chapter-4.pdf

CHAPTER 4: INVESTING IN FIXED INCOME SECURITIES LEARNING OBJECTIVES: After reading this chapter, the reader should understand about: x Basic characteristics of fixed income securities x Components of fixed income securities x Relationship between bond price and yield...

CHAPTER 4: INVESTING IN FIXED INCOME SECURITIES LEARNING OBJECTIVES: After reading this chapter, the reader should understand about: x Basic characteristics of fixed income securities x Components of fixed income securities x Relationship between bond price and yield x Alternative yield measure like YTM, Coupon Yield, Current yield x Interest rate risk x Duration of the bond 4.1 Overview of Fixed Income Securities Investors find it less exciting to talk about bonds or fixed income securities (bonds). A typical investor has more focus on equities when it comes to investment discussions. It is an irony because the global total market value of bonds is larger than the total market value of equity. As of 2020, global equity market capitalization was USD 105.8 trillion and global bond market outstanding was US$ 123.5 trillion.12 Generally, Government is the single largest issuer of bonds. Not only the size but also in terms of number of issues, bonds overtake equities as unlike equity, companies can issue many different bond issues outstanding at the same time. Governments issue bonds of many kinds and varied maturity profile. In India, the fixed income market is classified on the basis of the entities issuing fixed income securities. Fixed income securities are issued by legal entities such as the Central and State Governments, Public Bodies, Banks and Institutions, statutory corporations and other corporate bodies13. The fixed income instruments traded can be classified into the following segments on the basis of the issuer of these securities (Table 4.1): Table 4.1: Types of Fixed Income Instruments Market Segment Issuer Government Securities Central Government State Governments Public Sector Bonds Government Agencies / Statutory Bodies Public Sector Undertakings 12 https://www.sifma.org/wp-content/uploads/2021/07/CM-Fact-Book-2021-SIFMA.pdf 13 In India, the long-term debt securities issued by the Government of India or any of the State Government’s or undertakings owned by them or by development financial institutions are called as bonds. Instruments issued by other entities are called debentures. 72 Private Sector Bonds Corporates Banks Financial Institutions Government securities or G-Secs, constitute the largest segment of the Indian fixed income market. The next largest section of the rupee-denominated debt market is the corporate bond market. This segment has grown substantially in recent years. The Indian primary market in corporate debt is basically a private placement market with most of the corporate bond issues being privately placed among the wholesale investors i.e. the banks, financial institutions, mutual funds, large corporate & other large investors. This situation has restricted the retail participation in the bond market. The share of retail investors in corporate bond market is very small.14 The issue and trading of fixed income securities by each of these entities are regulated by different bodies in India. Government securities and securities issued by banks, non-banking finance companies (NBFCs) are regulated by the RBI. The issue of non-government securities comprising basically issues of corporate debt is regulated by SEBI. 4.2 Bond Characteristics Since bonds create fixed financial obligations on the issuers, they are referred as fixed income securities. The issuer of a bond agrees to 1) pay a fixed amount (known as coupon) periodically and 2) repay the fixed amount of principal (known as face value) at the date of maturity. The fixed obligations of the security are the most defining characteristic of bond. Mostly bonds make semi-annual coupon payments, though some may make annual, quarterly or monthly coupon payments. The coupon payment is always calculated as a fixed promised percentage applied on the face value of the bond. There are however zero coupon bonds which do not make any coupon payments. Typically, a zero coupon bond is issued for less than its face value and the face value is paid on the maturity date. Bonds have fixed maturity date beyond which they cease to exist as a legal financial instrument. Perpetual bonds, which do not have any maturity date exist forever. On the basis of term to maturity, bonds with a year or less than a year maturity are termed as money market securities. Long-term obligations with maturities in excess of 1 year, are referred as capital market securities. Thus, long term bonds as they move towards maturity become money market securities. The issue price, coupon, maturity period, face value, redemption value are important intrinsic features of a bond. The issue price would define the amount guaranteed capital gain a bond holder would enjoy if the bond is held till maturity. The coupon of a bond indicates the regular 14https://content.ftserussell.com/sites/default/files/research/ftse-sbi-indian-bond-index-series-jan-2019-final.pdf 73 income/coupon income that the bond holder will receive over the life (or holding period) of the bond. The term to maturity is the time period before a bond matures. All G-Secs are normally coupon bearing and have semi-annual coupon or interest payments with a tenor of between 5 to 30 years. Maturity period is also known as tenor or tenure. Though not found in common, sometimes corporate bonds might promise some premium on redemption, hence making the redemption value different than the face value (or par