Ppt 1-bond Market

Financial Institutions and Markets Prof. Manisha Sanghvi

Examination

Marks

Final Examination

60

Mid Term Examination

20

Presentation

10

Attendance / Class Participation

10

Total

100

Course Contents

 Introduction to Financial markets and Institutions  Bond Market  Money Market  Capital Market  Mutual Funds  Foreign Exchange  Investment Banking  Commercial Banking

Indian Financial System  The economic development of a nation is reflected by the progress of

the various economic units, broadly classified into corporate sector, government and household sector. While performing their activities these units will be placed in a surplus/deficit/balanced budgetary situations.  There are areas or people with surplus funds and there are those with a deficit. A financial system or financial sector functions as an intermediary and facilitates the flow of funds from the areas of surplus to the areas of deficit. A Financial System is a composition of various institutions, markets, regulations and laws, practices, money manager, analysts, transactions and claims and liabilities.

 Financial System;

The word "system", in the term "financial system", implies a set of complex and closely connected or interlined institutions, agents, practices, markets, transactions, claims, and liabilities in the economy. The financial system is concerned about money, credit and finance-the three terms are intimately related yet are somewhat different from each other. Indian financial system consists of financial market, financial instruments and financial intermediation. These are briefly discussed below

Financial Institutions  Includes institutions and mechanisms which

Affect generation of savings by the community  Mobilisation of savings  Effective distribution of savings 

 Institutions are banks, insurance companies,

mutual funds- promote/mobilise savings  Individual investors, industrial and trading companies- borrowers

Financial market  Defined as the market in which financial assets are created or transferred  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 or dividend.  Classification    

    

Money market (Short term instrument) Organized (Banks) Unorganized (money lenders, chit funds, etc.) Capital markets (Long term instrument) Primary Issues Market Stock Market Bond Market

 The most important distinction between the two????

Financial markets facilitate:   

The raising of capital The transfer of risk 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. These receipts are securities which may be freely bought or sold. In return for lending money to the borrower, the lender will expect some compensation in the form of interest or dividends. Financial markets could mean: 

Organizations that facilitate the trade in financial products. i.e. Stock exchanges facilitate the trade in stocks, bonds and warrants.



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

Financial Markets  OTC  Auction Market  Organized Market  Intermediation financial market

Types of Financial markets 

Capital markets 

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Commodity markets Money markets 

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Stock markets, which provide financing through the issuance of shares or common stock, and enable the subsequent trading thereof. Bond markets, which provide financing through the issuance of Bonds, and enable the subsequent trading thereof.

which provide short term debt financing and investment.

Derivatives markets 

which provide instruments for the management of financial risk.   

Futures Forward Options .

Insurance markets

 

which facilitate the redistribution of various risks. Foreign exchange markets

 

which facilitate the trading of foreign exchange. Credit market

 

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

The capital markets consist of primary markets and secondary markets. Newly formed (issued) securities are bought or sold in primary markets. Secondary markets allow investors to sell securities that they hold or buy existing securities.

Purpose of Financial Markets Purpose:  To facilitate the transfer of funds between borrowers and lenders  Trade TIME & RISK  Price discovery: Trading on secondary markets provides public

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

 Lower search costs: Since all trading parties converge to the

same location, matching is made easier

 Provides liquidity: investors can sell assets prior to maturity on

secondary markets to satisfy their time preference for consumption and diversification needs.

FM Participants

 Firms - Net Borrowers  Households (Individuals/Consumers)- Net Savers  Financial Institutions -Borrowers and Savers  Government (Federal/State/Local)

Money Market

 Main Function •To channelize savings into short term productive investments like working capital .

 Instruments in Money Market •Call

money market •Treasury bills market •Markets for commercial paper •Certificate of deposits •Bills of Exchange •Money market mutual funds •Promissory Note

Capital Markets Provided resources needed by medium and

large scale industries.

Purpose for these resources  Expansion  Capacity Expansion  Investments  Mergers and Acquisitions Deals in long term instruments and sources of

funds

Main Activity 

Functioning as an institutional mechanism to channelize funds from those who save to those who needed for productive purpose.



