Chapter 1: Introduction to Interest Rate, Interest Rate Instruments and Fixed Income Market

Understanding the Interest Rate Concept:

• Debt is a concept of “I owe You” where the borrower agrees to repay the borrowed money with an additional amount called interest.
• The interest rate is calculated as a percentage of the principal amount and the agreed-upon time period.
• Loans are formalized through agreements or notes, with loans being non-tradable and notes being tradable debt instruments.
• Interest rates apply to various borrowing and lending transactions, such as mortgages, personal loans, and corporate bonds.
• Interest rates are typically quoted as the annual percentage rate (APR), which represents the nominal annual interest rate.
• Interest rates vary based on factors like the loan amount, tenor, credit risk, and prevailing market conditions.

Factors Influencing Interest Rates:

• Demand for money: Economic activity and investor risk appetite influence the demand for funds, impacting interest rates.
• Supply of money: Central banks control the money supply and may adjust interest rates to manage inflation.
• Fiscal deficit and government borrowing: High fiscal deficits and increased government borrowing can lead to higher interest rates.
• Inflation: Higher inflation erodes the value of money, necessitating higher nominal interest rates to compensate.
• Global interest rates and foreign exchange rates: Investors seek higher returns in countries with higher interest rates, influencing domestic rates.
• Central bank actions: Central banks’ policy rate changes affect commercial interest rates and bond market yields.

Effective Rate:

• The effective interest rate differs from the nominal interest rate due to compounding effects.
• Compounding frequency affects the effective rate, which is the actual rate earned by an investor.
• The effective rate formula is [(1 + annual interest rate/n)^n – 1], where n is the number of compounding periods.

Nominal and Real Interest Rate:

• Nominal interest rate is the stated rate of a bond, while real interest rate accounts for inflation.
• Real interest rate = Nominal interest rate – Inflation rate.
• If inflation exceeds the coupon rate, the real interest rate becomes negative.

Fixed Income Securities:

• Fixed Income Securities are debt instruments that pay a fixed amount of interest to investors.
• Bonds and debentures are common types of fixed income securities issued by corporations and governments.
• Fixed income securities have fixed features including a specified maturity date and known cash flows.
• Key components of fixed income securities include the issue price, face value, coupon (interest), coupon frequency, interest payment dates, maturity date, call/put option dates, and redemption value.
• The issue price is the price at which bonds are issued to investors, usually the same as the face value.
• The face value represents the principal amount of the bond on which the coupon is calculated.
• Coupons are the periodic interest payments made to bondholders and are expressed as a percentage of the face value.
• Coupon frequency refers to how regularly an issuer pays the coupon, which can be monthly, quarterly, semi-annually, or annually.
• Interest payment dates are the dates on which the issuer pays the coupon to bondholders.
• The maturity date is the future date when the investor’s principal is repaid, marking the end of the security.
• Call and put options allow the issuer or investor to redeem the security before the maturity date.
• The redemption value is the amount paid by the issuer at maturity, which can be at a premium, discount, or par value.

Example:

• Security details: Face value of Rs 1,000, issued on April 01, 2021, for a 10-year period at Rs. 1,000, with a coupon of 7% paid every 6 months.
• Issue price: Rs 1,000
• Face value: Rs 1,000
• Coupon: 7%
• Coupon frequency: Half-yearly
• Interest payment dates: April 01st and October 01st
• Maturity date: April 01, 2031
• Put option: Not applicable
• Call option: Not applicable
• Redemption value: Rs 1,000

Presenting the information in a table format:

Type of Fixed Income Securities:

Classification based on issuers:

• Government Bonds/Sovereign Bonds/Gilt-edged Bonds: Issued by the government in domestic currency to support expenditures. Considered relatively low risk.
• Municipal Bonds: Issued by local authorities to fund projects such as infrastructure. Market is gradually growing.
• Corporate Bonds/Non-Convertible Debentures (NCDs): Issued by corporations to raise capital. Higher risk compared to government bonds.
• Securitized Debt: Monetizing illiquid loan assets into tradable bonds through a Special Purpose Vehicle (SPV).

Classification based on maturity:

• Overnight Debt/Borrowings: Short-term borrowings by banks from the money market or RBI.
• Ultra-Short-Term Debt (Money Market): Short-term borrowings up to one year, including instruments like Commercial Papers (CP) and Treasury Bills (TB).
• Short-Term Debt: Bonds with maturity up to 5 years.
• Medium-Term Debt: Bonds maturing in 5 to 12 years, the bulk of debt issuances.
• Long-Term Debt: Bonds with maturity beyond 12 years, often issued by the government.