value) The face value or par value of the bond is the original value of the obligation. It is similar to the principal on a loan. Face value of the bond is different from bond’s market price. This situation can arise when the interest rates prevailing in the market are different than the coupon rate promised on the bond. When coupons and the prevailing market rate of interest are not the same, market price of the bond can be lower or higher than principal value. If the market interest rate is above the coupon rate, the bond will sell at a discount to the par value. If the market rate is below the bond’s coupon, the bond will sell at a premium to the par value. This behaviour is mathematically quite intuitive. Let’s consider the example below. Let’s imagine that a bond with a face value of Rs.1000 has been issued for a period of 1 year, with a coupon rate of 12% p.a. and the coupon being paid on maturity. At the end of end of 1 year , i.e. on maturity the bond would repay the face value of Rs.1000. Therefore for any one who is interested to invest in this bond would have Rs. 1000 of outflow today and Rs. 1120 (Coupon of Rs.120 and Face Value of Rs. 1000) of inflow at the end of 1 year. Then the return in percentage to any investor who has invested in this bond would be (1120 – 1000) / 1000 = 12%. Because the investment was held for a period of 1 year, then the return is annual return. Going by the basic tenets of time value of money and compounding an investor who is ready to invest Rs.1000 today and seeks a return of 12% would expected Rs.1120 at the end of 1 year, and hence this bond would exactly match his investment preference. Depicting it mathematically: 1000 * ( 1.12) ^ 1 = 1120; where “(1.12)^1” is the future value interest factor, and this is compounding today’s cashflow to future date. OTHER WISE it could also be depicted in a discounting format. This approach would help someone to calculate what is the maturity value of an investment which is promising some interest rate. 1120 / (1.12)^1 = 1000; where “1/(1.12)^1” is the present value interest factor, and it is discounting a future cashflow to today. This approach would help someone to calculate what is the amount that needs to 74 be invested, in case an investment avenue is promising a definitive cashflow at the end of 1 year. That means an investor seeking 12% return should invest not more than Rs.1000 in this bond which is promising Rs.1120 at the end of 1 year. Then what should be the maximum amount an investor who seeks 15% p.a. return pay for the same bond? It would be Rs.1120 / (1.15)^1 = 973.91. Because only this amount would generate him a return of 15% p.a. In the same manner, an investor who wants only 8% would be ready to pay upto Rs.1120 /(1.08)^1 = 1037.40. An investor is paying either less or more than the face value not because the bonds are different. In fact, the bond characteristics in terms of face value, coupon rate, date of coupon payment, and the date of maturity are all fixed. Therefore the only thing which was making the difference was the expected rate of return. While the above example was that of an individual investor and the expected rate of return was clear in the investor’s mind. What if many investors are participating in a market and bidding for this bond. Logically one consensus interest would naturally emerge when the bond is finally bought or sold. But the issue is that this interest rate is not visible directly. Hence the fixed income markets reverse calculates this hidden or implied expected rate of return in a fixed income security, from its traded prices. This is referred to as “yield”. It should be clear that Yield on a bond is a consensus interest rate that emerged due to the demand and supply forces of the investors in the market, and their required rate of return was definitely influenced by the ongoing government benchmark interest rates. This inverse relationship between interest rates and bond prices as explained above is underlying the bond theorems, that “with all other things remaining the same, an increase in the market interest rates would decrease the prices of fixed income securities”. Another interesting thing about bonds is that unlike equity shares, government or companies can have many different bonds outstanding at the same time, but each of them could have a different maturity period and a coupon rates. These features of the bonds will be part of the indenture.15 Logically every new issue of a bond by a company would always provide coupon rates according to the then prevailing interest rates in the market rates. 4.2.1 Bonds with options Bonds can also be issued with embedded options.16 Some common types of bonds with embedded options are: bonds with call option, bonds with put option and convertible bonds. 15 Indenture is the legal agreement between two parties, in case of bond indenture the two parties are the bond issuer (borrower) and the investors (lender). 16 Options are financial derivatives that give buyers the right, but not the obligation, to buy or sell an underlying asset at an agreed-upon price at a future date, where the price is agreed upon today. 