Provides opportunities to various class of individuals and entities.

Primary Markets

Secondary Markets

When companies need financial resources for its expansion, they borrow money from investors through issue of securities.

The place where such securities are traded by these investors is known as the secondary market.

Securities issued b)Preference Shares c)Equity Shares d)Debentures

Securities like Preference Shares and Debentures cannot be traded in the secondary market.

Equity shares is issued by the under writers and merchant bankers on behalf of the company.

Equity shares are tradable through a private broker or a brokerage house.

People who apply for these securities are: b)High networth individual c)Retail investors d)Employees e)Financial Institutions f)Mutual Fund Houses g)Banks

Securities that are traded are traded by the retail investors,FI’s,MF’s etc

One time activity by the company.

Helps in mobilising the funds for the investors in the short run.

The Indian Capital Market  Market for long-term capital. Demand comes

from the industrial, service sector and government  Supply comes from individuals, corporates, banks, financial institutions, etc.  Can be classified into: Gilt-edged market  Industrial securities market (new issues and stock market) 

Major Reforms in Indian Capital Market  Setting up of SEBI  Introduction of free pricing in the primary capital market and abolition of  

  

capital control Standardization of disclosures in public issue Permission to FIIs to operate in the Indian capital market. Modernisation of trading infrastructure – on-line screen based electronic trading system Shift from account period settlement to (14 days) to rolling settlement (T+2) Safety and Integrity Measures – margining system, intra-day trading limit, exposure limit and setting up of trade/settlement guarantee fund Clearing of transactions through the clearing house

 Dematerialization of securities –Two depositories in the country  Reconstitution of Governing Boards of Stock Exchanges  Introduction of trading in equity derivative products  Indian corporate allowed to access  International capital markets through    

American Depository Receipts Global Depository Receipts Foreign Currency Convertible Bonds External Commercial Borrowings

Financial Institutions Specialize in market activities that help facilitate the  Transfer of funds between borrowers and lenders. They are frequently referred to as Financial Intermediaries (ie. act in the capacity as a go-between when financial markets are insufficient by themselves) Types of Financial Institutions:  Depository: Commercial Banks, Thrifts, Credit Unions, Savings and Loan  Non Depository: Investment companies (mutual funds), Pension funds, Insurance  Finance companies: Corporations that have financial arms such as, LIC housing finance, IDBI  Government Sponsored Enterprises (GSE)  Information collectors: Analysts, Rating agencies, Auditors  Market makers & dealers: Brokers, Specialist firms

Bond Market Session 2

Making money: Interest and capital gains There are two ways to make money from a bond – either by earning interest or capital gains. Let's say that you have a Rs 1,000 bond that pays 6% interest for five years. If you hold that bond until the very end of this term (known as the maturity date), you’ll collect five interest payments of Rs 60 for a total of Rs 300. Principal amount Rs 1000.00

Year 1 (6% interest on 1,000) 60.00

Year 2 (6% interest on 1,000) 60.00

Year 3 (6% interest on 1,000) 60.00

Year 4 (6% interest on 1,000) 60.00

Year 5 (6% interest on 1,000) 60.00

Total principal and interest (at maturity date of 5 years) 1,300.00

•You could also decide to sell that bond to someone else for $1,100. In that case you’d earn a capital gain of $100 (plus whatever interest payments you had received in the meantime). •Now, why would someone pay you $1,100 for a bond that only cost you $1,000?

