FIXED INCOME SECURITIES

- INTRODUCTION

Ritesh Nandwani

Faculty, NISM

INTRODUCTION

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WHAT IS FIXED INCOME SECURITY

A contractual agreement between the investor and the issuer,

wherein the investor loans money to the issuer that borrows the funds for a defined period of time at a fixed interest rate

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WHAT IS FIXED INCOME SECURITY

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WHAT IS FIXED INCOME SECURITY

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BASIC FEATURES & TERMINOLOGIES

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Pricing

• Face Value / Principal

• Issue Price

• Redemption Value

Interest

• Zero Coupon / Coupon bearing Bonds

• Coupon Rate (Fixed/Floating)

• Coupon Frequency

Tenure

• Single Repayment

• Amortization

Embedded Options

• Call / Put

• Conversion

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TYPES OF FIS

Issuer Maturity Coupon Option Redemptio

n

Govt. Short term Zero coupon Plain vanila Single

Govt. Bodies Medium term Fixed Rate Conversion Amortising

PSUs Long term Floating Rate Call

Banks / FIs Perpetual Put

Corporates

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FIS VS. EQUITY

PARAMETERS EQUITY DEBT

Ownership Owners Lenders

Risk High Risk Low Risk

Return Variable Fixed (generally)

Maturity Perpetual Fixed (generally)

Liquidation Hierarchy Last preference First preference

Voting Rights Yes No

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KEY PARTICIPANTS Issuers

• Govt. & Govt. Bodies/Authorities

• Banks/FIs

• Corporates

Investors

• Institutional Investors

• Banks, FIs., MFs, Insurance Companies, PFs, Pension Funds, FPIs, etc.

• Corporates

• Individual Investors

Intermediaries

• Merchant Banks / Primary Dealers

• Stock Exchanges

• Debenture Trustees

• Credit Rating Agencies

• Brokers / Market makers

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FIS ISSUERS IN INDIA Government

• Government Securities (G-Secs)

• Treasury bills (T-bills)

• Bonds issued by State Govt.s & UTs (SDLs)

Government Authorities

• Bonds issued by Govt. Controlled Institutions and PSUs

• Bonds issued by Local Bodies and Municipalities (Municipal Bonds)

Banks / Financial Institutions

• Bonds/NCDs

• CPs/CDs

Corporates

• Bonds/Debentures

• Preference Shares

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PRICING & YIELD

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PRICING OF BONDS

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YIELD TO MATURITY (YTM)

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YTM - An IRR or an interest rate that equates PV of all future CFs of a

bond to the current price of the bond

PRICE YIELD RELATIONSHIP

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PRICE YIELD RELATIONSHIP

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FACTORS AFFECTING BOND PRICES Coupon Direct relationship between coupon and Bond price

Interest rates on comparable bonds (Yield) Depends on various factors - Credit quality, Liquidity, Embedded options, Tenure, etc.

Inverse relationship between interest rates and Bond price

Tenor For zero coupon bonds, inverse relationship (assuming a flat or an upward sloping yield

curve)

For coupon bonds, relationship would depend on coupon rate and yield

Embedded Option Value of a callable bond = Value of similar plain vanilla bond - Value of the call option

Value of a putable bond = Value of similar plain vanilla bond + Value of the put option

Value of bond with conversion option = Value of similar plain vanilla bond + Value of the conversion option

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FACTORS AFFECTING YIELDS, & YIELD CURVE

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WHY DIFFERENT YIELDS?

Yield of a bond depends upon various factors:

Type of issuer

Perceived Credit risk

Term of the issue

Embedded options

Tax aspects

Expected liquidity

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TERM STRUCTURE OF INTEREST RATES

Term Structure of Interest Rates

- Graphical depiction of the relationship between the yield on bonds of the same credit quality but different maturities

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YIELD CURVES

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A FLAT YIELD CURVE

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BOND PRICE VOLATILITY & DURATION

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NEED OF A PARAMETER TO MEASURE RISK

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BOND PRICE VOLATILITY / INTEREST RATE RISK

Price Volatility on account of changes in interest rates

Refer Excel Illustration

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BOND PRICE VOLATILITY - KEY CHARACTERISTICS Inverse relationship between price and yield (interest rates)

For a small change in yield, price increase (on account of reduction in interest rates) and price

decrease (on account of same increase in interest rates) are roughly same

For a large change in yield, price increase (on account of reduction in interest rates) is higher

than the price decrease (on account of same increase in interest rates)

The higher the Maturity, the higher will be the price volatility

The lower the Current yield, the higher will be the price volatility

The lower the Coupon rate, the higher will be the price volatility

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MEASURING BOND PRICE VOLATILITY

Full Valuation Approach

Duration and Convexity

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FULL VALUATION APPROACH

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FULL VALUATION APPROACH - FOR A PORTFOLIO

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FULL VALUATION APPROACH

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DURATION Duration of a Bond measures the sensitivity of bond’s price to changes in interest rates or, more specific, to changes in Bond’s YTM

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MACAULAY DURATION

A weighted average of time to receipts of bonds future cash flows, where the weights are present values of the future cash flows

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MACAULAY DURATION - EXAMPLE

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MACAULAY DURATION - VISUALISATION

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MODIFIED DURATION

Modified duration provides an estimate of % change in price for a given change in yield

% change in price = (-Modified Duration * change in yield in %)

Example: If a bond has a Modified Duration of 4.5, then a 1% increase/decrease in yield would result in 4.5% decrease/increase in price

Modified duration provides only a linear estimate of % change in price and ignores the convexity of price curve

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MODIFIED DURATION Modified duration (Duration) provides an estimate of % change in price for a given change in yield

Duration is an approximation of risk. P (as estimated using duration) captures the linear changes in prices for changes in yield

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MODIFIED DURATION

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CONVEXITY

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PROPERTIES OF DURATION Macaulay Duration of a Zero coupon bond is always same as its maturity

For a coupon paying bond, Macaulay Duration would be lesser than its maturity

The greater the coupon, the lower would be the Duration, and vice-versa

The price estimated by the duration would always be an under-estimate, because of positive convexity of bonds For a small change in interest rate, the price estimated by duration would be closer to the

actual price

If interest rates changes are big, the price estimated by duration would be farther from actual price

The lower the current yield of the bond, the higher would be the duration

Further, as interest rates fall, the duration of the bond would rise

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WHERE DOES DURATION COME FROM

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WHERE DOES DURATION COME FROM

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DOLLAR DURATION & PRICE VALUE OF A BASIS POINT

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DOLLAR DURATION AND PVBP

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DURATION & CONVEXITY OF A PORTFOLIO

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ESTIMATING PRICE CHANGE USING DURATION & CONVEXITY Using Duration

% change in price = (-Modified Duration * change in yield in %)

Using Both Duration & Convexity

% change in price = (-Modified Duration * change in yield in

%) + (1/2 * Convexity Measure * (change in yield in %)2)

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LIMITATIONS OF DURATION & CONVEXITY

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LIMITATIONS OF DURATION & CONVEXITY

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LIMITATIONS OF DURATION & CONVEXITY

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BONDS WITH EMBEDDED OPTIONS

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PRICE YIELD RELATIONSHIP OF A CALLABLE BOND

BONDS WITH EMBEDDED OPTIONS

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PRICE YIELD RELATIONSHIP OF A PUTTABLE BOND

THANK YOU

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