75 A callable bond gives the issuer the right to redeem all or part of the outstanding bonds before the specified maturity date. Callable bonds are advantageous to the issuer of the security but they present investors with a higher level of reinvestment risk than non-callable bonds. The issuer will call the bond before its maturity only when the interest rates for similar bonds fall in market. The investor will receive the face value of the bond before its maturity, and will be forced to reinvest that money for the remaining period lower interest rates. This is called reinvestment risk. A put provision gives the bondholders the right to sell the bond back to the issuer at a pre- determined price on specified dates. Puttable bonds are beneficial to the bondholder by guaranteeing a pre-specified selling price at the redemption dates. A convertible bond is a combination of a plain vanilla bond plus an embedded equity call option. It gives the bondholder the right to exchange the bond for a specified number of common shares of the issuing company. 4.3 Determinants of bond safety Bonds being fixed income securities, are expected to generate a pre-specified stream of cashflows in terms of coupon and principal payment. The previous discussion on return while investing in a bond and the price of a bond, are all dependent on a fundamental assumption, that the bonds are literally default risk free. Meaning the coupon and principal repayment would be as much as promised, and will occur at the same time which is promised. Therefore safety aspects of bonds are tied to their probability of defaulting on these payments or possibility of delaying in the payments. This probability and possibility is the underlying phenomenon of credit risk to which bond holders are exposed. Credit Risk is, the risk of loss resulting when the issuer fails to make full and timely payments of interest and/or repayments of principal. The most important document to understand the safety aspects of the bond is its indenture. It is the legal agreement between the firm issuing the bond and the bondholders, providing the specific terms of the debt agreement. All the features of the bond i.e. its par value, coupon rate, maturity period, periodicity of coupon payments, collateral for the bond, seniority of the payments will be set forth in the indenture. Indenture also provides information on covenants. Covenants are clauses specifying the rights of the bond holders and restrictions on the bond issuers. Covenants are broadly of two kinds: Positive covenants and Negative covenants. Positive covenants are actions which issuers are required to do, whereas negative covenants specify what issuers are prohibited from doing. These are necessary to protect an investor’s investment in the debt security. 76 Companies issue different kinds of bonds. Some may be secured against some specified property of the issuer in the case of default. The value of the asset against which the bond is secured determines the quality of the bond. Some bonds are unsecured. These are backed by the promise of the issuer to pay coupon and principal on a timely basis. In such a situation, the credit worthiness of the issuer determines bond quality. To understand the probability of default by the issuer, most bond investors rely on Rating Agencies. Rating agencies play an integral role in bond markets. These agencies are specialized firms that determine the ability and willingness of the issuers to meet their financial obligations on time and as promised. The actual level of default risk faced on an investment depends on the financial situation of the borrower. Default risk can be assessed by tracking the credit rating of an investment. Credit rating agencies assign credit ratings after carrying out a detailed analysis of the issuer’s financial ability to honour the payments on time. These ratings are in the form of alphanumeric symbols. Rating is given for an instrument and not to a firm; so two different instruments issued by the same firm can have different ratings. The higher the credit rating, the lower is the default risk. SEBI has standardized the rating symbols used by the credit rating agencies so that investors are able to easily gauge the level of credit risk assigned to an instrument. The rating symbols and their definitions are reproduced below in Box 4.1 and Box 4.2. Rating agencies have their own methodology to gauge the creditworthiness of the issuer and also the probability that the particular instrument will not default. They use symbols to express their opinion. Typically, ratings are expressed as grades from ‘AAA’ to ‘D’ to communicate the relative level of credit risk. (See Box 4.1) Bonds with higher credit risk receive a lower credit rating from the bond rating firms and vice versa. Bond markets are also classified on the basis of creditworthiness reflected in the credit rating as investment grade and non-investment grade (speculative) bond market. 77 Box 4.1: Credit rating symbols and Definitions for Long Term Instruments Long term debt instruments: The instruments with original maturity exceeding one year Rating symbols should have CRA’s first name as prefix AAA - Instruments with this rating are considered to have the highest degree of safety regarding timely servicing of financial obligations. Such instruments carry lowest credit risk. AA - Instruments with this rating are considered to have high degree of safety regarding timely servicing of financial obligations. Such instruments carry very low credit risk. A - Instruments with this rating are considered to have adequate degree of safety regarding timely servicing of financial obligations. Such instruments carry low credit risk. BBB - Instruments with this rating are considered to have moderate degree of safety regarding timely servicing of financial obligations. Such instruments carry moderate credit risk. BB - Instruments with this rating are considered to have moderate risk of default regarding timely servicing of financial obligations. B - Instruments with this rating are considered to have high risk of default regarding timely servicing of financial obligations. C - Instruments with this rating are considered to have very high risk of default regarding timely servicing of financial obligations. D - Instruments with this rating are in default or are expected to be in default soon. Modifiers {"+" (plus) / "-"(minus)} can be used with the rating symbols for the categories AA to C. The modifiers reflect the comparative standing within the category. 