Risk and return bond return...3

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Risk and return bond return...3

  1. 1. 2 CONTENTS  Introduction  Features of the bond  Face Value  Coupon Rate  Periodicity of coupon payments  Maturity  Redemption Value  Types of Bonds  Fixed and Floating Rate Bonds  Indexed Bonds  Callable & Puttable Bonds  Zero Coupon and Deep Discount Bonds  Convertible Bonds  Cash Flow of the bond VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  2. 2. 3 CONTENTS  Pricing of bond/Yield on the bond  Deep Discount/Zero Coupon Bonds & STRIPS  Term Structure of Interest Rates  Theories of Term Structure  Duration of the Bond  Bond Rating  Bond Management Strategies VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  3. 3. 4 BONDS  Bonds have emerged as one of the prominent financial instruments of capital markets world over.  Bonds are the instruments of borrowings.  They promise a fixed return until their maturity and the payback of principal upon maturity. VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  4. 4. 5 FEATURES OF THE BOND  The terms and conditions for the issue of bonds are pre decided at the time of the issue as a part of bond indenture.  Main features of bond indenture are:  face value,  coupon rate,  periodicity of coupon payments,  maturity period, and  redemption value. VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  5. 5. 6 TYPES OF BONDS  Fixed rate and floating rate bonds  Indexed bonds  Callable /puttable bonds  Bonds that can be called by the issuer prior to the maturity are known as callable Bonds, while whose redeemable at the option of subscribers are known as puttable bonds  Redemption in lump sum /phased redemption VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  6. 6. 7 TYPES OF BONDS  Zero Coupon/Deep Discount Bonds  Bonds that do not pay any interest but are issued at discount to the face value and redeemed at face value are called Deep Discount Bonds  Convertible Bonds  Convertible bonds are those, which convert a part of the bond into equity shares. It combines the features of bonds and equity in a composite instrument VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  7. 7. 8 CASH FLOW OF THE BOND  Cash flows of bonds are made up of two components: the periodic coupon payments and principal repayment Time (months from 0 6 12 18 24 30 36 now) Coupon received 0 5 5 5 5 5 5 Principal paid (-) and -100 105 redeemed (+) Total cash flow -100 5 5 5 5 5 110 VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  8. 8. 9 PRICING OF BOND  The value of bond is arrived by discounting the future cash flows from the bonds at an appropriate discount rate  Discount rate must appropriately be adjusted for the  riskiness of the cash flows,  prevalent market conditions, and  timing of cash flows to truly reflect the expectations VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  9. 9. 10 VALUE OF THE BOND & DISCOUNT RATE Value of the Bond and Discount Rate 140 120 Value (Rs.) 100 80 60 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% Discount Rate (%) VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  10. 10. 11 VALUE OF THE BOND & DISCOUNT RATE  Discount rate is a function of risk. Higher the risk, higher the discount rate and consequently lower the price of bond When discount rate, r > coupon rate, i Price < Face Value When discount rate, r < coupon rate, i Price > Face Value When discount rate, r = coupon rate, i Price = Face Value VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  11. 11. 12 VALUE OF THE BOND AND RISK FREE RATE  Value of the bond does not rise above a certain maximum Bond Value and Risk Free Rate Price Risk Free Rate Discount Rate VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  12. 12. 13 VALUE OF THE BOND WITH TIME  The difference between the price and the redemption value narrows as maturity nears and price converges to its redemption value at maturity irrespective of the discount rate. Bond Price and Time Price Premium Bond Par Value= Redemption Value Discount Bond Maturity Time VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  13. 13. 14 YIELD ON THE BOND  There are four types of yields:  current yield;  yield to maturity;  realised yield and  yield to call (relevant only for callable bonds)  Current yield is the annual coupon payment divided by the current price. Interest Amount, Coupon x Face Value Current Yield (%) = x100 Current Price, P0 VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  14. 14. 15 YIELD TO MATURITY (YTM)  Yield to maturity (YTM) is the rate of return the investor earns if he holds the bond till maturity.  YTM satisfies the following Value of the bond = Price, P0 n Ct Rt = ∑ + 1 (1 + YTM)t (1 + YTM)n  A 5-year bond with 12% coupon payable annually selling at Rs. 90 would have YTM of r such that Price, P0 = 90.00 12 12 12 12 12 12 100 = + 2 + 3 + 4 + 5 + 6 + (1 + r) (1 + r) (1 + r) (1 + r) (1 + r) (1 + r) (1 + r)6 VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  15. 15. 16 YTM AND VALUE OF BOND  YTM considers the time value of money while calculating returns for the investor.  There is an inverse relationship between the price and the YTM of the bond. VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  16. 16. 