Introduction Bonds refer to debt instruments bearing interest on maturity. In simple terms, organizations may borrow funds by issuing debt securities named bonds, having a fixed maturity period (more than one year) and pay a specified rate of interest (coupon rate) on the principal amount to the holders. Bonds have a maturity period of more than one year which differentiates it from other debt securities like commercial papers, treasury bills and other money market instruments. Thus a bond is like a loan: the issuer is the borrower (debtor), the holder is the lender (creditor), and the coupon is the interest. Bonds provide the borrower with external funds to finance long-term investments, or, in the case of government bonds, to finance current expenditure . Bonds and stocks are both, securities but the major difference between the two is that (capital) stockholders have an equity stake in the company (i.e., they are owners), whereas bondholders have a creditor stake in the company (i.e., they are lenders). Another difference is that bonds usually have a defined term, or maturity, after which the bond is redeemed, whereas stocks may be outstanding indefinitely. An exception is a consol bond, which is a perpetuity (i.e., bond with no maturity).
Features of Bonds
The most important features of a bond are:
Nominal, Principal or Face Amount—The amount over which the issuer pays interest, and which has to be repaid at the end.
Issue price—The price at which investors buy the bonds when they are first issued. The net proceeds that the issuer receives are calculated as the issue price, less issuance fees, times the nominal amount.
Maturity date—The date on which the issuer has to repay the nominal amount. As long as all payments have been made, the issuer has no more obligations to the bond holders after the maturity date. The length of time until the maturity date is often referred to as the term or maturity of a bond.
Coupon—The interest rate that the issuer pays to the bond holders. Usually this rate is fixed throughout the life of the bond. The name coupon originates from the fact that in the past, physical bonds were issued which had coupons attached to them. On coupon dates the bond holder would give the coupon to a bank in exchange for the interest payment.
Coupon dates—The dates on which the issuer pays the coupon to the bond holders. It can be paid quarterly, semi-annually or annually.
TYPES OF BONDS Municipal Bonds: Municipal bonds are debt obligations issued by states, cities, countries and other governmental entities, which use the money to build schools, highways, hospitals, sewer systems, and many other projects for the public good. When you purchase a municipal bond, you are lending money to a state or local government entity, which in turn promises to pay you a specified amount of interest (usually paid semiannually) and return the principal to you on a specific maturity date. Not all municipal bonds offer income exempt from both federal and state taxes. There is an entirely separate market of municipal issues that are taxable at the federal level, but still offer a state—and often local—tax exemption on interest paid to residents of the state of issuance. Most of this municipal bond information refers to munis which are free of federal taxes.
Government Bonds : Government Bonds are securities issued by the Government for raising a public loan or as notified in the official Gazette. They consist of Government Promissory Notes, Bearer Bonds, Stocks or Bonds held in Bond Ledger Account. They may be in the form of Treasury Bills or Dated Government Securities.
Government Securities are mostly interest bearing dated securities issued by RBI on behalf of the Government of India. GOI uses these funds to meet its expenditure commitments. These securities are generally fixed maturity and fixed coupon securities carrying semi-annual coupon. Since the date of maturity is specified in the securities, these are known as dated Government Securities, e.g. 8.24% GOI 2018 is a Central Government Security maturing in 2018, which carries a coupon of 8.24% payable half yearly. Features of Government Securities
Issued at face value
No default risk as the securities carry sovereign guarantee.
Ample liquidity as the investor can sell the security in the secondary market
Interest payment on a half yearly basis on face value
No tax deducted at source
Can be held in D-mat form.
Rate of interest and tenor of the security is fixed at the time of issuance and is not subject to change.
Redeemed at face value on maturity
Maturity ranges from of 2-30 years.
Securities qualify as SLR investments (unless otherwise stated).
Mortgage and Asset Backed Bonds: Mortgage-backed securities (MBS) and asset-backed securities (ABS) represent the largest segment of the global bond market today. In simple terms, investing in MBS means lending your money to hundreds of individual mortgage borrowers across the country. In return for a higher yield than Treasury notes, investors are subject to added "prepayment" risk, meaning money invested may be repaid much sooner than maturity. Agency MBS Mortgage bonds which are guaranteed by a government agency or government-sponsored enterprise. Non Agency MBS Mortgage bonds which are issued by banks and financial companies not associated with a government agency. These securities have no credit guarantee other than the quality of the loans behind them, and any other structural credit protection provided by the terms of the bond deal they belong to. Asset Backed Securities Bonds that represent an investment in a pool of consumer or commercial loans. For example, auto loans or credit card loans are commonly pooled to make asset backed securities. For unknown historical reasons, bonds backed by high quality mortgage loans are considered Mortgage Backed Securities (MBS) despite the fact that technically they fall into the broader definition of Asset Backed Securities (ABS). Bonds backed by home equity loans and other home loans less than high quality are considered Asset Backed Securities.
