Fixed Income
This sub‑topic covers Fixed Income securities, their key characteristics, valuation methods and risk factors. It is essential for the Investment Adviser exam because most client portfolios contain bonds or similar instruments. Understanding how to compute yields and duration helps you answer quantitative questions confidently.
Learning Objectives
- 1Define Fixed Income and list its major types in India
- 2Identify the core features such as coupon, face value and maturity
- 3Apply present value, current yield and YTM formulas to price bonds
- 4Explain duration and the principal risks associated with Fixed Income
Definition and Importance of Fixed Income
Fixed Income refers to financial instruments that provide a predetermined stream of cash flows, usually in the form of interest or coupon payments, and return the principal at maturity. In the Indian context, these include government securities, corporate bonds, Treasury bills, and fixed deposits.
The predictable cash flows make Fixed Income a cornerstone for risk‑averse investors and for portfolio diversification. SEBI’s definition emphasizes that the instrument must have a fixed repayment schedule, which distinguishes it from equity.
For the NISM exam, you will be asked to identify the instrument, compute its yield, and assess its risk profile. Questions often test whether you can link the concept to client suitability under the Investment Adviser regulations.
Remember: the term “fixed” relates to the payment schedule, not necessarily the return amount, which can vary with market price.
Core Features of Fixed Income Instruments
Every Fixed Income security has a face value (or par) that is repaid at maturity. The periodic interest paid is called the coupon, expressed as a percentage of the face value.
The maturity period can range from a few days (Treasury bills) to several decades (long‑term bonds). The market price fluctuates with changes in prevailing interest rates, credit perception and liquidity.
Yield measures the effective return to the investor. While the coupon is fixed, the current yield and yield to maturity (YTM) vary with price. Knowing how to calculate these helps you answer exam items on bond pricing.
Other attributes include call/put options, convertibility and tax treatment, but the exam focuses mainly on coupon, price, maturity and yield.
Students often equate the coupon rate with the bond’s return. The coupon is fixed, but the actual return depends on the purchase price; use current yield or YTM for the correct answer.
Categories of Fixed Income Securities in India
Indian Fixed Income markets offer a variety of instruments. Government securities (G‑Sec) are issued by the Central Government and carry the lowest credit risk. Corporate bonds are issued by companies and offer higher yields to compensate for credit risk.
Treasury bills (T‑Bills) are short‑term discount instruments with maturities of 91, 182 or 364 days. Fixed deposits (FDs) offered by banks are also considered Fixed Income, though they are not tradable on secondary markets.
Each category differs in liquidity, taxability and typical investor base. The exam may ask you to match a feature (e.g., “zero‑coupon”) with the correct instrument.
Understanding these classifications helps you recommend suitable products under SEBI’s client‑suitability norms.
Comparison of Major Fixed Income Instruments in India
| Instrument | Typical Maturity | Coupon Type | Issuer | Credit Risk |
|---|---|---|---|---|
| Government Securities | 2–30 years | Fixed or Floating | Central Government | Lowest |
| Corporate Bonds | 5–10 years | Fixed | Companies | Higher than G‑Sec |
| Treasury Bills | 91‑364 days | Zero‑coupon (discount) | Central Government | Lowest |
| Bank Fixed Deposits | 7 days‑10 years | Fixed | Banks | Low to Moderate |
Valuation – Present Value of a Cash Flow
Bond pricing is based on discounting each future cash flow (coupon or principal) to its present value (PV) using the market‑required rate of return. The principle is the same as for any Fixed Income instrument.
The PV formula for a single cash flow is straightforward: divide the future amount by (1 + r)ⁿ, where r is the discount rate per period and n is the number of periods until receipt.
When multiple cash flows exist, you sum the PV of each. This concept underlies the calculation of current yield and YTM, which the exam tests extensively.
Remember to keep the rate and time units consistent (annual rate with years, monthly rate with months).