17 REALISED YIELD  Realised yield is the rate of return investor earns on bonds if he sells the bonds before its maturity. It has two components: annual coupons received till the date of sale and the capital appreciation realised on sale. n P0 x (1+ ry ) = TVn VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  17. 17. 18 YIELD TO CALL  Yield to call is the return the investors earn on the callable bonds till the time the bonds are called. It comprises of two components: annual coupons till the date of call and the call price.  For a 5-year 12% annual coupon bond trading at Rs. 90, callable after four years at Rs. 105 the YTC is computed as below: Value of the bond = Price, P0 = 90 n Ct Rt = ∑ t + 1 (1 + YTC) (1 + YTC)n 4 12 105 = ∑ t + 1 (1 + YTC) (1 + YTC)4 VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  18. 18. DEEP DISCOUNT/ZERO19 COUPON BONDS AND STRIPS  Zero coupon bonds do not pay any interest and instead provide all the returns in the form of capital gains.  They are issued at price substantially lower than the par value and are redeemed at par. Pr ice Be haviour of Ze r o Coupon Bond 30-Ye ar Ze r o Coupon Bond Discount Rate 10% 1,000 Bond Price (Rs.) 900 800 700 600 500 400 300 200 100 - Tim e (yr s .) VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  19. 19. 20 ZERO COUPON BONDS  The value of zero coupon bonds is arrived by discounting the par value (redemption price) at an appropriate discount rate  Coupon bearing bonds too can be made to look like zero coupon bonds if we treat all the coupon payments as separate instruments Face Value Value of Zero Coupon Bond = (1 + r)T VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  20. 20. 21 STRIPS  The process of segregating the coupon payments and redemption value and issuing them as separate securities is called stripping.  Each of the strips becomes a separate instrument that can be traded independently of the composite instrument.  These are known as STRIPS (Separate Trading of Registered Interest and Principal of Securities). VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  21. 21. 22 ADVANTAGES OF STRIPS  The advantages of stripping include  increased liquidity due to increased participation by small investors as coupon stripping results in instruments of smaller denominations,  larger number of securities available for trading providing depth to the market, and  fair pricing due to increased depth and participation. VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  22. 22. 23 TERM STRUCTURE OF INTEREST RATES  The timing of cash flows and the discount rates to be used are inter-dependent as the expectations of investors vary with the investment horizon. For example: Term of investment Yield 1 year 8% 2 years 9% 3 years 10% VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  23. 23. 24 TERM STRUCTURE OF INTEREST RATES  The relationship between the yield (interest rate) and the term of investment is called the term structure of interest rates. TERM STRUCTURE OF INTEREST RATES 11 10 10 9 9 8 Yield (%) 8 7 6 5 1 2 3 Term of Investment (Years) VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  24. 24. 25 YTM AND TERM STRUCTURE  Ideally the value of the bond must be arrived at with the discount rate appropriate with the timing of the cash flow as given by term structure of interest rates, rather that single discount rate for all the cash flows.  Value of the bond using single rate: 120 120 120 1000 Price, P0 = + + + (1+ 0.10) (1+ 0.10)2 (1+ 0.10)3 (1+ 0.10)3 = 109.09 + 99.17 + 90.16 + 751.31 = Rs.1049.73 ,  Value of the bond using discount rate as per the term structure: 120 120 120 1000 Price, P0 = + 2 + 3 + (1+ 0.08)(1+ 0.09) (1+ 0.10) (1+ 0.10)3 = 111.11+ 101.00 + 90.16 + 751.31 = Rs.1053.58 , VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  25. 25. 26 FINDING TERM STRUCTURE  Though the YTMs are observable the term structure of interest rates needs to be derived on some rationale basis.  Term structure of interest rates is hidden in the YTMs of bonds with progressive maturities.  YTMs of bonds with different maturities do not reflect the term structure unless all of them have only single cash flow attached with them. VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  26. 26. 27 FINDING TERM STRUCTURE  The most suitable method to arrive at term structure on interest rates is to get the yields on bonds with increasing maturities but that have single cash flow, as is the case with zero-coupon bonds. Bond Maturity Price Yield (Rs.) Zero Coupon Bond 1 Year 925.00 8.11% Zero Coupon Bond 2 Year 845.00 8.79% Zero Coupon Bond 3 Year 770.00 9.10% All bonds are redeemable at par with Rs. 1,000 FV Yields have been worked out using following: P0 = (1 + rn )n VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  27. 27. 28 IMPLIED FORWARD RATES  Term structure of interest rates not only provides expectations of returns with horizon of investment but also imply forward rates of interest.  For example 8% yield for 1 year investment and 9% for two year investment implies yield expectation of 10% for one year investment one year from now.  Under conditions of perfect market and well-informed investors the direct investment strategy (investing for two years) and roll over strategy (investing for one year and then rolling over for another year)must result in identical returns. VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  28. 28. 