Presentation on theme: "Chapter 12 Bond Prices and the Importance of Duration"— Presentation transcript:
1Chapter 12 Bond Prices and the Importance of Duration
2Outline Introduction Review of bond principles Bond pricing and returnsBond riskThe meaning of bond diversificationChoosing bondsExample: monthly retirement income
3IntroductionThe investment characteristics of bonds range completely across the risk/return spectrumAs part of a portfolio, bonds provide both stability and incomeCapital appreciation is not usually a motive for acquiring bonds
4Review of Bond Principles Identification of bondsClassification of bondsTerms of repaymentBond cash flowsConvertible bondsRegistration
5Identification of Bonds A bond is identified by:The issuerThe couponThe maturityFor example, five IBM “eights of 10” means $5,000 par IBM bonds with an 8% coupon rate and maturing in 2010
6Classification of Bonds IntroductionIssuerSecurityTerm
7Introduction The bond indenture describes the details of a bond issue: Description of the loanTerms of repaymentCollateralProtective covenantsDefault provisions
8IssuerBonds can be classified by the nature of the organizations initially selling them:CorporationFederal, state, and local governmentsGovernment agenciesForeign corporations or governments
9DefinitionThe security of a bond refers to what backs the bond (what collateral reduces the risk of the loan)
10Unsecured Debt Governments: Full faith and credit issues (general obligation issues) is government debt without specific assets pledged against itE.g., U.S. Treasury bills, notes, and bonds
11Unsecured Debt (cont’d) Corporations:Debentures are signature loans backed by the good name of the companySubordinated debentures are paid off after original debentures
12Secured Debt Municipalities issue: Revenue bonds Assessment bonds Interest and principal are repaid from revenue generated by the project financed by the bondAssessment bondsBenefit a specific group of people, who pay an assessment to help pay principal and interest
13Secured Debt (cont’d) Corporations issue: Mortgages Well-known securities that use land and buildings as collateralCollateral trust bondsBacked by other securitiesEquipment trust certificatesBacked by physical assets
14Term The term is the original life of the debt security Short-term securities have a term of one year or lessIntermediate-term securities have terms ranging from one year to ten yearsLong-term securities have terms longer than ten years
15Terms of RepaymentInterest onlySinking fundBalloonIncome bonds
16Interest Only Periodic payments are entirely interest The principal amount of the loan is repaid at maturity
17Sinking FundA sinking fund requires the establishment of a cash reserve for the ultimate repayment of the bond principalThe borrower can:Set aside a potion of the principal amount of the debt each yearCall a certain number of bonds each year
18BalloonBalloon loans partially amortize the debt with each payment but repay the bulk of the principal at the end of the life of the debtMost balloon loans are not marketable
19Income Bonds Income bonds pay interest only if the firm earns it For example, an income bond may be issued to finance an income-producing project
21AnnuitiesAn annuity promises a fixed amount on a regular periodic schedule for a finite length of timeMost bonds are annuities plus an ultimate repayment of principal
22Zero Coupon BondsA zero coupon bond has a specific maturity date when it returns the bond principalA zero coupon bond pays no periodic incomeThe only cash inflow is the par value at maturity
23Variable Rate BondsVariable rate bonds allow the rate to fluctuate in accordance with a market indexFor example, U.S. Series EE savings bonds
24Consols Consols pay a level rate of interest perpetually: The bond never maturesThe income stream lasts foreverConsols are not very prevalent in the U.S.
25DefinitionA convertible bond gives the bondholder the right to exchange them for another security or for some physical assetOnce conversion occurs, the holder cannot elect to reconvert and regain the original debt security
26Security-Backed Bonds Security-backed convertible bonds are convertible into other securitiesTypically common stock of the company that issued the bondsOccasionally preferred stock of the issuing firm, common stock of another firm, or shares in a subsidiary company
27Commodity-Backed Bonds Commodity-backed bonds are convertible into a tangible assetFor example, silver or gold
28Bearer Bonds Bearer bonds: Do not have the name of the bondholder printed on themBelong to whoever legally holds themAre also called coupon bondsThe bond contains coupons that must be clippedAre no longer issued in the U.S.