Where:
FV= Future cash flow amount in rupeesr= Discount rate per period (decimal, e.g., 0.08 for 8% p.a.)n= Number of periods until cash flow is receivedWorked Example
Given FV = 10,000 ₹, r = 8% p.a. (0.08), n = 3 years: Step 1: PV = 10000 / (1 + 0.08)^{3} Step 2: (1 + 0.08)^{3} = 1.2597 Step 3: PV = 10000 / 1.2597 = 7,940.58 ₹ Verification: 10000 / (1.08)^{3} = 7,940.58.
Scenario
An investor expects a coupon of 500 ₹ after 2 years. The market requires an 9% annual return.
Solution
Using the PV formula: PV = 500 / (1 + 0.09)^{2}. Compute (1.09)^{2} = 1.1881. Then PV = 500 / 1.1881 = 420.70 ₹. The present value of the coupon is 420.70 ₹.
Conclusion
The discounted value is lower than the nominal amount, illustrating why market price and yields differ from the coupon rate.
Yield Measures – Current Yield and Yield to Maturity
Current Yield is a quick measure of return, calculated as the annual coupon divided by the bond’s market price. It ignores capital gains or losses at maturity.
Yield to Maturity (YTM) represents the total annualised return if the bond is held to maturity, assuming all coupons are reinvested at the same rate. The exact YTM requires solving a present‑value equation, but the exam often provides an approximation formula.
Both yields are examined in the NISM syllabus. Current yield is useful for comparing income‑generating ability, while YTM is the benchmark for total return.
When the market price is above par, YTM will be lower than the coupon rate; when below par, YTM exceeds the coupon.
Where:
Annual Coupon= Total coupon payment received in a year (₹)Market Price= Current purchase price of the bond (₹)Worked Example
Given an annual coupon of 600 ₹ and a market price of 12,000 ₹: Step 1: Current Yield = 600 / 12000 Step 2: Current Yield = 0.05 = 5% Verification: 600 ÷ 12000 = 0.05 (5%).
Where:
C= Annual coupon payment (₹)F= Face (par) value of the bond (₹)P= Current market price of the bond (₹)n= Years to maturityWorked Example
Bond details: C = 800 ₹, F = 10,000 ₹, P = 9,200 ₹, n = 5 years. Step 1: (F - P)/n = (10,000 - 9,200)/5 = 800/5 = 160 ₹ Step 2: Numerator = C + 160 = 800 + 160 = 960 ₹ Step 3: Denominator = (F + P)/2 = (10,000 + 9,200)/2 = 19,200/2 = 9,600 ₹ Step 4: YTM ≈ 960 / 9,600 = 0.10 = 10% Verification: (800 + (10,000-9,200)/5) ÷ ((10,000+9,200)/2) = 0.10 (10%).
Scenario
A corporate bond has a face value of 10,000 ₹, a 7% annual coupon, is trading at 9,500 ₹, and matures in 4 years.
Solution
Current Yield = (0.07 × 10,000) / 9,500 = 700 / 9,500 = 0.0737 = 7.37%. For YTM approximation: C = 700 ₹, F = 10,000 ₹, P = 9,500 ₹, n = 4. (F‑P)/n = (10,000‑9,500)/4 = 500/4 = 125 ₹. Numerator = 700 + 125 = 825 ₹. Denominator = (10,000 + 9,500)/2 = 19,500/2 = 9,750 ₹. YTM ≈ 825 / 9,750 = 0.0846 = 8.46%. Verification steps match the calculations shown.
Conclusion
The bond’s current yield (7.37%) is lower than its YTM (8.46%) because it trades at a discount to par.
Do not answer yield questions with the coupon percentage alone. Always adjust for the market price using current yield or YTM formulas.
Interest‑Rate Sensitivity – Duration
Duration measures the weighted average time to receive a bond’s cash flows and indicates how much the bond’s price will change for a 1% change in interest rates. It is expressed in years.
