VALUATION OF FIXED INCOME SECURITIESSecurity AnalysisSemester 3

Valuation of Fixed Income SecuritiesStrategic Role of BondsBond TerminologyTypes of BondsValuation of BondsBond Yield MeasuresBond Price AnalysisRisk Associated with BondsForecasting Interest Rates and Determinants of Interest Rates

Valuation of Fixed Income SecuritiesTheories of Interest RatesAnalysis of Deep Discount BondsAnalysis of Convertible BondsAnalysis of Tax-Sheltered Fixed Income Securities

Valuation of Fixed Income SecuritiesDual Currency BondsEquity Index-linked BondsCommodity Linked Bull and Bear BondsSwap-linked Notes

Strategic Role of BondsBond returns have very low positive co-relation with returns of stocks, hence adding bond to a portfolio reduces risk significantly.Investment avenue for risk-averse investors.Different tax treatment of bond.Certainty of return of bond.Preferential right of a bond-holder over a shareholder in case of liquidation of company.

Fixed Income Securities MarketInstrumentsBondsDebenturesPreference SharesOther Convertible SecuritiesIssuersGovernmentQuasi Government BodiesCorporate (PSUs also)Municipal CorporationInvestorsRetail InvestorsMutual FundsPE FundsRecognized PFsTrustsRegulator RBI and SEBI

Bond ClassificationSecured versus Unsecured BondsSenior versus Subordinate BondsRegistered and Unregistered BondsConvertible and non-convertible bondsFloating rate bondsDebenturesIndexed linked bondsDeep Discount (Original Issue Discount) Bond

Bond TerminologyFace valueCoupon and frequency of interest paymentMaturity date, maturity and residual maturityRedemption premiumCall and put optionBond PriceBasis point

Bond TerminologyIndenture Covenants/ProvisionsLengthy and complex legal documentsSpells out the legal rights of holders, obligations of issuing company and restrictions on its operations as well as rights of holders and obligation of borrower in case of liquidationMaintains desirable risk profile throughout the life of security/investmentControls total amount of debt financing

Bond TerminologyIndenture Covenants/ProvisionsProtects holders priority on interest and principal payment in case of default and liquidationNegative pledgeLimitation on additional indebtedness Limitation on asset salesLimitation on restricted payments

Bond Market QuotationsNSE Whole Debt MarketRBI Negotiated Dealing SystemAccrued Interest and Settlement Value for bond deals

Bond Returns and PricesCurrent YieldCalculation formulaRelationship with priceMerits and demeritsTime Adjusted Value of BondValuation of Zero Coupon BondYield to Maturity IRRMethod of Approximation for YTMAssumptions Underlying YTM

Bond Returns and PricesExtensions of YTM Yield to Call and Yield to PutRealized Yield Its the actual yield earned by the investorEquates the future value of purchase price to the total cash flow realized on bond Depends upon reinvestment rate and holding period

Bond Returns and PricesCalculation of Expected Realized YieldProperties of The Realized YieldRI = RY = YTMRI > RY > YTMRI < RY < YTMFor longer maturity bonds, RY will be closer to RIFor shorter maturity bonds, RY will be closer to YTM.

Bond Returns and PricesBond Price-Yield RelationshipPrice and yield inversely relatedBond Price-Maturity RelationshipDirectly relatedBond Coupon-YTM-Price RelationshipIf coupon > YTM, then market price > face valueIf coupon < YTM, then market price < face valueIf coupon = YTM, then market price = face value

Principles of Bond Price MovementThe YTM is inversely related to the price of the bond.For a difference between the coupon and the YTM, the extent of change in the price of a bond depends on the remaining term to maturity. Longer the maturity, greater will be the price change.The increase in price of a bond due to changes interest rate will be at a diminishing rate as the term to maturity increases.

Principles of Bond Price MovementGiven the maturity, the increase in bond prices will be greater with decrease in YTM than the decrease in bond price with an equal increase in YTM.For any given change in YTM, the percentage price change will be higher for low coupon bonds than for high coupon bonds.A change in YTM affects the prices of bonds with higher YTM more than prices of bonds with lower YTM.

Bond Returns and PricesValuation of Preferred Shares/equityValuation of WarrantsWarrants are long term call optionValuation depends upon market price of shares and exercise price of warrantGraphical representation of relationship of warrant price and price of underlying shares

Bond Returns and PricesValuation of Convertible SecuritiesDepends upon conversion characteristicsGenerally, it is summation of PV of interest and principal and PV of equity shares receivable on conversionTerminology conversion rate, conversion value, investment value, conversion premium, investment premium, conversion parity price of share, current yields on share and bond, break-even period

Bond Returns and PricesAttractiveness of ConvertiblesConsideration for default riskProfitable in stable or declining interest rate scenarioReasonable break even periodInvestment premium < 15%Conversion premium

Bond Returns and PricesValuation of Tax Sheltered Fixed Income Securities/InvestmentTax saving at the time of investment and/or at the time of redemptionExamples ELSS, NSC

