Introduction to Interest Rate, Interest Rate Instruments and

Introduction to Interest Rate, Interest Rate Instruments and Fixed Income Market

• Definition: Interest rate is the amount charged on top of the principal by a lender to a borrower for the use of assets, expressed as a percentage of principal.
• Details: Interest rates are typically noted on an annual basis and are subjective, decided based on various factors such as inflation, liquidity, duration, central bank policy, and credit risk.

Key Concepts

• Interest Rate: The amount charged by a lender to a borrower for the use of assets, expressed as a percentage of principal.
• Risk-Free Interest Rate: Not explicitly defined in this section, but implied as the interest rate charged by a lender to a borrower with zero credit risk.
• Fixed Income Securities: Debt instruments that pay a fixed amount of interest to investors, such as bonds and debentures.
• Term Structure of Interest Rate: Not explicitly defined in this section, but implied as the relationship between interest rates and time to maturity.

Factors Influencing Interest Rates

• Macro Factors:
  • Demand for money
  • Supply of money
  • Fiscal deficit and government borrowing
  • Inflation
  • Global interest rates and foreign exchange rates
  • Central bank actions
• Micro Factors:
  • Maturity/Tenor of the bonds
  • Credit Risk
  • Seniority of Bonds
  • Security of Bonds
  • Liquidity of Bonds
  • Investor sentiments

Effective Interest Rate

• Definition: The effective interest rate is the rate that takes into account the compounding effect of interest.
• Formula: Effective interest rate = [ (1 + annual interest rate/n)^n – 1 ]

Nominal and Real Interest Rate

• Nominal Interest Rate: The stated interest rate of a bond.
• Real Interest Rate: The nominal interest rate adjusted for inflation.
• Formula: Real interest rate = Nominal interest rate – Rate of Inflation

Fixed Income Securities

• Definition: Debt instruments that pay a fixed amount of interest to investors, such as bonds and debentures.
• Key Components:
  • Issue Price
  • Face Value (FV)
  • Coupon (interest)

Introduction to Interest Rate, Interest Rate Instruments and (Part 2)

• Definition: Interest rate instruments are securities that offer a return in the form of interest payments, excluding the interest amount, on the maturity date.
• Details: The issuer may pay a premium above the face value at the time of maturity.

Key Concepts

• Coupon/Interest: Cash flows offered by a security at fixed intervals/predefined dates, expressed as a percentage of the face value of the security, giving the coupon rate.
• Coupon Frequency: How regularly an issuer pays the coupon to the holder, which can be monthly, quarterly, semi-annually, or annually.
• Interest Payment Dates: Dates on which interest/coupon is paid to bondholders by the issuer.
• Maturity Date: The date in the future on which the investor's principal will be repaid, and the security ceases to exist.
• Call/Put Option Date: The date on which the issuer or investor can exercise their rights to redeem the security before the maturity date.
• Maturity/Redemption Value: The amount paid by the issuer, other than coupon payment, which can be at a premium, discount, or par.

Type of Fixed Income Securities

• Bonds: Financial securities issued by a legal entity to raise funds, agreeing to refund/return the borrowed amount at the end of the contract period or at various time intervals.
• Classification of Bonds: Based on issuers, maturity, coupon, currencies, embedded options, security, priority of claims, purpose of issue, underlying, and taxation.

Classification of Fixed Income Securities Based on the Type of Issuer

• Government Bonds/Sovereign Bonds/Gilt Edged Bonds: Issued by the government, typically denominated in the domestic currency, and considered risk-free.
• Municipal Bonds: Issued by local authorities to fund projects, categorized based on the source of interest payments and principal repayments.
• Corporate Bonds: Issued by corporates to raise capital, with performance depending on future revenues and profitability.
• Securitized Debt: Created by monetizing illiquid loan assets into a liquid pool of tradable assets through a Special Purpose Vehicle (SPV).

Classification of Fixed Income Securities Based on Maturity/Redemption

• Overnight Debt/Borrowings: Typically borrowed by banks from the money market or RBI, which can be collateralized or clean.
• Ultra-Short-Term Debt (Money Market): Short-term borrowings up to one year, including instruments like Commercial Papers (CP), Certificate of Deposits (CD), and Treasury Bills (TB).
• Short Term Debt: Bonds with maturity spanning from 1 to 5 years, issued for cost effectiveness and operational flexibility.
• Medium Term Debt: Bonds maturing in 5 to 12 years, also referred to as intermediate bonds.
• Long Term Debt: Bonds with maturity beyond 12 years, often issued by the Government of India.
• Staggered Maturities: Bond issues packaged as a series of different bonds with different or staggered maturities.
• Perpetual Bonds (Consol Bonds): Bonds without a maturity date, continuing to pay coupons during the life of the company, often issued by banks to meet Tier-I Capital requirements.

Classification of Fixed Income Securities Based on Coupon

• Plain Vanilla Bonds: The simplest form of a bond with a fixed coupon and defined maturity, usually issued and redeemed at face value.
• Zero-Coupon Bonds: Discounted instruments that do not pay interest and are redeemed at the face value of the bond at maturity, with a single cash flow at maturity.

