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1. FINANCIAL MARKETS 04A BOND MARKETS

2. WHAT IS A BOND A bond is a fixed income debt security issued by the government or corporates.

3. BOND PRICING & VALUATION 3

4. BOND TERMINOLOGY 4

5. DEFINITION OF A BOND A bond is a legally binding agreement between a borrower (bond issuer) and a lender (bondholder ): The agreement specifies the principal amount of the loan. the size and timing of the cash flows: in dollar terms (fixed-rate borrowing) OR as a formula (adjustable-rate borrowing)

6. SOME TERMINOLOGY Maturity/term to maturity Face value Coupon rate, frequency Premium/par/discount bonds Premium/discount on redemption

7. MATURITY/TERM TO MATURITY The maturity date of a bond is the date on which the principal is to be repaid. Once a bond has been issued, the time remaining until maturity is referred to as the term to maturity or tenor of a bond. 7

8. FACE/ PAR VALUE The face value of a bond is the amount that is specified as such in the contract of issue. The amount of redemption proceeds as well as the coupon interest are determined by reference to face value. Though, they may not equal the face value . The face value is also referred to as the par value , of the bond. 8

9. In case of bonds redeemable at par, the face value coincides with maturity value , redemption value , or principal value of the bond. If a bond is redeemable above par value, it is said to be redeemable at a premium. If a bond is redeemable below par value, it is said to be redeemable at a discount. 9 REDEMPTION AT PAR/PREMIUM DISCOUNT

10. BOND PRICES & PAR VALUES A bond that is selling for more than its par value is said to be trading at a premium to par. A bond that is selling at less than its par value is said to be trading at a discount to par. A bond that is selling for exactly its par value is said to be trading at par. 10

11. COUPON RATES & FREQUENCY The coupon rate on a bond is the annual percentage of its par value that will be paid to bondholders. Some bonds make coupon interest payments annually, while others make semiannual, quarterly, or monthly payments. 11

12. EXAMPLE A $1,000 par value semiannual-pay bond with a 5% coupon would pay 2.5% of $1,000, or $25, every six months. 12

13. INTRINSIC VALUE OF AN INSTRUMENT 13

14. WHAT IS INTRINSIC VALUE? Intrinsic value of an asset is the ingrained worth of an asset as computed by a potential investor using an objective model e.g. DCF analysis, Black Scholes model of option pricing etc. 14

15. Intrinsic value is arrived at by means of an objective calculation or complex financial model rather than using the currently trading market price of that asset. 15

16. INTRINSIC VALUE IS INVESTOR SPECIFIC Intrinsic value is not only security-specific but also investor-specific. Every investor makes his own estimates about the inputs required for the model that he chooses to apply and arrives at his assessment of intrinsic value. 16

17. If we use the DCF model for intrinsic value, we discount the cash flows at the rate that encapsulates the investor’s own risk perception of the security.

18. INTRINSIC VALUE & MARKET TRADES A COMPARISON OF INTRINSIC VALUE WITH MARKET PRICE ENABLES IDENTIFICATION OF MISPRICED SECURITIES AND HENCE, POTENTIAL INVESTMENT OPPORTUNITIES. 18

19. KEY TAKEAWAYS In financial analysis, intrinsic value is the calculation of an asset's worth based on a financial model. By comparing intrinsic value with CMP, mispriced securities that may constitute potential investment opportunities are identified. 19

20. APPROACHES TO BOND VALUATION ARBITRAGE FREE PRICING 20

21. INTRINSIC VALUE IN THE AFP MODEL Intrinsic value as per the Arbitrage Free Pricing model of a financial security is the present value of all future cash flows attributable to that security discounted at the rate that is representative of the risk profile of these cash flows

22. RATIONALE OF THE AFP FORMULA Consider two investment portfolios: Portfolio A: A 2-year bond valued at P A at t=0 that yields: Cash flow of C 1 at the end of first year (t=1) Cash flow C 2 at the end of the second year (t=2) 22

23. Portfolio B: A deposit of an amount P 1 = C 1 /(1+S 01 ) at t=0 for one year @ S 01 yielding C 1 = P 1 (1+S 01 ) at the end of one year (t=1) and A deposit of an amount P 2 =C 2 /(1+S 02 ) 2 at (t=0) for two years @ S 02 yielding C 2 = P 2 (1+S 02 ) 2 at the end of two years (t=2) We assume for the moment that receipt of C 1 at the end of the first year and C 2 at the end of the second year is default free from both portfolios A & B. 23