29Registered Bonds Registered bonds show the bondholder’s name Registered bondholders receive interest checks in the mail from the issuer
30Book Entry BondsThe U.S. Treasury and some corporation issue bonds in book entry form onlyHolders do not take actual delivery of the bondPotential holders can:Open an account through the Treasury Direct System at a Federal Reserve BankPurchase a bond through a broker
31Bond Pricing and Returns IntroductionValuation equationsYield to maturityRealized compound yieldCurrent yieldTerm structure of interest ratesSpot rates
32Bond Pricing and Returns (cont’d) The conversion featureThe matter of accrued interest
33IntroductionThe current price of a bond is the market’s estimation of what the expected cash flows are worth in today’s dollarsThere is a relationship between:The current bond priceThe bond’s promised future cash flowsThe riskiness of the cash flows
34Valuation equations Annuities Zero coupon bonds Variable rate bonds Consols
36Annuities (cont’d)Separating interest and principal components:
37Annuities (cont’d) Example A bond currently sells for $870, pays $70 per year (Paid semiannually), and has a par value of $1,000. The bond has a term to maturity of ten years.What is the yield to maturity?
38Annuities (cont’d) Example (cont’d) Solution: Using a financial calculator and the following input provides the solution:N = 20PV = $870PMT = $35FV = $1,000CPT I = 4.50This bond’s yield to maturity is 4.50% x 2 = 9.00%.
39Zero Coupon BondsFor a zero-coupon bond (annual and semiannual compounding):
40Zero Coupon Bonds (cont’d) ExampleA zero coupon bond has a par value of $1,000 and currently sells for $400. The term to maturity is twenty years.What is the yield to maturity (assume semiannual compounding)?
41Zero Coupon Bonds (cont’d) Example (cont’d)Solution:
47Yield to MaturityYield to maturity captures the total return from an investmentIncludes incomeIncludes capital gains/lossesThe yield to maturity is equivalent to the internal rate of return in corporate finance
50Realized Compound Yield The effective annual yield is useful to compare bonds to investments generating income on a different time schedule
51Realized Compound Yield (cont’d) ExampleA bond has a yield to maturity of 9.00% and pays interest semiannually.What is this bond’s effective annual rate?
52Realized Compound Yield (cont’d) Example (cont’d)Solution:
53Current Yield The current yield: Measures only the return associated with the interest paymentsDoes not include the anticipated capital gain or loss resulting from the difference between par value and the purchase price
54Current Yield (cont’d) For a discount bond, the yield to maturity is greater than the current yieldFor a premium bond, the yield to maturity is less than the current yield
55Current Yield (cont’d) ExampleA bond pays annual interest of $70 and has a current price of $870.What is this bond’s current yield?
56Current Yield (cont’d) Example (cont’d)Solution:Current yield = $70/$870 = 8.17%
57Yield Curve The yield curve: Is a graphical representation of the term structure of interest ratesRelates years until maturity to the yield to maturityIs typically upward sloping and gets flatter for longer terms to maturity
59Theories of Interest Rate Structure Expectations theoryLiquidity preference theoryInflation premium theory
60Expectations TheoryAccording to the expectations theory of interest rates, investment opportunities with different time horizons should yield the same return:
61Expectations Theory (cont’d) ExampleAn investor can purchase a two-year CD at a rate of 5 percent. Alternatively, the investor can purchase two consecutive one-year CDs. The current rate on a one-year CD is 4.75 percent.According to the expectations theory, what is the expected one-year CD rate one year from now?
62Expectations Theory (cont’d) Example (cont’d)Solution:
63Liquidity Preference Theory Proponents of the liquidity preference theory believe that, in general:Investors prefer to invest short term rather than long termBorrowers must entice lenders to lengthen their investment horizon by paying a premium for long-term money (the liquidity premium)Under this theory, forward rates are higher than the expected interest rate in a year
64Inflation Premium Theory The inflation premium theory states that risk comes from the uncertainty associated with future inflation ratesInvestors who commit funds for long periods are bearing more purchasing power risk than short-term investorsMore inflation risk means longer-term investment will carry a higher yield
65Spot RatesSpot rates:Are the yields to maturity of a zero coupon securityAre used by the market to value bondsThe yield to maturity is calculated only after learning the bond priceThe yield to maturity is an average of the various spot rates over a security’s life
66Spot Rates (cont’d) Spot Rate Curve Yield to Maturity Interest Rate Time Until the Cash Flow
67Spot Rates (cont’d) Example A six-month T-bill currently has a yield of 3.00%. A one-year T-note with a 4.20% coupon sells for 102.Use bootstrapping to find the spot rate six months from now.
