par.
Semi-Annual Compounding (Standard Convention)
Most corporate and government bonds pay coupons semi-annually. The general formula adjusts for m compounding periods per year:
Quick Verification
- Per-period yield: 5% / 2 = 2.5%
- Number of periods: 8 × 2 = 16
- Coupon per period: $1,000 × 6% / 2 = $30
✅ The calculation above uses these exact inputs, confirming the price of $1,065.27.
Professional Pricing Insights
When trading between coupon dates, the buyer compensates the seller for accrued interest. The clean price (quoted) excludes accrued interest; the dirty price (invoice) includes it.
YTM is the internal rate of return assuming all coupons are reinvested at the same rate. It is the single discount rate that equates the bond’s price to its cash flows.
If coupon > YTM → Premium (price > par).
If coupon = YTM → Par (price = par).
If coupon < YTM → Discount (price < par).
Coupon bonds have lower duration than zero-coupon bonds of the same maturity, as interim cash flows reduce interest rate sensitivity.
Valuation Summary
The price of a coupon-bearing bond is the present value of its coupon annuity plus the discounted face value. This fundamental DCF approach underpins all fixed-income analytics, from relative value assessment to risk management.
© 2026 · Fixed-Income Valuation Desk Reference
Zero-Coupon Bond Valuation
The Core Valuation Formula
A zero-coupon bond makes no periodic interest payments. Its current market price is the present value of the single future cash flow — the face value at maturity. The discount rate used is the required yield (YTM) for the bond’s term and risk profile.
Where: P = current price | F = face value | r = yield per period | n = number of periods
Practical Example & Step-by-Step
Assume the following bond characteristics:
Bond Assumptions
- Face Value (F): $1,000
- Yield to Maturity (r): 5.0% (0.05) per annum
- Time to Maturity (n): 10 years
An investor pays ~$613.91 today to receive $1,000 at maturity, earning an annualized return of 5%.
Semi-Annual Compounding (Market Standard)
In many fixed-income markets, yields are quoted on a semi-annual bond basis. The formula adjusts to reflect the compounding frequency:
Semi-Annual Example
- Face Value: $1,000
- Yield (annual): 5%
- Maturity: 10 years
- Compounding: Semi-annual (m = 2)
With more frequent compounding, the present value is slightly lower ($610.27 vs. $613.91).
Critical Professional Considerations
Zero-coupon bonds have no accrued interest between payment dates, making pricing and settlement more straightforward than coupon bonds.
Even without cash interest, the annual accretion of the discount is treated as taxable income under Original Issue Discount (OID) rules in many jurisdictions.
If yield rises to 6%, the price falls to $558.39. If yield drops to 4%, price rises to $675.56 — illustrating the inverse relationship.
Zero-coupon bonds have the highest duration for a given maturity. Macaulay duration equals the exact time to maturity (n), making them extremely sensitive to interest rate moves.
Final Calculation Summary
The current market price of any zero-coupon bond is found by discounting the face value using the appropriate yield and compounding convention. The formula remains the bedrock of fixed-income pricing — rigorous, transparent, and essential for portfolio valuation.
© 2026 · Fixed-Income Valuation Desk Reference
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Question
(a) Consider a coupon bond that has a Tk. 1000 par value and a coupon rate of 10%. The bond is currently selling for Tk. 1200 and has 5 years to maturity. What is the bond’s yield to maturity?
(b) What is the price of a perpetual bond that has a coupon of Tk. 100 per year and a yield to maturity of 5%?
Solution
(a) Yield to Maturity (coupon bond)
(b) Perpetual bond price
Bond Price and Market Interest Relationship
Bond price fluctuates due to the fluctuation of the market interest rate. If market interest rate goes up and becomes higher than the coupon rate then bond’s price go down and vice versa. If market interest rate equals coupon rate then bond’s price equals face value or par value.
Credit Rating
- Definition: An assessment of the bond issuer’s creditworthiness, provided by rating agencies like Moody’s, S&P, or Fitch. Higher ratings indicate lower default risk.
- Example: A bond rated AAA is considered very safe, while a bond rated CCC is considered high-risk.
Default Risk
- Definition: The risk that the bond issuer will fail to make timely coupon payments or repay the face value at maturity.
- Example: A corporate bond from a financially unstable company has higher default risk than a U.S. Treasury bond.
Accrued Interest
- Definition: The interest that has accumulated since the last coupon payment but has not yet been paid.
- Example: If a bond pays a $30 coupon every 6 months and 3 months have passed since the last payment, the accrued interest is now $15.
Yield Curve
- Definition: A graph that plots the yields of bonds with the same credit quality but different maturity dates. It shows the relationship between yield and time to maturity.
