Chapter 13 Bond Selection

1. Chapter 13Bond Selection

2. Outline • Introduction • The meaning of bond diversification • Choosing bonds • Example: monthly retirement income

3. Introduction • In most respects selecting the fixed-income components of a portfolio is easier than selecting equity securities • There are ways to make mistakes with bond selection

4. The Meaning of Bond Diversification • Introduction • Default risk • Dealing with the yield curve • Bond betas

5. Introduction • It is important to diversify a bond portfolio • Diversification of a bond portfolio is different from diversification of an equity portfolio • Two types of risk are important: • Default risk • Interest rate risk

6. Default Risk • Default risk refers to the likelihood that a firm will be unable to repay the principal and interest of a loan as agreed in the bond indenture • Equivalent to credit risk for consumers • Rating agencies such as S&P and Moody’s function as credit bureaus for credit issuers

7. Default Risk (cont’d) • To diversify default risk: • Purchase bonds from a number of different issuers • Do not purchase various bond issues from a single issuer • E.g., Enron had 20 bond issues when it went bankrupt

8. Dealing With the Yield Curve • The yield curve is typically upward sloping • The longer a fixed-income security has until maturity, the higher the return it will have to compensate investors • The longer the average duration of a fund, the higher its expected return and the higher its interest rate risk

9. Dealing With the Yield Curve (cont’d) • The client and portfolio manager need to determine the appropriate level of interest rate risk of a portfolio

10. Bond Betas • The concept of bond betas: • States that the market prices a bond according to its level of risk relative to the market average • Has never become fully accepted • Measures systematic risk, while default risk and interest rate risk are more important

11. Choosing Bonds • Client psychology and bonds selling at a premium • Call risk • Constraints

12. Client Psychology and Bonds Selling at A Premium • Premium bonds held to maturity are expected to pay higher coupon rates than the market rate of interest • Premium bond held to maturity will decline in value toward par value as the bond moves towards its maturity date

13. Client Psychology & Bonds Selling at A Premium (cont’d) • Clients may not want to buy something they know will decline in value • There is nothing wrong with buying bonds selling at a premium

14. Call Risk • If a bond is called: • The funds must be reinvested • The fund manager runs the risk of having to make adjustments to many portfolios all at one time • There is no reason to exclude callable bonds categorically from a portfolio • Avoid making extensive use of a single callable bond issue

15. Constraints • Specifying return • Specifying grade • Specifying average maturity • Periodic income • Maturity timing • Socially responsible investing

16. Specifying Return • To increase the expected return on a bond portfolio: • Choose bonds with lower ratings • Choose bonds with longer maturities • Or both

17. Specifying Grade • A legal list specifies securities that are eligible investments • E.g., investment grade only • Portfolio managers take the added risk of noninvestment grade bonds only if the yield pickup is substantial

18. Specifying Grade (cont’d) • Conservative organizations will accept only U.S. government or AAA-rated corporate bonds • A fund may be limited to no more than a certain percentage of non-AAA bonds

19. Specifying Average Maturity • Average maturity is a common bond portfolio constraint • The motivation is concern about rising interest rates • Specifying average duration would be an alternative approach

20. Periodic Income • Some funds have periodic income needs that allow little or not flexibility • Clients will want to receive interest checks frequently • The portfolio manager should carefully select the bonds in the portfolio

21. Maturity Timing • Maturity timing generates income as needed • Sometimes a manager needs to construct a bond portfolio that matches a particular investment horizon • E.g., assemble securities to fund a specific set of payment obligations over the next ten years • Assemble a portfolio that generates income and principal repayments to satisfy the income needs

22. Socially Responsible Investing • Some clients will ask that certain types of companies not be included in the portfolio • Examples are nuclear power, military hardware, “vice” products

23. Example: Monthly Retirement Income • The problem • Unspecified constraints • Using S&P’s Bond Guide • Solving the problem

24. The Problem • A client has: • Primary objective: growth of income • Secondary objective: income • $1,100,000 to invest • Inviolable income needs of $4,000 per month

