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1、Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall,4-1,Chapter 4 Bond Price Volatility,Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall,4-2,Learning Objectives,After reading this chapter, you will understandthe price-yield relationship of an option-free bondthe fact
2、ors that affect the price volatility of a bond when yields changethe price-volatility properties of an option-free bondhow to calculate the price value of a basis pointhow to calculate and interpret the Macaulay duration, modified duration, and dollarduration of a bondwhy duration is a measure of a
3、bonds price sensitivity to yield changes,Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall,4-3,Learning Objectives (continued),After reading this chapter, you will understandthe spread duration measure for fixed-rate and floating-rate bondshow to compute the duration of a portfolio
4、and contribution to portfolio durationlimitations of using duration as a measure of price volatilityhow price change estimated by duration can be adjusted for a bonds convexityhow to approximate the duration and convexity of a bondthe duration of an inverse floaterhow to measure a portfolios sensiti
5、vity to a nonparallel shift in interest rates (key rate duration and yield curve reshaping duration),Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall,4-4,Exhibit 4-2 Shape of Price-Yield Relationship for an Option-Free Bond,Price,Maximum Price,Yield,Copyright 2010 Pearson Education
6、, Inc. Publishing as Prentice Hall,4-5,Price Volatility Characteristics of Option-Free Bonds,There are four properties concerning the price volatility of an option-free bond: Although the prices of all option-free bonds move in the opposite direction from the change in yield required, the percentage
7、 price change is not the same for all bonds. For very small changes in the yield required, the percentage price change for a given bond is roughly the same, whether the yield required increases or decreases. For large changes in the required yield, the percentage price change is not the same for an
8、increase in the required yield as it is for a decrease in the required yield. For a given large change in basis points, the percentage price increase is greater than the percentage price decrease.An explanation for these four properties of bond price volatility lies in the convex shape of the price-
9、yield relationship.,Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall,4-6,Price Volatility Characteristics of Option-Free Bonds (continued),Characteristics of a Bond that Affect its Price Volatility There are two characteristics of an option-free bond that determine its price volati
10、lity: coupon and term to maturity. First, for a given term to maturity and initial yield, the price volatility of a bond is greater, the lower the coupon rate. This characteristic can be seen by comparing the 9%, 6%, and zero-coupon bonds with the same maturity. Second, for a given coupon rate and i
11、nitial yield, the longer the term to maturity, the greater the price volatility. This can be seen in Exhibit 4-3 (See Overhead 4-9) by comparing the five-year bonds with the 25-year bonds with the same coupon.,Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall,4-7,Copyright 2010 Pear
12、son Education, Inc. Publishing as Prentice Hall,4-8,Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall,4-9,Measures of Bond Price Volatility,Money managers, arbitrageurs, and traders need to have a way to measure a bonds price volatility to implement hedging and trading strategies. T
13、hree measures that are commonly employed: price value of a basis point yield value of a price change duration,Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall,4-10,Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall,4-10,Measures of Bond Price Volatility (continued),
14、Price Value of a Basis Point The price value of a basis point, also referred to as the dollar value of an 01, is the change in the price of the bond if the required yield changes by 1 basis point.,Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall,4-11,Copyright 2010 Pearson Educatio
15、n, Inc. Publishing as Prentice Hall,4-11,Measures of Bond Price Volatility (continued),Yield Value of a Price Change Another measure of the price volatility of a bond used by investors is the change in the yield for a specified price change.,Copyright 2010 Pearson Education, Inc. Publishing as Prent
16、ice Hall,4-12,Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall,4-12,Measures of Bond Price Volatility (continued),Duration The Macaulay duration is one measure of the approximate change in price for a small change in yield:where P = price of the bond C = semiannual coupon interest (in dollars) y = one-half the yield to maturity or required yield n = number of semiannual periods (number of years times 2) M = maturity value (in dollars),
