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Bond Prices and Interest Rate Risk

Bond Prices and Interest Rate Risk. Chapter 5 Kidwell, Blackwell, Whidbee and Sias. The Time Value of Money. Investing—in financial assets or in real assets—means giving up consumption until later.

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Bond Prices and Interest Rate Risk

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  1. Bond Prices and Interest Rate Risk Chapter 5 Kidwell, Blackwell, Whidbee and Sias Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  2. The Time Value of Money • Investing—in financial assets or in real assets—means giving up consumption until later. • Positive time preference for consumption must be offset by adequate return. Opportunity cost of deferring consumption determines minimum rate of return required on a risk-free investment— • Present sums are theoretically invested at not less than this rate; • Future cash flows are discounted by at least this rate. • Time value of money is not really about inflation. • Inflation expectations affect discount rate, but • Deferred consumption has opportunity cost by definition. Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  3. Future Value or Compound Value The future value (FV) of a sum (PV) is FV = PV (1+i)n where iis the periodic interest rate and n is the number of compounding periods. Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  4. Present Value • The value today of a sum expected at a future time is given by • PV = FV * (1 / (1+i)^n) • With risk present, a premium will be added to the risk-free rate. • The higher the discount rate, the lower the present value. Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  5. Bond Pricing: What is a bond? • A form of loan—a debt security obligating a borrower to pay a lender principal and interest. • Borrower (issuer) promises contractually to make periodic payments to lender (investor or bondholder) over given number of years • At maturity, holder receives principal (or face value or par value). • Periodically before maturity, holder receives interest (coupon) payments determined by coupon rate. The coupon rate is set as a percentage of par on the face value of the bond Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  6. Bond Features • The bond indenture defines the terms of the contract. In general, the issuer promises to repay the principal amount and make coupon payments (most often semi-annually) over the life of the bond. • The par or face value of a bond is the amount the borrower owes the lender at maturity. Typically, $1000. • The maturity date is the date on which the principal is repaid. Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  7. How debt differs from equity • Debtholders do not have ownership or voting rights • Debt generally has a maturity date at which time the principal is repaid to the lender or owner of the debt. • Debt generally has fixed interest payments at specific dates • Bonds have first claim on the firm’s assets in the event of bankruptcy. Equity holders are “residual” claimants. Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  8. Types of Bonds • U.S. government bonds – The U.S. government is the largest individual issuer of bonds in our economy. • Used to finance the Federal budget • Generally considered the highest quality, or risk-free, debt • U.S. government has never defaulted and the markets are very liquid. Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  9. Types of Bonds • Corporate bonds • The corporate bond market is very large, very active and there are many large volume traders • Institutional investors, i.e., life insurance companies, pension funds, mutual funds, hold large amounts of the this debt • Corporations will have many bond issues trading at any given time • Corporate bond market is much less liquid than equity or U.S. government debt markets • Riskiness of corporate bonds varies across firms Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  10. Types of Bonds • Municipal bonds are issued by local or state governments and agencies • To fund local projects • These bonds can be quite risky – depending on the tax revenues of localities • International bonds are issued by foreign governments, or foreign corporations. • International bonds also have foreign exchange risk Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  11. Bond contracts • The contract for a bond is called its “indenture.” It lays out the financial terms of a bond and defines the contractual obligations between the borrower and the lender. • Name of the issuer • Maturity date and redemption value • Coupon rate – generally fixed but can be floating (or zero) • Dates of scheduled payments Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  12. Additional bond features that would be defined in the indenture • A call feature allows the firm to redeem or call a debt issue prior to maturity. Bonds are most likely to be called when interest rates have declined. • A sinking fund requires the gradual retirement of debt issue through repurchase or deposits to a sinking fund account. • Convertible debt is convertible at the option of the holder into common stock. Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  13. Bond features (continued) • Some bonds are sold with warrants which give the holder the option to purchase common stock. • Some bonds have “put” features which allow the holder to sell the bond back to the issuer under special circumstances. • Coupon rates on new bonds are usually fixed. • Coupon rates are generally chosen so that the bond will sell at or near par value when issued. Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  14. Bond features (continued) • Some bonds have coupon rates that float with treasury rates, LIBOR or commodity prices. • Original issue discount (OID) bonds are bonds issued with a coupon below prevailing rates. • Zero coupon bonds are OID bonds that pay no coupon payments at all. Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  15. What is a bond? Example • Par value = $1000 • Coupon rate = 5% • Issued today • Matures 30 years from today • Annual coupon payments • So, the holder receives (the issuer pays) : • $50 per year interest for 30 years (coupon rate * par value) • $1,000 par value at the end of year 30 Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  16. Bond pricing: Bond cash flows • Bondholder thus owns the right to a stream of cash flows: • Ordinary annuity of interest payments • Future lump sum in return of par value • These cash flows are discounted to their present value to find the bond’s value. • The same process can be used at any point during the life of the bond. Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  17. Bond Pricing: Present Value • Thus, the value or price of a bond is the present value of the future cash flows promised, discounted at the market rate of interest consistent with the riskiness of the promised cash flows. Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  18. PV of Bond Cash Flows • PB = Price of Bond • Ct = coupon at period t • Fn = Par value due at maturity • i = market interest rate (discount rate or market yield); and • n = number of periods to maturity Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  19. Bond Pricing: Principles • Cash flows are assumed to flow at end of the period and to be reinvested at i. Bonds typically pay interest semiannually. • Increasing i decreases price (PB); decreasing i increases price; thus bond prices and interest rates move inversely. • If market rate equals coupon rate, bond trades at par. • If coupon rate exceeds market rate, the bond trades above par—at a premium. • If market rate exceeds coupon rate, bond trades below par—at a discount. Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  20. Zero coupon bonds are “pure discount” securities • No periodic coupon payments. • Issued at discount from par. • Single payment of par value at maturity. • PB is simply PV of FV represented by par value, discounted at market rate. • PB = Fn / (1+i)^n Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  21. Risk factors in bonds Yield rewards investor for at least 3 risks: • Credit or default risk: chance that issuer may be unable or unwilling to pay as agreed. • Reinvestment risk: potential effect of variability of market interest rates on return at which payments can be reinvested when received. • Price risk: Inverse relationship between bond prices and interest rates. Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  22. Bond yields: Set by market • Discount rate at which bond price equals discounted PV of expected payments. • Measure of return ideally capturing impact of • Coupon payments • Income from reinvestment of coupons • Any capital gain or loss Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  23. Common Yield Measures • Yield to Maturity • Expected Yield • Realized Yield • Total Return Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  24. Yield to Maturity • Investor's expected yield if bond is held to maturity and all payments are reinvested at same yield. • Normally determined by iteration—try different discount rates until PB=present value of future payments. Analogous to IRR of a capital project. • The longer until maturity, the less valid the reinvestment assumption. Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  25. Computing Yield to Maturity • Investor buys 5% percent coupon (semiannual payments) bond for $951.90 • Bond matures in 3 years. • Solve the bond pricing equation for the interest rate (i) such that price paid for the bond equals PV of remaining payments due under the bond. Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  26. Computing Yield to Maturity • Solving either by trial and error or with a financial calculator results in yield to maturity of 3.4% semiannually, or 6.8% annually. Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  27. Expected Yield • Predicted yield for a given holding period (same procedure as YTM, but for some holding period shorter than maturity) Must forecast— Expected interest rate(s) Bond price at end of holding period Plug forecast results into bond pricing formula Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  28. Realized Yield • Investor’s ex-post or “hindsight” actual rate of return, given the cash flows actually received and their timing. May differ from YTM due to— • change in the amount or timing of promised payments (e.g. default). • change in market interest rates affecting premium or discount. Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  29. Computing Realized Yield • Investor pays $1,000 for 10-year 8% annual coupon bond; sells bond 3 years later for $902.63. • Solve for i such that $1,000 (the original investment) equals PV of 2 annual payments of $80 followed by a 3rd annual payment of $982.63 (the actual cash flows this investor received). Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  30. Computing Realized Yield • Solve by trial and error or with a financial calculator results in realized yield of 4.91% Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  31. Total Return • Yield metric that considers capital gains or losses as well as changes in reinvestment rate. • Find interest rate that compounds initial purchase price to sum of terminal value of bond plus future value of all coupon payments received (based on known or assumed reinvestment rate). Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  32. Computing Total Return • Terminal Value of Bond + Future Value of Reinvested Interest Coupons = Total Accumulated • PB = Total Accumulated / (1+i)^n • Solve for i Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  33. Total Return – Example • Expect to hold a bond for four years, 8% annual coupon. Price today is $1000 • Expect to sell the bond at 1098.35. Thus we expect interest rates to fall • What is the total return if we can reinvest the coupons at 7%? Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  34. Total Return • What is the future value of the coupon payments at t=4? • N=4, I=7, PV=0, PMT=80  FV = 360.49 • The future sale price is $1098.35. Thus total cash flows at t=4 is equivalent to $1098.35 + $360.49 • Find the IRR that shows return on: • 1000 = (1098.35 + 360.49) / (1 + I ) ^ 4  9.9% Chapter 5 Kidwell, Blackwell, Whidbee & Sias