78  Box 4.2: Credit Rating Symbols and Definitions for Short Term Debt instruments Short term debt instruments: The instruments with original maturity of upto one year Rating symbols should have CRA’s first name as prefix A1 – Instruments with this rating are considered to have very strong degree of safety regarding timely payment of financial obligations. Such instruments carry lowest credit risk. A2 - Instruments with this rating are considered to have strong degree of safety regarding timely payment of financial obligations. Such instruments carry low credit risk. A3 - Instruments with this rating are considered to have moderate degree of safety regarding timely payment of financial obligations. Such instruments carry higher credit risk as compared to instruments rated in the two higher categories. A4- Instruments with this rating are considered to have minimal degree of safety regarding timely payment of financial obligations. Such instruments carry very high credit risk and are susceptible to default. D - Instruments with this rating are in default or expected to be in default on maturity. Modifier {"+" (plus)} can be used with the rating symbols for the categories A1 to A4. The modifier reflects the comparative standing within the category. 4.4 Valuation of Bonds Since bonds are fixed income securities, generating a series of pre-specified cashflows, their value can be estimated adopting the discounting cashflow approach. The discounting cashflows approach uses the required rate of return of the investor and discounts all the future cashflows received from a bond, to arrive at the intrinsic value of the bond, at a particular point in time. The motivation to arrive at the value of a bond is to compare its intrinsic value with the ongoing market price, just like how an equity share is compared, and then judge whether it is overvalued or undervalued. Therefore, investment decisions in the bonds can also be taken by estimating their intrinsic values. When the intrinsic value of a bond is greater than the ongoing current market price, one could invest in it. Or else, if the investor is already holding the bond, then the bond could be sold. Alternatively, the investment and disinvestment decisions can also be taken by comparing the implied yield by investing in the bond at the ongoing current market price. If the calculated yield is greater than the required yield or required rate of return of the investor, then the investor can buy the bond. Similarly, if the yield is lesser than what the investor requires, then the bond could be sold. The following sections would discuss these further. 79 4.4.1. Intrinsic Value of a Bond The intrinsic value of a bond is the sum of present value of all future cash flows of the bond discounted at a required rate of return. ௡‫כ‬௖௙ ‫ݐ݊݁݉ݕܽܲ݊݋݌ݑ݋ܥ‬௧ ‫݁ݑ݈ܸܽ݊݋݅ݐ݌ܴ݉݁݀݁ݎ݋݁ݑ݈ܸܽ݁ܿܽܨ‬ ‫ܸܫ‬଴ ൌ  ෍ ൅ ‫ݎ‬ ‫ݎ‬ ௧ୀଵ ሺͳ ൅ ൬ ൰ሻ௧ ሺͳ ൅ ൬ ൰ሻ௡‫כ‬௖௙ ݂ܿ ݂ܿ IVo = Intrinsic Value of a Bond Coupont = is the periodic cashflow paid by the bond as promised. It is not the annual payment, but the actual amount that is adjusted to the frequency of coupon payment. Face Value or Redemption Value = It is the Par value of the bond which is promised to be repaid on the date of maturity. In case the bond promises an amount different than the face value, then it would be termed as redemption value. r = discount rate which is either the investor’s required rate or a comparable bond’s yield to maturity calculated at its ongoing market prices. The discounting rate needs to be adjusted to the frequency of coupon payment, so that discounting is in tune with the principle. t = is the time period when the coupon is paid. It is represented in the form of a digit. n = the time period when the payment of last coupon and the face value takes place on the date of maturity. It is also represented in the form of a digit adjusted to the frequency of coupon payment. cf = frequency of coupon payment in the bond. In case the bond pays coupons half-yearly, then the value it takes is 2, quarterly 4, monthly 12 and so on. It may be noted that whenever a bond paying coupons more than once in a year is being evaluated, then both the discounting rate and the maturity period need to be adjusted accordingly. Where the time period is multiplied with the frequency of coupon payment, and the discounting rate is divided by the frequency of coupon payment. The above equation needs to be solved using a mathematical calculator and one should be conversant with the aggregation operator used in the equation. Otherwise, the readymade interest rate factors can be used to calculate the intrinsic value. The interest rate factors are available as readymade tables where the rows are the periods and the columns are the discounting rates. Because coupons are annuities and the face value that is repaid at maturity 80 is a lumpsum payment, the following representation can achieve the same objective as shown in the previous equation. IVo = Coupon Payment (PVIFA r/cf, n*cf) + Face Value or Redemption Value (PVIF r/cf, n*cf) Where, PVIFA r, n*cf = It is the present value interest rate factor for annuity for discounting rate ‘r’ and for n * cf coupon payments. PVIF r, n*cf = It is the present value interest rate factor for discounting rate ‘r’ and for n * cf time period. Say for instance an investor with an expected rate of 14% p.a. is calculating the intrinsic value of a bond with a face value of Rs.1000, that is offering a semi-annual coupon of 12% p.a., and which has a remaining term to maturity of 5 years. The bond would be worth Rs.1000 at maturity. The intrinsic value of the bond can be calculated using the equation and the present value interest factors as follows. ହ‫כ‬ଶ ͸Ͳ௧ ͳͲͲͲ ‫ܸܫ‬଴ ൌ  ෍ ௧ ൅ ሺͳ ൅ ͲǤͳͶȀʹሻ ሺͳ ൅ ͲǤͳͶȀʹሻହ‫כ‬ଶ ௧ୀଵ Solving this would yield the answer 929.72. This can also be calculated using the interest rate factors as follows: IVo = 60 ( PVIFA 14%/2, 5 * 2) + 1000 (PVIF14%/2, 5 * 2) That is = 60 * (7.0236 ) + 1000 * (0.5083) = 421.42 + 508.30 = 929.72 Therefore the intrinsic value of the bond with the above face value, maturity date, and coupon payment is Rs.929.72. It may be noted that the value is lesser than the face value. This is in tune with the inverse relationship between interest rates and price of the bond discussed in the earlier paragraphs. Because the bond is paying a coupon of only 12% p.a., but the investor requires 14% p.a., based on the ongoing market interest rates, or the investor’s personal risk appetite or perception, the bond is not worth the face value, but something lesser than that. The intrinsic value of a bond can be also calculated using the excel “PRICE” function in the MS Excel as illustrated in Illustration 4.1. The intrinsic value of the same bond that is used the example above is also used for the illustration. The table represents the sheet in excel and columns A and B can be related to that in the excel sheet. The letters in red in column A exactly represent the inputs (according to syntax) of the “PRICE” function in MS Excel, and the values in column B need to be given as inputs into MS Excel to get the answer. The black 81 letters in column A in parenthesis are explanations to understand what does the word in red colour mean. The column B in the last shows the syntax for the MS Excel function to be used to get the answer for the intrinsic value of a bond. There might be a point of confusion when the words “YIELD” and “PRICE” are used in the function. However the clarity is “YIELD” should be considered as the required rate of return of the investor and not “YIELD TO MATURITY” of the bond. Similarly “PRICE” is the final output one would get, which is the intrinsic value of the bond at the required rate of return and not the “ONGOING CURRENT MARKET PRICE” Illustration 4.1: Calculating Intrinsic Value of a Bond in excel A B Settlement (the date on which the valuation is being done) 01-01-2022 Maturity (the date of maturity reckoned from date of valuation) 01-01-2027 Rate (Coupon rate depicted on per annum basis) 12% Yield (Discount rate applied or required rate of return of the investor) 15% Redemption (The value proportionately expressed per Rs.100) 100 Frequency (It takes a number 1 for yearly, 2 for half-yearly, 4 for 2 quarterly, 12 for monthly) Basis (indicates the day count convention that is used [Day count 0 basis: 0 or omitted = US (NASD) 30/360; 1 = Actual/actual; 2 = Actual/360; 3 = Actual/365; 4 = European 30/360) PRICE (The intrinsic value of a bond, which would be the answer) the =PRICE(Settlement, result in column should be multiplied by 10, because the answer is Maturity, Rate, for a bond with face value of Rs.100, and the face value of the bond Yield, Redemption, in our illustration is Rs.1000. The values in column B would result into Frequency, Basis) an answer 929.76 (Please input the values in MS Excel and verify by doing it yourself) 4.4.2. Bond Yield Measures Bond holders receive return from one or more of the following sources, when they buy bond: 1. The coupon payments made by the issuer; 2. The capital gain (or capital loss) when the bond is sold/matured; and 3. Income from reinvestment of the interest payments that is interest-on-interest. There are yield measures commonly used to measure the return from investing in a bond are briefly described below: 82 Coupon Yield: The coupon yield is the coupon payment as a percentage of the face value. It can be considered as a nominal interest payment on a fixed interest bond. Coupon yield = (Coupon Payment / Face Value) * 100 Illustration: Coupon: Rs. 8.24; Face Value: Rs. 100; Market Value: Rs. 103.00; Coupon yield = 8.24/100 = 8.24% Current Yield: The current yield is the coupon payment as a percentage of the bond’s current market price. Current yield = (Annual coupon rate / current market price of the bond) *100% Illustration: The current yield for a 10 year 8.24% coupon paying bond selling for Rs. 103.00 with a face value of Rs. 100 is calculated as below: Annual coupon interest = 8.24% x Rs. 100 = ₹8.24 Current yield = (8.24/103) X 100 = 8.00% Yield to Maturity: Yield to Maturity (YTM) is that rate which discounts the future cash flows from a bond, and makes the sum of the present values of such cashflows equal to the current market price of the bond. It is the rate of return that can be expected in a bond investment, when purchased at the ongoing market price, and when it is held until its maturity. YTM can also be considered as the Implied Rate of Return, or Internal Rate of Return of the bond. Mathematically, when we substitute the IVo in the formula of intrinsic value of a bond with the current market price, and then solve it to extract the ‘r’, then that ‘r’ would be the YTM. ௡‫כ‬௖௙ ‫ݐ݊݁݉ݕܽܲ݊݋݌ݑ݋ܥ‬௧ ‫݁ݑ݈ܸܽ݊݋݅ݐ݌ܴ݉݁݀݁ݎ݋݁ݑ݈ܸܽ݁ܿܽܨ‬ ܲ଴ ൌ  ෍ ൅ ሺͳ ൅ ‫ݎ‬Ȁ݂ܿሻ௧ ሺͳ ൅ ‫ݎ‬Ȁ݂ܿሻ௡‫כ‬௖௙ ௧ୀଵ Po= Current Market Price of the of bond All other variables are same as explained in the previous sections. Again a word