Bond Market - MMS

8/3/2019 Bond Market - MMS

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Financial Institutions

and Markets


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Indian Financial System

n The economic development of a nation is reflected by the progress of thevarious economic units, broadly classified into corporate sector, governmentand household sector. While performing their activities these units will beplaced in a surplus/deficit/balanced budgetary situations.

n There are areas or people with surplus funds and there are those with a

deficit. A financial system or financial sector functions as an intermediaryand facilitates the flow of funds from the areas of surplus to the areas ofdeficit. A Financial System is a composition of various institutions, markets,regulations and laws, practices, money manager, analysts, transactions andclaims and liabilities.


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n Financial System;The word "system", in the term "financial system", implies a set ofcomplex and closely connected or interlined institutions, agents,practices, markets, transactions, claims, and liabilities in theeconomy. The financial system is concerned about money, credit

and finance-the three terms are intimately related yet are somewhatdifferent from each other. Indian financial system consists offinancial market, financial instruments and financial intermediation.These are briefly discussed below


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Financial Institutions

n Includes institutions and mechanisms whichq Affect generation of savings by the communityq Mobilisation of savings

q Effective distribution of savingsn Institutions are banks, insurance companies,

mutual funds- promote/mobilise savingsn Individual investors, industrial and trading

companies- borrowers


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Financial marketn These assets represent a claim to the payment of a sum of money

sometime in the future and/or periodic payment in the form of interest ordividend. Classification

Money marketq (Short term instrument)q Organized (Banks)q Unorganized (money lenders, chit funds, etc.)

Capital marketsq (Long term instrument)

q Primary Issues Marketq Stock Marketq Bond Market


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Financial markets facilitate:

n The raising of capital

n The transfer of risk

n International trade

They are used to match those who want capital to those who have it. Typically a

borrower issues a receipt to the lender promising to pay back the capital. Thesereceipts are securities which may be freely bought or sold. In return for lendingmoney to the borrower, the lender will expect some compensation in the form ofinterest or dividends.

Financial markets could mean:

n Organizations that facilitate the trade in financial products. i.e. Stock exchanges

facilitate the trade in stocks, bonds and warrants.

n The coming together of buyers and sellers to trade financial products. i.e. stocks andshares are traded between buyers and sellers in a number of ways including: the useof stock exchanges; directly between buyers and sellers etc.


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Financial Markets

n OTCn Auction Marketn Organized Market


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Types of Financial markets

n Capital markets

n Stock markets, which provide financing through the issuance ofshares or common stock, and enable the subsequent trading thereof.

n Bond markets, which provide financing through the issuance ofBonds, and enable the subsequent trading thereof.

n Commodity markets

n

Money marketsq which provide short term debt financing and investment.

n Derivatives markets

q which provide instruments for the management of financial risk.

n Futures

n Forward

n Options

n Swaps


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n Insurance markets

q which facilitate the redistribution of various risks.n Foreign exchange markets

q which facilitate the trading of foreign exchange.n Credit market

q where banks, FIs and NBFCs purvey short, mediumand long-term loans to corporate and individuals.


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Purpose of Financial Markets

Purpose:n To facilitate the transfer of funds between borrowers and lendersn Trade TIME & RISK

n Price discovery: Trading on secondary markets provides public

information on asset prices (market price = last traded price of anasset)

n Lower search costs: Since all trading parties converge to the samelocation, matching is made easier

n Provides liquidity: investors can sell assets prior to maturity onsecondary markets to satisfy their time preference for consumptionand diversification needs.


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FM Participants

n Firms - Net Borrowersn Households (Individuals/Consumers)- Net Savers

n Financial Institutions -Borrowers and Saversn Government (Federal/State/Local)


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Money Market

Main FunctionTo channelize savings into short term productiveinvestments like working capital .

Instruments in Money MarketCall money marketTreasury bills marketMarkets for commercial paperCertificate of depositsBills of ExchangeMoney market mutual fundsPromissory Note

P i M k t S d M k t


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Primary Markets Secondary Markets

When companies need financialresources for its expansion, theyborrow money from investorsthrough issue of securities.

The place where such securities aretraded by these investors is knownas the secondary market.

Securities issueda)Preference Sharesb)Equity Sharesc)Debentures

Securities like Preference Shares andDebentures cannot be traded in thesecondary market.

Equity shares is issued by the under

writers and merchant bankers onbehalf of the company.

Equity shares are tradable through a

private broker or a brokerage house.

