Valuation of Fixed Income Securities [CS Tanuj Saxena]

Sr No




Zero Coupon / Deep Discount Bond

 - No coupon payment

 - Issued at discount and redeemed at Face Value or Premium

 - Also called Deep Discount Bond

 - Not Tradeable and Not Transferable


Convertible Bonds

 - Fully or Partially Convertible into Equity


Non  - Convertible Bond

 - No Convers in value


Floating Rate Bond

 - Have floating interest rate

 - Linked to another base interest rate (Repo Rate, MIBOR, LIBOUR), Treasury Interest Rate


Callable Bond

 - The right of the issuer company to call off or redeem bond after a specified period but before maturity.

 - the price of callable bond (Vcallable bond) is always lower than the price of a straight (non-callable) bond because the call option adds value to an issuer.

 - Vcallable bond = Vnon-callable bond – Vcall option


Puttable Bond

 - Put option is the right of bond holder to ask for redemption after a specified time but before maturity

 - Putable bonds offer a lower yield and is worth more than a non-putable bond.

 - Vputable bond = Vnon-putable bond + Vput option


Perpetual Bonds

 - Fixed Income Security with no maturity date

 - They are not redeemable

 - Pays steady interest

 - Such a bond is also referred to as a “Console


Tax Free Bonds

 - Interest income on these bond is exempt

 - Generally issued by infrastructure companies


Junk Bond

 - Bonds with high default risk

 - Higher coupon rate and high yield

 - Low Credit Rating


Bond Value with Semi Annual Interest

 - Interest divided by 2

 - Number of years multiplied by 2

 - Discount rate divided by 2


Value of bond and Discount rate



R > coupon rate

Price < Face Value


R < coupon rate

Price > Face Value


R = coupon rate

Price = face Value


Current Yield

 - Annual Coupon Payment divided by Current Price

 - Current Yield = Interest Amount  * 100

                                     Current Price 


Yield to Maturity

 - Reflects the yield with the price that the investor would earn if he holds the bond till maturity

 - Discount rate that equates the remaining cashflows of bond to the current price is YTM

 - YTM is also called IRR


Realised Yield or Holding Period Return

 - YTM is what the yield investor gets by holding it till maturity. If the investor sells the bond before maturity, he realises a different yield depending upon the exit price that affect the capital gains

 - Holding Period Return = Capital Gain + Coupon Payment *100

                                                              Purchase Price


Bond Duration

 - Measure the time structure of bond and bond interest rate risk

 - Average time taken for all interest coupon and principal to be recovered

 - Also called Macaulay's Duration


Modified Duration

 - Measurable change in value of a security in response to a change in interest rates

 - Modified duration follows the concept that interest rates and bond prices move in opposite directions

 - Modified Duration = Macualey Duration

                                                (1 + YTM/n)


Effective Duration

 - Duration calculation of bond that have embedded option

 - This measure of duration takes into account the fact that expected cash flows will fluctuate as interest rates change


Credit Spread

 - The difference in bond’s yield due to different credit rating is known as Credit Spread.

 - A credit spread is the difference in yield between a government bond and a debt security with the same maturity but of lesser quality


Clean Price / Flat Price / Quoted Price

 - Price excluding interest accrued


Dirty Price / Full Price

 - Price including interest accrued


Commercial Paper

 - Unsecured, Short Term Debt Instrument

 - Issued by Corporation

 - Maturity minimum 7 days and maximum 1 year

 - Minimum rating for issuing CP is "A"

 - Valued at Carrying Cost


Treasury Bills

 - Money Market Instrument

 - finance the short term requirement

 - Type of T Bills - 14Days, 91Days, 182 Days, 384 Days

 - Minimum amount of bid 25000


Certificate of Deposit

 - A negotiable money market instrument issued against funds deposited at a bank or other eligible financial institution for a specified time period

 - The maturity period of CDs issued by banks should not be less than 7 days and not more than one year, from the date of issue.

 - The maturity most quoted in the market is for 90 days


Embedded Options

 - An embedded option is a special condition attached to a security and, in particular, a bond, that gives the holder or the issuer the right to perform a specified action at some point in the future.

 - An embedded option is an inseparable part of another security, and as such does not trade by itself.

 - offers specific yet useful rights to the issuer to be used at a later stage


Nominal Interest Rate

 - Does not consider Inflation into account


Real Interest Rate

 - Does consider inflation into account

 - Real Interest rate = Nominal interest Rate

                                             (1 + inflation rate)^t


Interest Rate Swaps

 - The parties exchange cash flows based on a notional principal amount (this amount is not actually exchanged) in order to hedge against interest rate risk or to speculate.