29 THEORIES OF TERM STRUCTURE Expectations Hypothesis  The shape of yield curve is dependent upon the expectations of investors about the future interest rates. Liquidity Preference Hypothesis  Liquidity preference theory suggest that the term structure of the interest rates is governed by preferences of investors for liquidity. Preferred Habitat/Market Segmentation Theory  Preferred Habitat theory recognises that the investor have preferred investment horizons. Short-term investors invest in securities with short maturities and long-term investors prefer securities with long-term maturities. VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  29. 29. 30 DURATION OF THE BOND  Values of bonds change with the change in interest rates.  With change in interest rates all bonds do not change in value by the same amount. It depends upon the Duration of the bond.  Price sensitivity of the bond is measured by the term called Duration. VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  30. 30. 31 COMPUTING DURATION  Duration is the time weighted average of the present values of the cash flows of the bond as proportions of its price. n ∑t x PV of CFt 1 Duration of the Bond = P0 1 x CF1 2 x CF2 3 x CF3 4 x CF4 = + + + + .......... P0 (1 + r)1 (1 + r)2 (1 + r)3 (1 + r)4 VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  31. 31. 32 COMPUTING DURATION Time Cash flow PV (10%) Proportion Time x Proportion 1 80.00 72.73 8.14% 0.081 2 80.00 66.12 7.40% 0.148 3 80.00 60.11 6.73% 0.202 4 80.00 54.64 6.12% 0.245 5 80.00 49.67 5.56% 0.278 6 80.00 45.16 5.06% 0.303 VALUATION & MANAGEMENT OF BONDS CHAPTER 6 7 80.00 41.05 4.60%
  32. 32. 33 SENSITIVITY OF BOND PRICES  Due to convexity of bond price with interest rate the change in price of bonds is linear only approximately. Duration Volatility of the bond = - (1+ YTM/m) 6.091 6.091 =- =- = - 5.54 (1+ 0.1/1) 1.1 VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  33. 33. 34 PROPERTIES OF DURATION  Duration of low YTM bonds is higher and hence they are more sensitive as compared to high YTM bonds.  Duration of low coupon bonds is higher  Duration of bonds with longer term to maturity is higher  Duration is always shorter than the term to maturity and increases as maturity extends  Duration of a portfolio of bonds is weighted average of durations of bonds consisting it. Duration of Bond Portfolio=Dp = wiD1+w2D2+w3D3… VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  34. 34. 35 BOND RATING  Bond rating is an alphanumeric score given to debt issue of a firm by an independent specialised external agency.  It broadly signifies the level of risk associated with such an issue of debt.  Purpose of rating is to facilitate investors to make informed judgment for investing VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  35. 35. 36 BOND MANAGEMENT STRATEGIES Buy-and-Hold Strategy  The simplest of the strategy of managing the investment in bonds is buy-and-hold.  Buy-and-hold strategy has the advantage of least transaction cost. Bond Laddering  Bond laddering strategy is similar to buy- and-hold with the modification that the portfolio of bonds is chosen with staggered and progressive maturities. VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  36. 36. MATURITY VS. DURATION37 MATCHING – IMMUNISATION  The investors in bond primarily face two kinds of risks 1. Price Risk: Bonds prices change constantly, albeit not as much as stock prices, with the changing economic conditions that affect the YTM. 2. Reinvestment Risk: Reinvestment risk arises due to inability of the investors to reinvest the interim coupon payments at the desired rate. VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  37. 37. MATURITY VS. DURATION38 MATCHING – IMMUNISATION  By matching maturity with the planned investment horizon the price risk is eliminated but the re-investment risk remains.  By making holding period equal to the duration of the bond the portfolio can be immunized from change in value due to change in interest rates. VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  38. 38. MATURITY VS. DURATION39 MATCHING – IMMUNISATION  Matching investment horizon with duration rather than maturity of the bond keeps terminal wealth constant. 1,800 Terminal Value TERMINAL VALUE 1,400 M aturity M atching 1,000 Duration M atching 600 0 1 2 3 4 5 at 10% at 5% at 20% Time (Years) VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  39. 39. 40 RIDING THE YIELD CURVE  The strategy is used with rising yield curve to get higher returns by selling the bond rather than holding it till maturity.  a zero coupon bond with two years remaining for maturity.  The rising yield curve with yields of 7% for one-year term and 8% for two-year term.  Buy and hold till maturity:  The current price of the bond would be Rs. 857.34 (1,000/1.082).  If planned horizon of investment is two years the investor would lock-in the return of 8%. VALUATION & MANAGEMENT OF BONDS CHAPTER 6
  40. 40. 41 RIDING THE YIELD CURVE Buy and sell after one year:  if investor sells the bond after one year the bond would trade at a price higher than expected.  With 8% yield the price should be Rs. 925.92 (1,000/1.08).  But since after one year the time left for maturity is one year only the new price of the bond should be Rs. 934.58 (1,000/1.07) consistent with the yield curve.  The investor would realise a return of 9% if the bond is sold one year after investment. VALUATION & MANAGEMENT OF BONDS CHAPTER 6

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