People who apply for these securitiesare:a)High networth individualb)Retail investorsc)Employeesd)Financial Institutionse)Mutual Fund Housesf)Banks

Securities that are traded are tradedby the retail investors,FIs,MFs etc

One time activity by the company. Helps in mobilising the funds for the

investors in the short run.


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The Indian Capital Market

n Market for long-term capital. Demand comesfrom the industrial, service sector andgovernment

n Supply comes from individuals, corporates,banks, financial institutions, etc.

n Can be classified into:q Gilt-edged marketq Industrial securities market (new issues and stock

market)

M j R f i I di C i l


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Major Reforms in Indian CapitalMarket

n Setting up of SEBI

n Introduction of free pricing in the primary capital market andabolition of capital control

n Standardization of disclosures in public issue

n Permission to FIIs to operate in the Indian capital market.Modernization of trading infrastructure on-line screen basedelectronic trading system

n Shift from account period settlement to (14 days) to rollingsettlement (T+2)

n

Safety and Integrity Measures margining system, intra-day tradinglimit, exposure limit and setting up of trade/settlement guaranteefund

n Clearing of transactions through the clearing house


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n Dematerialization of securities Two depositories in the country

n Reconstitution of Governing Boards of Stock Exchanges

n Introduction of trading in equity derivative products

n Indian corporate allowed to access

n International capital markets throughq American Depository Receiptsq Global Depository Receiptsq Foreign Currency Convertible Bondsq External Commercial Borrowings


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Bond (Debt) Market

Session 2


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What is a Bond?

You've just loaned your neighbour $1,000so that he can renovate his home. He'spromised to pay you 6% interest each yearfor the next 5 years, and then hell give you

back your money. A bond works much the same way yougive a company $1,000 and they pay you afixed rate of interest for a specified period

of time, after which they return yourprincipal. Governments (federal, provincialand municipal) and corporations use bondsto raise the capital they need to expand.


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You could also decide to sell that

bond to someone else for $1,100. Inthat case youd earn a capital gain of$100 (plus whatever interestpayments you had received in the

meantime).

Now, why would someone pay you$1,100 for a bond that only cost you

$1,000?


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Selling bonds

Your $1,000 bond pays 6% interest. Since youbought that bond, however, interest rates have gonedown. Similar companies are now only offering a 5%interest rate on their bonds. Your original rate looks

pretty good to another investor. So you can sell that6% bond at a higher cost than you paid for it, which iscalled selling for a premium.

However, if interest rates have gone up, and similarcompanies are now offering 8%, you may have to sellyour bond for less which is known as selling at adiscount.

Interest rates and bond prices, then, are like a see-saw when interest rates go down, bond prices go up

(and vice versa).


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Bond Issuers

n Government Bondsn Municipal Bondsn Corporate Bondsn International Bonds

q Eurobondq Foreign bondsq

Global Bonds


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Corporate Bonds

n Corporate bonds are debt securities issued by private and publiccorporations. Companies issue corporate bonds to raise money fora variety of purposes, such as building a new plant, purchasingequipment, or growing the business.

n When one buys a corporate bond, one lends money to the "issuer,"

the company that issued the bond. In exchange, the companypromises to return the money, also known as "principal," on aspecified maturity date. Until that date, the company usually paysyou a stated rate of interest, generally semiannually.


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Wholesale Debt Marketn The Wholesale Debt Market segment deals in fixed income securities and is

fast gaining ground in an environment that has largely focused on equities.

n The Wholesale Debt Market (WDM) segment of the Exchange commencedoperations on June 30, 1994. This provided the first formal screen-basedtrading facility for the debt market in the country.

n This segment provides trading facilities for a variety of debt instruments

including Government Securities, Treasury Bills and Bonds issued by PublicSector Undertakings/ Corporates/ Banks like Floating Rate Bonds, ZeroCoupon Bonds, Commercial Papers, Certificate of Deposits, CorporateDebentures, State Government loans, SLR and Non-SLR Bonds issued byFinancial Institutions, Units of Mutual Funds and Securitized debt by banks,financial institutions, corporate bodies, trusts and others.

n

Large investors and a high average trade value characterize this segment.Till recently, the market was purely an informal market with most of thetrades directly negotiated and struck between various participants. Thecommencement of this segment by NSE has brought about transparencyand efficiency to the debt market.


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Retail Debt Market

n With a view to encouraging wider participation of all classes ofinvestors across the country (including retail investors) ingovernment securities, the Government, RBI and SEBI haveintroduced trading in government securities for retail investors.