 - Types of Swaps

 - Plain Vanila Swap

 - Cross Currency Swaps

 - G Sec linked Swaps

 - Used to convert

1. From floating rate of interest to fixed rate of interest

2. from fixed rate of interest to floating rate of interest


Accrual Swaps

 - the interest on one side accrues only when the floating reference rate is within a certain range.

 - form of discrete time-switch option in which the interest on one side accrues only if certain conditions are met.


Soverign Bond

 - Issued by national government

 - can be denominated in foreign currency or domestic currency

 - Offered at catchy discounts


State and Local Government Bond

 - Debt obligation issued by states, cities, countries and other governmental entities

 - Usually denominated in domestic currency

 - If a state government is close to default on its debt the media often refer to this as a sovereign debt crisis.


Semi Government / Agency Bond

 - Issued by State or Local Government

 - Issued to fund infrastructure projects


Corporate Debt Securities

 - Issued to raise money for business purpose

 - Pays higher interest rates than government bonds

 - Issued by Corporates

 - Mostly maturity is more than a year

 -  issued for less than a year - called Commercial Paper


Interest rate Cap

 - a type of interest rate derivative in which the buyer receives payments at the end of each period in which the interest rate exceeds the agreed strike price.


Interest rate Floor

 - a derivative contract in which the buyer receives payments at the end of each period in which the interest rate is below the agreed strike price.


Risk associated with embedded option

 - Risk of Reinvestment

 - Limited Price Appreciation



Seprate Trading of Registered Interest and Principal of Securities





Short Term Bond

1 to 3 years


Medium Term Bond

3 to 10 years


Long Term Bond

more than 10 years


Treasury Bills pays interest at 

Coupon Rate Semi Annually


Treasury Bills are traded on

Secondary Market


Maturity of Long Term Debt Instrument

More than 12 months


Who is not allowed to do transaction in debt instrument

Secondary Dealers


In the……………. Strategy, funds are evenly allocated to bonds in each of several different maturity classes



A newly issued Sovereign Bonds are sold to public via:



"A" Credit Rating

Capacity to pay interest plus principal is slightly susceptibly to adverse economic condition


"AAA" Credit Rating

Capacity to pay interest plus principal is high


"D" Credit Rating

Currently in Default


First Credit Rating Agency of India is

Credit Rating Information Services of India Limited (CRISIL)


Call Auction

 - The point at which buyers set maximum prices to buy and sellers the minimum selling price for a security or exchange is called Call Auction



Valued at


Treasury Bills

Carrying Cost


Commercial papers/ certificate of deposits of tenor less than one year

Carrying Cost


Security Receipts

Net present value given by the issuing reconstruction company


Which bond permit bond holder to invest the Interest income again in host bond

bunny bonds


The type of bond in which the payments are made on the basis of inflation index is classified as 

Purchasing power bond


An investor who buys the separated principal from the bond, knows as __________ receives an amount equal to the face value of bond when it matures



Yield Curve

Modified Duration


Commercial Paper

7 days


When the investor is unable to sell the debt product quickly as there are few buyers for it. He may then have to sell it at a lower price or wait till maturity is called?

Liquidity Risk


The reinvestment of periodic interest received may happen at a lower rate depending on the prevailing interest rate at that time is called

Reinvestment Risk


If inflation rates change during the lifetime of a debt product, interest payment fixed at a past date becomes inadequate in today’s terms is called

Inflation Risk


When the market interest rate rises above the rate of a debt instrument, the demand for it falls and, hence, the market price of the debt product also falls is called

Interest Rate Risk


………is a long-term, unsecured debt instrument with a lower claim on assets and income than other classes of debt, while ……………bond issue is secured by the issuer’s property:

A subordinated debenture, mortgage


For equitable non-callable bond, callable bond is:.



For Equitable non-puttable bond, the puttable bond is



Leaverage is 

Compounding of Risk


Backwardation is condition where

Spot Prices exceeds forward prices


Correlation is

A notion from probability


Annuity is

An annuity is a series of payments in equal time periods, guaranteed for a fixed number of



Volatility is measured as 



………… the embedded option that allows the issues to redeem a bond prior to the maturity date at a predetermined price and date

Issuer Call


……………… the embedded option that allows the bond holder to request for the bond to

be redeemed by the issuer

Bondholders puts


A bond issued with the embedded “change of control put” option means

The right of investor to request for the bonds to be redeemed by the issuer in the event of

a takeover of the company


Bond with issuer call option is trade at



Bond with issuer put option is trade at



The exercise price of a ………reimbursed the lendor for an amount of up to the approximate

present value of lost interest for the remaining term of the lost contract?

