【正文】 Chapter 12 FIXEDINCOME ANALYSIS Chapter 12 Questions ? What different bond yields are important to investors? ? How are the following major yields on bonds puted: current yield, yield to maturity, yield to call, and pound 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? Chapter 12 Questions ? When yields change, what characteristics of a bond cause differential price changes for individual bonds? ? What do we mean by the duration of a bond, how is it puted, and what factors affect it? ? What is modified duration and what is the relationship between a bond’s modified duration and its volatility? Chapter 12 Questions ? What is the convexity for a bond, what factors affect it, and what is its effect on a bond’s volatility? ? Under what conditions is it necessary to consider both modified duration and convexity when estimating a bond’s price volatility? 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 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: – P is 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 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 priceyield 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 The Yield Model The yield on the bond may be puted when we know the market price tnitt YCP )1(1?? ??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 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 ine 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 Realized (horizon) yield 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. Current Yield ? Similar to dividend yield for stocks, this measure is important to ine oriented investors CY = C/P ? where: – CY = the current yield on a bond – C = the annual coupon payment of t