Selling bonds •Your $1,000 bond pays 6% interest. Since you bought that bond, however, interest rates have gone down. 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 that 6% bond at a higher cost than you paid for it, which is called selling for a premium. •However, if interest rates have gone up, and similar companies are now offering 8%, you may have to sell your bond for less – which is known as selling at a discount. •Interest rates and bond prices, then, are like a seesaw – when interest rates go down, bond prices go

Bond Issuers  Government Bonds  Municipal Bonds  Corporate Bonds  International Bonds

Eurobond  Foreign bonds  Global Bonds 

Bonds terminology  Issuer

A bond is a debt security, similar to an I.O.U. When you purchase a bond, you are lending money to a government, municipality, corporation, federal agency or other entity known as the issuer.  Par Value  It is the value stated on the face of the bond.  It represents the amount the firm borrows and promises to repay at the time of the maturity.  It is also known as the principal, face value, or par value.  Par value will vary depending on the type of bond. Most corporate bonds have a Rs 100 face value, sometimes it can be Rs 1000.  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 on a bond, the bond will have to be sold below par value (at a 

 Maturity 

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



Maturity is the length of time before the principal is returned on a bond. It is also called term-to-maturity. At the time of maturity, the issuer is no longer obligated to make interest payments. Maturities range significantly, from 1 year to 40+ years for some corporate bonds. The bonds of different maturities will behave somewhat differently. For example, bonds with long-term maturities will be more sensitive to changes in interest rates. Shorter term bonds are more stable and, because you are more likely to hold it to maturity, are more predictable. There are some circumstances where a bond will be "called" before maturity. Short-term notes: maturities of up to 4 years; Medium-term notes/bonds: maturities of five to 12 years; Long-term bonds: maturities of 12 or more years.

 Coupon  









The coupon rate is the interest rate that is paid out to the bond holder. The name derives from the old system of payment, in which bond holders would need to send in coupons in order to receive payment. The coupon is set when the bond is issued and is usually expressed as an annual percentage of the par value of the bond. Payments usually occur every six months, but this can vary. If there is a 5% coupon on a Rs 1000 face value bond, the bondholder will receive Rs 50 every year. If two bonds with equal maturities and face values pay out different coupons, the prices of these bonds will behave differently in the secondary market. For example, the bond with a lower coupon rate will be less expensive because the bondholder is going to be getting more of his/her return from the return of principal at maturity than will the holder of a bond with a higher coupon. There are some bonds that do not pay out any coupons; these are called zero-coupon bonds .

CREDIT RATINGS 

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 the specific revenue sources securing the bond.

Credit Ratings Credit Risk

Moody's

Standard and Poor's

Prime

Aaa

AAA

AAA

Excellent

Aa

AA

AA

Upper Medium

A

A

A

Lower Medium

Baa

BBB

BBB

Speculative

Ba

BB

BB

Very Speculative

B, Caa

B, CCC, CC

B, CCC, CC, C

Default

Ca, C

D

DDD, DD, D

Fitch

Types of Bonds I. Classification on the basis of Variability of Coupon  Zero Coupon Bonds 



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. No interest (coupon) is paid to the holders and hence, there are no cash inflows in zero coupon bonds. The difference between issue price (discounted price) and redeemable price (face value) itself acts as interest to holders. The issue price of Zero 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.

Floating Rate Bonds  In some bonds, fixed coupon rate to be provided to the holders is not specified. Instead, the coupon rate keeps fluctuating from time to time, with reference to a benchmark rate. Such types of bonds are referred to as Floating Rate Bonds. For better understanding let us consider an example of one such bond from IDBI in 1997. The maturity period of this floating rate bond from IDBI was 5 years. The coupon for this bond used to be reset half-yearly on a 50 basis point mark-up, with reference to the 10 year yield on Central Government securities (as the benchmark). This means that if the benchmark rate was set at “X” %, then coupon for IDBI’s floating rate bond was set at “(X + 0.50)” %.

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

Coupon rate in some of these bonds also have floors and caps. For example, this feature was present in the same case of IDBI’s floating rate bond wherein there was a floor of 13.50% (which ensured that bond holders received a minimum of 13.50% irrespective of the benchmark rate). On the other hand, a cap (or a ceiling) feature signifies the maximum coupon that the bonds issuer will pay (irrespective of the benchmark rate). These bonds are also known as Range Notes. More frequently used in the housing loan markets where coupon rates are reset at longer time intervals (after one year or more), these are well known as Variable Rate Bonds and Adjustable Rate Bonds. Coupon rates of some bonds may even move in an opposite direction to benchmark rates. These bonds

 Fixed 

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 maturity you will receive the Rs 1000 back.

