1. INVESTMENTS: Analysis and Management Third Canadian Edition INVESTMENTS: Analysis and Management Third Canadian Edition W. Sean Cleary Charles P. Jones Prepared by Khalil Torabzadeh University of Lethbridge

2. Chapter 11 Bond Yields and Prices

3. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Calculate the price of a bond. Explain the bond valuation process. Calculate major bond yield measures, including yield to maturity, yield to call, and horizon return. Account for changes in bond prices. Explain and apply the concept of duration. Learning Objectives

4. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Intrinsic value  Is an estimated value  Present value of the expected future cash flows  Required to compute intrinsic value Expected future cash flows Timing of expected cash flows Discount rate, or required rate of return by investors Bond Valuation Principle

5. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Value of a coupon bond: Bond Valuation Where P = The price of bond today (time period 0) C = the regular coupons or interest payments F = the face value of the bond n = the number of periods to maturity r = the appropriate discount rate or market yield

6. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Bond Valuation Biggest problem is determining the discount rate or required yield, r Required yield is the current market rate earned on comparable bonds with the same maturity and credit risk

7. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 The basic Components of Interest Rates: o Short-term riskless rate  Provides foundation for other rates RF ≈ RR + EI Where RF = short-term T- bill rate RR = the real risk-free rate of interest EI = the expected rate of inflation Bond Yields

8. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Maturity differentials  Term structure of interest rates Accounts for the relationship between time and yield for bonds the same in every other respect Risk premium  Yield spread or yield differential  Associated with issuer’s particular situation Interest Rates

9. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Measures of Bond Yields They include: o Current Yield o Yield to Maturity o Yield to Call o Realized (horizon) Yield

10. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Defined as the ratio of the coupon interest to the current market price, C/P Uses the current market price instead of the face amount of a bond ($1,000) Not a true measure of the return – does not account for the difference between bond’s purchase piece and eventual redemption at par value Current Yield

11. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Yield to maturity (YTM)  Rate of return on bonds most often quoted for investors  Promised compound rate of return received from a bond purchased at the current market price and held to maturity  Equates the present value of the expected future cash flows to the initial investment Similar to internal rate of return Yield to Maturity

12. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Solve for YTM (semi-annual coupons): Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM Yield to Maturity

13. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Yield to a specified call date and call price Substitute number of periods until first call date for and call price for face value (semi- annual coupons) Applies to callable bonds Yield to Call

14. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 For:(1) longer-term bonds (2) bonds with higher coupon rates (i.e., have more money to reinvest) NO reinvestment risk for “Zeroes” Reinvestment Risk

15. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates Can only be calculated after investment period is over Horizon return analysis  Bond returns based on assumptions about reinvestment rates Realized Yield

16. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Over time, bond prices that differ from face value must change Bond prices move inversely to market yields The change in bond prices due to a yield change is directly related to time to maturity and inversely related to coupon rate Bond Price Changes

17. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Holding maturity constant, a rate decrease will raise prices a greater percent than a corresponding increase in rates will lower prices Price Market yield Bond Price Changes

18. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Important considerations  Different effects of yield changes on the prices and rates of return for different bonds  Maturity inadequate measure of a bond’s economic lifetime  A measure is needed that accounts for both size and timing of cash flows Measuring Bond Price Volatility: Duration

19. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 A measure of a bond’s lifetime, stated in years, that accounts for the entire pattern (both size and timing) of the cash flows over the life of the bond The weighted average maturity of a bond’s cash flows  Weights determined by present value of cash flows Duration

20. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Need to time-weight present value of cash flows from bond Duration depends on three factors  Maturity of the bond  Coupon payments  Yield to maturity Calculating Duration

21. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Duration increases with time to maturity, but at a decreasing rate  For coupon paying bonds, duration is always less than maturity  For zero coupon-bonds, duration equals time to maturity Duration increases with lower coupons Duration increases with lower yield to maturity Duration Relationships

22. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Allows comparison of effective lives of bonds that differ in maturity, coupon Used in bond management strategies, particularly immunization Measures bond price sensitivity to interest rate movements, which is very important in any bond analysis Why is Duration Important?

23. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Modified Duration = D* = D/(1+r) D* can be used to calculate the bond’s percentage price change for a given change in interest rates It works well for “small” changes in interest rates and parallel shifts in the term structure of interest rates. Estimating Price Changes Using Duration

24. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Refers to the degree to which duration changes as the yield to maturity changes  Price-yield relationship is convex Duration equation assumes a linear relationship between price and yield Convexity largest for low coupon, long-maturity bonds, and low yield to maturity Convexity

25. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 To obtain maximum price volatility, investors should choose bonds with the longest duration Duration is additive  Portfolio duration is just a weighted average of each individual bond’s duration Duration measures volatility, which is one of the aspect of risk in bonds Duration Conclusions

26. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Appendix 11A Treasury Bill Yields and Prices T-bill are sold in Canada on a discount basis

27. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Appendix 11B Effective Duration For option-free bonds  Effective Duration = Modified Duration For bonds with embedded options  Effective Duration ≠ Modified Duration

28. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Appendix 11B Effective Convexity Percentage change in bond price = Duration effect + Convexity effect = (- Effective duration) (Δy) + (Convexity) (Δy) 2

29. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Appendix 11C Convertible Bonds Convertible Bonds  Bonds that are convertible into a specified number of C/S Terminology ie. How many shares per bond

30. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Where “r” is the required rate of return on identical (similar) non-convertible bonds. Appendix 11C Convertible Bonds

31. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Conversion Premium = Market price of convertible – Conversion value Minimum (Floor) Value = Maximum (straight bond value; conversion value) Appendix 11C Convertible Bonds

32. Cleary Jones/Investments: Analysis and Management, 3 rd Canadian Edition, Chapter 11 Why Issue/Buy Convertibles? Investors  income (interest) but at lower rate  participate in share price appreciation Firm  “lower” coupons  delayed equity financing (when share price rises)  usually have call feature attached

33. Copyright © 2009 John Wiley & Sons Canada, Ltd. All rights reserved. Reproduction or translation of this work beyond that permitted by Access Copyright (The Canadian Copyright Licensing Agency) is unlawful. Requests for further information should be addressed to the Permissions Department, John Wiley & Sons Canada, Ltd. The purchaser may make back-up copies for his or her own use only and not for distribution or resale. The author and the publisher assume no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information contained herein. Copyright