Duration of BondsActual life/tenor of bondMaturity of a bond and duration of a bondDuration WA measure of a bonds life. Various time periods at which the bond generates cash flows are weighted according to the relative size of the present values of the cash flow.The idea of duration was first propounded by Fredrick Macaulay in 1938

Duration of BondsCalculation of duration of a bondFormula of calculating duration as suggested by Fredrick MacaulayA simplified formula to calculate durationFormula suggested by Prof. G. HawawiniRelationship between coupon, YTM, maturity and durationDuration - a fulcrum that balances present values of cash flows of a bond on a time scale

Bond Duration PropertiesFor all bonds paying periodic coupons, duration < term to maturityFor zero coupon or single period bonds, duration = term to maturityFor perpetual bonds, duration = (1 + YTM)/YTMMaturity and duration are directly relatedDuration and YTM are inversely related

Bond Duration PropertiesDuration and market price of the bond are directly related.Coupon/frequency of coupon payment and duration of a bond are inversely related.Duration of a bond declines as the bond approaches maturity.

Bond DurationInterest rate risk and interest rate elasticityInterest rate elasticity and durationModified Duration Modified Duration as a Measure of Bond VolatilityRupee DurationPrice Value of a Basis Point(PV01) a variant of rupee duration

Duration of Bond PortfolioConsider the portfolio as a single bondMap portfolio cash flows into various buckets. Find present value of cash flows using portfolio YTM as discount rate. Apply regular formula to calculate portfolio duration.Weighted duration of the portfolio can be calculated using individual duration of bonds and applying weight according to the market price of the bond.

Limitations of Macaulay and Modified DurationDuration is not static. Bond investment strategies based on duration values needs to be regularly fine tuned.Estimation of price change for small change in yield only. For large yield changes, price change for two bonds having equal duration will be unequal because of different convexity.All the limitations of YTM is applicable to duration also.

Limitations of Macaulay and Modified DurationNot applicable for option embedded and floating rate bonds because of basic assumption that intermittent cash flows are not affected by changes in yield. ( the answer is Effective Duration)Not applicable for large yield changes.Not applicable for non-parallel shift in yield curve. ( answer is Key Rate Duration)

Effective Duration of BondsAddresses limitations of Macaulay and Modified DurationConsiders changes in cash flow due to changes in yield and also due to embedded optionsFormula for calculating Effective DurationUses interest rate model and related bond price modelFor option free bonds, Macaulays Duration = Effective Duration

Key Rate DurationAddresses the problem of non-parallel shift in yield curveIntroduced by Thomas HoNot a single duration measure, but a vector of numbers defining price sensitivity of a security over the entire domain of possible movement of yield curve.Possible to construct a portfolio of bonds with embedded options using zero coupon bonds.

Duration and convexityEffective Duration > maturityNegative Effective DurationEmpirical durationRegression model of bond pricing

Application of the Concept of DurationImmunization of the portfolio against interest rate risk.Estimation of price change for a bond/portfolio due to interest rate change.Extended applicationDuration of equity dividend discount model and dividend yield model

Convexity of BondsConvexity the shape of the curve representing relationship of bond price and yieldOne of the bond theorem - Given the maturity, the increase in bond prices will be greater with decrease in YTM than the decrease in bond price with an equal increase in YTM.Convexity an important tool to study bond characteristics

Convexity of BondsPrices of bonds with high convexity will increase more with decrease in YTM and will fall less with increase in YTMDuration is the first and convexity is the second approximation of price changes for bondsDuration good for small changes in YTMConvexity good for both small and large changes in YTM

Convexity of BondsConvexity also indicates changes in yieldConvexity is second derivative of price with respect to yieldRelationship of convexity, coupon, maturity and yield of a bondCoupon and convexity inversely relatedMaturity and convexity directly relatedYield and convexity inversely relatedDuration and convexity directly related

Convexity of bondsConvexity effect on price change of bonds due to changes in yieldComputation of convexity for a bondPrice change for a bond due to convexityEffective ConvexityConvexity of Option Embedded Bonds

Risk Associated with BondsSystematic RiskPurchasing power risk/inflation risk/interest rate riskReinvestment riskIndicated through sovereign rating of a countryAlso, non-diversifiableUnsystematic RiskBusiness and financial riskApproximated through the process of credit rating

Term Structure of Interest RatesYield curve definition and various shapesSignificance of Zero Coupon Yield CurveShift in the shape of yield curve from rising, to flat to declining as economic condition changesExplanation of term structure of interest rates

Term Structure of Interest Rates

Term Structure HypothesisShape of Yield CurveFlatRisingDecliningHumpedPure Expectationshort term interest rates are not expected to changeshort term interest rates are expected to increase.short term interest rates are expected to decreaseshort term interest rates are expected to increase initially and then decrease.Liquidity Preferencethere is no liquidity premium on long term rates over short term ratespositive liquidity premium over increasing term.negative liquidity premium over increasing term.liquidity premium positive upto certain term, then negative.Segmentationdemand and supply are matched over all maturities.excess supply of short maturity instruments.excess supply of long maturity instruments.excess supply of mid-term instruments.

Thank youMayank Patel