Introduction to Interest Rate, Interest Rate Instruments and (Part 3)

• Fixed Income Securities: These securities provide regular cash flows and are generally used by long-term fixed income investors such as pension funds and insurance companies to gauge and offset the interest rate risk of these firms’ long-term liabilities.
• Types of Fixed Income Securities:
  • Floating Rate Bonds (FRBs): Linked to a benchmark interest rate, with coupon rates reset on each coupon payment date.
  • Caps and Floor: Instruments that cap interest payment obligations if interest rates rise, or provide a floor to protect investor interests.
  • Inverse Floater: Bonds with coupon rates inversely related to benchmark rates.
  • Inflation Indexed Bonds: FRBs that protect investors from rising prices by being indexed to inflation measures.
  • Step Up/Down Bonds: Bonds with coupon rates that increase or decrease over time.
  • Deferred Coupon Bonds: Bonds that do not pay interest in initial years but pay high interest later.
  • Deep Discount Bonds: Zero-coupon bonds issued at a high discount to face value.

Classification of Fixed Income Securities

• Based on Embedded Options:
  • Straight Bonds: Bonds that pay interest at regular intervals and return principal at maturity.
  • Bond with Call Option: Bonds that give the issuer the right to call back the bond before maturity.
  • Bond with Put Option: Bonds that give the investor the right to seek redemption before maturity.
  • Bond with Call and Put Option: Bonds that give both issuer and investor the right to redeem before maturity.
• Based on Security:
  • Secured Debt: Bonds backed by specific assets of the issuer.
  • Unsecured Debt: Bonds issued without specific collateral.
  • Credit Enhanced Bonds: Bonds with credit enhancement strategies to improve credit worthiness.
• Based on Seniority:
  • Senior Debt: Bonds with higher priority in repayment hierarchy.
  • Subordinated Debt: Bonds with lower priority in repayment hierarchy.

Other Instruments

• Annuities: Financial products that provide monthly payments over a certain period.
• AT1 (Additional Tier-1) Bonds: Perpetual bonds issued by banks to shore up their core capital base.
• AT2 Bonds: Subordinated debt instruments issued by banks to meet Tier 2 capital requirements.
• Convertible Bonds: Bonds that can be converted to equity shares at a specified time.
• REITs (Real Estate Investment Trusts): Trusts that invest in commercial real estate assets.
• InvITs (Infrastructure Investment Trusts): Trusts that invest in the infrastructure sector.
• Green Bonds: Fixed-income instruments specifically earmarked for climate and environmental projects.

Introduction to Interest Rate, Interest Rate Instruments and (Part 4)

• Definition: Debt securities are typically asset-linked and backed by the issuing entity's balance sheet, carrying the same credit rating as their issuers' other debt obligations.
• Details: Various types of debt securities include:
  • Tax-free bonds: Issued by government enterprises to raise funds for a particular purpose, with absolute tax exemption on interest.
  • Tax Saving Bonds: Offer tax benefits to owners, with a minimum lock-in period, and taxable interest earned.
  • Asset Linked Bonds: Provide better credit enhancement to investors, linked to underlying assets, with payable capability depending on the asset's market performance.
  • Environment, Social and Governance (ESG) Debt Securities: Issued in accordance with international frameworks, adapted to suit Indian requirements, as specified by SEBI.
  • Masala Bonds: Rupee-denominated bonds issued outside India by Indian entities, helping to raise money in local currency from foreign investors.

Equity Securities v/s Debt Securities

• Key differences:
  • Equity securities indicate ownership, while debt securities represent a loan to the company.
  • Equity securities have no maturity date, whereas debt securities typically have a maturity date.
  • Equity securities offer variable returns, while debt securities provide a predefined return in the form of interest payments.
  • Equity shareholders have voting rights, whereas debt securities do not.

Advantages of Debt Compared to Equity

• Benefits:
  • Debt is a long-term source of capital for borrowers.
  • Borrowing through debt does not reduce the control of the company for the borrower.
  • Lenders have priority over equity holders in case of bankruptcy.
  • Interest on debt is tax-deductible, reducing the weighted average cost of capital.
  • Raising debt capital through private placement is generally less complicated.

Disadvantages of Debt Compared to Equity

• Drawbacks:
  • Certain debt instruments may put restrictions on the company's core activities.
  • Debt must be repaid, resulting in liquidity outflow.
  • Debt repayment causes cash flow risk and may jeopardize the company's growth plans.
  • High leverage can increase the risk of default.
  • Debt obligations are fixed, regardless of market conditions.

Concept of Risk-Free Interest Rate

• Definition: The interest rate applicable to transactions with no credit risk, typically involving a sovereign government borrowing in its home currency.
• Details:
  • Credit risk: The risk of default by the borrower.
  • Price Risk (Interest Rate Risk): The uncertainty in the movement of interest rates, impacting the value of debt securities.
  • Reinvestment risk: The risk of reinvesting interim payments at unknown future interest rates.
  • The risk-free rate is the benchmark for all valuations, representing the return without risk.

Term Structure of Interest Rates

• Definition: The relationship between interest rates and the term (or tenor) of borrowing/lending period.
• Details: The market quotes rates for standard terms/tenors, and the term structure of interest rates is a crucial concept in finance.