- Example: A normal yield curve slopes upward, indicating that longer-term bonds have higher yields than shorter-term bonds.
Spread
- Definition: The difference in yield between two bonds, often used to compare corporate bonds to risk-free government bonds.
- Example: If a corporate bond yields 6% and a Treasury bond yields 4%, the spread is 2%.
Dirty Price
- Definition: The bond price including accrued interest.
- Example: If a bond’s clean price is $950 and accrued interest is $25, the dirty price is $975.
Clean Price
Definition: The bond price excluding accrued interest.
Example: If a bond’s dirty price is $975 and accrued interest is $25, the clean price is $950.
Classification of Bond
Callable Bond
- Definition: A bond that the issuer can redeem before its maturity date, usually at a premium to the face value.
- Example: A callable bond with a face value of $1,000 might be callable at $1,050 after 5 years.
Puttable Bond
- Definition: A bond that allows the bondholder to sell it back to the issuer at a predetermined price before maturity.
- Example: A puttable bond with a face value of $1,000 might allow the bondholder to sell it back to the issuer at $1,020 after 3 years.
Zero-Coupon Bond
- Definition: A bond that does not pay periodic coupons. It is issued at a discount to face value and repays the face value at maturity.
- Example: A zero-coupon bond with a face value of $1,000 might be issued at $800 and repay $1,000 at maturity.
Government Bonds:
- Issued by central or state governments.
- Considered risk-free in stable economies.
- Example: Treasury Bonds, Treasury Bills (T-Bills).
Corporate Bonds:
- Issued by companies to finance operations or expansion.
- Higher risk than government bonds but offers better returns.
- Example: Debentures, Convertible Bonds.
Municipal Bonds:
- Issued by local governments or municipalities.
- Often tax-free for investors in the issuing jurisdiction.
Certificates of Deposit (CDs):
- Fixed-term deposits offered by banks with a guaranteed return.
- Low risk and insured up to a certain limit.
Fixed Deposit Receipts (FDRs):
- Offered by banks with fixed tenure and fixed interest rates.
- Non-tradable in secondary markets.
Preference Shares (Fixed Dividend):
Hybrid security offering fixed dividends before common shareholders receive dividends.
Treasury Bills (T-Bills):
- Short-term securities issued by the government (typically less than one year).
- Issued at a discount and redeemed at face value.
Floating Rate Bonds:
Bonds with variable interest rates that adjust periodically based on market conditions.
Differentiate between Zero Coupon Bond and Coupon Bearing Bond.
Zero coupon bonds and coupon-bearing bonds are two distinct types of fixed-income securities that differ in their structure, interest payments, and investment appeal. The key differences are outlined below:
| Feature | Zero Coupon Bond | Coupon Bearing Bond |
| Definition | A bond that does not pay periodic interest but is issued at a discount and matures at face value. | A bond that pays periodic interest (coupon payments) to bondholders until maturity. |
| Interest Payments | No periodic interest payments; all interest is accrued and paid at maturity. | Regular interest payments (annually, semi-annually, or quarterly) based on a fixed or floating coupon rate. |
| Price at Issuance | Issued at a deep discount to its face value. | Issued at or near its face value. |
| Maturity Value | Redeemed at full face value, with the difference being the earned interest. | Redeemed at face value, with periodic interest already paid over time. |
| Risk & Volatility | Higher interest rate risk and price volatility due to no interim cash flow. | Lower price volatility as regular coupon payments reduce reinvestment risk. |
| Suitability | Suitable for long-term investors seeking capital appreciation. | Suitable for investors seeking regular income and stable returns. |
| Example | A 10-year zero coupon bond issued at $600 matures at $1,000. The $400 gain represents the investor’s return. | A 10-year coupon bond with a 5% annual interest rate pays $50 annually and returns the principal at maturity. |
Importance of Fixed Income Securities/Bond in Banking
- Asset Management: Banks invest in fixed-income securities for liquidity and stable returns.
- Loan Pricing Benchmark: Government bond yields influence lending rates.
- Risk Diversification: Helps balance portfolio risks by providing steady income.
- Liquidity Management: Short-term instruments like T-Bills help banks manage cash flow efficiently.
Debenture
A debenture is a type of unsecured bond that is not backed by collateral but relies on the creditworthiness and reputation of the issuer. It is commonly issued by corporations to raise long-term capital.
Key Features:
- Unsecured Debt: No physical asset backing
- Fixed or Floating Interest Rate
- Convertible or Non-Convertible: Some debentures can be converted into equity shares
- Higher Risk than Secured Bonds
Example:
A company issues a 7-year debenture with a 6% coupon rate, but since it is not backed by any assets, investors rely on the company’s financial health to receive payments
Conclusion
Zero coupon bonds provide long-term growth without regular income, while coupon-bearing bonds offer steady interest payments, making them suitable for income-focused investors. The choice between the two depends on an investor’s financial goals, risk appetite, and investment horizon. Debenture is not backed by any direct assets/collateral so it is as more risky than bond.
