CHAPTER SEVEN: BOND ANALYSIS AND INVESTMENT pdf

CHAPTER SEVEN: BOND ANALYSIS AND INVESTMENT 06/08/2011 1 Bond Values • Bond values are discussed in one of two ways: – The dollar price – The yield to maturity • These two methods are equivalent since a price implies a yield, and vice-versa 06/08/2011 2 Bond Yields • There are several ways that we can describe the rate of return on a bond: – Coupon rate – Current yield – Yield to maturity – Modified yield to maturity – Yield to call – Realized Yield 06/08/2011 3 The Coupon Rate • The coupon rate of a bond is the stated rate of interest that the bond will pay • The coupon rate does not normally change during the life of the bond, instead the price of the bond changes as the coupon rate becomes more or less attractive relative to other interest rates • The coupon rate determines the dollar amount of the annual interest payment: Annual Pmt Coupon Rate Face Value  06/08/2011 4 The Current Yield • The current yield is a measure of the current income from owning the bond • It is calculated as: CY Annual Pmt Face Value  06/08/2011 5 The Yield to Maturity • The yield to maturity is the average annual rate of return that a bondholder will earn under the following assumptions: – The bond is held to maturity – The interest payments are reinvested at the YTM • The yield to maturity is the same as the bond’s internal rate of return (IRR) 06/08/2011 6 The Modified Yield to Maturity • The assumptions behind the calculation of the YTM are often not met in practice • This is particularly true of the reinvestment assumption • To more accurately calculate the yield, we can change the assumed reinvestment rate to the actual rate at which we expect to reinvest • The resulting yield measure is referred to as the modified YTM, and is the same as the MIRR for the bond 06/08/2011 7 The Yield to Call • Most corporate bonds, and many older government bonds, have provisions which allow them to be called if interest rates should drop during the life of the bond • Normally, if a bond is called, the bondholder is paid a premium over the face value (known as the call premium) • The YTC is calculated exactly the same as YTM, except: – The call premium is added to the face value, and – The first call date is used instead of the maturity date 06/08/2011 8 The Realized Yield • The realized yield is an ex-post measure of the bond’s returns • The realized yield is simply the average annual rate of return that was actually earned on the investment • If you know the future selling price, reinvestment rate, and the holding period, you can calculate an ex-ante realized yield which can be used in place of the YTM (this might be called the expected yield) 06/08/2011 9 Calculating Bond Yield Measures • As an example of the calculation of the bond return measures, consider the following: – You are considering the purchase of a 2-year bond (semiannual interest payments) with a coupon rate of 8% and a current price of $964.54. The bond is callable in one year at a premium of 3% over the face value. Assume that interest payments will be reinvested at 9% per year, and that the most recent interest payment occurred immediately before you purchase the bond. Calculate the various return measures. – Now, assume that the bond has matured (it was not called). You purchased the bond for $964.54 and reinvested your interest payments at 9%. What was your realized yield? 06/08/2011 10 [...]... duration of bond 1 is longer than that of bond two, so you would expect bond 1 to gain more if rates actually drop – Pbond 1, 8%= 920.15; Pbond 1, 7%= 959.00; gain = 38.85 – Pbond 2, 8%= 1159.71; Pbond 2, 7%= 1205.01; gain = 45.30 • Bond 1 has actually changed by less than bond 2 What happened? Well, if we figure the percentage change, we find that bond 1 actually gained by more than bond 2 • %Dbond 1 =... partial derivative of the bond valuation equation wrt the yield 06/08/2011 33 Why is Duration Better than Term? • Earlier, it was noted that duration is a better measure than term to maturity To see why, look at the following example: • Suppose that you are comparing two five-year bonds, and are expecting a drop in yields of 1% almost immediately Bond 1 has a 6% coupon and bond 2 has a 14% coupon Which... preferred habitat hypothesis because it contends that interest rates are determined by supply and demand and that different investors have preferred maturities from which they do no stray • There is not much support for this hypothesis S D S D Insurance Companies Banks 06/08/2011 27 Bond Price Volatility • Bond prices change as any of the variables change: – Prices vary inversely with yields – The longer... bonds is: – Value the bond as of the last payment date – Take that value forward to the current point in time This is the total price that you will actually pay – To get the quoted price, subtract the accrued interest • We can also start by valuing the bond as of the next coupon date, and then discount that value for the fraction of the period remaining 06/08/2011 15 Valuing Bonds Between Coupon Dates... years, semiannual payments of $50, and a required return of 7% per year) • As of period 0 (today), the bond is worth $1,079.93 As of next period (with only 5 remaining payments) the bond will be worth $1,067.73 Note that: 1067.73  1079.931.035  50 1 P1 P0 Interest earned • So, if we take the period zero value forward one period, you will get the value of the bond at the next period including the... month and year Not all fixed-income markets use the same convention: – 30/360 – 30 days in a month, 360 days in a year This is used in the corporate, agency, and municipal markets – Actual/Actual – Uses the actual number of days in a month and year This convention is used in the U.S Treasury markets • Two other possible day count conventions are: – Actual/360 – Actual/365 • Obviously, when valuing bonds... year 06/08/2011 12 Bond Valuation in Practice • The preceding examples ignore a couple of important details that are important in the real world: – Those equations only work on a payment date In reality, most bonds are purchased in between coupon payment dates Therefore, the purchaser must pay the seller the accrued interest on the bond in addition to the quoted price – Various types of bonds use different... 06/08/2011 28 Measuring Term to Maturity • It is difficult to compare bonds with different maturities and different coupons, since bond price changes are related in opposite ways to these variables • Macaulay developed a way to measure the average term to maturity that also takes the coupon rate into account • This measure is known as duration, and is a better indicator of volatility than term to maturity... Duration is calculated as: N D  t 1 Pmt t  t  1  i t Bond Pr ice • So, Macaulay’s duration is a weighted average of the time to receive the present value of the cash flows • The weights are the present values of the bond s cash flows as a proportion of the bond price 06/08/2011 30 Calculating Duration • Recall our earlier example bond with a YTM of 5% per six-months: -964.54 40 40 0 D 40 1,000... regarding the number of days in a month and year 06/08/2011 13 Valuing Bonds Between Coupon Dates (cont.) • Imagine that we are halfway between coupon dates We know how to value the bond as of the previous (or next even) coupon date, but what about accrued interest? • Accrued interest is assumed to be earned equally throughout the period, so that if we bought the bond today, we’d have to pay the seller . CHAPTER SEVEN: BOND ANALYSIS AND INVESTMENT 06/08/2011 1 Bond Values • Bond values are discussed in one of two ways: – The dollar price –. referred to as the modified YTM, and is the same as the MIRR for the bond 06/08/2011 7 The Yield to Call • Most corporate bonds, and many older government bonds, have provisions which allow. coupon rate of a bond is the stated rate of interest that the bond will pay • The coupon rate does not normally change during the life of the bond, instead the price of the bond changes as