24. Then, for both portfolios A & B: The cash flows at the end of first year (t=1) & second year (t=2) are both identical. The riskiness of the recovery of cash flows from both portfolios is the same ( riskfree ). There are no cash flows except at t=0, t=1 and t=2 years Thus, the portfolios A & B must cost the same at all times so that: P A =P 1 +P 2 =C 1 /(1+S 01 )+C 2 /(1+S 02 ) 2 24

25. GENERALIZATION 25 MATURITY RISK

26. WHY INDICATE INTEREST RATES WITH INDICES? TERM STRUCTURE OF INTEREST RATES 26 INTEREST RATES ARE USUALLY A FUNCTION OF MATURITY. THIS PHENOMENON IS CALLED TERM STRUCTURE OF INTEREST RATES

27. STEPS IN VALUATION OF BONDS To value bonds we need to: Estimate future cash flows Size (how much) and Timing (when) Assess the risk of realizing these cash flows Select the appropriate discount rate based on risk assessment Discount future cash flows at an appropriate rate:

28. Bond cash flows are largely non-discretionary and determined by the contract of issue. For assessing the riskiness of the realizability of these cash flows and default probabilities recourse may be had to the instrument’s creditr ratings. 28

29. SEMIANNUAL COUPONS Adjust the coupon payments by dividing the annual coupon payment by 2 Adjust the discount rate by dividing the annual discount rate by 2 The time period t in the present value formula is treated in terms of 6-month periods rather than years, hence double the number of periods.

30. VALUE OF BOND WITH SEMI-ANNUAL COUPONS 30 The factor of ½ appears in the denominator because even the half-yearly rates are quoted on annualized (per annum) basis.

31. IMPORTANT The factor of ½ appears in the denominator because even the half-yearly rates are quoted on annualized (per annum) basis. The compounding time point is assumed to coincide with the coupon payments. 31

32. EXAMPLE Calculate the intrinsic value of a 10% semi-annual bond of the face value of INR 1,000 that has exactly 1.50 years to maturity. The bond has just made a coupon payment and the spectrum of risk adjusted interest rates is as follows: 6 months maturity: 8% p.a. 12 months maturity: 9% p.a. 18 months maturity 10% p.a. 32

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34. MEASURES OF RETURN IN FIXED INCOME SECURITIES 34

35. YIELD MEASURES Nominal Yield or Coupon Rate Current Yield Yield to Maturity Annualized Realized Yield or Annualized Holding Period Yield or Effective Annual Yield

36. CONTENTS CURRENT YIELD YIELD TO MATURITY YTM & RISKINESS YTM: AN INTERPRETATION SPOT RATES, YTM & PRICE CAVEAT YTM & COUPON RATE IMPLIED ASSUMPTIONS OF YTM ISSUES WITH YTM: REINVESTMENT RATE PORTFOLIO YTM ANNUALIZED HOLDING PERIOD YIELD 36

37. SOURCES OF INCOME IN FIXED INCOME INVESTMENTS COUPONS INTEREST ON REINVESTED INTEREST CAPITAL GAINS 37

38. COMMON MEASURES OF RETURN CURRENT YIELD YIELD TO MATURITY HOLDING PERIOD YIELD 38

39. CURRENT YIELD   39

40. WHAT IS YTM? YTM is the discount rate that equates the present value of future cash flows from the instrument to its current market price (including accrued interest). 40

41. WHAT IS YTM? YTM is the discount rate that equates the present value of future cash flows from the instrument to its current market price (including accrued interest). 41

42. OBSERVATION For a given price, the YTM depends on relative distribution of cash flows. In other words, YTM depends on: the magnitude of the cash flows and the timing of the cash flows. 42

43. YTM & RISKINESS YTM is a risk adjusted discount rate that encapsulates the market’s perception of the riskiness of the realizability of the cash flows from the instrument. For a given bond, YTM depends on the riskiness of the cash flows since the price will incorporate the riskiness in the realization of these cash flows. 43

44. Therefore, two bonds with identical cash flows may trade at different YTMs if their risk as perceived by the market is different because the price will adjust accordingly. The more risky bond would quote at a lower price and hence a higher YTM. 44

45. CONVERSE If two bonds carry similar risk perceptions in the market, they would have the same YTM notwithstanding that their cash flow patterns are different. The prices would adjust to make the YTMs equal. 45

46. YTM: AN INTERPRETATION The YTM may be interpreted as some kind of average for the term structure of market interest rates. Captures the term structure in one single interest rate.