25. The Problem (cont’d) • You decide: • To invest the funds 50-50 between common stocks and debt securities • To invest in ten common stock in the equity portion (see next slide) • You incur $1,500 in brokerage commissions

26. The Problem (cont’d)

27. The Problem (cont’d) • Characteristics of the fund: • Quarterly dividends total $3,001 ($12,004 annually) • The dividend yield on the equity portfolio is 2.44% • Total annual income required is $48,000 or 4.36% of fund • Bonds need to have a current yield of at least 6.28%

28. Unspecified Constraints • The task is meeting the minimum required expected return with the least possible risk • You don’t want to choose CC-rated bonds • You don’t want the longest maturity bonds you can find

29. Using S&P’s Bond Guide • Figure 13-1 is an excerpt from the Bond Guide: • Indicates interest payment dates, coupon rates, and issuer • Provides S&P ratings • Provides current price, current yield

30. Using S&P’s Bond Guide (cont’d)

31. Solving the Problem • Setup • Dealing with accrued interest and commissions • Choosing the bonds • Overspending • What about convertible bonds?

32. Setup • You have two constraints: • Include only bonds rated BBB or higher • Keep the average maturities below fifteen years • Set up a worksheet that enables you to pick bonds to generate exactly $4,000 per month (see next slide)

33. Setup (cont’d)

34. Dealing With Accrued Interest and Commissions • Bond prices are typically quoted on a net basis (already include commissions) • Calculate accrued interest using the mid-term heuristic • Assume every bond’s accrued interest is half of one interest check

35. Choosing the Bonds • The following slide shows one possible solution: • Stock cost: $494,000 • Bond cost: $557,130 • Accrued interest: $9,350 • Stock commissions: $1,500 • Do you think this solution could be improved?

37. Overspending • The total of all costs associated with the portfolio should not exceed the amount given to you by the client to invest • The money the client gives you establishes another constraint

38. What About Convertible Bonds? • Convertible bonds can be included in a portfolio • Useful for a growth of income objective • People buy convertible bonds in hopes of price appreciation • Useful if you otherwise meet your income constraints

39. Immunization Strategies • A portfolio of bonds is said to be immunized (from interest rate risk) if its payoff at some future date is independent of the future levels of interest rates. • Immunization is closely related to the concept of duration.

40. Immunization consists of matching the duration of the portfolio’s assets and liabilities (obligations). • Suppose a firm has a future obligation Q. The prevailing interest rate is r, and the liability is N periods away. • The present value of this liability is denoted by V0=Q/(1+r)N.

41. Now suppose that the firm is currently hedging this liability with a bond whose value VB = V0 and whose coupon payments are denoted by P1,…,PN. • We thus have:

42. Suppose now that interest rates change from r to r+Dr. The new values of the future obligation and of the bond are:

43. Rearranging terms and recalling that V0=VB yields the following expression: • The left-hand side represents the duration of the bond, while the right-hand side represents the duration of the obligation (Since the obligation consisted of only one payment, the duration is its maturity).

44. In conclusion, in order for a portfolio to be immunized, you need to have: • DURATIONASSETS = DURATIONLIABILITIES • Caveat: this works only if the interest rates of various maturities all change in the same manner, i.e. if the yield curve shifts upward or downward in a parallel shift.

45. Immunization Example • You need to immunize an obligation whose present value V0 is $1,000. The payment is to be made 10 years from now, and the current interest rate is 6%. The payment is thus the future value of 1,000 at 6%, therefore it is: 1,000(1.06)10 = $1,790.85 • The Excel spreadsheet on the next slide shows three bonds that you have at your disposition to immunize the liability.

48. Values 10 years later, assuming interest rates do not change (The goal of getting $1,790.85 is still met)

49. Values 10 years later, assuming interest rates change to 5% right after we buy the bonds (The goal of getting $1,790.85 is not met by Bond 1 anymore)

50. Observations • If interest rates go down to 5%, Bond 1 does not meet the requirement anymore. • Bond 3, on the other hand, exceeds the payment that must be made in year 10. • The ability of Bond 2 to meet the obligation is barely affected. Why? Because its duration is 10 years, exactly matching the duration of the liability. Pick Bond 2.