 Payable at Maturity 

Receive no payments until maturity and at that time you receive principal plus the total interest earned compounded semi-annually at the initial interest rate.

II. Classification on the Basis of Variability of Maturity  Callable Bonds 



The issuer of a callable bond has the right (but not the obligation) to change the tenor of a bond (call option). The issuer may redeem 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. This embedded option helps issuer to reduce the costs when interest rates are falling, and when the interest rates are rising it is helpful for the holders.

 Puttable Bonds 





The holder of a puttable bond has the right (but not an obligation) to seek redemption (sell) from the issuer at any time before the maturity date. In riding interest rate scenario, the bond holder may sell a bond with low coupon rate and switch over to a bond that offers higher coupon rate. Consequently, the issuer will have to resell these bonds at lower prices to investors. Therefore, an increase in the interest rates poses additional risk to 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 to attract investors.

 Convertible Bonds 





The holder of a convertible bond has the option to convert the bond into equity (in the same value as of the bond) of the issuing firm (borrowing firm) on pre-specified terms. This results in an automatic redemption of the bond before the maturity date. The conversion ratio (number of equity of shares in lieu of a convertible bond) and the conversion price (determined at the time of conversion) are prespecified at the time of bonds issue. Convertible bonds may be fully or partly convertible. For the part of the convertible bond which is redeemed, the investor receives equity shares and the non-converted part remains as a bond.

III. Classification on the basis of Principal Repayment  Amortizing Bonds 



Amortizing Bonds are those types of bonds in which the borrower (issuer) repays the principal along with the coupon over the life of the bond. The amortizing schedule (repayment of principal) is prepared in such a manner that whole of the principle is repaid by the maturity date of the bond and the last payment is done on the maturity date. For example - auto loans, home loans, consumer loans, etc.

Debt Instruments Type

Typical Features

Central Government Securities

Medium – long term bonds issued by RBI on behalf of GOI. Coupon payment are semi annually

State Government Securities

Medium – long term bonds issued by RBI on behalf of state govt. Coupon payment are semi annually

Government – Guaranteed Bonds

Medium – long term bonds issued by govt agencies and guaranteed by central or state govt. Coupon payment are semi annually

PSU

Medium – long term bonds issued by PSU. 51% govt equity stake

Corporate

Short - Medium term bonds issued by private companies. Coupon payment are semi annually

Risk Associated with Investing in Bonds  Interest Rate Risk  The price of the bond will change in the opposite direction from the change in interest rate. As interst rate rises the bond price decreases and vice versa.  If an investor has to sell a bond prior to the maturity date, it means the realisation of capital loss.  This risk depends on the type of the bond; callable puttable etc????  Reinvestment Income or Reinvestment Risk  The additional income from such reinvestment called interest on interest, depends on the prevailing interest rate levels at the time of reinvestment.

 Call Risk  The issuer usually retains this right in order to have flexibility to refinance the bond in the future is market interest rate drops below the coupon rate  Disadvantage for investors for callable bond: cash flow pattern not known with certainty, interest rate drop, capital appreciation will reduce.  Credit Risk 



If the issuer of a bond will fail to satisfy the terms of the obligation with respect to the timely payment of interest and repayment of the amount borrowed. Yield = market yield + risk associated with credit risk

 Inflation Risk 



Purchasing power risk arises because of the variation in the value of cash flow from the security due to inflation. Eg: ???

 Exchange Rate Risk 

Risk associated with the currency value for nonrupee denominated bonds. Eg: US treasury bond

 Liquidity Risk  Its depends on the size of the spread between bid and ask price quoted. Wider the spread is risky.  For investors keeping till maturity, this is uminportant.  Market to market should be calculated portfolio value.  Volatility Risk 

Value of bond will increase when expected interest rate volatility increases.

 Risk Risk  Natural uncertainty.  Avoid securities in which knowledge is less.