Introduction to Interest Rate, Interest Rate Instruments and (Part 5)

• Money Market: The money market deals with short-term debt instruments, including:
  • Overnight (ON)
  • 1-week (1W)
  • 2-week (2W)
  • 1-month (1M) to 1-year (1Y) at monthly intervals
• Bond Market: The bond market involves longer-term debt instruments, including:
  • 2Y, 5Y, 7Y, 10Y, 15Y, 20Y, 25Y, 30Y, and 40Y
• Interest Rate Determination: Interest rates differ based on the borrower's credit risk, with rates directly quoted for sovereign borrowers and add-on credit spreads for non-sovereign borrowers
• Term Structure of Interest Rates (Yield Curve): A graphical representation of interest rates against terms, including:
  • Risk-free Curve: Represents the ultimate opportunity cost
  • AAA Curve, BBB Curve, etc.: Reflect the price of credit risk for different credit ratings
• Factors Influencing Interest Rates: Demand-supply for money, liquidity, seasonal demand-supply for credit, foreign portfolio investment inflows and outflows, bunching of tax and government payments, inflation outlook, and capital expenditure by industry and businesses
• Central Bank's Role: Monitors and controls short-term interest rates in developed economies, while influencing long-term rates in developing and emerging economies through tools like repo, reverse repo, bank rate, cash reserve ratio, statutory liquidity ratio, and open market operations

Types of Yield Curves

• Normal Yield Curve: Upward sloping, indicating higher yields for higher maturities, reflecting higher inflation-risk premium and expectations for economic growth
• Inverted Yield Curve: Short-term yields are higher than long-term yields, often seen when the market expects interest rates to fall, indicating a worsening economic situation or recession
• Flat Yield Curve: Yields remain constant irrespective of time to maturity, indicating no extra premium for higher maturities, often seen later in the economic cycle with higher inflation expectations and tighter monetary policy
• Humped Yield Curve: Short-term and long-term yields are lower than medium-term yields, resulting from various economic factors

Term Structure Shifts

• Parallel Shift: All rates move in the same direction by the same extent
• Steepening: The difference between long-term and short-term rates rises or widens, with the curve shifting in an anti-clockwise direction
• Flattening: The difference between long-term and short-term rates falls or narrows, with the curve shifting in a clockwise direction
• Twist: Both rates move in opposite directions
• Convexity Change: Both rates move in the same direction but by different extents, or one rate remains constant while the other changes

Introduction to Interest Rate, Interest Rate Instruments and (Part 6)

• Interest Rate: The interest rate is the percentage at which interest is paid on a loan or investment. It is usually expressed as a percentage per annum.
• Interest Rate Instruments: These are financial instruments that have interest rates associated with them, such as bonds, loans, and deposits.
• Types of Interest Rates: There are two main types of interest rates: Simple Interest and Compound Interest.
• Simple Interest (SI): Simple interest is calculated only on the principal amount, without taking into account any interest accrued in previous periods.
• Compound Interest (CI): Compound interest is calculated on both the principal amount and any accrued interest in previous periods.

Key Concepts

• Conversion of Rate into Amount: The market practice is to always quote interest rate as percentage per annum, but in the settlement of transaction, the interest rate is converted into interest amount.
• Parameters for Conversion: The conversion requires the following parameters to be specified: payment frequency, compounding frequency, and day count fraction.
• Simple Interest Formula: Simple interest (SI) = Principal * Interest rate p.a. * Time in years
• Compound Interest Formula: Interest for Year 1 (I1) = Principal * Interest rate p.a. * (Time which is 1 year)

Single Period Investment

• Definition: When investment is made for a single period (like a year), the investor gives money today and receives the principal and promised interest at the end of that period.
• Future Value: Future Value for one period = Principal * (1 + Interest Rate %) or FV = PV (1 + r%)
• Present Value: PV = FV/ (1 + r%)

Multi-period Investment

• Definition: When multiple periods are involved in an investment, the present value would be calculated assuming reinvestment of the future stream of income at the agreed rate.
• Future Value: Future Value = Principal * (1 + Interest Rate)time or FV = PV (1 + r) t
• Present Value: PV = FV/(1 + r) t

Day Count Fraction

• Definition: It specifies how to convert the payment period into year fraction (e.g. 6M = 0.5Y).
• Types of Day Count Conventions:
  • Actual/Actual Day Counting: This takes into account the actual number of days between the last coupon date and the next coupon date.
  • 30/360 (European) Day Counting: This day count convention considers all months are equal and have fixed 30 days in a month and 360 days in a year.
  • Actual/365 Day Counting: In this convention, the coupon days are calculated as actual number of days in between two dates but the year is considered as 365 days.
  • Actual/360 Day Counting: In this convention, the coupon days are calculated as actual number of days in between two dates but the year is considered as containing 360 days.

Accrued Interest

• Definition: Accrued interest is a market practice peculiar to bond market. Accrued interest applies only when a bond is a coupon bond (or any other instrument for which coupon for the current interest period is known).
• Clean Price: The price at which the bond is negotiated.
• Dirty Price (Invoice Price): The price at which the bond is settled.

Introduction to Interest Rate, Interest Rate Instruments and Accrued Interest

• Accrued Interest: The interest accrual at coupon rate from the previous coupon date to the settlement date of the trade. It is the amount of interest that has accumulated on a bond since the last coupon payment.
• Dirty Price: The price of a bond that includes accrued interest. It is calculated as the clean price plus accrued interest.
• Clean Price: The price of a bond that excludes accrued interest.
• Day Count Convention: A method used to calculate accrued interest. Common day count conventions include Actual/Actual and 30/360.