  35. Current yield • Investors may be holding a bond for only a short period of time (~1 year) • In this case, they are interested in the “current yield.” • The current yield is the amount of the annual coupon divided by the current market price of the bond Bonds and Their Valuation

  36. Current yield • A bond trades today at $900 and pays an annual coupon of $90. What is the current yield on the bond if purchased today? • Current yield = Annual coupon / current trading price = 90 / 900 = 10% Bonds and Their Valuation

  37. Other bond value measures • Yield to call – what is the yield of the bond if it is paid off as of its yield date. • Note that the corporation may also pay a premium to face value at the call as compensation to investors for early retirement of the debt • This is a bond feature that would have been known in the indenture and would have been priced in the initial issue price. Bonds and Their Valuation

  38. Obtaining Bond Information • On line bond information • Listings include coupon rate, maturity year, current yield, trading volume, closing price, and net change in price from previous day. • Also, see Moody’s or Standard & Poor’s bond guides. Or, EDGAR (www.sec.gov) for the indentures and information about the bond contract and issuing firm. Bonds and Their Valuation

  39. The Yield Curve is not Flat • When the yield curve is not flat (I.e., when observed yields are not the same for all maturities), the correct procedure for valuing a bond promising a stream of known cash payments is to discount each of the payments at the rate corresponding to a pure discount bond of its maturity and then add the resulting individual values. • The yield to maturity can be found from this calculation. Bonds and Their Valuation

  40. Example: Bond Valuation • Suppose you are valuing a bond that pays annual coupons of 10% on the face value of $1000. The bond matures in three years. • The cash flows associated with the bond are as follows: • CF at t=1  $100 • CF at t=2  $100 • CF at t=3  $1100 Bonds and Their Valuation

  41. Example: Bond Valuation • You know that the yield of a 1-year pure discount bond is 5.5%, of a 2-year pure discount bond is 6.0% and of a 3-year pure discount bond is 6.5%. • What is the price you are willing to pay for the bond? • What is the yield to maturity of the bond? Bonds and Their Valuation

  42. Example: Bond Valuation • Value each of the cash flows at its respective yield. • Price = $100 / (1+.055) + $100 / (1.06)^2 + $1100 / (1.065)^3 = $1094.42 • What is the yield to maturity on this bond: • N=3, PV= -$1094.42, PMT=$100, FV=$1000  I= 6.4389 Bonds and Their Valuation

  43. Variation in Bond Prices • Bond prices (and YTMs) will vary with many factors: • Creditworthiness of the issuer • Maturity • Coupon rate • Tax considerations • Bond features – callability, convertibility, etc. • Closeness to maturity Bonds and Their Valuation

  44. Bond Price Volatility • Next class! Chapter 5 Kidwell, Blackwell, Whidbee & Sias

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