Trading in this retail debt market segment (RDM) on NSE has beenintroduced w.e.f. January 16, 2003. Trading shall take place in theexisting Capital Market segment of the Exchange.

In the first phase, all outstanding and newly issued centralgovernment securities would be traded in the retail segment. Other

securities like state government securities, T-Bills etc. would beadded in subsequent phases.


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Bonds Terminology

n Issuer

q Government, municipality, corporation, federal agency or otherentity known as the issuer.

n Par Value

q It is the value stated on the face of the bond.

q It represents the amount the firm borrows and promises to repayat the time of the maturity.

q It is also known as the principal, face value, or par value.q It is important to remember that bonds are not always sold at par

value. In the secondary market, a bond's price fluctuates with

interest rates. If interest rates are higher than the coupon rate ona bond, the bond will have to be sold below par value (at a"discount"). If interest rates have fallen, the price will be higher.


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n Maturity

q It is also called term-to-maturity. At the time of maturity, the issueris no longer obligated to make interest payments.

q Maturities range significantly, from 1 year to 40+ years for somecorporate bonds.

q Short-term notes: maturities of up to 5 years;q Intermediate term or Medium-term: maturities of five to 12 years;q Long-term bonds: maturities of 12 or more years.


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n Couponq The coupon rate is the interest rate that is paid out to the bond holder.q The name derives from the old system of payment, in which bond

holders would need to send in coupons in order to receive payment.

q The coupon is set when the bond is issued and is usually expressed asan annual percentage of the par value of the bond.

q Coupon payment can be annually, semi annually, quarterly or monthly.q There are some bonds that do not pay out any coupons; these are

called zero-coupon bonds .


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n Yield to Maturityq The rate of return anticipated on a bond if it is held

until the maturity date. YTM is considered a long-term bond yield expressed as an annual rate. Thecalculation of YTM takes into account the currentmarket price, par value, coupon interest rate andtime to maturity. It is also assumed that all couponsare reinvested at the same rate. Sometimes this is

simply referred to as "yield" for short.


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CREDIT RATINGSn Each of the agencies assigns its ratings based on an in-depth analysis of the issuer's

financial condition and management, economic and debt characteristics, and thespecific revenue sources securing the bond.


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Types of Bonds

I. Classification on the basis of Variability of Coupon

n Zero Coupon Bondsq Zero Coupon Bonds are issued at a discount to their face value and at

the time of maturity, the principal/face value is repaid to the holders. Nointerest (coupon) is paid to the holders and hence, there are no cashinflows in zero coupon bonds.

q

The difference between issue price (discounted price) and redeemableprice (face value) itself acts as interest to holders. The issue price ofZero Coupon Bonds is inversely related to their maturity period, i.e.longer the maturity period lesser would be the issue price and vice-versa. These types of bonds are also known as Deep Discount Bonds.


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n Floating Rate Bondsq Reference rate + quoted margin (LIBOR + Q. margin)

q Floors

q Caps

n Fixedq Stays same until maturity; ie: buy a Rs 1000 bond with 8% fixed interest

rate and you will receive Rs 80 every year until maturity and at maturityyou will receive the Rs 1000 back.

n Payable at Maturityq Receive no payments until maturity and at that time you receive

principal plus the total interest earned compounded semi-annually at theinitial interest rate.


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II. Classification on the Basis ofVariability of Maturity

n Callable Bondsq The issuer of a callable bond has the right (but not the obligation)

to change the tenor of a bond (call option). The issuer mayredeem a bond fully or partly before the actual maturity date.These options are present in the bond from the time of original

bond issue and are known as embedded options.q This embedded option helps issuer to reduce the costs when

interest rates are falling, and when the interest rates are rising itis helpful for the holders.


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n Puttable Bonds

q The holder of a puttable bond has the right (but not an obligation)to seek redemption (sell) from the issuer at any time before thematurity date.

q In riding interest rate scenario, the bond holder may sell a bond

with low coupon rate and switch over to a bond that offers highercoupon rate. Consequently, the issuer will have to resell thesebonds at lower prices to investors.

q Therefore, an increase in the interest rates poses additional riskto the issuer of bonds with put option (which are redeemed at

par) as he will have to lower the re-issue price of the bond toattract investors.


