201104010上海交大一

201104010上海交大一

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Unformatted text preview: 2011年6月CFA一级强化班讲义 Fixed Income 讲师:康昊昱 金程高级培训师 日期:2011年4月10日 地点: ■ 上海 □ 北京 □深圳 上海金程国际金融专修学院 R61: Features of Debt Securities Negative covenants (can’t do….) • Can’t sell assets that have been pledged as collateral • Can’t claim that the same assets back several debt issues simultaneously • Can’t borrow additional money unless certain financial conditions are met Affirmative covenants (can do….) • Maintenance of certain financial ratios (ROE、Debt ratio、ROA) • If this value of ratio is not maintained, the bonds could be considered to be in default Some types of bonds • Zero-coupon bonds: 到期日偿还面值,期间没有利息的支付,折价发行 • Step-up notes : 利率按照时间的拖长不断的递增,增加偿债成本 • Deferred-coupon bonds: 利息延迟支付,复利累计到期末进行总付 2-59 100% Contribution Breeds Professionalism 100% R61: Features of Debt Securities Some types of bonds • Floating-rate bonds: 浮动利率债券,随着基准利率的变化而变化,定期 进行一次调整,相当于无数固定利率债券的组合 New coupon rate = reference rate +/- quoted margin • Inverse floater ——coupon rises when a reference interest rate decreases • Example: coupon rate = 12% - reference rate • Caps:利率上限——有利于issuer • for issuer: long a call option; for bondholder: short a call option • Floor:利率下限——有利于bondholder • for issuer:short a put option; for bondholder:long a put option • Collar:同时设定利率上限与下限 • for issuer:long a call option and short a put option • for bondholder:short a call option and long a put option 3-59 100% Contribution Breeds Professionalism 100% R61: Features of Debt Securities Accrued interest, full price (dirty price) and clean price Trading day T1 T1 Accrued interest = Coupon × T1 + T2 T2 t Coupon date1 Coupon date2 clean price = dirty price-accrued interest 在trading day获得的包含T1时段利息的价格 Example: 3-year bond, coupon rate 10%, par 1000,(semiannual)buy at 8%, the period between the settlement date and the next coupon period is 58 days,there are 183days in the coupon period, what is accrued interest? Accrued interest =(1000*0.1/2)*(1-58/183)=50*(1-0.3169)=34.155 4-59 100% Contribution Breeds Professionalism 100% R61: Features of Debt Securities provisions for redemption and retirement of bonds • Amortizing Securities——类似年金 Make periodic interest and principal payments over the life of the bond,将 末期支付的本金平摊在平时期间:住房按揭。若每期支付相同,则每期支付 额中,利息占比下降,本金占比上升 Equal payment 0 1 2 3 4 5 • Prepayment options: 提前偿付权——for issuer • 提前偿付权有利于发行人,可以根据自身现金流状况提前偿还所欠余额,对 债券人而言,打乱其现金流的确定性 • Price of straight bond without option and price of bond embedded with prepayment option? 5-59 100% Contribution Breeds Professionalism 100% R61: Features of Debt Securities provisions for redemption and retirement of bonds • Bullet Bond——Pay only interest until maturity (non-amortizing) • Call provisions——可赎回条款:Is valuable when interest rates lower than the coupon rate (The firm call its bonds and refinance at lower interest rates). • Non-refundable vs. Non-callable Bonds • Nonrefundable Bonds prohibit the call of an issue using the proceeds from a lower coupon bond issue. • A bond may be callable but not refundable. • Non-callable Bonds are more common than nonrefundable bonds. • Call protection, is more powerful than the refunding 将禁止用赎回的资金按照较低的市场利率重新融资——non-refundable options • Call protection period:赎回锁定期 • Currently callable——锁定期已过,可随时赎回 • 可赎回条款对发行人有利,可以随时赎回债券 6-59 100% Contribution Breeds Professionalism 100% R61: Features of Debt Securities Embedded options favor the issuers: options favor the issuers: • The right to call the issue. The right to call the issue. • The prepayment option. The prepayment • Accelerated sinking fund provision. • The caps on a floater. The caps on a floater. Embedded options favor the bondholders: • Conversion provisions.——相当于一个看涨期权 Conversion provisions.—— • The put option——可由bondholder主张由发行人赎回债券 The put option—— • The floor on a floater. The floor on a floater. 7-59 100% Contribution Breeds Professionalism 100% R62: Risks associated with investing in bonds Risks Associated with Investing in Bonds • Interest Rate Risk: the effect of changes in the prevailing market rate of interest on bond values. • Yield Curve Risk: arises from the possibility of changes in the shape of the yield curve. 久期可以衡量收益率曲线上同等幅度的利率变动带来的风险, 但一旦收益率曲线形状发生变化,久期则无法衡量 • Call Risk: arises from the fact that when interest rate fall, a callable bond investor’s principal may be returned and must be reinvested at the new lower rates. Call protection reduces call risk, when interest rates are more volatile, callable bonds have relatively more call risk • Prepayment Risk: is similar to call risk. Prepayments are principal repayments in excess of those required on amortizing loans. 