Corporate Bonds Corporate bonds are debt obligations issued by private and public corporations. They are typically issued in multiples of 1,000 and/or 5,000. Companies use the funds they raise from selling bonds for a variety of purposes, from building facilities to purchasing equipment to expanding their business. When you buy a bond, you are lending money to the corporation that issued it. The corporation promises to return your money (also called principal) on a specified maturity date. Until that time, it also pays you a stated rate of interest, usually semiannually. The interest payments you receive from corporate bonds are taxable. Unlike stocks, bonds do not give you an ownership interest in the issuing corporation.
Zero Coupon Bonds Zero coupon bonds are bonds that do not pay interest during the life of the bonds. Instead, investors buy zero coupon bonds at a deep discount from their face value, which is the amount a bond will be worth when it "matures" or comes due. When a zero coupon bond matures, the investor will receive one lump sum equal to the initial investment plus the imputed interest, which is discussed below. The maturity dates on zero coupon bonds are usually long-term. These long-term maturity dates allow an investor to plan for a long-range goal, such as paying for a child’s college education. With the deep discount, an investor can put up a small amount of money that can grow over many years. The price of a zero-coupon bond can be calculated by using the following formula:
How is the Zero Coupon Bond Effective Yield Formula Derived? The formula for calculating the effective yield on a discount bond, or zero coupon bond, can be found by rearranging the present value of a zero coupon bond formula: This formula can be written as This formula will then become By subtracting 1 from the both sides, the result would be the formula where: F = Face value r = investor's required annual yield / 2 t = number of years until maturity x 2
Risks of Investing in Bonds Interest rate risk When interest rates rise, bond prices fall; conversely, when rates decline, bond prices rise. The longer the time to a bond’s maturity, the greater its interest rate risk. Reinvestment risk When interest rates are declining, investors have to reinvest their interest income and any return of principal, whether scheduled or unscheduled, at lower prevailing rates. Inflation risk Inflation causes tomorrow’s rupee to be worth less than today’s; in other words, it reduces the purchasing power of a bond investor’s future interest payments and principal, collectively known as “cash flows.” Inflation also leads to higher interest rates, which in turn leads to lower bond prices. Market risk The risk that the bond market as a whole would decline, bringing the value of individual securities down with it regardless of their fundamental characteristics. Default risk The possibility that a bond issuer will be unable to make interest or principal payments when they are due. If these payments are not made according to the agreements in the bond documentation, the issuer can default
Call risk Some corporate, municipal and agency bonds have a “call provision” entitling their issuers to redeem them at a specified price on a date prior to maturity. Declining interest rates may accelerate the redemption of a callable bond, causing an investor’s principal to be returned sooner than expected. In that scenario, investors have to reinvest the principal at the lower interest rates. If the bond is called at or close to par value, as is usually the case, investors who paid a premium for their bond also risk a loss of principal. In reality, prices of callable bonds are unlikely to move much above the call price if lower interest rates make the bond likely to be called. Liquidity risk The risk that investors may have difficulty finding a buyer when they want to sell and may be forced to sell at a significant discount to market value. they are due and therefore default. Event risk The risk that a bond’s issuer undertakes a leveraged buyout, debt restructuring, merger or recapitalization that increases its debt load, causing its bonds’ values to fall, or interferes with its ability to make timely payments of interest and principal. Event risk can also occur due to natural or industrial accidents or regulatory change. (This risk applies more to corporate bonds than municipal bonds.)
Credit Rating Agencies rate the debt instruments of companies. They do not rate the companies, but their individual debt securities. Rating is an opinion regarding the timely repayment of principal and interest thereon; It is expressed by assigning symbols, which have definite meaning. A rating reflects default risk. Ratings are not a guarantee against loss. They are simply opinions based on analysis of the risk of default. They are helpful in making decisions based on particular preference of risk and return. A company, desirous of rating its debt instrument, needs to approach a credit rating agency and pay a fee for this service. The determinants of ratings The default-risk assessment and quality rating assigned to an issue are primarily determined by three factors - i) The issuer's ability to pay: Ratio analysis is used to analyse the present and future earning power of the issuing corporation and to get insight into the strengths and weaknesses of the firm. ii) The strength of the security owner's claim on the issue: To assess the strength of security owner's claim, the protective provisions in the indenture (legal instrument specifying bond owners' rights), designed to ensure the safety of bondholder's investment, are considered in detail. iii) The economic significance of the industry and market place of the issuer: The factors considered in regard to the economic significance and size of issuer includes: nature of industry in which issuer is, operating (specifically issues like position in the economy, life cycle of the industry, labour situation, supply factors, volatility etc.), and the competition faced by the issuer (market share, technological leadership, production efficiency, financial structure, etc.)