Time value of Money  Present value of money

PV = Pn

1 (1+r)n

Present value of an Ordinary Annuity  When the same amount of rupees is received

each year or paid each year is referred to as an annuity.  When the first payment is received one period from now is called as an ordinary annuity. PV = 1 1-

A

(1+r)n r

Question  Suppose that an investor expects to receive

Rs 100 at the end of each year for the next eight year. Interest rate 9%  When the first payment is received one period from now is called as an ordinary annuity. PV = 1 1-

100

(1.09)8

0.09 100 [5.534811] = Rs 533.48

Bond Pricing  Reason –

Indicate the yield received  Should the bond be purchased 

 Priced at – Premium, Discount, or at Par

Calculating Bond Price  Sum of the present values of all expected

coupon payments plus the present value of the par value at maturity.

C = coupon payment, ordinary annuity n = number of payments i = interest rate, or required yield M = value at maturity, or par value

Session 3 Yield YTM Duration

Question 1  Calculate the Bond price for a 20 year 10%

coupon bond with a par value of Rs 1000. Lets suppose the yield on this bond is 11%. The cash flows for this bond are as follows: 40 semi anually coupon payment of Rs 50  Rs 1000 to be received 40 six month period from now. 

Solution 50

1-

1 (1.055)40 0.055

 Rs 50 1- 0.117463

0.055 = Rs 802.31 + 117.46 = Rs 919.77

1000

+

(1.055)40

+

Rs 100 8.51332

Question 2  Calculate the Bond price for a 20 year 10%

coupon bond with a par value of Rs 1000. Lets suppose the yield on this bond is 6.8%. The cash flows for this bond are as follows: 40 semi anually coupon payment of Rs 50  Rs 1000 to be received 40 six month period from now. 

Solution 50

1-

1 (1.034)40

1000

+

0.034

= Rs 1084.51 + 262.53 = Rs 1,347.04

(1.034)40

 Calculate the Bond price for a 20 year 10%

coupon bond with a par value of Rs 1000. Lets suppose the yield on this bond is 10%. The cash flows for this bond are as follows: 40 semi anually coupon payment of Rs 50  Rs 1000 to be received 40 six month period from now. Ans Rs 1000 

Price Yield Relationship  When yield increases, investor would not buy

the issue because it offers a below market yield; the resulting lack of demand would cause the price to fall.  When yield decreases ??????  This is how bond price falls below its par value.  When bond sells below its par value, it is said to be selling at a discount

 Coupon rate is less than the required yield

Price is less than the par ( Discount Bond)  Coupon rate is equal to the required yield Price is equal to the par  Coupon rate is more than the required yield Price is more than the par ( premium Bond)

 A fundamental property of a bond is that its

price changes in the opposite direction from the change in the required yield  As the required yield increases, the present value of cash flow decreases; hence the price decreases.  As the required yield decreases, the present value of cash flow increases; hence the price

price

yield

Premium and Discount Bonds

Pricing Zero-Coupon Bonds  No coupon payment until maturity. Because of this,

the present value of annuity formula is unnecessary.  Calculate the price of a zero-coupon bond that is maturing in 5 years, has a par value of $1,000 and required yield of 6%....?

Determine the Number of Periods  Determine the Yield 

Determining Interest Accrued  Accrued interest is the fraction of coupon payment

that the bond seller earns for holding the bond for a period of time between bond payments

The amount that the buyer pays the seller is the agreed upon the price plus accrued interest. This is referred as a Dirty bond prices  The price of a bond without accrued interest is called the Clean bond prices 

Eg: On March 1, 2003, X is selling a corporate bond with a face value of $1,000 and 7% coupon paid semi-annually. The next coupon payment after March 1, 2003, is expected on June 30, 2003. What is the interest accrued on the bond?

Bond Basics  Two basic yield measures for a bond are its coupon

rate and its current yield.