8-59 100% Contribution Breeds Professionalism 100% R62: Risks associated with investing in bonds Risks Associated with Investing in Bonds • Reinvestment Risk: the fact that when market rates fall, the cash flows from fixed-income securities must be reinvested at lower rates, reducing the returns an investor will earn. 再投资风险与利率风险反向变化,即使债券没有赎回与提前偿付条款,同样存 在再投资风险,因为收到的现金流随时都将再投资,哪种有一种债券不存在 再投资风险? • Credit Risk: the risk that the creditworthiness of a fixed-income security’s issuer will deteriorate, increasing the required return and decreasing the security’s value. • Liquidity Risk: has to do with the risk that the sale of a fixed-income security must be made at a price less than fair market value because of a lack of liquidity for a particular issue. 9-59 100% Contribution Breeds Professionalism 100% R62: Risks associated with investing in bonds Risks Associated with Investing in Bonds • Exchange-Rate Risk: arises from the uncertainty about the value of foreign currency cash flows to an investor in terms of his home-country currency. • Inflation Risk: the uncertainty about the amount of goods and services that a security’s cash flows will purchase.所有投资产品都面临通胀风险 • Volatility Risk: is present for fixed-income securities that have embedded options. The effect of changes in interest rate volatility on values of bonds with embedded options. 期权定价公式得出:波动性越大,权利价值越高 • Event Risk: encompasses the risks outside the risks of financial markets, such as the risks posed by natural disasters and corporate takeovers. • Sovereign Risk: changes in governmental attitudes and policies toward the repayment and servicing of debt. 10-59 100% Contribution Breeds Professionalism 100% R62: Risks associated with investing in bonds Relationship of Coupon rate, yield, price Premium Coupon rate > Required market yield, bond price > par value Par Coupon rate = Required market yield, bond price = par value Discount Coupon rate < Required market yield, bond price < par value Interest risk • 利率风险:即债券价格对利率变化的敏感程度,价格对利率变化越敏感,价格 波动的可能性就越高 • 通常用久期duration来衡量利率风险,久期越高,利率风险越高 duration = - percentage change in bond price yield change in percent • Exercise: A bond has a duration of 7.2, if the yield decreases from 8.3% to 7.9%, calculate the approximate percentage change in the bond price 11-59 100% Contribution Breeds Professionalism 100% R62: Risks associated with investing in bonds Maturity, Coupon, and Embedded Options affect the Bond’s Interest Rate Risk Maturity The price of the bond with longer maturity will change more for a given change in yield. Higher duration Coupon rate The price of the bond with higher coupon rate will change less for a given change in yield. Lower duration Caps Embedded options(callable &putable ) Floors call The value of bond with embedded options is less sensitive to interest rate changes. Lower duration put • 表中四种嵌入期权,均限制了利率变动的范围,caps & floor直接限定变动区 间;赎回与回收条款约束了利率变动对债券价格的影响,利率过低,issuer 将行使call,利率过高,bondholder将行使put 12-59 100% Contribution Breeds Professionalism 100% R62: Risks associated with investing in bonds • V callable bond = V option-free bond - V call option • If r↑, value of the embedded call option↓, callable bond value fall less than comparable option free bond • If r↓, option-free bond increase more than callable bond. • In general, the value of a callable bond is less sensitive to interest rate changes than an otherwise identical option-free bond. price • 左图可以看出,谁的久期 更低(利率风险更小)? • Callable bond只在利率下 Call option value Call price 跌时有可能行权,因此在 一定利率水平以上,不附 权债券重合 Option-free bond value callable bond value yield 13-59 100% Contribution Breeds Professionalism 100% R62: Risks associated with investing in bonds • Floating-Rate Security • Floating-rate securities has less interest rate risk, but still has it. • Time Lag: there is a lag between the time when the market yield changes and coupon rate is reset. The greater the gap, the greater the bond price fluctuation. • Fixed Margin: the required margin (non-constant) does not match quoted margin (constant). • Caps: the reference rate↑→ the cap rate reached →market yields↑→ floater’s price↓ • 在reset day前后,利率风险的大小不同,利率调整之后,一定期限内息 票率将无法按照市场利率调整,面临较高的利率风险 • 距离reset day越近,利率风险越小 yield 14-59 100% Contribution Breeds Professionalism 100% R62: Risks associated with investing in bonds Duration • Duration is a measure of the percentage change in bond price duration = price sensitivity of a security yield change in percent to changes in yield • 久期是一种加权平均到期时间 Percentage price change= - duration ×yield change in % • Dollar duration = duration ×1%×bond price , 1%代表收益率变动100个BP • Dollar duration 