bonds and valuation

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Fixed income securities



1. Valuation of Fixed Income Securities 2. Introduction to Bond Markets 3. Yield and Conventions4. Spot and Forward Rates5. Terminology and characteristics of Bonds/Types of fixed income securities:Central Government securitiesState Government securitiesGovernment-guaranteed bondsPSU bondsCorporate debenturesMoney market instruments and preferred stockValuation/Pricing of bonds, Bond Yields6. Term structure of interest rates


Companies and governments need money for developmental activitiesThey can borrow from banks or raise money from the public by issuing bondsA bond is nothing but a loan for which the public is the lenderA bond can be considered as an IOU given by the borrower (issuer) to the lender (investor)The issuer of the bonds pays interest to the lender at a pre-determined rate and scheduleBonds are called as fixed-income securities as the investor is aware of the exact amount he will get back if he holds the security till maturity

Definition and features

A bond represents a contract under which a borrower promises to pay interest and principal on specific dates to the holder of the bond.

The most important things to note in a fixed income instrument are Issuer Example BOB,ICICI, L&T, SBI, Hindalco, NHB, NABARD, Railway finance corpn. Coupon or interest Ex. 8%, 9%, 10%, Zero CouponTenure Say 5 yrs., 10 yrs, 15 yearsMaturity date the date on which the borrower repays the amountInterest payment schedule Monthly, Quarterly, Semi Annually, Annually, Compounded, Simple, FloatingRatings AA, AA+Pre closure options Call after 5 years, Put after 5 years, 1 % interest penalty.Issue price or value At par, At discount


Differences between bond and equity

BondBonds are debt instrumentsAn investor becomes a creditor to the organisationA bond holder has a higher claim on the assetsHe does not have a share in the profits he gets only principal and interest

Stocks and sharesShares are equity An investor becomes an owner in an organisation he has voting rightsA shareholder is paid only after all the debt payments are madeHe has a right to share in the profits of the company he is paid dividend depending on the amount of profits


Why invest in bonds?

Bonds are not as volatile as the stock marketsThey provide a fixed income and thus are safe retirement plansThey are good investments for short term horizons when money is required for a definite purposeIf a person is in his 20s and 30s, a majority of investment can be in equities, whereas if a person is in his middle age, a majority of investments must be in fixed income securities


Who issues Bonds?

Central GovernmentState GovernmentPublic sector UndertakingsPrivate Sector Companies


Bond Market - How it evolved into a market

Investors had a general perception that bonds with longer maturity give higher returns.Some investors who had bought these bonds wanted to exit, but the issuer was not ready to buy it backThere were some who sensed that they can sell their bonds and make capital gainsThere were some regulatory requirements due to which people wanted to sellThere were some changes in the risk profile of the issuer and holders wanted to offloadAs the category of Available for sale increased and more investors flocking to buy bonds round the year, it created what is called the bond market


Bond Market

The National Stock exchange has a Wholesale debt Market segment. It is a market for high value transactions

The retail trade in corporate debt securities is done primarily on the capital market segment of the NSE and the debt segment of the Bombay Stock exchange


Trade timings

Trading in the WDM segment is open on all days except Saturdays, Sundays and other holidays, as specified by the Exchange.


Monday to Friday

Same Day Settlement (Government Securities)

10.00 hrs to 15.00 hrs

Other Day Settlement (Government Securities)

10.00 hrs to 17.15 hrs

Same Day and Other Day Settlement (Non-Government Securities)

10.00 hrs to 18.15 hrs


Phases of trade

Trading on WDM segment is divided into three phases as under:Pre-Open Market PhaseThe pre-open period commences from 9.00 hrs This period allows the trading member/Participant to:set up counter party exposure limitsset up Market Watch (the security descriptor)make inquiriesMarket Open PhaseThe system allows for inquiries of the following activities when the market is open for trading:Order EntryOrder ModificationOrder CancellationTrade Cancellation


Phases of trade

Post Market Phase (also called SURCON)During the period of SURCON (SURveillance and CONtrol) a trading member gets only inquiry access with a facility to request for trade cancellation. On completion of SURCON the trading system processes data and gets the system ready for the next day.


Risk associated with bonds


Risk associated with bonds


Bond Valuation

RequirementsAn estimate of expected cash flowsAn estimate of the required rate of return

The formula :

P=A*(1+r)-1 / r(1+r) + M/ (1+r)

P= Present Value in rupeesA= Annual coupon amountn= Number of years to Maturityr= Periodic required returnM= Maturity Value


A bond specimen copy


Term structure of Interest rates

Term structure of interest rates is the variation of yields of bonds with similar risk profiles with the terms of bondsInterest rates depend onTimeLevel of riskMarket trendsIdentical bonds (same risk profile, liquidity, tax structures) with different terms to maturity have different interest rates

Yield curves

The term structure of interest rates is shown by the yield curveIt is a graph that plots the yields of similar-quality bonds against their maturities, ranging from shortest to longest.The yield curve is generally indicative of future interest rates, which are indicative of an economy's expansion or contractionTherefore, yield curves and changes in yield curves can convey a great deal of information.

Yield curves


























1000/1.08= 925.931000/(1.08*1.10) = 841.751000/(1.08*1.10*1.11) = 758.33



Yield curves

Types of yield curves

Types of yield curves

Normal Yield curve upward sloping depicts normal economic conditions growth at a normal rateSteeply +ve sloping yield curve is an indicator of an economic recovery and found at the end of a recessionInverted yield curve downward sloping rare and abnormal market conditions Long term rates are lower than short term ratesFlat yield curve Finally, a flat yield curve exists when there is little or no difference between short and long term yields market is sending mixed signals Short term rates may rise, Long term may fall

Spot and forward rates

Let us consider 2 zero coupon bonds with a maturity value of Rs.1000Bond A is a 1 year bond with a rate of 8%Bond B is a 2 year bond with a rate of 10%I will be able to buy these bonds today at the above rates. So we refer to this as the spot rate.

Present value of both bonds can be easily calculated




Bond A


Bond B




Forward rates

Let us say I had invested Rs.826.45, it would grow as below 826.45 X (1.10) The above when expressed as below gives us the forward rate 826.45 X (1.10) = 826.45 X 1.08 X 1.1204

When an individual invests in a two-year zero coupon bond yielding 10 percent, his wealth at the end of two years is the same as if he received an 8 percent return over the first year and a 12.04 percent return over the second year. This hypothetical rate over the second year, 12.04 percent, is called the forward rate.

More generally, given the 1 year (r1) and the 2 year (r2) spot rates, we can calculate the forward rate as below f = (1+r2) 1+r1

Characteristics of Yield curves

Three characteristics of yield curvesThe change in yields of different term bonds tend to move in the same directionThe yields of short term bonds are more volatile than the long term bondsThe yields of long term bonds tend to be higher than the short term bonds

Three theories to explain yield curves

The expectations theoryThe liquidity preference hypothesisThe segmented market hypothesis

Expectation Hypothesis

The Expectation hypothesis states that different term bonds can be viewed as a series of 1-period bonds with yields of each bond equal to the expected short term interest rate for that period.The forward interest rates are unbiased estimates of future interest ratesThe expectation hypothesis is about maximization of utility of money in the form of higher expected return over the long term horizonAccordingly present long term interest rate is just an average of the current short term rates and one period forward rates

Expectation hypothesis








Liquidity Preference Theory

This theory pro