RATING METHODOLOGY Key areas considered in a rating include the following: i) Business Risk : To ascertain business risk, the rating agency considers Industry's characteristics, performance and outlook, operating position (capacity, market share, distribution system, marketing network, etc.), technological aspects, business cycles, size and capital intensity. ii) Financial Risk : To assess financial risk, the rating agency takes into account various aspects of its Financial Management (e.g. capital structure, liquidity position, financial flexibility and cash flow adequacy, profitability, leverage, interest coverage), projections with particular emphasis on the components of cash flow and claims thereon, accounting policies and practices with particular reference to practices of providing depreciation, income recognition, inventory valuation, off-balance sheet claims and liabilities, amortization of intangible assets, foreign currency transactions, etc. iii) Management Evaluation : Management evaluation includes consideration of the background and history of the issuer, corporate strategy and philosophy, organizational structure, quality of management and management capabilities under stress, personnel policies etc. iv) Business Environmental Analysis : This includes regulatory environment, operating environment, national economic outlook, areas of special significance to the company, pending litigation, tax status, possibility of default risk under a variety of scenarios.
CREDIT RATING AGENCIES IN INDIA CRISIL : This was set-up by ICICI and UTI in 1988, and rates debt instruments. Nearly half of its ratings on the instruments are being used. CRISIL evaluation is carried out by professionally qualified persons and includes data collection, analysis and meeting with key personnel in the company to discuss strategies, plans and other issues that may effect ,evaluation of the company. The rating ,process ensures confidentiality. , Once the company decides to use rating, CRISIL is obligated to monitor the rating over the life of the debt instrument. Symbol (Rating category). Description (with regard to the likelihood of meeting the debt obligations on time) AAA Highest Safety AA High Safety A Adequate Safety BBB Moderate Safety BB Inadequate Safety B High Risk C Substantial Risk D Default
ICRA : ICRA was promoted by IFCI in 1991. The factors that ICRA takes into consideration for rating depend on the nature of borrowing entity. The inherent protective factors, marketing strategies, competitive edge, competence and effectiveness of management, human resource development policies and practices, hedging of risks, trends in cash flows and potential liquidity, financial flexibility, asset quality and past record of servicing of debt as well as government policies affecting the industry are examined. Symbol (Rating category). Description (with regard to the likelihood of meeting the debt obligations on time) LAAA highest-credit-quality & lowest credit risk. LAA high-credit-quality & low credit risk. LA adequate-credit-quality & average credit risk. LBBB moderate-credit-quality & higher than average credit risk. LBB inadequate-credit-quality & high credit risk. LB risk-prone-credit-quality & very high credit risk. LC poor-credit-quality & limited prospect of recovery. LD lowest-credit-quality & low prospect of recovery.
CARE : CARE is a credit rating and information services company promoted by IDBI jointly with investment institutions, banks and finance companies. The company commenced its operations in October 1993.In January 1994, CARE commenced publication of CAREVIEW, a quarterly journal of CARE ratings. In addition to the rationale of all accepted ratings, CAREVIEW often carries special features of interest to issuers of debt instruments, investors and other market players. Symbol (Rating category). Description (with regard to the likelihood of meeting the debt obligations on time) CARE AAA highest-credit-quality & lowest credit risk. CARE AA high-credit-quality & low credit risk. CARE A adequate-credit-quality & average credit risk. CARE BBB moderate-credit-quality & moderate credit risk. CARE BB moderate credit risk. CARE B high credit risk. CARE C Very high credit risk. CARE D Default or expected to be default.