68Spot Rates (cont’d) Example (cont’d) Solution: Use the T-bill rate as the spot rate for the first six months in the valuation equation for the T-note:
69The Conversion Feature Convertible bonds give their owners the right to exchange the bonds for a pre-specified amount or shares of stockThe conversion ratio measures the number of shares the bondholder receives when the bond is convertedThe par value divided by the conversion ratio is the conversion priceThe current stock price multiplied by the conversion ratio is the conversion value
70The Conversion Feature (cont’d) The market price of a bond can never be less than its conversion valueThe difference between the bond price and the conversion value is the premium over conversion valueReflects the potential for future increases in the common stock priceMandatory convertibles convert automatically into common stock after three or four years
71The Matter of Accrued Interest Bondholders earn interest each calendar day they hold a bondFirms mail interest payment checks only twice a yearAccrued interest refers to interest that has accumulated since the last interest payment date but which has not yet been paid
72The Matter of Accrued Interest (cont’d) At the end of a payment period, the issuer sends one check for the entire interest to the current bondholderThe bond buyer pays the accrued interest to the sellerThe bond sells receives accrued interest from the bond buyer
73The Matter of Accrued Interest (cont’d) ExampleA bond with an 8% coupon rate pays interest on June 1 and December 1. The bond currently sells for $920.What is the total purchase price, including accrued interest, that the buyer of the bond must pay if he purchases the bond on August 10?
74The Matter of Accrued Interest (cont’d) Example (cont’d)Solution: The accrued interest for 71 days is:$80/365 x 71 = $15.56Therefore, the total purchase price is:$920 + $15.56 = $935.56
78Interest Rate RiskInterest rate risk is the chance of loss because of changing interest ratesThe relationship between bond prices and interest rates is inverseIf market interest rates rise, the market price of bonds will fall
79Default RiskDefault risk measures the likelihood that a firm will be unable to pay the principal and interest on a bondStandard & Poor’s Corporation and Moody’s Investor Service are two leading advisory services monitoring default risk
80Default Risk (cont’d)Investment grade bonds are bonds rated BBB or aboveJunk bonds are rated below BBBThe lower the grade of a bond, the higher its yield to maturity
82DefinitionConvenience risk refers to added demands on management time because of:Bond callsThe need to reinvest coupon paymentsThe difficulty in trading a bond at a reasonable price because of low marketability
83Call Risk If a company calls its bonds, it retires its debt early Call risk refers to the inconvenience of bondholders associated with a company retiring a bond earlyBonds are usually called when interest rates are low
84Call Risk (cont’d) Many bond issues have: Call protection A period of time after the issuance of a bond when the issuer cannot call itA call premium if the issuer calls the bondTypically begins with an amount equal to one year’s interest and then gradually declining to zero as the bond approaches maturity
85Reinvestment Rate Risk Reinvestment rate risk refers to the uncertainty surrounding the rate at which coupon proceeds can be investedThe higher the coupon rate on a bond, the higher its reinvestment rate risk
86Marketability RiskMarketability risk refers to the difficulty of trading a bond:Most bonds do not trade in an active secondary marketThe majority of bond buyers hold bonds until maturityLow marketability bonds usually carry a wider bid-ask spread
92Theorem 3 Higher coupon bonds have less interest rate risk Money in hand is a sure thing while the present value of an anticipated future receipt is risky
93Theorem 4When comparing two bonds, the relative importance of Theorem 2 diminishes as the maturities of the two bonds increaseA given time difference in maturities is more important with shorter-term bonds
94Theorem 5Capital gains from an interest rate decline exceed the capital loss from an equivalent interest rate increase
95Duration as A Measure of Interest Rate Risk The concept of durationCalculating duration
96The Concept of Duration For a noncallable security:Duration is the weighted average number of years necessary to recover the initial cost of the bondWhere the weights reflect the time value of money
97The Concept of Duration (cont’d) Duration is a direct measure of interest rate risk:The higher the duration, the higher the interest rate risk
98Calculating DurationThe traditional duration calculation:
100Calculating Duration (cont’d) The closed-end formula for duration:
101Calculating Duration (cont’d) ExampleConsider a bond that pays $100 annual interest and has a remaining life of 15 years. The bond currently sells for $985 and has a yield to maturity of 10.20%.What is this bond’s duration?
