1. 10 C h a p t e r Bond Prices and Yields second edition Fundamentals of Investments Valuation & Management Charles J. Corrado Bradford D. Jordan McGraw Hill / IrwinSlides by Yee-Tien (Ted) Fu

2.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 2 Bond Prices and Yields Our goal in this chapter is to understand the relationship between bond prices and yields, and to examine some of the fundamental tools of bond risk analysis used by fixed-income portfolio managers. Goal

3.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 3 Bond Basics  A bond essentially is a security that offers the investor a series of fixed interest payments during its life, along with a fixed payment of principal when it matures.  So long as the bond issuer does not default, the schedule of payments does not change.  When originally issued, bonds normally have maturities ranging from 2 years to 30 years, but bonds with maturities of 50 or 100 years also exist.  Bonds issued with maturities of less than 10 years are usually called notes.  A very small number of bond issues have no stated maturity, and these are referred to as perpetuities or consols.

4.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 4 Bond Basics  U.S. Treasury bonds are straight bonds.  Special features may be attached, creating convertible bonds, “putable” bonds, “putable” bonds have a put feature that grants bondholders the right to sell their bonds back to the issuer at a special put price. Straight bond An IOU that obligates the issuer to pay to the bondholder a fixed sum of money (called the principal, par value, stated value or face value) at the bond’s maturity, along with constant, periodic interest payments (called coupons) during the life of the bond.

5.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 5 Bond Basics  Two basic yield measures for a bond are its coupon rate and current yield.

6.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 6 Bond Basics  example1, suppose a $1,000 par value bond pays semiannual coupons of $40. The annual coupon is then $80, and stated as a percentage of par value the bond's coupon rate is  $80 / $1,000 = 8%.  example2, suppose a $1,000 par value bond paying an $80 annual coupon has a price of $1,032.25.  The current yield is $80 / $1,032.25 = 7.75%.

7.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 7 Straight Bond Prices and Yield to Maturity Yield to maturity (YTM) The discount rate that equates a bond’s price with the present value of its future cash flows.

8.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 8 Straight Bond Prices and Yield to Maturity Bond price = present value of all the coupon payments + present value of the principal payment whereC=annual coupon, the sum of 2 semiannual coupons FV=face value M=maturity in years

9.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 9 Straight Bond Prices and Yield to Maturity  Suppose a bond has a $1,000 face value, 20 years to maturity, an 8 percent coupon rate, and a yield of 9 percent. What’s the price?

10.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 10  At simple interest:  P = A/(1 + nr)  At interest compounded annually:  P = A/(1 + r)n  At interest compounded q times a year:  P = A/(1 + r/q)nq

11.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 11 Straight Bond Prices and Yield to Maturity

12.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 12 Premium and Discount Bonds  Bonds are commonly distinguished according to the relative relationship between their selling price and their par value.  Premium bonds:price > par value YTM < coupon rate  Discount bonds:price < par value YTM > coupon rate  Par bonds:price = par value YTM = coupon rate

13.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 13 Premium and Discount Bonds

14.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 14 Premium and Discount Bonds  In general, when the coupon rate and YTM are held constant … for discount bonds: the longer the term to maturity, the greater the discount from par value, and for premium bonds: the longer the term to maturity, the greater the premium over par value.

15.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 15 Premium and Discount Bonds  Example 10.2: Premium and Discount Bonds. Suppose a bond has a $1,000 face value, with eight years to maturity and a 7 percent coupon rate. If its yield to maturity is 9 percent, does this bond sell at a premium or discount? Verify your answer by calculating the bond’s price.  Since the coupon rate is smaller than the yield, this is a discount bond.