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n Convertible Bonds

q The holder of a convertible bond has the option to convert thebond into equity (in the same value as of the bond) of the issuingfirm (borrowing firm) on pre-specified terms.

q This results in an automatic redemption of the bond before the

maturity date. The conversion ratio (number of equity of shares inlieu of a convertible bond) and the conversion price (determinedat the time of conversion) are pre-specified at the time of bondsissue.

q Convertible bonds may be fully or partly convertible. For the part

of the convertible bond which is redeemed, the investor receivesequity shares and the non-converted part remains as a bond.


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III. Classification on the basis ofPrincipal Repaymentn Amortizing Bonds

q Amortizing Bonds are those types of bonds in which the borrower(issuer) repays the principal along with the coupon over the life ofthe bond.

q The amortizing schedule (repayment of principal) is prepared in

such a manner that whole of the principle is repaid by thematurity date of the bond and the last payment is done on thematurity date. For example - auto loans, home loans, consumerloans, etc.

D bt I t t


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Debt InstrumentsType Typical Features

Central Government Securities Medium long term bonds issued by RBI onbehalf of GOI.

Coupon payment are semi annually

State Government Securities Medium long term bonds issued by RBI onbehalf of state govt.


Government Guaranteed Bonds Medium long term bonds issued by govt

agencies and guaranteed by central or stategovt.


PSU Medium long term bonds issued by PSU.

51% govt equity stake

Corporate Short - Medium term bonds issued by privatecompanies.


s ssoc a e w nves ng n


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s ssoc a e w nves ng nBonds

n Interest Rate Riskn The price of the bond will change in the opposite direction

from the change in interest rate. As interest rate rises thebond price decreases and vice versa.

n If an investor has to sell a bond prior to the maturity date, it

means the realisation of capital loss.n This risk depends on the type of the bond; callable puttable

etc????

n Reinvestment Income or Reinvestment Riskn The additional income from such reinvestment called

interest on interest, depends on the prevailing interest ratelevels at the time of reinvestment.


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n Call Riskn The issuer usually retains this right in order to have

flexibility to refinance the bond in the future is marketinterest rate drops below the coupon rate

n

Disadvantage for investors for callable bond: cash flowpattern not known with certainty, interest rate drop, capitalappreciation will reduce.

n Credit Riskn If the issuer of a bond will fail to satisfy the terms of the

obligation with respect to the timely payment of interestand repayment of the amount borrowed.n Yield = market yield + risk associated with credit risk


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n Inflation Riskn Purchasing power risk arises because of the variation in

the value of cash flow from the security due to inflation.n Eg: ???

n Exchange Rate Riskn Risk associated with the currency value for non-rupee

denominated bonds. Eg: US treasury bond


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n Liquidity Riskn Its depends on the size of the spread between bid and ask

price quoted. Wider the spread is risky.n For investors keeping till maturity, this is uminportant.

n Market to market should be calculated portfolio value.n Volatility Risk

n Value of bond will increase when expected interest ratevolatility increases.

n Risk Riskn Natural uncertainty.n Avoid securities in which knowledge is less.


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Time value of money


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Time value of Money

n Present value of moneyq One timeq Annuity

n Future value of moneyq One timeq Annuity


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Question

n Suppose an instrument promises to pay Rs5,000,000 seven years from now with nointerim cash flows. Assuming rate of interest

is 10%. What is the present value of thisinvestment?

n Rs 2,565,791


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Present value of an OrdinaryAnnuity

n When the same amount of rupees is receivedeach year or paid each year is referred to asan annuity.

n When the first payment is received oneperiod from now is called as an ordinaryannuity.

PV = 1- 1

A (1+r)n

r

Q i


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Question

n Suppose that an investor expects to receiveRs 100 at the end of each year for the nexteight year. Interest rate 9%. Calculate PV ofthe receivable amount.PV = 1- 1

100 (1.09)8 0.09

100 [5.534811] = Rs 533.48


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Bond Pricing

n Reason q Indicate the yield receivedq Should the bond be purchased

n Priced at Premium, Discount, or at Par

l l i d i


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Calculating Bond Price

n Sum of the present values of all expected couponpayments plus the present value of the par value atmaturity.

C = coupon payment, ordinary annuityn = number of payments

i = interest rate, or required yieldM = value at maturity, or par value


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Eg: Calculate the price of a bond with a par value of $1,000 to bepaid in 10 years, coupon rate of 10%, and required yield of12%.....?

