1 / 27

Chapter 12

Chapter 12. FIXED-INCOME ANALYSIS. Chapter 12 Questions. What different bond yields are important to investors? How are the following major yields on bonds computed: current yield, yield to maturity, yield to call, and compound realized (horizon) yield?

alijah
Download Presentation

Chapter 12

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 12 FIXED-INCOME ANALYSIS

  2. Chapter 12 Questions • What different bond yields are important to investors? • How are the following major yields on bonds computed: current yield, yield to maturity, yield to call, and compound realized (horizon) yield? • What factors affect the level of bond yields at a point in time? • What economic forces cause changes in the yields on bonds over time?

  3. The Fundamentals of Bond Valuation • Like other financial assets,the value of a bond is the present value of its expected future cash flows: Vj = SCFt/(1+k)t

  4. The Fundamentals of Bond Valuation • To incorporate the specifics of bonds: P = S(Ci/2)/(1+Ym/2)t + Pp /(1+Ym/2)2n • This is the present value model where: • Pis the current market price of the bond • n is the number of years to maturity • Ci is the annual coupon payment • Ym is the yield to maturity of the bond • Pp is the par value of the bond

  5. Bond Price/Yield Relationships • Bond prices change as yields change, and have the following relationships: • When yield is below the coupon rate, the bond will be priced at a premium to par value • When yield is above the coupon rate, the bond will be priced at a discount from its par value • The price-yield relationship is not a straight line, but rather convex (This is convexity) • As yields decline, prices increase at an increasing rate • As yield increase, prices fall at a declining rate

  6. The Yield Model The yield on the bond may be computed when we know the market price Where: P = the current market price of the bond Ct= the cash flow received in period t Y = the discount rate that will discount the cash flows to equal the current market price of the bond

  7. Computing Bond Yields Yield Measure Purpose Coupon rate Measures the coupon rate or the percentage of par paid out annually as interest Current yield Measures current income rate Promised yield to maturity Measures expected rate of return for bond held to maturity Promised yield to call Measures expected rate of return for bond held to first call date Measures expected rate of return for a bond likely to be sold prior to maturity. It considers specified reinvestment assumptions and an estimated sales price. It can also measure the actual rate of return on a bond during some past period of time. Realized (horizon) yield

  8. Current Yield • Similar to dividend yield for stocks, this measure is important to income oriented investors CY = C/P • where: • CY = the current yield on a bond • C = the annual coupon payment of the bond • P = the current market price of the bond

  9. Promised Yield to Maturity • Widely used bond yield figure • Assumes • Investor holds bond to maturity • All the bond’s cash flow is reinvested at the computed yield to maturity Solve for Y that will equate the current price to all cash flows from the bond to maturity, similar to IRR

  10. Promised Yield to Maturity • For zero coupon bonds, the only cash flow is the par value at maturity. This simplifies the calculation of yield. P = 1,000/(1+Ym/2)2n • Where n is the number of years to maturity.

  11. Promised Yield to Call • When a callable bond is likely to be called, yield to call is the more appropriate yield measure than yield to maturity • As a rule of thumb, when a callable bond is selling at a price equal to par value plus one year of interest, the value should be based on yield to call

  12. Calculating Promised Yield to Call Where: P = market price of the bond Ct = annual coupon payment nc = number of years to first call Pc = call price of the bond

  13. Realized Yield • The horizon yield measures yield when the investor expects to sell the bond (for a price of Pf in hp time periods) prior to maturity or call

  14. Calculating Future Bond Prices • Expected future bond prices are an important calculation in several instances: • When computing horizon yield, we need an estimated future selling price • When issues are quoted on a promised yield, as with municipals • For portfolio managers who frequently trade bonds

  15. Calculating Future Bond Prices Where: Pf= estimated future price of the bond Ci = annual coupon payment n = number of years to maturity hp = holding period of the bond in years Ym = expected semiannual rate at the end of the holding period