16.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 16 Premium and Discount Bonds  Example 10.3: Premium Bonds Consider two bonds, both with a 9 percent coupon rate and the same yield to maturity of 7 percent, but with different maturities of 5 and 10 years. Which has the higher price? Verify your answer by calculating the prices.  First, since both bonds have a 9 percent coupon and a 7 percent yield, both bonds sell at a premium. Based on what we know, the one with the longer maturity will have a higher price.  We can check these conclusions by calculating the prices as follows:

17.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 17 Premium and Discount Bonds

18.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 18 Premium and Discount Bonds  Example 10.4: Discount Bonds Now consider two bonds, both with a 9 percent coupon rate and the same yield to maturity of 11 percent, but with different maturities of 5 and 10 years. Which has the  higher price? Verify your answer by calculating prices.  These are both discount bonds. (Why?) The one with the shorter maturity will have a higher price. To check, the prices can be calculated as follows:

19.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 19 Premium and Discount Bonds

20.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 20 Relationships among Yield Measures  Since the current yield is always between the coupon rate and the yield to maturity (unless the bond is selling at par) … for premium bonds: coupon rate > current yield > YTM for discount bonds: coupon rate < current yield < YTM for par value bonds: coupon rate = current yield = YTM

21.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 21 A note on bond price quotes  Clean price : the price of a bond net of accrued interest, this the price that is typically quoted.  Dirty price : the price of a bond including accrued interest, also known as the full or invoice price, this is the price the buyer actually pays.

22.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 22 Calculating Yields  To calculate a bond’s yield given its price, we use the straight bond formula and then try different yields until we come across the one that produces the given price.  To speed up the calculation, financial calculators and spreadsheets may be used.

23.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 23 Yield to Call  A callable bond allows the issuer to buy back the bond at a specified call price anytime after an initial call protection period, until the bond matures.

24.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 24 Yield to Call  Yield to call (YTC) is a yield measure that assumes a bond issue will be called at its earliest possible call date. whereC=constant annual coupon CP=call price of the bond T=time in years to earliest possible call date YTC=yield to call assuming semiannual coupons Callable bond price

25.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 25 Interest Rate Risk  The yield actually earned or “realized” on a bond is called the realized yield, and this is almost never exactly equal to the yield to maturity, or promised yield. Interest rate risk The possibility that changes in interest rates will result in losses in a bond’s value.

26.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 26 Interest Rate Risk and Maturity

27.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 27 Reinvestment Risk  A simple solution is to purchase zero coupon bonds. In practice however, U.S. Treasury STRIPS are the only zero coupon bonds issued in sufficiently large quantities, and they have lower yields than even the highest quality corporate bonds. Reinvestment rate risk The uncertainty about future or target date portfolio value that results from the need to reinvest bond coupons at yields not known in advance.

28.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 28 Price Risk versus Reinvestment Rate Risk  Interest rate increases act to decrease bond prices (price risk) but increase the future value of reinvested coupons (reinvestment rate risk), and vice versa. Price risk The risk that bond prices will decrease. Arises in dedicated portfolios when the target date value of a bond or bond portfolio is not known with certainty.

29.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 29 Immunization  It is possible to engineer a portfolio such that price risk and reinvestment rate risk offset each other more or less precisely. Immunization Constructing a portfolio to minimize the uncertainty surrounding its target date value.

30.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 30 Chapter Review  Bond Basics  Straight Bonds  Coupon Rate and Current Yield  Straight Bond Prices and Yield to Maturity  Straight Bond Prices  Premium and Discount Bonds  Relationships among Yield Measures

31.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 31 Chapter Review  More on Yields  Calculating Yields  Yield to Call  Interest Rate Risk and Malkiel’s Theorems  Promised Yield and Realized Yield  Interest Rate Risk and Maturity  Malkiel’s Theorems

32.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 32 Chapter Review  Duration  Macaulay Duration  Modified Duration  Calculating Macaulay’s Duration  Properties of Duration  Dedicated Portfolios and Reinvestment Risk  Dedicated Portfolios  Reinvestment Risk

33.  2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 10 - 33 Chapter Review  Immunization  Price Risk versus Reinvestment Rate Risk  Immunization by Duration Matching  Dynamic Immunization