Coupon payments are made semi-annually to bond holders andthat the next coupon payment is expected in 6 months

n Determine the Number of Coupon Payments

n Determine the Value of Each Coupon Payment

n Determine the Semi-Annual Yield

n Plug the Amounts Into the Formula


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Bond price isless than its par

value i.e, extraincentive toinvest in the

bonds


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Price Yield Relationship


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Price Yield Relationship

n When yield increases, investor would notbuy the issue because it offers a belowmarket yield; the resulting lack of demandwould cause the price to fall.

n When yield decreases ??????n This is how bond price falls below its par

value.n When bond sells below its par value, it is

said to be selling at a discount


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n Coupon rate is less than the required yieldPrice is less than the par ( Discount

Bond)

n Coupon rate is equal to the required yieldPrice is equal to the par

n Coupon rate is more than the requiredyield

Price is more than the par ( premiumBond)


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n A fundamental property of a bond is that itsprice changes in the opposite directionfrom the change in the required yield

n As the required yield increases, thepresent value of cash flow decreases;hence the price decreases.

n As the required yield decreases, thepresent value of cash flow increases;hence the price


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Session 3

Yield YTM Duration


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Question 1

n Calculate the Bond price for a 20 year10% coupon bond with a par value of Rs1000. Lets suppose the yield on this bond

is 11%. The cash flows for this bond areas follows:q 40 semi anually coupon payment of Rs 50q Rs 1000 to be received 40 six month period

from now.


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Solution

50 1- 1 1000

(1.055)4 + (1.055)400.055

n Rs 50 1- 0.117463 + Rs 1000.055 8.51332

= Rs 802.31 + 117.46

= Rs 919.77


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Question 2


is 6.8%. The cash flows for this bond areas follows:q 40 semi anually coupon payment of Rs 50q Rs 1000 to be received 40 six month period

from now.


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Solution

50 1- 1 1000

(1.034)40 + (1.034)400.034

= Rs 1084.51 + 262.53

= Rs 1,347.04


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is 10%. The cash flows for this bond areas follows:q 40 semi anually coupon payment of Rs 50q Rs 1000 to be received 40 six month period

from now.Ans Rs 1000


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Assignment 1

n Find out different factor that affect risk freerate?


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Pricing Zero-Coupon Bonds

n No coupon payment until maturity. Because of this,the present value of annuity formula is unnecessary.

n Calculate the price of a zero-coupon bond that ismaturing in 5 years, has a par value of $1,000 and

required yield of 6%....?q Determine the Number of Periodsq Determine the Yield

i i


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Determining InterestAccruedn Accrued interest is the fraction of coupon payment

that the bond seller earns for holding the bond for aperiod of time between bond payments

q The amount that the buyer pays the seller is

the agreed upon the price plus accruedinterest. This is referred as a Dirty bond prices

q The price of a bond without accrued interest iscalled the Clean bond prices


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Accrued Interest

q Interest accrues linearly during coupon period

Last

Coupon

Date

Next

Coupon

Date

Settlement

Date


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Eg: On March 1, 2010, X is selling a corporate bond witha face value of $1,000 and 7% coupon paid semi-

annually. The next coupon payment after March 1, 2010,is expected on June 30, 2010.What is the interest accrued on the bond?


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Yield


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Bond Basics

n Two basic yield measures for a bond are its couponrate and its current yield.

valueParcouponAnnualrateCoupon =

priceBond

couponAnnualyieldCurrent =

Yield


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Yield

n Yield is the return you actually earn on thebond--based on the price you paid and the

interest payment you receiven Two Types of Yields:

q Current Yield: annual return on the dollar amount paidfor the bond and is derived by dividing the bond's interestpayment by its purchase price

q Yield To Maturity: total return you will receive by holdingthe bond until it matures or is called.


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Yield

n From the time a bond is originally issued until the dayit matures, its price in the marketplace will fluctuateaccording to changes in market conditions or creditquality.

n The constant fluctuation in price is true of individualbonds-and true of the entire bond market-with every change in the level ofinterest rates typically having an immediate, andpredictable, effect on the prices of bonds.


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Yield

1. Current yield:Annual coupon receipts/ Market price of the bond

n. It does not consider:

n Time value of moneyn Complete series of future cash flow

n. It compares a pre-specified coupon with the current

market price, it is called as current yield.


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Example

n The current yield for a 15 years 7%coupon bond with a par value of Rs 1000,selling for Rs 769.40

Current yield = Rs 70 = 9.10%

Rs769.40


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Yield to Maturity

n Given a pre-specified set of cash flows and a price,the YTM of a bond is that rate which equates thediscounted value of the future cash flows to thepresent price of the bond.