Computation of Accrued Interest

• Actual/Actual Method: Calculates accrued interest based on the actual number of days between the previous coupon date and the settlement date.
• 30/360 Method: Calculates accrued interest based on a 30-day month and a 360-day year.

Example of Accrued Interest Calculation

• For a 6.90% bond paying semi-annually, with a previous coupon date of January 13, 2021, and a settlement date of March 5, 2021:
  • Using the Actual/Actual method: Accrued interest = 6.90% * (51/181) = 0.972099
  • Using the 30/360 method: Accrued interest = 6.90% * (52/180) = 0.996667
• Dirty Price Calculation: Dirty price = clean price + accrued interest. For example, if the clean price is Rs. 101.50 and the accrued interest is Rs. 0.9967, the dirty price would be Rs. 102.4967.

Importance of Accrued Interest

• Deterministic vs. Stochastic Changes: Accrued interest is a deterministic change, meaning it is known in advance. In contrast, changes in interest rates and credit ratings are stochastic, meaning they are unknown and unpredictable.
• Monitoring Stochastic Changes: Traders prefer to monitor stochastic changes, as they are more relevant to the bond's value.

Introduction to Spot Rate (Zero Rate) and Holding Period Return

• Spot Rate (Zero Rate): The return on investment that is realized over a specific period, taking into account the compounding of interest.
• Holding Period Return (HPR): The return on investment that is realized over a specific period, including the effects of reinvestment of interim cash flows.

Calculation of Spot Rate and Holding Period Return

• Formula for Spot Rate: Spot rate = (F/P)^(1/(N*C)) - 1, where F is the final amount received, P is the initial amount invested, N is the number of years, and C is the compounding frequency.
• Example of Spot Rate Calculation: If Rs 100 grows into Rs 150 over three years, the spot rate can be calculated as (150/100)^(1/(3*1)) - 1 = 14.4714% per annum.

Coupon, Current Yield, and Yield-to-Maturity

• Coupon Income: The regular flow of money or return to the investor as promised by the borrower.
• Current Yield: The ratio of the annual coupon payment to the bond's current market price.
• Yield-to-Maturity: The total return on investment, including the coupon payments and the capital gain or loss, over the life of the bond.

Types of Bonds and Their Characteristics

• Zero-Coupon Bonds: Bonds that do not pay coupons, but instead pay the face value at maturity.
• Floating Rate Bonds: Bonds that pay coupons based on a benchmark interest rate, such as a treasury bill rate.
• Government Securities: Bonds issued by governments to finance their activities.

Introduction to Interest Rate, Interest Rate Instruments and Yield Measures

• Interest Rate Risk: Changes in interest rates can affect the market value of bonds. If interest rates rise, the market value of a bond with a fixed interest rate will decrease, and if interest rates fall, the market value will increase.
• Term Premium: A term premium is the excess return demanded by investors for holding a long-term bond over a shorter-term bond. This premium reflects the additional risk and uncertainty associated with lending for longer periods.
• Reinvestment Income: The income earned from reinvesting periodic interest or coupon payments from a bond. The yield to maturity (YTM) assumes that all future coupons are reinvested at the same rate as the YTM.

Yield Measures

• Current Yield: The simplest measure of yield, calculated as the annual coupon payment divided by the clean price of the bond.
• Yield to Maturity (YTM): The most widely used yield measure, which assumes that the investor holds the bond until maturity and reinvests all future coupons at the same rate as the YTM.
• Bond Equivalent Yield (BEY): A yield measure used for money market instruments, which annualizes the return on a short-term instrument to make it comparable to longer-term bonds.
• Discount Yield: A yield measure used for bonds purchased at a discount and held until maturity, which calculates the expected return based on the discount from face value.
• Effective Yield: The equivalent annual yield that produces the same final amount as a nominal interest rate compounded over a year.

Determining Cash Flow, Yield, and Price of Bonds

• Cash Flows: The known future payments from a bond, including coupon payments and the return of principal at maturity.
• Discount Factors: The present value of future cash flows, calculated using the market interest rate or yield.
• Present Value: The sum of the discounted cash flows, which represents the current price of the bond.
• Pricing a Bond: Involves calculating the cash flows, discount factors, and present value of the bond using the market interest rate or yield.

Introduction to Interest Rate, Interest Rate Instruments and Valuation

• Bond Valuation: The value of a bond is calculated as the sum of the discounted value of its future cash flows.
• Discount Factors (DF): The discount factors are used to calculate the present value of the bond's cash flows.
• Present Value Interest Factor (PVIF): The sum of all discount factors is known as the PVIF, which is used to calculate the bond's value.

Key Concepts in Bond Valuation

• Annual Coupon Paying Bond: The value of an annual coupon paying bond is calculated using the formula: Value = (Annual Coupon * PVIF) + (Face Value * PV of last maturity).
• Semi-Annual Coupon Paying Bond: The value of a semi-annual coupon paying bond is calculated using the formula: Value = (Coupon * PVIF) + (Face Value * DF for the maturity year).
• Frequency of Payments: The frequency of payments (n) affects the valuation of bonds, with more frequent payments resulting in a higher value.