47. SPOT RATES, YTM & PRICE There is 1-1 correspondence between price and YTM of a given bond and given spot rates. A given spectrum of spot rates uniquely determine the price of a given bond and, therefore, the YTM .

48. COUPON, YTM & PRICE Bond prices and YTM are inversely related. The value of a bond would be equal to its face value only when the coupon interest rate and YTM are equal. The value of a bond would be higher (lower) than its face value when the coupon interest rate is higher (lower) than YTM.

49. EFFECTIVE ANNUAL YIELD ANNUALIZD HOLDING PERIOD YIELD   49

50. EXAMPLE You are given the following with respect to a level coupon bond: Coupon Rate: 30% p.a. Frequency of coupons: Annual Term to maturity: 2 years Face Value: 1,000 Redemption Value: 1,500 One Year Spot Rate S(0,1): 8% p.a. annually compounded Two-Year Spot Rate S(0,2): 12% p.a. annually compounded What is the intrinsic value of the bond ? Assuming that the current market price of the bond equals its intrinsic value, what is its yield to maturity (in % p.a.)? 50

51. EXAMPLE You are given the following information with regard to an annuity bond: Face Value of the bond: 1,00,000 Traded Price: 1,00,000 Equal Annuity Payments Annual Term to Maturity: 2 years One Year Spot Rate S(0,1), annual compounding 10% p.a. Two Year Spot Rate S(0,2), annual compounding: 20% p.a. The bond makes equal annual payments to the holder of the bond over a two year period. Calculate the YTM of the bond? 51

52. EXAMPLE Consider a bond portfolio X comprising of one bond Y and one bond Z. Both bonds are annual level coupon bonds redeemable at par value of 1,000. They are also trading at par. Bond Y is a three year bond trading at a YTM of 20% p.a. annually compounded. Bond Z pays an annual coupon of 25% and has two years to maturity. What is the YTM of the portfolio X based on the aggregate cash flows from the portfolio? 52

53. EXAMPLE Consider the following data in respect of a bond investment: Face Value of bond: 1,000 Coupon Rate: 10% Coupon Frequency: Annual Redemption Value (Par): 1,000 Term to Maturity at purchase: 5 years YTM at purchase: 12% p.a. annually compounded Holding Period: 2 years YTM at sale of bond: 11% p.a. annually compounded The investor does not reinvest the coupons received by him during his holding period of two years. What is the effective annual yield earned by the investor (in % p.a. annually compounded)? 53

54. EXAMPLE Consider the following data in respect of a bond investment: Face Value of bond: 1,000 Coupon Rate: 10% Coupon Frequency: Annual Redemption Value (Par): 1,000 Maturity at purchase: 5 years YTM at purchase: 12% p.a. annually compounded Holding Period: 1 year YTM at sale of bond: 10% p.a. annually compounded Calculate the total cash flow received by the investor including the coupon on date of liquidation of the investment at the end of the holding period. 54

55. TYPES OF RISK IN BONDS Default Risk Interest Rate Risk Reinvestment Rate Risk Price Risk Inflation Risk Liquidity Risk Call Risk

56. INTEREST RATE RISK 56

57. 57 1 P H H+1 T 2 H

58. INTEREST RATE RISK Since the price of a bond fluctuates with market interest rates, the risk that an investor faces when investing in a bond portfolio is that: ( i ) the price of the bond at end of holding period will decline if market interest rates rise UNANTICIPATEDLY. This risk is referred to as price risk. (ii) the income from reinvestment of coupons may not yield the desired return if interest rate fall. This is called reinvestment rate risk.

59. YTM AND BOND PRICE 800 1000 1100 1200 1300 $1400 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Discount Rate Bond Value 6 3/8 When the YTM > coupon, the bond trades at a discount. P Q YIELD PRICE CURVE Non linearity. Slope is negative. Slope increases with YTM.

60. CONVEXITY OF PRICE-YIELD CURVE Non linearity. First derivative is negative. Slope is negative, θ is in second quadrant. Second derivative is positive. Hence, the curve is convex to the origin.