The most common measure in the NISM syllabus is Macaulay Duration, calculated by weighting each cash flow by the time until receipt and dividing by the bond price.
A higher duration means greater price volatility. Short‑term instruments like T‑Bills have low duration, while long‑term corporate bonds have high duration.
Understanding duration helps you answer exam items on price sensitivity and client suitability for risk‑averse investors.
Where:
t= Time period (years) of cash flow CF_tCF_{t}= Cash flow at time t (₹), including coupons and principal at maturityr= Yield to maturity per period (decimal)n= Total number of periods until maturityWorked Example
Bond: Face 1,000 ₹, 5% annual coupon, 3‑year maturity, YTM = 6%. Cash flows: 50 ₹ each year, 1,050 ₹ at year 3. PV of CFs: Year1 = 50/(1.06)^1 = 47.17, Year2 = 50/(1.06)^2 = 44.50, Year3 = 1,050/(1.06)^3 = 882.00. Weighted numerator: (1×47.17) + (2×44.50) + (3×882.00) = 47.17 + 89.00 + 2,646.00 = 2,782.17. Denominator (price) = 47.17 + 44.50 + 882.00 = 973.67. Duration = 2,782.17 / 973.67 = 2.86 years. Verification: Weighted sum ÷ price = 2.86 years.
Scenario
A 7% annual coupon bond with face value 10,000 ₹ matures in 5 years. Current price is 9,800 ₹ and YTM is 6.5%.
Solution
Cash flows: 700 ₹ each year, 10,700 ₹ at year 5. Discount each cash flow at 6.5%: Year1 PV = 700/1.065 = 657.28, Year2 PV = 700/1.065^2 = 617.36, Year3 PV = 579.55, Year4 PV = 543.73, Year5 PV = 10,700/1.065^5 = 7,782.44. Sum of PVs = 657.28+617.36+579.55+543.73+7,782.44 = 10,180.36 (approx price). Weighted numerator = (1×657.28)+(2×617.36)+(3×579.55)+(4×543.73)+(5×7,782.44) = 657.28+1,234.72+1,738.65+2,174.92+38,912.20 = 44,717.77. Duration = 44,717.77 / 10,180.36 = 4.39 years. Verification: Weighted sum ÷ price ≈ 4.39 years.
Conclusion
The bond’s duration of 4.39 years indicates moderate price sensitivity; a 1% rise in rates would roughly reduce its price by 4.39%.
Average Yields of Common Fixed Income Instruments (India)
⭐Exam Takeaways
- Fixed Income securities provide predetermined cash flows and are classified by issuer, maturity and coupon structure.
- Core features – face value, coupon, maturity, market price – determine yield calculations.
- Current Yield = Annual Coupon ÷ Market Price; it ignores capital gains/losses.
- Yield to Maturity (approx.) = [C + (F‑P)/n] ÷ [(F+P)/2]; reflects total return if held to maturity.
- Macaulay Duration measures weighted average time to cash‑flow receipt and gauges price sensitivity to interest‑rate changes.
Practice Questions
7 questions on Fixed Income
What does the term "Fixed Income" refer to in the context of financial instruments?
A bond pays an annual coupon of ₹600 and is currently priced at ₹12,000. What is its current yield?
Which Fixed Income instrument in India is issued at a discount and does not pay periodic coupons?
When a bond trades above its face (par) value, how does its Yield to Maturity (YTM) compare to its coupon rate?
Using the approximation formula, what is the Yield to Maturity (YTM) for a bond with C=₹800, F=₹10,000, P=₹9,200 and n=5 years?
A 3‑year bond with a face value of ₹1,000 pays a 5% annual coupon and has a YTM of 6%. What is its Macaulay Duration (rounded to two decimal places)?
For a bond with face value ₹10,000, a 7% annual coupon, trading at ₹9,500 and maturing in 4 years, which is higher: the current yield or the approximated YTM?