Valuation of Bonds with Different Maturities and Frequencies

• Bonds with Maturities Less Than One Year: The value of a bond with a maturity less than one year is calculated using the formula: V = Face Value / (1 + R% * n).
• Zero Coupon Bond: The value of a zero coupon bond is calculated using the formula: V = Face Value / (1 + R%)^n.
• Semi-Annual Yield: The semi-annual yield is used to calculate the value of a bond with semi-annual coupon payments.

Valuation of Bonds at Non-Coupon Dates

• Dirty Price: The dirty price is the present value of the bond, which includes the accrued interest.
• Clean Price: The clean price is the value of the bond excluding the accrued interest.
• Accrued Interest: The accrued interest is the interest that has accrued since the last coupon payment date.

Spot Rate and Bond Price

• Spot Rate (Zero Rate): The spot rate is the true return on investment, which considers premium/discount in bond price, capital gain/loss at redemption, and reinvestment of interim income.
• Bond Price: The bond price is calculated by discounting the cash flows at the appropriate zero rates from the prevailing term structure of zero rates.

Introduction to Interest Rate, Interest Rate Instruments and (Part 10)

• Bond Price Determination: The bond price is determined by the term structure of zero rates, not by demand-supply for the bond itself. The demand-supply forces that affect bond prices are related to the demand-supply for money, which in turn determines the zero rates.
• Return Measures for Bonds: In a coupon bond (or annuity), there are multiple return measures, each corresponding to the cash flows. To simplify interpretation, these rates are averaged into a single number called the Yield to Maturity (YTM).
• Yield to Maturity (YTM): YTM is derived from the bond price and is used as another way of quoting bond price. It is not a true return measure and has several drawbacks, including:
  • Assuming a flat term structure of zero rates, which is inconsistent with reality.
  • Being inconsistent for bonds with different coupons but the same maturity.
  • Assuming different reinvestment rates simultaneously.
• Price-Yield Relationship: The relationship between a bond's price and its yield is inverse and non-linear. The price-yield curve can be used to compare the relative effective riskiness of two bonds.
• Factors Affecting Price Volatility: The price volatility of a bond is affected by its term to maturity, coupon rate, and yield to maturity. Specifically:
  • Longer-term bonds are more volatile than shorter-term bonds.
  • Higher-coupon bonds are less volatile than lower-coupon bonds.
  • Bonds with higher yields to maturity are less volatile than those with lower yields to maturity.
• Relation between Coupon Rate, Yield, Price, and Par Value: Bonds can trade at par when the coupon rate equals the current market yield. If the coupon rate is lower than the market yield, the bond trades at a discount, and if it's higher, the bond trades at a premium.
• Price-Time Path of a Bond: The price of a bond over time is affected by its initial price (par, discount, or premium) and the required rate. As a bond approaches its maturity date, its price is "pulled to par," meaning it moves towards its face value.

Introduction to Interest Rate, Interest Rate Instruments and Risk Measures

• Interest Rate Risk: The change in the price or value of a bond with respect to the change in market interest rates.
• Price Volatility: The variability in the price of a bond due to changes in interest rates.
• Duration: A measure of the time-weighted average of the present value of a bond's future cash flows.

Key Concepts

• Price-Yield Curve: A graphical representation of the relationship between the price of a bond and its yield.
• Convexity: The shape of the price-yield curve, which explains the difference in price changes depending on the zone of yield movement.
• Macaulay Duration: The weighted average of the time to get the future cash flows from a bond, measured in units of years.

Risk Measures

• Price Risk: The risk that the price of a bond will change due to changes in interest rates.
• Reinvestment Risk: The risk that the cash flows from a bond will be reinvested at a lower interest rate than the original bond.
• Interest Rate Risk: The risk that changes in interest rates will affect the price or value of a bond.

Properties of Price Volatility

• The percentage change in price due to a change in yield will be different for different bonds.
• When yield changes are very small, the percentage price change for a given bond remains more or less the same.
• When yield changes are large, the price change for the bond is different for the same increase and decrease in the yield.
• When yields fall, the price changes are bigger than the price changes when yield rises by the same magnitude.

Duration and Macaulay Duration

• Duration: A measure of the time-weighted average of the present value of a bond's future cash flows.
• Macaulay Duration: The weighted average of the time to get the future cash flows from a bond, measured in units of years.
• Macaulay duration is influenced by the bond's coupon rate, term to maturity, and yield to maturity.
• Macaulay duration is inversely related to the coupon rate and yield to maturity.

Introduction to Interest Rate, Interest Rate Instruments and Duration

• Definition: Duration is a measure of the average time to receive all future cash flows from a bond, making the present value of these cash flows equal to the current market price.
• Details: It takes into account the timing and amount of all cash flows, including coupon payments and the return of principal, to estimate the sensitivity of a bond's price to changes in interest rates.

Key Concepts

• Duration Calculation: The duration of a bond can be calculated using the formula: Mac Duration = ∑(PV(CFt) * t) / Market Price of Bond, where PV(CFt) is the present value of the cash flow at time t, and t is the time period of the cash flow.
• Weighted Average Maturity: The weighted average maturity of a bond changes with yield changes, affecting the payback period. If interest rates increase, the payback period decreases, and vice versa.
• Duration Characteristics:
  • Coupon: Higher coupon bonds have smaller durations because a larger part of the cash flows is received in the early stages.
  • Yield to Maturity (YTM): Duration decreases with increases in YTM, as higher yields have a greater damping effect on the present value of distant coupons.
  • Maturity: Duration increases with maturity, but at a decreasing rate, and eventually stagnates after a certain maturity level is reached.

