Part - IX Fundamentals of Debt Securities

1. Part - IX Fundamentals of Debt Securities

2. Basics • What is debt? • It is a financial claim. • Who issues is? • The borrower of funds • For whom it is a liability • Who holds it? • The lender of funds • For whom it is an asset

3. Basics (Cont…) • What is the difference between debt and equity? • Debt does not confer ownership rights on the holder. • It is merely an IOU • A promise to pay interest at periodic intervals and to repay the principal itself at a prespecified maturity date.

4. Basics (Cont…) • It has a finite life span • The interest payments are contractual obligations • Borrowers are required to make payments irrespective of their financial performance • Interest payments have to be made before any dividends can be paid to equity holders. • In the event of liquidation • The claims of debt holders must be settled first • Only then can equity holders be paid.

5. Nomenclature • Debt securities are referred to by a variety of names. • Bills • Notes • Bonds • Debentures • In the U.S. a debenture is an unsecured bond. • In India the terms are used interchangeably.

6. U.S. Treasury Securities • They are fully backed by the federal government. • Consequently they are devoid of credit risk or the risk of default. • The interest rate on such securities is used as a benchmark for setting rates on other kinds of debt.

7. U.S. Treasury Securities (Cont…) • The Treasury issues three categories of marketable securities. • T-bills are discount securities • They are issued at a discount from their face values and do not pay interest. • T-notes and T-bonds are sold at face value and pay interest periodically.

8. U.S. Treasury Securities (Cont…) • T-bills are issued with a original time to maturity of one year or less. • Consequently they are Money Market instruments. • T-notes and T-bonds have a time to maturity exceeding one year at the time of issue. • They are therefore Capital Market instruments.

9. Plain Vanilla & Bells and Whistles • The most basic form of a bond is called the Plain Vanilla version. • This is true for all securities, not just for bonds. • More complicated versions are said to have `Bells and Whistles’ attached.

10. Face Value • It is the principal value underlying the bond. • It is the amount payable by the borrower to the lender at maturity. • It is the amount on which the periodic interest payments are calculated.

11. Term to Maturity • It is the time remaining in the life of the bond. • It represents the length of time for which interest has to be paid as promised. • It is represents the length of time after which the face value will be repaid.

12. Coupon • The coupon payment is the periodic interest payment that has to be made by the borrower. • The coupon rate when multiplied by the face value gives the dollar value of the coupon. • Most bonds pays coupons on a semi-annual basis.

13. Example of Coupon Calculation • Consider a bond with a face value of $1000. • The coupon rate is 8% per annum paid semi-annually. • So the bond holder will receive 1000 x 0.08 ___ = $40 every six months. 2

14. Yield to Maturity (YTM) • Yield to maturity is the rate of return that an investor will get if he buys the bond at the prevailing market price and holds it till maturity. • In order to get the YTM, two conditions must be satisfied. • The bond must be held till maturity. • All coupon payments received before maturity must be reinvested at the YTM.

15. Value of a Bond • A bond holder gets a stream of contractually promised payments. • The value of the bond is the value of this stream of cash flows. • However you cannot simply add up cash flows which are arising at different points in time. • Such cash flows have to be discounted before being added.

16. Price versus Yield • Price versus yield is a chicken and egg story, that is, we cannot say which comes first. • If we know the yield that is required by us, we can quote a price accordingly. • Similarly, once we acquire the asset at a certain price, we can work out the corresponding yield.

17. Bond Valuation • A bond is an instrument that will pay identical coupon payments every period, usually every six months, for a number of years, and will then repay the face value at maturity. • The periodic cash flows obviously constitute an annuity. • The terminal face value is a lump sum payment.

18. Bond Valuation (Cont…) • Consider a bond that pays a semi-annual coupon of $C/2, and which has a face value of $M. • Assume that there are N coupons left, and that we are standing on a coupon payment date. • That is, we are assuming that the next coupon is exactly six months away. • The required annual yield is y, which implies that the semi-annual yield is y/2.

19. Bond Valuation (Cont…) • The present value of the coupon stream is:

20. Bond Valuation (Cont…) • The present value of the face value is:

21. Bond Valuation (Cont…) • So the price of the bond is:

22. Illustration • IBM has issued a bond with a face value of $1,000. • The coupon is 8% per year to be paid on a semi-annual basis, on July 15 and January 15 every year. • Assume that today is 15 July 2002 and that the bond matures on 15 January 2022. • The required yield is 10% per annum.

23. Illustration (Cont…)

24. Par, Discount & Premium Bonds • In the above example, the price of the bond is less than the face value of $1,000. • Such a bond is called a Discount Bond, since it is trading at a discount from the face value. • The reason why it is trading for less than the face value is because the required yield of 10% is greater than the rate of 8% that the bond is paying by way of interest.