Classification based on coupon:

• Plain Vanilla Bonds: Bonds with fixed coupons and defined maturity, redeemed at face value.
• Zero-Coupon Bonds: Discounted instruments with no interest payments, redeemed at face value.
• Floating Rate Bonds: Coupons linked to a benchmark interest rate, coupon rate reset periodically.
• Inflation Indexed Bonds: FRBs indexed against inflation measures like WPI or CPI.
• Step Up/Down Bonds: Coupons increase or decrease over time.
• Deferred Coupon Bonds: No interest paid initially, high interest paid later.
• Deep Discount Bonds: Zero coupon bonds issued at a high discount to face value.

Classification based on embedded options:

• Straight Bonds: Basic bonds that pay regular fixed coupons and principal at maturity.
• Bonds with Call Option: Issuer can call back the bond before maturity if interest rates are low.
• Bonds with Put Option: Investor can seek redemption before maturity if interest rates are high.
• Bonds with Call and Put Option: Both issuer and investor can redeem the bond before maturity.

Classification based on security:

• Secured Bonds: Bonds backed by specific assets of the issuer.
• Unsecured Bonds: Bonds without specific collateral.
• Senior/Junior Bonds: Varying priority of claims in the company’s assets during liquidation.

Equity Securities vs. Debt Securities

Advantages of Debt Compared to Equity

Disadvantages of Debt Compared to Equity

Concept of Risk-Free Interest Rate

The risk-free rate serves as a benchmark for valuations, representing the return without risk. Other financial instruments carry various risks, leading to the demand for a premium above the risk-free rate. Market risk and reinvestment risk can be eliminated by holding bonds until maturity or investing in zero-coupon instruments.

Conversion of Rate into Amount:

• Interest rates are typically quoted as a percentage per annum in the market.
• However, during the settlement of transactions, the interest rate needs to be converted into an interest amount.
• The conversion requires specifying parameters such as payment frequency, compounding frequency, and day count fraction.

Simple Interest (SI) and Compound Interest (CI):

• Simple interest (SI) is an interest rate without any reinvestment option.
• When interest is accrued for multiple periods, it becomes necessary to differentiate between simple interest (SI) and compound interest (CI).
• Compound interest involves reinvesting the money received at different points in time to earn a higher effective rate of return.
• The simple interest rate remains the same from year to year, while the compound interest rate increases each year.

Formulas for Simple Interest and Compound Interest:

• Simple interest (SI) = Principal * Interest rate p.a. * Time in years
• Compound interest (CI) calculations involve interest earned on the principal and previously earned interest:
• Interest for Year 1 (I1) = Principal * Interest rate p.a. * (Time, which is 1 year)
• Interest for Year 2 (I2) = (Principal + I1) * Interest rate p.a. * (Time, which is 1 year)
• Interest for Year 3 (I3) = (Principal + I1 + I2) * Interest rate p.a. * (Time, which is 1 year)
• And so on…

Example:

• Consider an investment of ₹100 earning 8% p.a. over five years.
• A comparison of simple interest and compound interest for each year would look like this:

Table: Comparison of Simple Interest and Compound Interest

Chart: Simple Vs Compound Interest

Single Period Investment:

• When making an investment for a single period, the investor gives money today and receives the principal and promised interest at the end of that period.
• The investor only earns simple interest in a single period.
• The future value (FV) for a single period investment can be calculated using the formula:
• FV = PV * (1 + Interest Rate %)
• PV = FV / (1 + r%)

Multi-period Investment:

• In multi-period investments, the future value is calculated assuming reinvestment of the future stream of income at the agreed rate.
• The future value (FV) for a multi-period investment can be calculated using the formula:
• FV = PV * (1 + Interest Rate)^time
• PV = FV / (1 + r)^t

Day Count Fraction (or Day Count Basis):

• Day count fraction refers to how the payment period is converted into a year fraction.
• It depends on the method of counting the number of days in the payment period and the total number of days in a year.
• Different day count conventions exist, such as Actual/Actual, 30/360 (European), Actual/365, and Actual/360.
• The convention used may vary across different markets and countries.

Accrued Interest

• Accrued interest is a market practice specific to the bond market.
• It applies to coupon bonds or instruments with known coupon rates for the current interest period.
• In the secondary market, there are two prices: clean price (negotiated price) and dirty price (settled price).
• Dirty price is always higher than the clean price by the amount of accrued interest.
• Accrued interest is the interest accrual at the coupon rate from the previous coupon date to the settlement date of the trade.