Written By-Md Kollol Hossain, CEO, CapitalinsightBD
How to calculate Current Market Price of a Bond and YTM, visit here.
To know the difference between Bond and Equity, visit here.
জিরো কুপন বন্ড এবং কুপন বিয়ারিং বন্ডের মধ্যে পার্থক্য করুন।
জিরো কুপন বন্ড এবং কুপন-বিয়ারিং বন্ড হল দুটি স্বতন্ত্র ধরণের স্থির-আয়ের সিকিউরিটি যা তাদের কাঠামো, সুদ প্রদান এবং বিনিয়োগের আবেদনে ভিন্ন। মূল পার্থক্যগুলি নীচে বর্ণিত হল:
| বৈশিষ্ট্য | জিরো কুপন বন্ড | কুপন বিয়ারিং বন্ড |
| সংজ্ঞা | এমন একটি বন্ড যা পর্যায়ক্রমিক সুদ প্রদান করে না কিন্তু ছাড়ে জারি করা হয় এবং অভিহিত মূল্যে পরিপক্ক হয়। | এমন একটি বন্ড যা পরিপক্কতা পর্যন্ত বন্ডহোল্ডারদের পর্যায়ক্রমিক সুদ (কুপন প্রদান) প্রদান করে। |
| সুদের অর্থপ্রদান | কোনও পর্যায়ক্রমিক সুদ প্রদান করা হয় না; সমস্ত সুদ মেয়াদপূর্তিতে জমা হয় এবং পরিপক্কতার সময় প্রদান করা হয়। | নিয়মিত সুদের অর্থপ্রদান (বার্ষিক, অর্ধ-বার্ষিক, বা ত্রৈমাসিক) একটি নির্দিষ্ট বা ভাসমান কুপন হারের উপর ভিত্তি করে। |
| ইস্যুতে মূল্য | তার অভিহিত মূল্যের উপর গভীর ছাড়ে জারি করা হয়। | এর অভিহিত মূল্যে বা তার কাছাকাছি জারি করা হয়। |
| পরিপক্কতা মূল্য | পূর্ণ অভিহিত মূল্যে খালাস করা হয়, পার্থক্যটি অর্জিত সুদ সহ। | অভিহিত মূল্যে খালাস করা হয়, সময়ের সাথে সাথে ইতিমধ্যেই পর্যায়ক্রমিক সুদ প্রদান করা হয়। |
| ঝুঁকি এবং অস্থিরতা | অন্তর্বর্তীকালীন নগদ প্রবাহ না থাকার কারণে উচ্চ সুদের হার ঝুঁকি এবং মূল্যের অস্থিরতা। | নিয়মিত কুপন পেমেন্টের ফলে মূল্যের অস্থিরতা হ্রাস পায়, যা পুনঃবিনিয়োগের ঝুঁকি হ্রাস করে। |
| উপযুক্ততা | দীর্ঘমেয়াদী বিনিয়োগকারীদের জন্য উপযুক্ত যারা মূলধন বৃদ্ধি পেতে চান। | নিয়মিত আয় এবং স্থিতিশীল রিটার্ন চাইছেন এমন বিনিয়োগকারীদের জন্য উপযুক্ত। |
| উদাহরণ: | ৬০০ টাকয় জারি করা ১০ বছরের শূন্য কুপন বন্ড ১,০০০ টাকায় পরিপক্ক হয়। | ৪০০ টাকা লাভ বিনিয়োগকারীর রিটার্নকে প্রতিনিধিত্ব করে। ৫% বার্ষিক সুদের হার সহ ১০ বছরের কুপন বন্ড বার্ষিক ৫০ টাকা প্রদান করে এবং পরিপক্কতার সময় মূলধন ফেরত দেয়। |
উপসংহার
শূন্য কুপন বন্ড নিয়মিত আয় ছাড়াই দীর্ঘমেয়াদী প্রবৃদ্ধি প্রদান করে, অন্যদিকে কুপন-বহনকারী বন্ডগুলি স্থির সুদের অর্থ প্রদান করে, যা আয়-কেন্দ্রিক বিনিয়োগকারীদের জন্য উপযুক্ত করে তোলে। দুটির মধ্যে পছন্দ বিনিয়োগকারীর আর্থিক লক্ষ্য, ঝুঁকি গ্রহণের ক্ষমতা এবং বিনিয়োগের দিগন্তের উপর নির্ভর করে।
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