25. Par, Discount & Premium Bonds • If the required yield were to equal the coupon rate, the bond would sell for $1,000. • Such bonds are said to be trading at Par. • If the required yield were to be less than the coupon rate the price will exceed the face value. • Such bonds are called Premium Bonds, since they are trading at a premium over the face value.

26. Zero Coupon Bonds • A Plain Vanilla bond pays coupon interest every period, typically every six months, and repays the face value at maturity. • A Zero Coupon Bond on the other hand does not pay any coupon interest. • It is issued at a discount from the face value and repays the principal at maturity. • The difference between the price and the face value constitutes the interest for the buyer.

27. Illustration • Microsoft is issuing zero coupon bonds with 5 years to maturity and a face value of $10,000. • If you want a yield of 10% per annum, what price will you pay? • The price of the bond is obviously the present value of a single cash flow of $10,000, discounted at 10%.

28. Illustration (Cont…) • In practice, we usually discount the face value using a semi-annual rate of y/2, where y in this case is 10%. • This is to facilitate comparisons with conventional bonds which pay coupon interest every six months.

29. Zero Coupon Bonds • Zero coupon bonds are called zeroes by traders. • They are also referred to as Deep Discount Bonds. • They should not be confused with Discount Bonds, which are Plain Vanilla bonds which are trading at a discount from the face value.

30. Valuation in between Coupon Dates • While valuing a bond we assumed that we were standing on a coupon payment date. • This is a significant assumption because it implies that the next coupon is exactly one period away. • What should be the procedure if the valuation date is in between two coupon payment dates?

31. The Procedure for Treasury Bonds • Calculate the actual number of days between the date of valuation and the next coupon date. • Include the next coupon date. • But do not include the starting date. • Let us call this interval N1.

32. Treasury Bonds (Cont…) • Calculate the actual number of days between the coupon date preceding the valuation date and the following coupon date. • Once again include the ending date but exclude the starting date. • Let us call this time interval as N2.

33. Treasury Bonds (Cont…) • The next coupon is then k periods away where

34. Illustration • There is a Treasury bond with a face value of $1,000. • The coupon rate is 8% per annum, paid on a semi-annual basis. • The coupon dates are 15 July and 15 January. • The maturity date is 15 January 2022. • Today is 15 September 2002.

35. No. of Days Till the Next Coupon Date

36. No. of Days between Coupon Dates

37. Treasury Bonds (Cont…) • K = 122/184 = .6630 • This method is called the Actual/Actual method and is often pronounced as the Ack/Ack method. • It is the method used for Treasury bonds in the U.S.

38. The Valuation Equation • Wall Street professionals will then price the bond using the following equation.

39. Valuation • In our example

40. The 30/360 Approach • The Actual/Actual method is applicable for Treasury bonds in the U.S. • For corporate bonds in the U.S. we use what is called the 30/360 method. • In this method the number of days between successive coupon dates is always taken to be 180. • That is each month is considered to be of 30 days.

41. The 30/360 Approach (Cont…) • The number of days from the date of valuation till the next coupon date is calculated as follows. • The start date is defined as • D1 = (month1, day1,year1) • The ending date is defined as • D2 = (month2,day2,year2)

42. The 30/360 Approach (Cont…) • The number of days is then calculated as • 360(year2 – year1) + 30(month2 – month1) + (day2 – day1)

43. Additional Rules • If day1 = 31 then set day1 = 30 • If day1 = 30 or has been set equal to 30, then if day2 = 31, set day2 = 30 • If day1 is the last day of February, then set day1 = 30

44. Examples of Calculations

45. Pricing of A Corporate Bond • Let us assume that the bond considered earlier was a corporate bond rather than a Treasury bond.

46. Pricing (Cont…)

47. 30/360 European Convention • In this convention, if day2 = 31, then it is always set equal to 30. • So the additional rules are: • If day1 = 31 then set day1 = 30 • If day2 = 31 then set day2 = 30 • If day1 is the last day of February, then set day1 = 30

48. Examples of Calculations

49. Other Conventions • Actual/365 Convention • In this case the year is considered to have 365 days, while calculating the denominator, even in leap years. • Actual/365 Japanese • This is used for Japanese Government Bonds (JGBs) • It is similar to the Actual/365 method. • The only difference is that in this case, the extra day in February is ignored in leap years, while calculating both the numerator and the denominator.

50. Accrued Interest • The price of a bond is the present value of all the cash flows that the buyer will receive when he buys the bond. • Thus the seller is compensated for all the cash flows that he is parting with. • This compensation includes the amount due for the fact that the seller is parting with the entire next coupon, although he has held it for a part of the current coupon period.