  16. Adjusting for Differential Reinvestment Rates • The yield calculations implicitly assume reinvestment of early coupon payments at the calculated yield • If expectations are not consistent with this assumption, we can compound early cash flows at differential rates over the life of the bond and then find the yield based on an “Ending wealth” measure, which is calculated from the differential rates

  17. Yield Adjustments for Tax-Exempt Bonds • In order to compare taxable and tax-exempt bonds on an “equal playing field” for an investor, we calculate the fully taxable equivalent yield (FTEY) for tax-free bonds based on their returns FTEY = Tax-Free Annual Return/(1-T) • Where T is the investor’s marginal tax rate

  18. What Determines Interest Rates? • Inverse relationship with bond prices • Changes in interest rates have an impact on bond portfolios, in particular rising interest rates • It is therefore important to learn about what determines interest rates and to gain some insight as to forecasting future interest rates

  19. Forecasting interest rates • Interest rates are the cost of borrowing money, or the cost of “loanable funds” • Factors that affect the supply of loanable funds (through saving) and the demand for loanable funds (borrowing) affect interest rates • The goal is to monitor these factors, and to anticipate changes in interest rates and to be well-positioned to either benefit from the forecast or at least be protected from adverse changes in rates

  20. Determinants of Interest Rates • Nominal interest rates (i) can be broken down into the following components: i = RFR + I + RP where: • RFR = real risk-free rate of interest • I = expected rate of inflation • RP = risk premium • The key is to anticipate changes in any of these factors

  21. Determinants of Interest Rates • Alternatively, we can break down interest rate factors into two groups of effects: • Effect of economic factors • real growth rate • tightness or ease of capital market • expected inflation • supply and demand of loanable funds • Impact of bond characteristics • credit quality • term to maturity • indenture provisions • foreign bond risk (exchange rate risk and country risk)

  22. Determinants of Interest Rates Term structure of interest rates • One important source of interest rate variability is the time to maturity • The yield curve shows the relationship between bond yields and time to maturity at a point in time • Yield curve shapes • Rising curve (common) when rates are modest • Declining curve when rates are relatively high • Flat curves can happen any time • Humped when high rates are expected to decline • Note: usually relatively flat beyond 15 years

  23. Determinants of Interest Rates Term Structure Theories (what explains the changing shape of the yield curve?) • Expectations hypothesis • The shape of the yield curve depends on expected future interest rates and inflation rates • An upward-sloping curve indicates expectations of higher rates in the future • We can use this hypothesis to compute implied future (forward) interest rates • Yields of different maturities continually adjusting to estimates of future interest rates

  24. Determinants of Interest Rates Term Structure Theories • Liquidity preference hypothesis • Indicates that long term rates have to pay a premium over short term rates because: • Investors need a premium to compensate for the added price risk associated with long-term bonds • Borrowers are willing to pay higher rates on long-term debt to avoid refinancing risk • Works well in combination with the expectations hypothesis to explain the normal upward slope of the yield curve

  25. Determinants of Interest Rates Term Structure Theories • Segmented market hypothesis • Asserts that different investors, in particular institutions, have different maturity needs, so have “preferred habitats” along the yield curve • Interest rates in differentiated maturity markets are determined by unique supply and demand factors in those markets

  26. Determinants of Interest Rates • Term Structure and Trading • Knowledge of the term structure can aid in bond market trading strategies • For example, if the yield curve is sharply downward sloping, rates are likely to fall – lengthen bond maturities to take the most advantage of price appreciation as interest rates fall in the future

  27. Determinants of Interest Rates Yield Spreads • Bond investing strategies can focus on predicting various changing yield spreads, which exist between: • Segments: government bonds, agency bonds, and corporate bonds • Sectors: prime-grade municipal bonds versus good-grade municipal bonds, AA utilities versus BBB utilities • Different coupons within a segment or sector • Maturities within a given market segment or sector

More Related