102Calculating Duration (cont’d) Example (cont’d)Solution: Using the closed-form formula for duration:
105Bond Selection - Introduction In most respects selecting the fixed-income components of a portfolio is easier than selecting equity securitiesThere are ways to make mistakes with bond selection
106The Meaning of Bond Diversification IntroductionDefault riskDealing with the yield curveBond betas
107Introduction It is important to diversify a bond portfolio Diversification of a bond portfolio is different from diversification of an equity portfolioTwo types of risk are important:Default riskInterest rate risk
108Default RiskDefault risk refers to the likelihood that a firm will be unable to repay the principal and interest of a loan as agreed in the bond indentureEquivalent to credit risk for consumersRating agencies such as S&P and Moody’s function as credit bureaus for credit issuers
109Default Risk (cont’d) To diversify default risk: Purchase bonds from a number of different issuersDo not purchase various bond issues from a single issuerE.g., Enron had 20 bond issues when it went bankrupt
110Dealing With the Yield Curve The yield curve is typically upward slopingThe longer a fixed-income security has until maturity, the higher the return it will have to compensate investorsThe longer the average duration of a fund, the higher its expected return and the higher its interest rate risk
111Dealing With the Yield Curve (cont’d) The client and portfolio manager need to determine the appropriate level of interest rate risk of a portfolio
112Bond Betas The concept of bond betas: States that the market prices a bond according to its level of risk relative to the market averageHas never become fully acceptedMeasures systematic risk, while default risk and interest rate risk are more important
113Choosing Bonds Client psychology and bonds selling at a premium Call riskConstraints
114Client Psychology and Bonds Selling at A Premium Premium bonds held to maturity are expected to pay higher coupon rates than the market rate of interestPremium bond held to maturity will decline in value toward par value as the bond moves towards its maturity date
115Client Psychology & Bonds Selling at A Premium (cont’d) Clients may not want to buy something they know will decline in valueThere is nothing wrong with buying bonds selling at a premium
116Call Risk If a bond is called: The funds must be reinvestedThe fund manager runs the risk of having to make adjustments to many portfolios all at one timeThere is no reason to exclude callable bonds categorically from a portfolioAvoid making extensive use of a single callable bond issue
118Specifying Return To increase the expected return on a bond portfolio: Choose bonds with lower ratingsChoose bonds with longer maturitiesOr both
119Specifying GradeA legal list specifies securities that are eligible investmentsE.g., investment grade onlyPortfolio managers take the added risk of noninvestment grade bonds only if the yield pickup is substantial
120Specifying Grade (cont’d) Conservative organizations will accept only U.S. government or AAA-rated corporate bondsA fund may be limited to no more than a certain percentage of non-AAA bonds
121Specifying Average Maturity Average maturity is a common bond portfolio constraintThe motivation is concern about rising interest ratesSpecifying average duration would be an alternative approach
122Periodic IncomeSome funds have periodic income needs that allow little or not flexibilityClients will want to receive interest checks frequentlyThe portfolio manager should carefully select the bonds in the portfolio
123Maturity Timing Maturity timing generates income as needed Sometimes a manager needs to construct a bond portfolio that matches a particular investment horizonE.g., assemble securities to fund a specific set of payment obligations over the next ten yearsAssemble a portfolio that generates income and principal repayments to satisfy the income needs
124Socially Responsible Investing Some clients will ask that certain types of companies not be included in the portfolioExamples are nuclear power, military hardware, “vice” products
125Example: Monthly Retirement Income The problemUnspecified constraintsUsing S&P’s Bond GuideSolving the problem
126The Problem A client has: Primary objective: growth of income Secondary objective: income$1,100,000 to investInviolable income needs of $4,000 per month
127The Problem (cont’d) You decide: To invest the funds between common stocks and debt securitiesTo invest in ten common stock in the equity portion (see next slide)You incur $1,500 in brokerage commissions
129The Problem (cont’d) Characteristics of the fund: Quarterly dividends total $3,001 ($12,004 annually)The dividend yield on the equity portfolio is 2.44%Total annual income required is $48,000 or 4.36% of fundBonds need to have a current yield of at least 6.28%
130Unspecified Constraints The task is meeting the minimum required expected return with the least possible riskYou don’t want to choose CC-rated bondsYou don’t want the longest maturity bonds you can find
131Using S&P’s Bond Guide Figure 11-4 is an excerpt from the Bond Guide: Indicates interest payment dates, coupon rates, and issuerProvides S&P ratingsProvides current price, current yield
133Solving the Problem Setup Dealing with accrued interest and commissionsChoosing the bondsOverspendingWhat about convertible bonds?