of caution, that if the frequency of coupon payment is more than once in an year, then accordingly the ‘r’ that is extracted needs to be annualised by multiplying with the frequency of coupon 83 payment. For instance if the solved ‘r’ is 5% for a semi-annual coupon paying bond, then YTM per annum basis would be 5% * 2 = 10%. The calculation of YTM involves a trial-and-error procedure. Therefore one has to try by using different values in the ‘r’ and try to equate it to the current market price using the calculator. Because very rarely does a rate without decimal match the true YTM, so extrapolation is required to arrive at the accurate YTM. Instead MS Excel has a function ‘YIELD’ which calculates the YTM of a bond, given all its details and the current market price, for a face value of Rs.100. Continuing the above example used to calculate the intrinsic value, and by considering the current market price of the bond to be Rs.975, the YTM would be calculated in MS Excel as shown in illustration 4.2. Illustration 4.2: Calculating Yield to Maturity of a Bond in excel A B Settlement (the date on which the bond is going to be purchased) 01-01-2022 Maturity (the date of maturity reckoned from date of purchase) 01-01-2027 Rate (Coupon rate depicted on per annum basis) 12% Price (Current Market Price of the Bond, expressed per Rs.100) 97.5 Redemption (The value proportionately expressed per Rs.100) 100 Frequency (It takes number 1 for yearly, 2 for half-yearly, 4 for 2 quarterly, 12 for monthly) Basis (indicates the day count convention that is used [Day count 0 basis: 0 or omitted = US (NASD) & INDIA 30/360; 1 = Actual/actual; 2 = Actual/360; 3 = Actual/365; 4 = European 30/360) [see box 4.3 for Day count convention] YIELD (The Yield to Maturity would be 12.69%, when the cell is =YIELD(Settlement, formatted to percentage with two decimals. (Please input the values Maturity, Rate, in MS Excel and verify by doing it yourself) Price, Redemption, Frequency, Basis) 84  Box 4.3: Day Count convention Day count convention refers to the method used for arriving at the holding period (number of days) of a bond to calculate the accrued interest. As the use of different day count conventions can result in different accrued interest amounts, it is appropriate that all the participants in the market follow a uniform day count convention. For example, the conventions followed in Indian market for bonds is 30/360, which means that irrespective of the actual number of days in a month, the number of days in a month is taken as 30 and the number of days in a year is taken as 360. Whereas in the money market the day count convention followed is actual/365, which means that the actual number of days in a month is taken for number of days (numerator) whereas the number of days in a year is taken as 365 days. Hence, in the case of T-Bills, which are essentially money market instruments, money market convention is followed. In some countries, participants use actual/actual, some countries use actual/360 while some use 30/actual. Hence the convention changes in different countries and in different markets within the same country (e.g. Money market convention is different than the bond market convention in India). As previously discussed when market interest rates rise, the prices of a bonds fall. Conversely, if the market interest rates decline, the prices of bonds rise. In other words, the yield of a bond is inversely related to its price. The relationship between yield to maturity and coupon rate of bond may be stated as follows: x When the market price of a bond is less than its face value, i.e., the bond is selling at a discount, then YTM would be > Coupon Yield. x When the market price of a bond is more than its face value, i.e., the bond is selling at a premium, then YTM would be < Coupon Yield. x When the market price of a bond is equal to its face value, i.e., the bond is selling at par, then YTM would be = Coupon Yield. Yield to call In the case of bonds with an embedded call feature another measure of Yield is also popularly calculated by the markets along with Yield to Maturity. It is known as Yield to Call. The name comes from the entitlement retained by the issuing entity to repay amounts on the bond prior to its maturity. The amount repaid might not be equal to the face value, because it is being 85 paid prior to the date of maturity. Depending on the market interest rates forecasted by the issuer, the amount repaid, in a call may be higher or lower than the face value(par value). The price and date at which a bond can be called is mentioned at the time of issue. and it is referred to as “Call Price”. Sometimes the issuing entities give a schedule of dates along with their respective Call Prices, when the decision to call can be taken any time within a given range of dates. Yield to call measures the estimated rate of return for bond held till the first call date. The formula used to calculate the Yield to Maturity can be used to calculate the Yield to Call too. In this formula the “Face Value or Redemption Value” variable is substituted with “Call Price”. Then ‘n’ in the equation can be taken as the period till the date of the first call. Usually when there is nothing mentioned specifically, then the first call date is considered as the date on which Call would happen, and the Yield to Call at this date is calculated. ௡‫כ‬௖௙ ‫ݐ݊݁݉ݕܽܲ݊݋݌ݑ݋ܥ‬௧ ‫݁ܿ݅ݎ݈݈ܲܽܥ‬ ܲ଴ ൌ  ෍ ௧ ൅ ሺͳ ൅ ‫ݎ‬Ȁ݂ܿሻ ሺͳ ൅ ‫ݎ‬Ȁ݂ܿሻ௡‫כ‬௖௙ ௧ୀଵ Every other term in the equation means the same as discussed above. For instance, a 20 year old bond paying 12% coupon, semi-annually, and redeeming at par value of Rs.1000 is currently selling at