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## CHAPTER 8

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**CHAPTER 8**BOND VALUATION AND RISK Dr David P Echevarria**BOND VALUATION**The value of any debt claim is equal to the sum of the discounted future cash flows. The discount [interest] for future cash flows is a function of the level of riskiness for a particular bond and is termed the Yield to Maturity (YTM). Bond valuation model; • Vb = Coupon * PVIFA + Face Value * PVIF Dr David P Echevarria**BOND VALUATION**• Valuation of Bonds with Annual, Semi-annual, or quarterly Payments • Two cash streams are expect for each bond • Coupons • Face or maturity value • Coupons valued like an annuity • Face Value a single discounted future cash flow • Methods for computing Bond Market Values • Bond Tables • Financial Calculators (preferred) Dr David P Echevarria**BOND VALUATION**• Impact of Interest Rate Movements on Bond Prices • Bond Prices move in the Opposite Direction to Interest Rates. • Bonds will sell at discounts or premiums or equal to Face values • Interest Rates move in the Same Direction as Inflationary Expectations • Interest Rates move in the Same Direction as Perceived Riskiness Dr David P Echevarria**BOND VALUATION**• Factors Affecting Bond Price Interest Rate Sensitivity • The time remaining to maturity; direct relationship • The size of the coupon payments • The frequency of coupon payments; i.e., annual, Semi-, quarterly, monthly • Measuring Sensitivity to Interest Rate Movements: Duration • As duration increases, the greater the sensitivity to interest rate fluctuations • Importance of determining the investment horizon • Key strategy for immunizing the yield on a bond portfolio Dr David P Echevarria**BOND VALUATION**• Determination of Bond Yields • Yield to Maturity (YTM) • Current Yield • Tax treatment of gains and loses • Premiums • Discounts • Using Expectations to Manage Total Returns on Bond Portfolios • If you know were interest rates are going you know where bond prices are going • Riding the yield curve or betting on the movement of interest rates Dr David P Echevarria**BOND PORTFOLIO MANAGEMENT**• Use of Duration as an Immunization Strategy "A portfolio of bonds is immunized from interest rate risk if the duration of the portfolio equals the desired investment horizon" Fisher and Weil • Requires a known investment horizon; when do you need the cash? • Involves periodic adjustment in portfolio composition; see #3 below • Increase in YTM after the position is set results in a decrease in duration and vice-versa (Reinvestment of cash flows at higher rates than original YTM) • Duration affected by calls, serial redemptions, and sinking fund provisions Dr David P Echevarria**Managing Bond Risk: Duration**Dr David P Echevarria**Duration for a Zero Coupon Bond**Effects of Coupon Rates on Duration: As coupon rates increase, duration decreases and vice-versa. As YTM decrease, duration increases and vice versa. The duration for a zero-coupon bond is equal to its maturity. Dr David P Echevarria**BOND PORTFOLIO MANAGEMENT**• Use of Derivative Securities as Hedges • Interest rate futures, as well as options on futures • May also involve currency hedges • SWAP agreements may also be used Dr David P Echevarria**HOMEWORK QUESTIONS**• What cash flows are associated with bond investments? • What effects do interest rate increases (decreases) have on; • Market values of bonds? • Current yields? • Yields to maturity? • Duration measures? • What does it mean when a bond sells at par, at a discount, at a premium? • What does it mean to immunize a bond portfolio? • What information is necessary in order to make good bond investments? Dr David P Echevarria