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YTM

n Yield to maturity (YTM) is the interest rate (i) that equates thepresent value of cash flow payments received from a debtinstrument with its value today.

n It is the most accurate measure of interest rates.

n The yield to maturity is the annual return annual rate

(discounted) earned over a bond kept until maturity.n The yield to maturity is the discount rate estimated

mathematically that equals the cash flow of payment of interestand principal received with the purchasing price of the bond.

n This term is also referred to as internal rate of return or as the

expected rate of return of the bond and it is the yield in whichmost bond investors are interested in.


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n The yield-to-maturity depends on two assumptions:n The bonds are held to maturityn The interest payments received are reinvested at the

same rate as the yield-to-maturity

n In reality matching the yield-to-maturity rate from theinterest received is difficult because interest rates arechanging constantly. The interest received is usuallyreinvested at different rates from the stated yield-to-maturity rate.


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n The yield is the interest rate that will makethe present value of cash flow equals tothe bond price.

n

YTM is calculated same way as IRR, thecash flows are those that the investorwould realized by holding the bond tillmaturity.

n To compute the YTM requires a trial anderror method


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Yield of Bond

Eg: You hold a bond whose par value is $100 but has a currentyield of 5.21% because the bond is priced at $95.92. The bondmatures in 30 months and pays a semi-annual coupon of 5%.

l


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Example

n Calculate the YTM for a 15 years 7%coupon bond with a par value of Rs 1000.Lets suppose the bond price is Rs 769.42.The cash flows for this bond are asfollows:q 30 semi anually coupon payment of Rs 35q Rs 1000 to be received 30 six month period

from now.


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769.42 = Rs 35 1- 1 1000 1 (1+y)30 + (1+y)30

y


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n Trial and error method

Annual Interestrate

PV of 30 paymentsof Rs 35

PV of Rs 1000 30periods from now

PV of cash flows

9 % 570.11 267 837.11

9.5% 553.71 248.53 802.24

10% 538.04 231.38 769.42

11.5 % 532.04 215.45 738.49

11 % 508.68 200.64 709.32

Question?


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n The following three bonds, each of which has a parvalue of Rs 1000 and pays coupon semi-annually

n Calculate the Yield to maturity for three bonds

Bond Coupon rate (%) Number of yearsto maturity

Price (Rs)

A 7 5 884.20

B 8 7 948.90

C 9 4 967.70

Question?


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Click to edit Master subtitle style

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YTC, YTP, Bond PriceVolatility & Duration

Session 3

Yield to Call (YTC)


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Yield to Call (YTC)n Yield to call (YTC) is the interest rate that investors

would receive if they held the bond until the calldate. The period until the first call is referred to asthe call protection period.

n Yield to call is the rate that would make the bond'spresent value equal to the full price of the bond.

Essentially, its calculation requires two simplemodifications to the yield-to-maturity formula:

YTC


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YTC

n When the bond may be called and at whatprice are specified at the time the bond isissued.

n

The price at which bond may be called isreferred to as the call price.

E l


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Example

n Consider an 18 years 11% coupon bondpayable semi annually with a maturity valueof Rs 1000 selling at Rs 1169. suppose thatthe first call date is 8 years from now and thatthe call price is Rs 1055.

n Call price = 1055n N = 8*2 = 16 m

n C = 1000*11%/2 = 55n Bond price = 1169

Solution


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1169 = Rs 55 1- 1 1055 1 (1+y)16 + (1+y)16

y

n 8.54% is the yield to first call

Yield to Put (YTP)


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Yield to Put (YTP)

n This mean that the bond holder can force the issuer to

buy the issue at a specified pricen Yield to put (YTP) is the interest rate that investors would

receive if they held the bond until its put daten To calculate yield to put, the same modified equation for

yield to call is used except the bond put price replaces thebond call value and the time until put date replaces thetime until call date

n M = put pricen

n = number of periods until assumed put date.