Prepayment option


Interest rate derivative can be classified into ___ categories



………………….is a form of interest rate swap in which the floating payment is based on the

interest rate at the end of the specified period

In arrear swap


A Swap is called ..………swap if you are the party paying the floating leg and therefore

receiving the fix leg:



A Swap is called ..………swap if you are the party paying the fix leg and therefore receiving

the floating leg:



Effective duration

A duration calculation for bonds that have embedded options



 - When bond mature, the issuer does not have the cash on hand to repay bondholders, it can issue new bonds and use proceeds either to redeem the older bonds or to exercise a call option

 - This process is called Refunding


Bullet Bond

 - the entire principal amount of the bond is repaid at maturity.


Fully Amortized Bond

 - where periodic interest and equal principal repayments are made over the life of the bond, such that the bond is full repaid at maturity.


Partially Amortized Bond

 - where only a small partial amount of principal is repaid over the bond’s life, with a bigger lump sum balloon payment made at maturity of the bond. In essence, it is a hybrid between a fully amortizing and a bullet bond.


Sinking Fund

 - issuer repays a specific portion of the principal amount every year throughout the bond’s life or after a specified date. A sinking fund arrangement has a lower credit risk but higher reinvestment risk for investors.


Bond Public Offering



Underwritten Offering

An investment bank agrees an offering price with the issuer, and buys the whole bond issue at that price, and takes the risk of reselling it to other investors.


Best efforts offering

Opposite to an underwritten offering, the investment bank here just acts as a broker and sells as many securities as it can without taking underwriting risk. The unsold bonds are returned to the issuer


Shelf registration

type of public offering where the issuer can sell the entire bond issue in tranches. All they need to do is file a single document with the regulator to describe potential future bond issuances, which saves admin and registration fees.



 - Governments bonds are usually sold to investors via auction.


Yield Spread Measures



G - Spread

 - yield spread of a bond over the benchmark government bond yield


I - Spread

 - yield spread of a bond over the standard swap rate of same tenure and currency.


Z - Spread / Zero Volatility / Static Spread

 - the constant spread above benchmark government spot curve such that the present value of cash flows equals price of bond


Option Adjusted Spread

 - OAS = Z Spread - Option Value


Money Duration

 - measures the price change in units of currency in which the bond is dominated, given a change in annual yield to maturity.


4 C's of Credit Analysis

 - Capacity

 - collateral

 - Covenants

 - Character


Key Rate Duration

 - (PV_ − PV+)/(2×0.01×PV0)


the key rate duration can be used to measure

 - The sensitivity in a security’s price to a 1% change in yield for a specific maturity.


Effective Duration

 - (P(1) - P(2)) / (2 x P(0) x Y)


The taxability risk premium compensates bond holders for which

 - A bond’s unfavourable tax status


Swap yield

 - Determine by computing the price on each leg and then calculating the yield of each leg given those value


Credit Quality

 - Credit Quality is an indicator of the ability of the issuer of the fixed income security to pay back his Obligation

 - Usually assesed by Independent rating agency


Forward Contract

 - Contract to trade in a particular asset (which may be another security) at a particular price on a pre specified date


Forward Rate Agreement

 - Is an agreement to lend a money on a particular date in the future at a rate that is determined today


Future Contract

 - Standardized forward contract that is traded on an exchange and where the counter party ( the party with which the contract has been signed) is the exchange itself


Overnight Interest Rate

 - Floating rate is overnight rate (NSE MIBOR) and the fixed rate is paid in exchange of the compounded floating rate over a certain period


Call Money

 - Money that is lent for one day in money market


Notice Money

 - Money that is lent for more than 1 day but less than 15 days in money market


Term Money

 - Money lent for 15 days or more in the interbank market


FIMMDA Circulars



Central Government Securities

All CG securities which qualify for SLR as well as which do not qualify for SLR will be valued as per prices (yields) published by FIMMDA / FBIL.


State Government Securities

FIMMDA / FBIL will publish the prices (yields) for all the State Government Securities calculated in accordance with “para 3.6.2 of RBI Master Circular for banks dated July 1, 2015” or modified guidelines if any as per Benchmark Committee’s recommendations in this regard

Advertise With Us

Click here to read the disclaimer

Write a Comment

  • This is an excellent article. This is, in my opinion, one of the best posts ever written. Your work is excellent and inspiring. Thank you very much. Retro Bowl game


    23-09-2022 / 09:24:04 AM