Timeline of Dates:

Ownership and Entitlement:

• Between the previous coupon date and settlement date, the seller owns the bond and is entitled to receive the interest accrual for that period.
• Between the settlement date and the next coupon date, the buyer owns the bond and is entitled to the interest accrual for that period.
• Whichever party owns the bond on the next coupon date receives the coupon for the full period.

Computation of Accrued Interest:

• The computation of accrued interest depends on the day count convention used.
• Two examples are shown for different day count conventions: Actual/Actual and 30/360 (E).

Example 1: Actual/Actual

• Bond details: 6.90% coupon bond paying semi-annually
• Previous coupon date: January 13, 2021
• Next coupon date: July 13, 2021
• Accrued interest on March 5:
• AI = 6.90 * (2/51) = 0.972099

Example 2: 30/360 (E)

• Bond details: 6.90% coupon bond paying semi-annually
• Previous coupon date: January 13
• Next coupon date: July 13
• Accrued interest on March 5:
• AI = 6.90 * (52/180) = 0.996667

Calculation of Dirty Price:

• If the clean price of the bond is Rs. 101.50, then dirty price = clean price + accrued interest.
• Dirty price = Rs. 101.50 + Rs. 0.9967 = Rs. 102.4967.

Market Pricing and Accrued Interest:

• Accrued interest is not included in the market price (clean price) of the bond.
• If accrued interest is incorporated in the market price, the bond price would exhibit a periodic rise-and-fall pattern between coupon dates.
• Traders focus on stochastic changes (unknown changes) rather than deterministic changes (known changes), which include accrued interest.

Accrued Interest in Bond Market vs. Accrued Dividend in Equity Market:

• Accrued interest is specific to the bond market.
• In the equity market, there is no equivalent concept of accrued dividend.
• Dividend amounts are known after the company announces them, so the concept of accrued dividend can be applied between the announcement date and ex-dividend date.
• The contribution of dividends to the total return from equity is negligible compared to coupons in bonds, making accrued dividend less significant.

Spot Rate (Zero Rate) and Holding Period Return

Return on Investment:

• Return on investment is a crucial measure of performance.
• It is expressed as a rate per annum.
• Income before the investment term needs to be reinvested until the term.
• Compounding at intervals less than a year is incorporated if required.

Computation of Return:

Return = [(F/P)^(1/(N*C))] – 1

Where:

• F = Final amount received (face value)
• P = Initial amount invested (market price)
• N = Number of years
• C = Compounding frequency

Examples of Returns with Different Compounding Frequencies:

Realized Return (Zero Rate or Spot Rate):

• The realized return is the true return.
• It represents the return earned per annum for each compounding period, with interest automatically reinvested at the same rate until the investment term ends.
• It is also known as zero rate or spot rate.

Computing True Return:

• True return or zero rate can be readily computed for zero-coupon securities (discount instruments) because there are no interim cash flows.
• For coupon bonds and annuities, true return cannot be computed due to interim cash flows that require reinvestment until maturity.
• Reinvestment rates are unknown until the reinvestment time, making true return known only at the end of the investment period (ex post).

Approximate Measures of Return for Coupon Bonds and Annuities:

• Since holding period return (HPR) can only be computed ex post, other approximate measures of return are developed for coupon bonds and annuities.
• These measures include coupon, current yield, and yield-to-maturity.

Using Spot Rates (Zero Coupon Yield Curve):

• The yield-to-maturity yield curve assumes a constant rate for reinvested coupons during the bond’s life, ignoring the time value of money aspect.
• To account for the time value of money, spot rates or zero coupon yield curves are used.

Comparison of Bond Yield Measures

Note: Yield measures provide a way to compare the attractiveness of different bonds and assess their returns. Current yield is a simple measure that compares coupon income to the bond’s price. Yield to maturity considers all future cash flows and is the most widely observed yield measure. Bond equivalent yield and discount yield are specific to money market instruments. Effective yield calculates an equivalent annual yield considering compounding.

Determining Cash Flow, Yield, and Price of Bonds

• A bond is valued using known future cash flows based on the promised coupon and principal.
• Cash flows, discount factors, and bond prices can be calculated using the bond pricing equation.
• Example: Annual coupon paying bond with 10% interest rate, 5 years residual maturity, and a market yield of 8%.