Duration Relationships

• Coupon and Duration: Inversely related; higher coupons mean lower duration.
• YTM and Duration: Inversely related; higher yields mean lower duration.
• Maturity and Duration: Duration increases with maturity, but not exponentially.
• Zero-Coupon Bonds: Duration is equal to maturity, as there are no intervening cash flows.

Portfolio Duration

• Definition: The duration of a portfolio is the weighted average of the durations of the bonds in the portfolio.
• Calculation: Duration of a portfolio = ∑(wi * DURi), where wi is the weight of each bond in the portfolio, and DURi is the duration of each bond.

Modified Duration

• Definition: An adjusted measure of Macaulay duration to estimate a bond's price sensitivity to changes in interest rates.
• Calculation: Modified Duration = Macaulay Duration / (1 + (YTM / number of coupon periods per year)).
• Example: For a bond with a Macaulay duration of 5.34, the modified duration would be 5.34 / (1 + 4.5%) = 5.11.

Price Value of a Basis Point (PV01)

• Definition: The change in price of a bond for a 1 basis point (0.01%) change in yield.
• Calculation: PV01 = 0.01 * Modified Duration / 100 * Bond Price = (Bond price * Modified Duration) / 10000.

Convexity Measure

• Definition: A measure of the degree to which the price-yield relationship of a bond is non-linear.
• Importance: Convexity is important for large changes in interest rates, as duration alone may not accurately estimate price changes.
• Example: The table shows the actual price change and the price change implied by modified duration for different interest rate shocks, highlighting the error in using duration alone for large rate changes.

Introduction to Interest Rate, Interest Rate Instruments and (Part 13)

• Interest Rate Sensitivity: The error in approximating the bond price changes using modified duration gets larger as the interest shocks become larger.
• Duration Limitations: Duration underestimates the price change in case of interest rate fall and overestimates the price change in case of an increase in interest rate.
• Convexity: Measures how the bond's duration—and by implication, its price—will change depending on how much interest rates change.

Key Concepts

• Convexity Formula: Convexity = Σ [((CFt) / (1 + Y)^t) * t * (t+1)] / (P * (1 + Y)^2)
• Convexity Calculation: Can be tedious and long, especially if the bond is long term and has numerous cash flows.
• Convexity Approximation: Convexity = (P+ + P- - 2P0) / (2 * P0 * (Δy)^2)
• Convexity Adjustment: Convexity Adjustment = Convexity × 100 × (Δy)^2
• Convexity Relationships:
  • Coupon is inversely related to convexity.
  • Yield to maturity is inversely related to convexity.
  • Convexity is positively related to maturity of the bond.
  • Portfolio convexity is weighted sum of individual bond’s convexity.

Duration and Convexity Effect on Price Change

• Change in Price: Change in price = Duration effect + Convexity effect
• Example: % Change in price = {-10.66*(-0.02)} + {10081.96(-0.02)^2}
• Result: % Change in price = 21.32% + 3.28% = 24.60% (Estimated price change 24.60% approx.)

Role of the Debt Market

• Debt Market: Facilitates borrowing of funds using debt instruments to investors having varied risk appetite.
• Fixed Income Securities: Debt instruments are more popularly referred to as “Fixed Income Securities” due to fixed and known periodic interest or cash flows.
• Importance of Debt Markets: A well-developed debt market helps the Government to raise debt at a reasonable cost, lowers the borrowing cost for all, and provides greater pricing efficiency.

Importance of Debt Markets

• Government Debt: The Government generally issues the largest amount of debt to fund its expenditure.
• Corporate Bond Market: Helps an economic entity to raise funds at a cheaper cost.
• Debt Market Functions: Brings together large number of buyers and sellers to price the debt instruments efficiently, reduces degree of banking support for the economy, and helps the banking system with better Asset-Liability Management.

Primary and Secondary Debt Market in India

• Debt Market: Deals in both the Government debt as well as in non-Government debt instruments.
• Market Functionaries: Issuers like Government and Corporate firms, intermediaries like merchant bankers and brokers selling debt, and investors like commercial banks, collective investment schemes like mutual funds, pension funds, insurance companies, retail investors, etc.

Introduction to Interest Rate, Interest Rate Instruments and (Part 14)

• Debt Market Participants: The three critical participants in the debt market are:
  • Issuers: Governments, commercial banks, public sector companies, private corporate firms, etc.
  • Intermediaries: Investment banks and merchant banks who help issuers to sell bonds to the investors.
  • Investors: Private corporate treasuries, collective investment vehicles like mutual funds, insurance companies, commercial banks, pension funds, high net-worth individuals, etc.
• Regulators: The Reserve Bank of India (RBI) and the Securities and Exchange Board of India (SEBI) are the main regulators in the Indian debt market.
• Debt Market Segments: The Indian debt market has three distinct segments based on issuer category:
  • Government Debt (G-sec) Market: Government of India issues dated papers, Treasury Bills, and State governments issue State Development Loans.
  • Public Sector Units (PSU) and Banks: PSU and banks issue instruments to raise resources from the market.
  • Private Sector: Private sector raises resources through issuance of debt papers.