E l f YTP


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Example of YTP

n Consider an 18 years 11% coupon bondpayable semi annually issue selling Rs 1169.assume that issue is putable at par (Rs 1000)in five years.

n Put price = 1000n N = 5*2 = 10 mn C = 1000*11%/2 = 55

Solution


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Solution

1169 = Rs 55 1- 1 1000 1 (1+y)10 + (1+y)10

y

n 6.94% 7% is the yield to put


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Bond price volatility

Volatility of Bond Prices in theSecondary Market


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Secondary Market

n Maturityn Yieldn Credit rating

n Current interest rate

Price Yield Relationship for


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pSix Hypothetical Bonds

n 9% coupon bond with 5 years to maturityn 9% coupon bond with 25 years to maturityn 6% coupon bond with 5 years to maturityn 6% coupon bond with 25 years to maturityn 0% coupon bond with 5 years to maturityn 0% coupon bond with 25 years to maturity

Price Volatility Characteristicsof Option Free Bonds


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of Option- Free Bonds(Properties)n Although the prices of all the option free

bonds move in the opposite direction fromthe change in yield required, the percentageprice change is not the same for all bonds.

n For very small changes in the yield required,the percentage price change for a given bonfis roughly the same, whether the yield

required increases or decreases


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n For large changes in the required yield, thepercentage price change is not the same foran increase in the required yield as it is for adecrease in the required yield

n For a given change in basis point, thepercentage price increase is greater than thepercentage price decrease. (Long position:

Potential capital gain is more than the capitalloss, Short position: )


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Bond Price Volatility Duration & Convexity

Session 4

Characteristics of a Bond that


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Affect its Price Volatilityn There are two characteristics of an option

free bonds that determine its price volatility:Coupon and Term to Maturity


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n Long maturities in portfolio:n Investors who wants to increase a portfolios price

volatility because they expect interest rate to fall, all otherfactors being constant, should hold for long maturity

n Short maturities in portfolio:

Effects of Yield to Maturity


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Effects of Yield to Maturityn Price change for a 100 Basis point change in

yield for a 9% 25 yrs bond trading at differentyield level

Yield level (%) Initial price (Rs) New price (Rs) Price decline(Rs)

Percent decline(%)

7% 123.46 110.74 12.72 10.308 110.74 100 10.74 9.70

9 100 90.87 9.13 9.13

10 90.87 83.87 7.80 8.58

11 83.87 76.37 6.71 8.0812 76.37 70.55 5.81 7.61

13 70.55 65.50 5.05 7.16

14 65.50 61.08 4.42 6.75

Measures of Bond Price


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Volatility

Three measures:n Price value of a basis pointn Yield value of a price change

n Duration

Price value of a basis point


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n Price Value of a Basis Point refers to the change in theprice of a bond if the yield changes by 1 basis point(0.01%)

n If the price of Security A falls by 20 paise when the yield

rises by 0.01% and the price of Security B falls by 25paise for the same rise in the yield

Yield value of a price change


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n Yield Value of a Price change refers to thechange in the yield of a security for aspecified change in the price of the security.

n

The smaller the yield value, the pricevolatility would be greater since even a smallchange in the yield would change the priceconsiderably.

DURATION


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DURATION

n In CAPM, Beta is a measure of a shares sensitivity tochanges in an index.

n An analogous measure is calculated for bonds: it is calledDuration.

n Duration is a measure of the sensitivity of the price of abond to a change in interest rates.n The duration measure allows us to evaluate the relative

exposure to interest rate risk, of bonds with differingpatterns of coupon payments.

n Duration is a measure of how quickly the (present) valueof a bond is returned.

Duration


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u a o

n It is a measurement of how long, in years, it takes for theprice of a bond to be repaid by its internal cash flows.

n Formula:

Duration = Weighted Average of PV ofCash Flows

Present Value of Cash Flowsn The answer will give a measure of the average life of the

bond in a present value sense.n A bonds with a low duration gets most of its value from

cash flows occurring early.

Macaulays Duration


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Macaulay s Duration

n Macaulays definition: a weighted average term tomaturity where all cash flows are in terms of theirpresent value.

n Macaulays duration measure takes into account both

interim and final coupon payments, weighting earliercash flows as being more important than latter ones.n This is done by calculating the present value of each

cash-flow payment.

n As a result earlier coupon payments have higher present

value than later coupon payments.

Computation of Macaulays


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duration

n D = Macaulays durationn Ci = Cash-flow in period in N = Number of semi-annual time periodsn F = Redemption valuen y= YTM per period (prior to changes in interest rates)n P = current price of the bond

q The answer will give a measure of the average life of the bond ina present value sense.

q A bonds with a low duration gets most of its value from cashflows occurring early.