Cash Flows and Discount Factors using 8% Yield:

Bond Value Calculation:

• Bond value is the sum of all discounted values of future cash flows.
• Example calculation: Bond value = (10 * 3.9927) + (100 * 0.6806) = ₹39.9270 + ₹68.0600 = ₹107.9870.

Valuation of Semi-Annual Coupon Paying Bond:

• Bond paying coupons twice a year with a 10% annual coupon rate.
• Cash flows and discount factors are adjusted for semi-annual compounding.
• Example calculation: Bond value = (5 * 8.1109) + (100 * 0.675564) = ₹40.5545 + ₹67.5564 = ₹108.1109.

Valuing Bonds with Maturities Less Than One Year:

• Formula to calculate the value of a bond maturing before one coupon cycle.
• Example formula: Value = Face Value / ((1 + R% * n) / 365)

Valuing Zero Coupon Bond:

• Calculation of bond equivalent yield price for zero coupon bonds.
• Example formula: Value = Face Value / (1 + R%)^(n * t)

Valuing Bonds at Non-Coupon Dates:

• Dirty price is the present value of the bond, including accrued interest.
• Dirty price = Clean price + Accrued Interest.
• Calculation involves discounting cash flows from the previous coupon date to the settlement date.

Spot Rate Bond Price and YTM:

• Spot rate (zero rate) is the true return on investment.
• Market price of a bond is calculated using cash flows discounted at appropriate zero rates.
• Bond prices are determined by the term structure of zero rates.

Risk Measures:

• Fixed Income Securities: Risks associated with fixed income securities include credit risk, price risk, liquidity risk, and reinvestment risk.
• Sovereign Government Bonds: If the issuer is a sovereign government, there is usually no credit risk because the government will not default in its own currency.
• Zero-Coupon Bonds: Zero-coupon bonds have no reinvestment risk as there are no interim cash flows to be reinvested until maturity.
• Price Risk and Reinvestment Risk: Price risk and reinvestment risk work in opposite ways. When market interest rates rise, bond prices fall, but reinvestment income rises. The opposite happens when market interest rates fall.
• Price Volatility Characteristics: Bonds with longer maturities generally have higher sensitivity to interest rate changes compared to shorter maturity bonds. Price volatility is key to managing risk in fixed income securities.
• Price-Yield Relationship: The relationship between bond price and yield can be observed on a Price-Yield curve, which shows the price sensitivity of bonds at different yields.
• Price Sensitivity: The price changes for small changes in yield may not be the same across the yield curve. Longer bonds tend to have higher price sensitivity than short duration bonds.
• Volatility: Price volatility increases with larger changes in yield. Standard deviation of price changes is higher for larger yield changes.
• Percentage Change in Price: The percentage change in price due to a change in yield differs for different bonds based on their coupons, maturities, and traded yields.
• Convexity: The Price-Yield curve is convex, explaining the difference in price changes depending on the zone of yield movement.
• Macaulay Duration: Macaulay duration is the weighted average of the time to receive future cash flows from a bond. It is measured in years and influenced by coupon rate, term to maturity, and yield to maturity.
• Duration Adjustments: Duration measures the bond’s weighted average maturity and changes with yield changes. It helps compare bonds in terms of their effective payback periods.
• Macaulay Duration Formula: Macaulay duration is calculated using the weighted average of cash flows’ time periods and discount factors.
• Duration and Maturity: Duration does not increase exponentially with the maturity of a bond and stagnates after reaching a maturity level.
• Duration Calculation: Duration can be calculated using the present value of cash flows, time periods, and discount factors. Spreadsheet tools can assist in the calculation.

Role of the Debt Market:

1. Debt market is part of the capital market, along with the equity market, and plays a vital role in financing the economy.
2. It consists of fixed income securities, such as bonds and loans, which are bought and sold by investors.
3. The debt market facilitates the transfer of funds from those who have excess cash to those in need of financing.
4. It provides a platform for borrowers, including businesses and governments, to raise funds through debt instruments.
5. Debt instruments are essentially loans or IOUs that promise regular coupon or interest payments and repayment of the principal amount.
6. The debt market enables risk management through derivative instruments derived from underlying assets.
7. Structured finance, a component of the debt market, combines financing with risk management.
8. Companies use debt and equity financing to meet their financial needs, with debt representing borrowed money and equity representing ownership in the company.
9. Governments also borrow from the debt market to finance development projects and social expenditures.
10. The debt market offers a variety of instruments to match the duration and purpose of borrowing.
11. Proper assessment of available financing options is crucial for maintaining a balanced level of leverage.