Key Concepts

• Government Securities: Government of India issues Floating Rate Bonds, Inflation Indexed Bonds, Special Securities, and Cash Management Bills.
• PSU Bonds: Popular among investors due to their perceived low risk.
• Commercial Banks: Issue short-term papers like Certificate of Deposits (CDs) and long-term bonds.
• Private Corporates: Issue instruments like Bonds, Debentures, Commercial Papers (CPs), Floating Rate Notes (FRNs), Zero Coupon Bonds (ZCBs), etc.
• Debt Security Markets: Government Securities Market, Corporate Bond Market, and Money Market.

Primary and Secondary Market of Government Securities

• Primary Market: Debt instruments are issued in the primary market where initially they are subscribed by various investors.
• Secondary Market: Investors trade in government securities in the secondary market.
• Primary Market Instruments: Treasury bills and government dated securities.
• Auction Process: Government securities and Treasury Bills are issued through auctions (yield-based or price-based auctions) conducted by RBI.

Auction Participants

• Competitive Bidding: Meant for well-informed institutional investors who bid at a specific price/yield.
• Non-Competitive Bidding (NCB): For small and retail investors who submit their bid indirectly through an Aggregator/Facilitator.

Secondary Market for G-Secs

• Negotiated Dealing System-Order Matching (NDS-OM): An anonymous screen-based electronic order matching module.
• Over the Counter (OTC)/Telephone Market: G-Sec trading can also be done over telephonic negotiations.
• NDS-OM-Web: Enables Gilt Account Holders to control their orders and get access to real-time live quotes on NDS-OM.
• Stock Exchanges: Provide trading platforms to cater to the needs of retail investors.
• RBI Retail Direct Scheme: A one-stop solution to facilitate investment in Government Securities by individual investors.

SEBI Registered Stock Brokers

• Access to NDS-OM: SEBI-registered non-bank brokers can access NDS-OM through Master Direction - Reserve Bank of India (Access Criteria for NDS-OM) Directions.
• Separate Business Unit (SBU): Stock brokers can participate in Government Securities market in the NDS-OM under a SBU.

Clearing and Settlement of Government Securities

• Delivery versus Payment System-III (DvP-III): Securities and funds are settled on a net basis.
• Clearing Corporation of India Ltd. (CCIL): Guarantees settlement of trades on the settlement date by becoming a central counter-party (CCP) to every trade.
• Settlement Cycle: All outright secondary market transactions in G-Secs are settled on a T+1 basis.

Introduction to Interest Rate, Interest Rate Instruments and (Part 15)

• Open Market Operations (OMOs): OMOs are market operations conducted by the RBI to adjust rupee liquidity conditions in the market by selling or purchasing G-Secs.
• Repurchase or Buyback of G-Secs: The process of buying back existing securities by the Government of India and State Governments to reduce cost, improve liquidity, and manage cash effectively.
• Government Securities Lending Transactions: Enable market participants to borrow and lend G-Secs for a fee, with the borrower returning the security and the lender returning the collateral at the end of the agreed period.
• Holding of G-Secs: G-Secs can be held in physical or dematerialized (demat) form, with demat being the safest and most convenient option, eliminating custody-related problems.

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

• Public Issuance: An invitation to the public to subscribe to debt securities through a prospectus, with SEBI regulations governing the process.
• Private Placement: An offer of sale of debt securities to a select group of people or institutions, with the face value of a listed debt security being Rs. One lakh.
• Electronic Book Mechanism / Electronic Bidding Platform (EBP): Mandatory for private placement issuance of debt securities and non-convertible redeemable preference shares with an issue size of Rs. 20 crore or more.
• SEBI Regulations: Govern the issuance and listing of debt securities, with the SEBI (Issue and Listing of Non-Convertible Securities) Regulations, 2021 being the main regulations for corporate debt securities.

Key Concepts

• G-Secs: Government securities issued by the Government of India to finance its fiscal deficit.
• RBI: The Reserve Bank of India, responsible for conducting OMOs and regulating the G-Secs market.
• SEBI: The Securities and Exchange Board of India, responsible for regulating the issuance and listing of debt securities.
• EBP: Electronic Book Mechanism / Electronic Bidding Platform, used for private placement issuance of debt securities and non-convertible redeemable preference shares.
• Demat: Dematerialized form of holding G-Secs, which eliminates custody-related problems and facilitates hassle-free trading and maintenance of securities.

Introduction to Interest Rate, Interest Rate Instruments and (Part 16)

• Primary Market: The issuer has an option to avail an ‘anchor portion’ within the base issue size, with a maximum allocation of 30%/40%/50% of the base issue size, depending on the instrument rating.
• Bidding Process: In open bidding, bid information is available to the market during the bidding window, while in closed bidding, it is disclosed post-bidding.
• Secondary Market Mechanism of Corporate Bonds: The secondary market of corporate bonds is mainly institutional and operates over-the-counter (OTC), with transactions reported on an exchange reporting platform for market dissemination and bilateral settlement on a DVP-I mechanism through a clearing corporation.
• Request for Quote (RFQ) Platform: The RFQ platform provides market participants with a range of options to seek quotes and respond to quotes, promoting pre-trade transparency in debt security transactions.
• Regulatory Measures: SEBI has introduced various circulars to improve the functioning of the RFQ platform, including permitting stock brokers to place bids on behalf of clients and modifying the face value of listed debt securities.