Internationally acclaimed credit rating agencies such as Moody's , Standard and Poor's , Duff and Fitch have been offering rating services to bond issuers over a very long time. The bond issuers pay the rating agency to evaluate the quality of the bond issue in order to increase the information flow to investors and hopefully increase the demand for their bonds. The rating agency determines the appropriate bond rating by assessing various factors. Rating Category of Credit Agency Firms Moody's Explanation Aaa Best quality Aa High quality A Higher-medium grade Baa Medium grade Ba Possess speculative elements B Generally lack characteristics of desirable investment Caa Poor standing; may be in default Ca Speculative in a high degree; often in default C Lowest grade
Standard & Poor's Explanation AAA Highest grade AA High grade A Upper medium grade BBB Medium grade BB Lower medium grade B Speculative CCC-CC Outright speculation C Reserved for income bonds DDD-DD In default, with rating indicating relative salvage value
Value of a bond
The value of a debt security today is the present value of the promised future cash flows- the interest and the maturity value. Therefore, the present value of a debt is the sum of the present value of the interest payments and the present value of the maturity value.
B 0 = I 1 / (1 + k d ) 1 + I 2 / (1 + k d ) 2 + I 3 / ( 1+ k d ) 3 +………….. I 1+ B n / (1 + k d ) n
B 0 =Present value of security
B n =Maturity value of security
I = Interest payment
k d =Yield
Relation between the coupan rate, Price of the bond and the yield
If coupan rate > Yield, the security is worth more than its face value—It sells at premium
If coupan rate < Yield, the security is worth less than its face value—It sells at discount
If coupan rate = Yield, the security is valued at face value.
The yield of a bond is, the return on bond.The yield is expressed as an annual percentage of the face value. However, yield is a little more complicated than the coupan rate. There are several different measures of yield:
Nominal yield: It is equal to coupon rate; that is the return on the bond without accounting for any outside factors. If you purchase a bond at par value and hold to maturity, this will be the annual return you receive on the bond.
Current yeild: It is a measure of the return on the bond in relation to the current price.
Yield to call: The rate of return that an investor would earn if he bought a callable bond at its current market and held it until the call date given that th bond was called on the call date.
Yield to Maturity
Yield To Maturity The rate of return that an investor would earn if he bought the bond at its current market price and held it until maturity, is called as YTM Alternatively,it represents the discount rate which equates the discounted value of a bonds’s future cash flows to its current market price. YTM is the overall return on the bond if it is held to maturity. It reflects all the interest payment that are available through maturity and the principal that will be repaid,and assumes that all coupan payments will be reinvested at the current yield on the bond. This is the most valuable measure of yield because it reflects the total income that you can receive. YTM= [I+ (M-P)/N] / [ (M+P)/2] Where, I=Annual Interest Payment M=Maturity Value P=Purchase price or current price of bond N= Maturity period
Duration Of Bond The term duration is a measurement of how long in years it takes for the price of a bond to be repaid by its internal cash flows. Since a zero coupon bond doesn’t pay any intermediate cash flows and the entire money is available only on maturity, duration of a zero coupon bond is equal to maturity period. On the same lines since coupon bonds, pays coupons, we get our price much earlier to maturity period. Therefore, duration of a coupon bond will always be less than maturity period. Macaulay Duration The formula usually used to calculate a bond's basic duration is the Macaulay duration, which was created by Frederick Macaulay in 1938, although it was not commonly used until the 1970s. Macaulay duration is calculated by adding the results of multiplying the present value of each cash flow by the time it is received and dividing by the total price of the security. The formula for Macaulay duration is as follows: n = number of cash flows i = required yield M = maturity (par) value t = time to maturity C = cash flow P = bond purchase price
Steps for calculation:
Determine the bond cash flows till maturity.
Determine the PV factor using YTM.
Multiply the PV Factor into cash flows to find present value of cash flows.
Add the PV of all cash flows to determine the market value of the bond.
Divide each year’s cash flows by the market value of bond.
Multiply this factor by the corresponding years i.e. 1 figure by 1, year 2 figure by 2 etc.
The sum of all final values is the duration.
Modified Duration Modified duration is a modification of the Macaulay duration to estimate interest rate risk, calculating the change in a bond’s price to a change in its yield to maturity. This is the approximation of the percentage change in the price of the bond to the percentage change in yield. For bonds without any embedded features, bond price and interest rate move in opposite directions, so there is an inverse relationship between modified duration and an approximate 1% change in yield . Because the modified duration formula shows how a bond's duration changes in relation to interest rate movements, the formula is appropriate for investors wishing to measure the volatility of a particular bond. Modified duration is calculated by the following formula: OR
Duration Application: Calculating bond value change Duration measures interest rate risk , i.e., changes in present value of securities when interest rates change. Knowing duration we can calculate the price sensitivity as follows: Percent change in bond value = DM * change in yield Where, DM=Modified duration If yield rates rose from 10% to 10.5%, a 0.5% increase in rates, Macaulay’s formula would predict a percent change in value as: Percent change in bond value = DM * numerical change in stated yield. 4 = – 2.6439 * (+ 0.5) = – 1.3220% The price change calculated by MDuration would be $898.49 * –1.322% = –$11.88 The new bond price would be approximately $898.49 – $11.88 = $886.61. We can confirm the percent change and new price by entering these data into a spreadsheet: The change takes place in the PV Factor as a result of the change in market yield.