Annual coupon Coupon rate = Par value Annual coupon Current yield = Bond price

10-64

Yield  Yield is the return you actually earn on the

bond--based on the price you paid and the interest payment you receive  Two Types of Yields: 



Current Yield: annual return on the dollar amount paid for the bond and is derived by dividing the bond's interest payment by its purchase price Yield To Maturity: total return you will receive by holding the bond until it matures or is called.

Yield n



Current yield: Annual coupon receipts/ Market price of the bond It does not consider:  



Time value of money Complete series of future cash flow

It compares a pre-specified coupon with the current market price, it is called as current yield.

Example  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 Rs769.40

= 9.10%

Yield to Maturity 

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

YTM  Yield to maturity (YTM) is the interest rate (i) that equates the

  



present value of cash flow payments received from a debt instrument with its value today. It is the most accurate measure of interest rates. The yield to maturity is the annual return annual rate (discounted) earned over a bond kept until maturity. The yield to maturity is the discount rate estimated mathematically that equals the cash flow of payment of interest and principal received with the purchasing price of the bond. 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 which most bond investors are interested in.

YTM n

P=Σ t=1

C (1+y)n

+

M (1+y)n

P= Price of the bond C = coupon payment N = No. of years left to maturity M = Maturity value Y = yield to maturity

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

 The yield is the interest rate that will make the

present value of cash flow equals to the bond price.  YTM is calculated same way as IRR, the cash flows are those that the investor would realized by holding the bond till maturity.  To compute the YTM requires a trial and error method

Example  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 as follows: 30 semi anually coupon payment of Rs 35  Rs 1000 to be received 30 six month period from now. 

769.42 = Rs 35

1-

1

1000 30

(1+y) y

+

1 30

(1+y)

 Trial and error method Annual Interest rate

PV of 30 payments of Rs 35

PV of Rs 1000 30 periods 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

Would you prefer to buy a 10-year, 10% annual coupon bond or a 10-year, 10% semiannual coupon bond, all else equal? The semiannual bond’s effective rate is: m

2

 iNom   0.10 EFF% =  1 +  − 1 = 1+  − 1 = 10.25% m 2    10.25% > 10% (the annual bond’s effective rate), so you would prefer the semiannual bond.

Calculating Yield for Callable and Puttable Bonds  A callable bond's valuations must account for the

issuer's ability to call the bond on the call date  The puttable bond's valuation must include the buyer's ability to sell the bond at the pre-specified put date.  The yield for callable bonds is referred to as yield-to-call, and the yield for puttable bonds is referred to as yield-to-put.

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

investors would receive if they held the bond until the call date. The period until the first call is referred to as the call protection period.  Yield to call is the rate that would make the bond's present value equal to the full price of the bond. Essentially, its calculation requires two simple modifications to the yield-to-maturity formula:

YTC  When the bond may be called and at what

price are specified at the time the bond is issued.  The price at which bond may be called is referred to as the call price.

Example  Consider an 18 years 11% coupon bond

payable semi annually with a maturity value of Rs 1000 selling at Rs 1169. suppose that the first call date is 8 years from now and that the call price is Rs 1055.  Call price = 1055  N = 8*2 = 16 m  C = 1000*11%/2 = 55  Bond price = 1169

Solution 1169 = Rs 55

1-

1

1055 16

(1+y)

+

y

 8.54% is the yield to first call

1 16

(1+y)

Yield to Put (YTP)  This mean that the bond holder can force the issuer  

 

to buy the issue at a specified price. Yield to put (YTP) is the interest rate that investors would receive if they held the bond until its put date. To calculate yield to put, the same modified equation for yield to call is used except the bond put price replaces the bond call value and the time until put date replaces the time until call date. M = put price n = number of periods until assumed put date.

Example of YTP  Consider an 18 years 11% coupon bond

payable semi annually issue selling Rs 1169. assume that issue is putable at par (Rs 1000) in five years.  Put price = 1000  N = 5*2 = 10 m  C = 1000*11%/2 = 55

Solution 1169 = Rs 55

1-

1

1000 10

(1+y)

+

y

 6.94% ≈ 7% is the yield to put

1 10

(1+y)