Key Concepts in Money Market

• Money Market: A short-term market that handles instruments with maturities ranging from 1 day to 1 year, used by governments, banks, and corporate entities to manage short-term fund requirements.
• Participants: Public Sector Banks, Private Sector Banks, Foreign Banks, Co-operative Banks, Financial Institutions, Insurance Companies, Mutual Funds, Primary Dealers, and Non-Banking Financial Companies (NBFCs) participate in the money market.
• Segments: The money market is divided into two segments: borrowing and lending with or without collaterals, and asset market involving the purchase and sale of money market instruments.

Money Market Instruments

• Call Money: An avenue for unsecured lending and borrowing of funds, restricted to Scheduled Commercial Banks (SCBs) and Primary Dealers (PDs), with transactions reported on the Reserve Bank of India’s NDS-CALL platform.
• Notice Money: An extension of the interbank call market for uncollateralized lending and borrowing of funds for a period beyond overnight and up to 14 days.
• Term Money: An extension of the interbank call market for uncollateralized lending and borrowing of funds for a period between 15 days and 1 year.
• Market Repo: A type of repo contract where funds are borrowed via the sale of securities with an agreement to repurchase the same at a future date, with interest incorporated in the repurchase price.
• Triparty Repo: A type of repo contract with a third-party intermediary between the borrower and lender, known as the Triparty Agent (TPA), which selects, pays, and settles the collateral.
• Treasury Bills (T-bills): Zero-coupon securities issued by the Government of India for short-term borrowing, considered part of the money market as they mature within a year from issue.
• Cash Management Bills (CMBs): Very short-term T-bills used for cash management purposes.

Introduction to Interest Rate, Interest Rate Instruments and (Part 17)

• Management Bills (CMBs): CMBs are issued by the Government of India to fund temporary mismatches in its cash flow, with maturities less than 91 days.
• Commercial Paper (CP): A CP is used by Indian corporates to raise short-term unsecured funds, with maturities between 7 days and one year, and is governed by RBI regulations.
• Certificate of Deposit (CD): A CD is a negotiable, unsecured money market instrument issued by a bank as a Usance Promissory Note, with maturities between 7 days and one year.
• Repo in Corporate Bond/Corporate Debt Securities: Repo in corporate bonds was introduced by RBI in 2010, allowing participants to borrow against eligible securities, including listed corporate bonds and debentures, CPs, and CDs.
• Exchange Traded Tri-party Repo in Corporate Debt Securities: Tri-party repo on corporate debt securities is available for trading on exchanges, with a Tri-party Agent acting as an intermediary between the borrower and lender.

Importance of the Call Money Market

• Call Money Market: The call money market enables banks to even out their day-end demand and supply of overnight funds, with call money being the second most liquid asset after cash.
• Overnight MIBOR: The Mumbai Interbank Outright Rate (MIBOR) benchmark rate is based on overnight call money market transactions, administered by the Financial Benchmarks India Pvt. Ltd. (FBIL).

Economic Utility of Repo Market

• Repo Market: The repo market is used by traders for funding their positions and taking positions in the market to execute their views on interest rates.
• Short Selling: Short selling is allowed in certain securities and for certain entities, with the short selling entity required to borrow the security from the repo market to make deliveries.

Role of Regulators

• Reserve Bank of India (RBI): RBI manages the borrowing of the Central and State Governments, acts as the regulator for the Money market and the G-Sec market, and governs instruments issued by Commercial Banks and other Institutions regulated by it.
• Securities and Exchange Board of India (SEBI): SEBI is the regulator for the corporate bond market, including instruments issued by Commercial Banks and PSUs, with a maturity of more than one year.

Role of Credit Rating Agencies

• Credit Rating Agencies (CRAs): CRAs provide information about the riskiness of a debt instrument or a company, with ratings representing a CRA's evaluation of the qualitative and quantitative information pertaining to the prospective debtor.
• Credit Ratings: Credit ratings are assigned by CRAs to instruments, with the highest quality bonds commonly referred to as "AAA", while the least creditworthy are termed as "junk".
• Common Scale of Ratings:
  • AAA to BBB-: Investment Grade
  • BB+ to CCC-: Non-investment or Junk Grade
  • D: Default Rating
  • Short term Scale: A1+ to D

Introduction to Interest Rate, Interest Rate Instruments and (Part 18)

• Credit Spread: The credit spread is the price of credit risk. It is the difference in yield between a credit-risky bond and a credit-risk-free bond of similar maturity.
• Term Structure of Rates:
  • If the long-term rate is higher than the short-term rate, the shape of the term structure of rates is Normal/positive.
  • If the long-term rate is lower than the short-term rate, the shape of the term structure of rates is Inverted/negative.
  • If the long-term rate is equal to the short-term rate, the shape of the term structure of rates is Flat.
• Accrued Interest: The concept of accrued interest applies to Coupon bond. Accrued interest is the interest that has been earned by a bondholder since the last coupon payment.
• Modified Duration: If the coupon of the bond increases, its Modified Duration will decrease (other things remaining constant). Modified duration measures the sensitivity of a bond's price to changes in interest rates.