Importance of Debt Markets:

1. A well-developed debt market helps the government raise funds at a reasonable cost to finance its expenditures.
2. A liquid debt market reduces borrowing costs for all participants and enhances pricing efficiency.
3. It allows corporations to issue bonds, enabling them to raise funds at a lower cost compared to bank loans.
4. A well-functioning debt market brings together buyers and sellers, facilitating efficient pricing of debt instruments.
5. By distributing risk among many investors, a developed debt market reduces the reliance on the banking sector for financing.
6. It assists the banking system in better asset-liability management.
7. The presence of a liquid debt market attracts collective investment schemes and encourages retail investors to invest directly in debt.
8. Long-term investors, such as pension funds and insurance companies, benefit from a well-developed debt market to match and manage their liabilities effectively.
9. The primary debt market allows governments and corporates to directly sell their securities to investors through auctions or private placements.
10. The secondary debt market provides liquidity and acts as an exit route for investors, while also providing important information for price discovery and credit risk assessment.
11. However, debt issuance involves various regulations, underwriting, credit rating, and coordination with issue managers, requiring a developed legal framework and clear bankruptcy codes.
12. Regulatory costs associated with debt issuances can be a barrier for smaller borrowers, who often prefer bank loans.

Primary and Secondary Debt Market in India

Participants:

1. Issuers: Government, corporate firms, commercial banks, public sector companies, private corporate firms, etc.
2. Intermediaries: Merchant bankers, brokers
3. Investors: Commercial banks, mutual funds, pension funds, insurance companies, retail investors, etc.

Regulators: Reserve Bank of India (RBI) and Securities and Exchange Board of India (SEBI)

Segments of the Indian Debt Market:

1. Government debt (G-sec) market: Government of India issues dated papers, treasury bills, and State governments issue State Development Loans.
2. Public sector units (PSU) and Banks: Issuing instruments to raise resources from the market.
3. Private sector: Raising resources through issuance of debt papers.

Types of Debt Instruments:

1. Government Securities: Floating Rate Bonds, Inflation Indexed Bonds, Special Securities, Cash Management Bills, Ujwal Discom Assurance Yojana (UDAY) Bonds.
2. PSU Bonds: Popular among investors due to perceived low risk.
3. Commercial Banks: Issue short-term papers like Certificate of Deposits (CDs) and long-term bonds.
4. Private Corporates: Issue instruments like Bonds, Debentures, Commercial Papers (CPs), Floating Rate Notes (FRNs), Zero Coupon Bonds (ZCBs).

Primary Market of Government Securities:

• Government securities & Treasury Bills are issued through auctions conducted by RBI.
• Auctions can be multiple price auctions or uniform price auctions.
• Competitive Bidding: Well-informed institutional investors bid at specific price/yield.
• Non-Competitive Bidding: Small and retail investors bid without mentioning price/yield and get securities at the weighted average price/yield.

Secondary Market of Government Securities:

• Trading takes place through Negotiated Dealing System-Order Matching (NDS-OM), Over the Counter (OTC)/Telephone Market, NDS-OM-Web, and Stock Exchanges.
• Settlement is done through Delivery versus Payment System-III (DvP-III) on a T+1 basis.
• Recently, RBI introduced the Retail Direct Scheme for retail investors to invest in Government securities.

Open Market Operations (OMOs):

• RBI conducts sale/purchase of Government Securities to adjust rupee liquidity conditions in the market.

Repurchase or Buyback of G-Secs:

• Governments buy back existing securities from holders to reduce cost, improve liquidity, or manage cash flows.
• Buybacks can be done through auctions or through the secondary market route.

Holding of G-Secs:

• G-Secs can be held in physical form or dematerialized form (SGL Account or Gilt Account).
• Holding in demat form is safer and more convenient.
• G-Secs can also be held in a dematerialized account with a depository.

Primary and Secondary Market of Corporate Bonds / Non-Convertible Debentures:

• Corporate bonds are mainly issued on a private placement basis.
• Public issuance requires listing on recognized stock exchanges.
• Private placement is made to institutional investors.
• Private placement issuance is now mandated to be done through electronic book mechanism / electronic bidding platform (EBP).
• Participants enroll with EBPs and bid on the platform for better price discovery.
• Exchanges provide unique codes to participants for participation in the EBP platform.

Money Market:

Rating Agencies:

Note: Ratings may vary slightly between different credit rating agencies.