61. YTM AND BOND PRICE: CONVEXITY 800 1000 1100 1200 1300 $1400 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Discount Rate Bond Value 6 3/8 P Q Negative first derivative: Price and YTM are inversely related. Positive 2 nd derivative: Slope increases with YTM. These two together imply that the magnitude of the slope is decreasing with YTM thereby establishing convexity. YIELD PRICE CURVE

62. For a given decrease in yield, the percentage price increase is greater than the percentage price decrease for an equal increase in yield. IMPACT OF CONVEXITY

63. MEASURES OF INTEREST RATE RISK DOLLAR VALUE PER BASIS POINT (DV01) MACAULAY’S DURATION & CONVEXITY MODIFIED DURATION INTEREST RATE ELASTICITY

64. DOLLAR VALUE PER BP DOLLAR VALUE PER BASIS POINT (DV01) IS THE CHANGE IN BOND PRICE CORRESPONDING TO A CHANGE OF ONE BASIS POINT IN THE YIELD It is given by the negative slope of the price/yield curve:

65. 65 MACAULAY’S DURATION

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68. 68 DURATION AS DCF WEIGHTED AVERAGE TIME A bond’s (annual) Macaulay duration is calculated as the weighted average of : the number of years until each of the bond’s promised cash flows, where the weights are the present values of each cash flow as a percentage of the bond’s full value.

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70. Between coupon dates, the Macaulay duration of a coupon bond decreases with the passage of time and then goes back up significantly at each coupon payment date. 70 DURATION OF COUPON BONDS

71. EXAMPLE 1 Consider a 12% coupon bond with an yield to maturity of 18% and 5 years remaining to maturity. a. What is the bonds current price, assuming annual coupons? b. What is the bond’s Duration? Convexity? c. What percentage price change might you expect if the yield to maturity suddenly increased to 25%? Calculate using Duration alone and then using both Duration & Convexity. d. What would be the exact percentage price change?

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75. 75 MODIFIED DURATION

76. MODIFIED DURATION: DEFINITION The modified duration of a bond at a given YTM is the negative of percentage change in price of the bond for a 1% change in YTM. Since price & YTM are inversely related, modified duration returns a positive number for a conventional bond. 76

77. INTEREST RATE ELASTICITY

78. RECAP

79. PROBLEM Consider a 10% annual coupon bond with a maturity of two years. The bond is quoting at a YTM of 18% p.a. Coupons will be paid at the end of the first and second year. Redemption at a discount of 25% to face value will be made at the end of second year. Calculate the bond’s Macaulay’s duration (in years) & convexity (in years 2 ). 79

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83. PROBLEM On the basis of the value of duration & convexity arrived at in the previous question, , calculate the price change (in %) corresponding to a 5% increase in the ytm from the above figure. 83

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86. Nevertheless, the extent to which these effects would cancel each other also depends on the holding period of the investor. The longer the holding period, the greater would be the effect on reinvested income of an interest rate change and smaller would be the effect on price since the bond would be closer to maturity and hence, fewer coupons would be available for discounting . IMPACT OF HOLDING PERIOD ON BOND RETURNS

87. In fact, there exists a holding period at which both these effects exactly annul each other. This holding period turns out to be the Macaulay’s duration as proved below: 87

88. DURATION:IMPORTANT PROPERTIES The Macaulay Duration of a zero equals its maturity. Macaulay Duration of a perpetuity does not depend on coupon rates (D=(1+y)/y)..

89. DURATION AND COUPON RATES For practically realizable values, duration of all types of bonds (par, premium and discount) decreases with increase in coupon rate . This is because as coupon increases a greater proportion of the cashflows are realized by the investor earlier.

90. DURATION AND MATURITY Duration of par and premium bonds always increases with increasing maturity. For discount bonds, there is a critical value of maturity, upto which duration would increase with maturity. If maturity exceeds this critical value, then duration will start decreasing with maturity for discount bonds .