Bond Convexity: Convexity measures the rate of change in modified duration as yield change. Convexity refers to the shape of the price-yield relationship and can be used to refine the modified duration approximation of the sensitivity of prices to interest rate changes. Bond Convexity is defined formally as the degree to which the duration changes when the yield to maturity changes . It can be used to account for the inaccuracies of the Modified Duration approximation. On top of that, if we assume two bonds will provide the same duration and yield then the bond with the greater convexity will be less affected by interest rate change.
Application of Convexity The convexity improves the duration approximation for bond price changes. In other words, knowing convexity, we can find a better approximations of bond price change for every change in yield, than what we can find using duration. It is a measure of the relationship between bond prices and bond yields that demonstrates how the duration of a bond changes as the interest rate changes. Convexity is used as a risk-management tool, and helps to measure and manage the amount of market risk to which a portfolio of bonds is exposed. The formula is:
1. A bond of Rs. 1000 bearing a coupon rate of 12% is redeemable at par in 10 year. Find out the value of the bond if:
Required rate of return is 12%
Required rate of return is 14% and the maturity period is 8 yrs
Required rate of return is 12% and redeemable at Rs.1050 after 10 years.
2. A bond of Rs.1000 bearing a coupon rate of 12% p.a. payable half-yearly is redeemable after 4 years at par. Find out the value of the bond given that required rate of return is 14%.
3. A bond of Rs.10000 bearing coupon rate 12% and redeemable in 8 yrs at par is being traded at Rs. 10600. Find out YTM of the bond.
4. Bond A has face value of Rs.100, Coupon rate 15%p.a., maturity period 6 years, maturity value Rs.100 and current market price 89.5 and YTM is 18%.Calculate duration of bonds.
5. A 5 year bond with 8% coupon rate and maturity value of Rs.1000 is currently selling at Rs.925. Find YTM.
6. The following data is available for a XYZ Bond, face value Rs.1000, Coupon rate 16%p.a., life of bond 6 yrs, maturity value Rs.1000,current market price 964.5.
You are required to calculate:
YTM 2)Duration of bond 3)Volatility of bond
7.Two bonds A & B have a par value of Rs.10000 and YTM of 9%.Both mature after 4 years. A pays annual coupon of 10% and B pays annual coupon of7.5%. Calculate duration of both bonds A & B.
8. The following data is available for a bond:
Calculate YTM, Duration & volatility of this bond.
9. A bond can be acquired with a 4 year maturity. The bond has a coupon of 12% payable annually and is priced in the market at Rs.100. What is the duration of the bond? What would be the percentage change in price if interest rates rose to 13%.
Face Value Rs.1ooo Coupon 16%p.a. Years to maturity 6 Years Redemption Value Rs.1000 Current market price Rs. 950
10. Bonds A & B carry coupon rates of 4% & 12% respectively. Both bonds have 10 years to maturity and pays interest annually. If the discount rate (YTM) on both bonds rises from 8% to 10%, Calculate the expected % change in the bonds prices. 11. The following data are available for a bond: What is the current market price, duration and volatility of this bond? Calculate the expected market price, if we witness an increase in required yield by 75 basis points. Face Value Rs. 1000 Coupon Rate 16% Maturity Period 6 Yrs Redemption Value Rs.1000 YTM 17%
12. Calculate convexity given the following with respect to a coupon bond.
Coupon rate= 6%, Term= 5 years, yield to maturity= 7 %(3.5% semi annually) and Price=Rs. 958.42
13. Determine the convexity of an 8% coupon bond with two years to maturity an a zero coupon bond with 20 years to maturity. The yield-to-maturity on these bond is 10% p.a. Find out the price change of the zero coupon bond,and 8% coupon bond, if the yield changes to 11% using:
Using duration formula
Actual bond price formula
14. Calculate the price of a zero-coupon bond that is maturing in five years, has a par value of Rs.1,000 and a required yield of 6%.
15. Calculate the yield of a zero-coupon bond that is maturing in ten years, has a par value of Rs.1,000 and purchase price is Rs. 540.