D=[1 * C1/(1+y) + 2 * C2/(1+y)2 + ... + N * CN/(1+y)N + N * F/(1+y)N ] / P

Example - Macaulay Duration


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Example - Macaulay Duration

n A 10% coupon bond with a par value of Rs100 on 1.1.2010. Coupons are paid semi-annually; 1 January and 1 July. The bond willbe redeemed at par on 1.7.2011.

n What is the bond's duration?

n Semi-annual coupon payments = Rs 5


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n Semi-annual cash-flows:

1.1.10 (100)

1.7.10 51.1.11 5

1.7.11 105

y= 5%n Since Par value = market value YTM = Ci )

Duration:

D = [1 * 5/(1+0.05) + 2 * 5/(1+0.05)2 + 3 * 105/(1+0.05)3]100


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D = 2.8594 semi-annual periods (i.e. 1.43 years),

Peroid PV of CF Duration Cal

1 4.76 4.76

2 4.535 9.07

3 90.7 272.11Total 285.94

2.86

Duration 1.43

Example


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pFive Year Bond

Par Value = Rs. 10,000 , Coupon rate = 8%, YTM = 10%,

Maturity = 5 Years

Time Cash Flow PV Multiplier PV Weighted PV

1 800 0.909091 727.27 727.27

2 800 0.826446 661.16 1,322.31

3 800 0.751315 601.05 1,803.16

4 800 0.683013 546.41 2,185.64

5 10800 0.620921 6,705.95 33,529.75

9,241.84 39,568.14

Duration = 39,568.14 / 9,241.84 = 4.2814 Yrs


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For each of the two basic types of bonds theduration is the following:

Zero-Coupon Bond

Vanilla Bond

Duration of a Zero CouponBond


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Bond

Durationof a Vanilla orStraight Bond


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Straight Bond

ModifiedDuration


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n Accounts for changing interest rates.

n Indicates the percentage change in the price of a bondfor a given change in yield.

n Modified duration formula shows how a bond'sduration changes in relation to interest rate

movements.Formula:

Modified Duration = Macaulay Duration

1 + Yield to Maturity

Example


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Eg: Currently a bond is selling at $1,000 or par,which translates to a yield to maturity of 7.5%semi annually. Calculated Macaulay duration is4.26

Modified Duration = 4.26 = 4.101 + 0.0375

PROPERTIES OF DURATION


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n The duration measure, being the firstderivative of the price function, depends onthe following factors:

n Time to maturity

n Coupon payments and frequency of couponpayments in a year, and

n Yield to maturity.

Question?


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Question?

n Calculate the Bond duration and Modifiedbond for the bond with the face value of Rs1000 for 5 years coupon rate is 10% semiannually. YTM is 10%


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5/3/12 Total 8107.82

Period Cash Flow PV Cash Flow Duration Calc

0 ($1,000.00)

1 50.00 47.62 47.62

2 50.00 45.35 90.70

3 50.00 43.19 129.584 50.00 41.14 164.54

5 50.00 39.18 195.88

6 50.00 37.31 223.86

7 50.00 35.53 248.74

8 50.00 33.84 270.74

9 50.00 32.23 290.07

10 1,050.00 644.61 6,446.09


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n Duration is 4.05 (8107.82/ 1000/2)n Modified duration is 3.86 (4.05 /1.05)

Question 1


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Question 1

n Calculate the Bond duration and Modifiedbond for the bond with the face value of Rs1000 for 5 years coupon rate is 10% semiannually. YTM is 8%. First calculate Bond

Price

n Bond duration is 4.22

n Modified Duration 4.06

Question 2


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Question 2

n Calculate the Bond duration and Modifiedbond for the bond with the face value of Rs1000 for 5 years coupon rate is 10% semiannually. YTM is 12%

n Bond duration is 4.01n Modified Duration 3.78


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Types of Yield Curves


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Three Main Patterns


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1. Normal Yield Curve:

This is the yield curveshape that forms duringnormal market conditions.

Investors expect higheryields for fixed income

instruments with long-termmaturities that occurfarther into the future.

As general currentinterest rates increase, the

price of a bond willdecrease and its yield willincrease. Maturity

Yield


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2. Flat Yield Curve:

A flat yield curve usuallyoccurs when the market ismaking a transition thatemits different butsimultaneous indications ofwhat interest rates will do.

When the yield curve isflat, investors can maximizetheir risk/return tradeoff bychoosing fixed-incomesecurities with the least risk,

or highest credit quality.

Maturity

Yield


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3. Inverted Yield Curve:The inverted yield

curve indicates that themarket currentlyexpects interest rates todecline as time movesfarther into the future,which in turn means themarket expects yields

of long-term bonds todecline.

Yield

Maturity

Bond Market - MMS

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