Rs. 1180. Suppose the first call date is 8 years from today, and the issuer is going to call it at Rs. 1050, then the r which will equate the cashflows to the current market price would be the Yield to Call. ଼‫כ‬ଶ ͸Ͳ ͳͲͷͲ ͳͳͺͲ ൌ  ෍ ௧ ൅  ሺͳ ൅ ‫ݎ‬ሻ ሺͳ ൅ ‫ݎ‬ሻ଼‫כ‬ଶ ௧ୀଵ The same can be solved easily with MS Excel by using the tweaking the “Yield Function” as shown in illustration 4.3. Illustration 4.3: Calculating Yield to Call of a Bond in excel A B Settlement (the date on which the bond is going to be purchased) 01-01-2022 Maturity (the date of maturity reckoned from date of purchase) 01-01-2030 Rate (Coupon rate depicted on per annum basis) 12% Price (Current Market Price of the Bond, expressed per Rs.100) 118 Redemption (The value proportionately expressed per Rs.100) 105 Frequency (It takes number 1 for yearly, 2 for half-yearly, 4 for 2 quarterly, 12 for monthly) Basis (indicates the day count convention that is used [Day count 0 basis: 0 or omitted = US (NASD) & INDIA 30/360; 1 = Actual/actual; 2 = Actual/360; 3 = Actual/365; 4 = European 30/360) 86  YIELD (The Yield to Call would be 9.21%, when the cell is formatted to =YIELD(Settlement, percentage with two decimals. Maturity, Rate, Price, Redemption, Frequency, Basis) 4.5 Measuring Price Volatility of bonds Market price of a bond is a function of four factors: (1) Par value of the bond; (2) Coupon rate of the bond; (3) Maturity period i.e. no. of years to maturity and (4) Prevailing market interest rate. There are mathematical proofs that demonstrate the following relationships between yield (interest rate) changes and bond price behaviour: 1. Bond prices and the interest rates have inverse relationship. 2. Bond price volatility is inversely related to coupon. Bonds with higher coupons show smaller percentage price fluctuation for a given change in interest rates. For example, if many bonds with same maturity period of 10 years are taken, experiencing the same change in YTM say from 5% to 6%, the smaller coupon bond will experience the larger percentage price change. If a zero coupon bond is also included in the example, it will experience the largest percentage price change. 3. Bond price volatility is directly related to term to maturity, longer maturity bonds experience larger price changes for a given change in yields. Bond price volatility increases at a diminishing rate as term to maturity increases. 4. Bond price movements resulting from equal absolute increases or decreases in yield are not symmetrical. A decrease in yield raises bond prices by more than an increase in yield of the same amount lowers prices. 4.5.1. Interest rate risk Interest Rate Risk is defined as the risk emanating from changes in the market interest rates. As discussed above, market price of the bond reflects the present value of all future cash flows of the bond. The discount rate used to calculate the present value is the function of prevailing interest rates over various maturities. If the interest rate in the economy increases, the discounting factor to find out the present value of the future cash flows also increases, resulting in the fall in the value of the bond. A related concept to interest rate risk is reinvestment rate risk. Reinvestment risk is when the investor may not be able to reinvest the intermittent cash flows (coupons) at yields prevalent at the time of making the investment due to either decrease or increase in interest rates prevailing at the time of receipt of cash flows by investors. Yield to maturity computation 87 implicitly assumes that all coupon cash flows will be reinvested at yield to maturity. If, after the purchase of the bond, interest rates decline, the coupon cash flows will be reinvested at rates below the yield to maturity. Conversely, if interest rates increase, the coupon cash flows will be reinvested at rates above yield to maturity. 4.5.2 Concept of Duration One of the popular measures of measuring interest rate risk in a bond is Macaulay’s Duration and another derived indicator from it is Modified Duration. By construct both the measures are expressed in number of years. Hence the popular understanding that Duration is some kind of time period in which the bond investor would recoup the initial investment, from the cashflows from the bond. However theoreticians caution this interpretation of Duration. Alternatively they suggest, that it is a good measure of price sensitivity of a Bond for a given change in the market interest rates, yields, or required rates of return of the bond investor. Duration also shares the same properties of a bond as discussed in the Price Volatility segment in Section 4.5.1 Modified Duration is calculated as Macaulay’s Duration in Years / (1 + YTM adjusted to frequency of coupon payment) Say for instance the Macaulay’s Duration is 5 years and the YTM p.a. is 12%, and the frequency of coupon payment is half-yearly. Then the Modified Duration is 5 / (1 + 0.12/2) OR 5 / (1.06) = 4.72 years. The approximate change in price of a bond for a given change in market interest rates can be estimated using the modified duration as follows % change in the price = - Modified Duration * Change in market interest rates in decimals. Continuing the above example, if the modified duration of a bond is 4.72 years and there is a change in the market interest rates or yields from 2.5% to 2.7%. The expected percentage change in the price of the bond will be - 4.72 * 0.002 = - 0.944%. i.e. due to the negative relationship between interest rates and the bond prices, an increase in interest rates would decrease the prices of the bond. 88 4.5.2.1. Determining Macaulay’s Duration Duration (also known as