91. PRICE SENSITIVITY Hence, two effects interact due to interest rate shifts: DURATION EFFECT PRICE EFFECT

92. The duration effect of par & premium bonds increases with maturity. The price of a premium bond increases with maturity while that of a par bond remains constant. It follows that price sensitivity of premium and par bonds will always increase with maturity. PRICE SENSITIVITY VS MATURITY OF PREMIUM BONDS

93. PRICE SENSITIVITY & MATURITY OF DISCOUNT BONDS For discount bonds, there is a critical value of maturity, upto which duration would increase with maturity. If maturity exceeds this critical value, then duration will start decreasing with maturity for discount bonds . The price of a discount bond decreases with maturity. 95

94. For short term discount bonds, the duration effect dominates and sensitivity increases to start with. As maturity increases, the decrease due to price effect also becomes significant and the sensitivity starts decreasing gradually until a limiting value corresponding to a perpetuity is reached. 96

95. BOND MARKETS 97

96. SEGMENTATION OF BOND MARKETS The bond market is segmented as follows: The government bond market: This comprises of Central & State Government securities floated by governments for borrowing money to meet their fiscal deficits. These are fixed income instruments. They are dated sovereign securities issued by the RBI on behalf of the government. The corporate bond market: This market consists of FI bonds, PSU bonds & corporate bonds & debentures.

97. PRIMARY & SECONDARY MARKETS On the basis of buyers, there are two types of bond markets: Primary Market: The primary market is the one where the original bond issuer directly sells new debt securities to investors. Secondary Market: The bonds bought in the primary market can be further traded in the secondary market.  The retail investor can also make bond investments indirectly through debt based mutual funds.

98. WHOLESALE & RETAIL MARKETS The wholesale debt market system (WDM) allows trading in bonds of all kinds and varieties issued by Central or State Governments, PSUs and private sector corporations. This is the market segment where most institutionl players trade in debt instruments. In this segment of the NSE, the size of the deals is usually large. The Retail Debt Market (RETDEBT) is also available for retail investors interested in bonds/debentures trading. The RETDEBT segment of the NSE provides a trading platform for small players. This is a measure to facilitate individual level investors to trade in government securities. The RETDEBT facility is available on nEAT for retail investors in the debt segment of NSE.

99. PRIVATE PLACEMENT OF BONDS In view of the limited investor interest in bond investments, private placement of bonds has become a viable route to raising debt capital. Much of the funds mobilization in bond issuances comes from private placements.

100. COMMON BROKERS/ TRADING PLATFORMS FOR BOND INVESTMENTS Several online platforms facilitate bond investments for individual investors, such as GoldenPi , Wint Wealth, and BondsIndia Coin

101. BOND MARKET PLAYERS The market includes a diverse range of participants, including individual investors, institutional investors like mutual funds insurance companies and financial institutions. 

102. DATED GOVERNMENT SECURITIES Dated government securities are long term securities and carry a fixed or floating interest rate paid on face value. The frequency of interest payments is usually half-yearly. The tenor of dated securities can be upto 30 years.

103. STRUCTURE OF THE GOVERNMENT SECURITIES MARKET The investors in this market can be classified into different segments such as: Wholesale market which comprises of players such as banks, Fis, insurance companies, primary dealers & mutual funds; Middle segment comprises of corporates, PFs, NBFCs & co-operative banks; Retail segment consisting of individuals & non-institutional investors.

104. TRADING IN THE GOVERNMENT SECURITIES MARKET Governemnt securities may be held by investors either in physical form on in dematerialized form. However, it is mandatory for RBI regulated investors to hold and transact these securities in demat form. In the primary GSM, the dated securities are issued and priced through the market process (auctions) for a better price discovery. The securities may be traded in the secondary market either through ( i ) OTC or (ii) negotiated dealing system or (iii) stock exchanges. Transactions undertaken between market participants in the OTC/telephone market are to be reported on the NDS platform within 15 minutes after the deal is finalized. The settlement cycle for dated security auction is T+1.

105. COMMON BOND STRUCTURES 107

106. PLAIN VANILLA BOND ZERO COUPON BONDS DEEP DISCOUNT BONDS BALLOON REPAYMENT BONDS AMORTIZING BOND BONDS WITH SINKING FUND PROVISIONS FLOATING RATE NOTES/BONDS 108

107. FLOATERS WITH CAPS & FLOORS INVERSE FLOATER STEP UP & STEP DOWN COUPON BONDS CREDIT-LINKED COUPON BOND DEFERRED COUPON BOND INDEX LINKED BONDS INFLATION-LINKED BONDS EMBEDDED OPTIONS 109

108. CONVERTIBLE BONDS BONDS WITH WARRANTS 110