134Setup You have two constraints: Include only bonds rated BBB or higherKeep the average maturities below fifteen yearsSet up a worksheet that enables you to pick bonds to generate exactly $4,000 per month (see next slide)
135Setup (cont’d) Security Price Jan. Feb. March April May June 3,000 AAC $51,000$3801,000 BBL50,0003702,000 XXQ49,000$4005,000 XZ52,000$2707,000 MCDL53,0001,000 ME2,000 LN51,0005004,000 STU47,0002603,000 LLZ2906,000 MZN43,000170Equities$494,000$1,420$1,060$530
136Dealing With Accrued Interest and Commissions Bond prices are typically quoted on a net basis (already include commissions)Calculate accrued interest using the mid-term heuristicAssume every bond’s accrued interest is half of one interest check
137Choosing the Bonds The following slide shows one possible solution: Stock cost: $494,000Bond cost: $557,130Accrued interest: $9,350Stock commissions: $1,500Do you think this solution could be improved?
138Bonds Security Price Jan. Feb. March April May June $80,000 Empire 71/2s02$86,400$3,000$80,000 Energen 8s0782,900$3,200$100,000 Enhance 61/4s03105,500$3,370$80,000 Enron 65/8s0384,500$2,650$90,000 Enron 6.7s0697,200$3,010$100,000 Englehard 6.95s28100,630$3,470Bonds subtotal$557,130Total income$4,420$4,260$3,900$4,070$4,000
139OverspendingThe total of all costs associated with the portfolio should not exceed the amount given to you by the client to investThe money the client gives you establishes another constraint
140What About Convertible Bonds? Convertible bonds can be included in a portfolioUseful for a growth of income objectivePeople buy convertible bonds in hopes of price appreciationUseful if you otherwise meet your income constraints
141Immunization Strategies A portfolio of bonds is said to be immunized (from interest rate risk) if its payoff at some future date is independent of the future levels of interest rates.Immunization is closely related to the concept of duration.
142Immunization consists of matching the duration of the portfolio’s assets and liabilities (obligations).Suppose a firm has a future obligation Q. The prevailing interest rate is r, and the liability is N periods away.The present value of this liability is denoted by V0=Q/(1+r)N.
143Now suppose that the firm is currently hedging this liability with a bond whose value VB = V0 and whose coupon payments are denoted by P1,…,PM.We thus have:
144Suppose now that interest rates change from r to r+Dr Suppose now that interest rates change from r to r+Dr. The new values of the future obligation and of the bond are:
145Rearranging terms and recalling that V0=VB yields the following expression: The left-hand side represents the duration of the bond, while the right-hand side represents the duration of the obligation (Since the obligation consisted of only one payment, the duration is its maturity).
146In conclusion, in order for a portfolio to be immunized, you need to have: DURATIONASSETS = DURATIONLIABILITIESCaveat: this works only if the interest rates of various maturities all change in the same manner, i.e. if the yield curve shifts upward or downward in a parallel shift.
147Immunization ExampleYou need to immunize an obligation whose present value V0 is $1,000. The payment is to be made 10 years from now, and the current interest rate is 6%. The payment is thus the future value of 1,000 at 6%, therefore it is:1,000(1.06)10 = $1,790.85The Excel spreadsheet on the next slide shows three bonds that you have at your disposition to immunize the liability.
150Values 10 years later, assuming interest rates do not change (The goal of getting $1, is still met)
151Values 10 years later, assuming interest rates change to 5% right after we buy the bonds (The goal of getting $1, is not met by Bond 1 anymore)
152ObservationsIf interest rates go down to 5%, Bond 1 does not meet the requirement anymore.Bond 3, on the other hand, exceeds the payment that must be made in year 10.The ability of Bond 2 to meet the obligation is barely affected. Why? Because its duration is 10 years, exactly matching the duration of the liability. Pick Bond 2.
153We can compute and plot the bonds’ terminal values in year 10