Macaulay Duration) of a bond is popularly known as a measure of time taken to recover the initial investment in present value terms. Duration is expressed in number of years. Based on the calculation involved, it is interpreted as Weighted Average Time to recover the initial investment in the bond (the current market price). It is always less than or equal to the overall life (to maturity) of the bond in years. Only a zero coupon bond (a bond with no coupons) will have duration equal to its remaining maturity. Theoreticians also believe that the price sensitivity of a bond to changes in interest rates can be approximated by the bond's duration. The significance of duration is that greater the duration, more volatile is bond’s price or return on bond investment, for given changes in the level of interest rates. Duration of a bond can be calculated in two ways one is Manually and the other using MS Excel Calculating Duration in MS Excel: Duration can be calculated in MS Excel using the “DURATION” function in the finance functions. The syntax is = DURATION (Settlement date, Maturity date, Coupon Rate, Yield to Maturity, Frequency of Coupon payments, Basis) Illustration 4.4: A bond is currently selling at Rs.1168.51 generating a yield to maturity of 9%, when the bond is paying a coupon of 12%, its face value is Rs.1000, and the balance term to maturity is 8 years. The YTM of the bond can be calculated as 9% p.a., using the bond data. A B Settlement (the date on which the bond is going to be purchased) 01-01-2022 Maturity (the date of maturity reckoned from date of purchase) 01-01-2030 Rate (Coupon rate depicted on per annum basis) 12% Yield (Yield to Maturity at Current Market Price of the bond) 9% Frequency (It takes number 1 for yearly, 2 for half-yearly, 4 for 2 quarterly, 12 for monthly) Basis (indicates the day count convention that is used [Day count 0 basis: 0 or omitted = US (NASD) & INDIA 30/360; 1 = Actual/actual; 2 = Actual/360; 3 = Actual/365; 4 = European 30/360) DURATION (The answer is in years, and it will be 5.569 years) =YIELD(Settlement, Maturity, Rate, Yield, Frequency, and Basis) Manual Calculation of Macaulay’s Duration of Bond: To calculate the duration of a bond, one needs the current market price, the coupon rate, the face value of the bonds, the balance term to maturity, and the YTM of the bond at the ongoing market price, and the frequency of 89 coupon payment. Later the following step by step approach can be followed to arrive at the Duration of the bond. 1. Calculate the YTM of a bond using the current market price, balance term to maturity, coupon rate, and face value, and the final redemption value (Usually at par) 2. Calculate the coupons for each time period when the bond pays the coupons, till the bond’s maturity date 3. Arrive at the present values of the coupons and the final repayment value of the bond, using the interest rate factors calculated using YTM adjusted for the frequency of coupon payment. 4. Now multiply each of the cashflow at each point in time, with the digit representing the time when the cashflow is received. For instance, when calculating the duration of a semi-annual coupon paying bond with remaining life of 5 years, the digits representing the time periods would be 1 to 10. 5. Add all the products of the present value of cashflows and their respective time periods. 6. Finally divide the sum of the weighted present value of cashflows with the current market price of the bond. This gives the Duration in days. Time Coupon/Cashflow PV interest PV of Time * PVCFs factor @ 4.5% Coupons/Cashflows 1 Rs.60 0.9569 57.4163 57.4163 2 Rs.60 0.9157 54.9438 109.88 3 Rs.60 0.8763 52.5778 157.733 4 Rs.60 0.8385 500.3137 201.255 5 Rs.60 0.8024 48.1471 240.735 6 Rs.60 0.7679 46.0737 276.442 7 Rs.60 0.7348 44.0897 308.628 8 Rs.60 0.7032 42.1911 337.529 9 Rs.60 0.6729 40.3743 363.368 10 Rs.60 0.6439 38.6357 386.357 11 Rs.60 0.6162 36.9719 406.691 12 Rs.60 0.5897 35.3798 424.558 13 Rs.60 0.5643 33.8563 440.132 14 Rs.60 0.5399 32.3984 453.577 15 Rs.60 0.5167 31.0032 465.048 16 Rs.60 0.49447 29.6682 474.691 16 Rs.1000 0.49447 494.47 7911.52 Total 1168.51 13015.60 Sum of PV of Cashflows = 1168.51 (Which is nothing but the current market price) Sum of Weighted PV of Cashflows = 13015.60 90 Duration = (Sum PV of Weighted Cashflows / Sum of PV of Cashflows) / Frequency of Coupon Payment Macaulay’s Duration = (13015.60 / 1168.51) / 2 = 5.569 (We can see that both manual and MS Excel answers are the same). Modified Duration = 5.569 Years / (1.0450) = 5.33 91 Chapter 4: Sample Questions 1) Government securities carry practically no risk of________ and, hence are called risk-free or gilt-edged instruments. a) Tradability b) liquidity c) default d) negotiability 2) ______________ risk arises from the fact that income flows received from an investment at the coupon rate may not be able to earn the same interest. a) Re-investment b) Default risk c) Credit risk d) None of the above 3) The feature that allows the issuing firms to retire the bonds before the maturity by paying a prescribed price is called ____________. a) Callability (call option) b) Putability (put option) c) Convertibility d) Redemption 4) Typical putability (put option) feature of a bond _________________________. a) Gives the bond holders the option to convert the bond into another security, typically the common stock of the firm issuing the convertible bonds b) Gives the holder the right, under certain circumstances to sell the bond back to the issuer c) Allows the issuing firms to retire the bonds before the maturity by paying a prescribed price d) Allows the investor to redeem the bond 92