衡量久期导致的债券价格绝对值的变化(当收益率变动1%时) • Exercise:A bond is currently trading at $1,034.5, has a yield of 7.38%, and has a duration of 8.5. If the yield rises to 7.77%, calculate the new price of the bond? The percentage price change = - (7.77% - 7.38%)×8.5 = 3.315% 债券价格将下跌3.315%,因此债券价格为$1,000.21 15-59 100% Contribution Breeds Professionalism 100% R62: Risks associated with investing in bonds • Yield curve: the graphical depiction of relationship between yield and maturity • Portfolio duration is appropriate for parallel shifts of the yield curve. • Yield Curve Risk: decreases in portfolio value from changes in the shape of the yield curve. (i.e., non-parallel shifts, key rate duration,二级三级的定量 分析知识点) • 组合中不同债券的期限不 yield 同,因此久期不同,对应的 A non-parallel shift 收益率曲线也不同 • 利率变化对价格变动的敏感 A parallel shift 度不同,同等幅度市场利率 Initial Yield Curve 的变动,带来的价格变化 Yield Curve 同,反映在收益率曲线的形 状上,非平行移动 maturity 16-59 100% Contribution Breeds Professionalism 100% R62: Risks associated with investing in bonds Disadvantages of a callable or prepayable security to an investor • Disadvantage 1: much less certain cash flow stream. • Disadvantage 2: the investor is exposed to reinvestment risk. • Disadvantage 3: an up limit on bonds’ price appreciation. Reinvestment risk——再投资风险与利率风险此消彼长 • 利率风险:越早拿到越好,暴露在外不安全 • 再投资风险:越晚拿到越好,以免以较低的收益率进行再投资 A security has more reinvestment risk when • The coupon is higher so that interest cash flows are higher • It has a call feature • It is an amortizing security • It contains a prepayment option Reinvestment risk is minimized with low or zero-coupon bond issues or when time horizons are short. 17-59 100% Contribution Breeds Professionalism 100% R62: Risks associated with investing in bonds Forms of Credit Risk • Default Risk: the risk that a bond will fail to make promised/scheduled payments. • Credit Spread Risk: an increase in credit spread increases the required yield and decreases the price of a bond. • Downgrade risk: credit rating agency will lower a bond’s rating, then the yield required will increase and price of bond will decrease. Credit Ratings • Give bond purchasers an indication of the risk of default. • It’s an indication of the relative probability of default across the range of companies and bonds. investment grade speculative (junk bond or high yield bond) 18-59 AAA, AA, A and BBB normal speculative bond BB and B highly speculative CCC, CC and C currently in default D 100% Contribution Breeds Professionalism 100% R62: Risks associated with investing in bonds Liquidity Risk • The primary measure of liquidity is called the market bid-ask spread. That is, the size of the spread between the bid price (the price at which a dealer is willing to buy a security) and the ask price (the price at which a dealer is willing to sell a security). Exchange-Rate or Currency Risk • The uncertainty about the value of foreign currency. Inflation risk • Unexpected inflation risk or purchasing-power risk. Event Risk • Disasters, Corporate Restructurings & Regulatory Issues Sovereign Risk • Changes in Governmental Attitudes and Policies 19-59 100% Contribution Breeds Professionalism 100% R62: Risks associated with investing in bonds Volatility Risk ——只适用于含权的债权 • 根据BS公式,标的的波动与期权价格正相关 • 无论是call option 还是put option,波动越大,权利的价格越高 Type of embedded option Value of option when volatility high Value of bond when volatility high Volatility risk when volatility high Callable bonds high low high Putable bonds high high low • Callable bond的价格低于不含权的债权,期权价格越高,callable bond价值 越低,波动风险越高 • Putable bond的价格高于不含权的债权,期权价格越高,putable bond价值越 高,波动风险越低 20-59 100% Contribution Breeds Professionalism 100% R63: Overview of bond sectors and instruments U.S. Treasuries Fixed-Principal Treasuries Treasury Bills 一年以下 折价发行 Treasury Notes 1年以上 10年以下 Inflation-Indexed Treasuries (TIPS) Treasury Bonds 10年以上 Treasury Strips (Created by private sector) Coupon Strips 半年计息 半年计息 21-59 100% Contribution Breeds Professionalism 100% Principal Strips R63: Overview of bond sectors and instruments Treasury Inflation-Protected Securities(TIPS) • Structured to protect investors from inflation. • Auctioned 5-, 10- and 20-year TIPS. • Pay semiannual coupons. • Their principal is indexed to inflation. • Coupons fluctuate with inflation. • At maturity, investors receive the final coupon and the greater of the inflationadjusted principal or the original principal. TIPS coupon payments = inflation-adjusted par value ×stated coupon rate/2 • 之所以用2去除,是因为Notes与bond一般都是半年付一次息 • Example: 100,000 par value TIPS with a 3% coupon rate, set at issuance. Six months later the annual rate of inflation (CPI) is 4%. The par value will be 102,000, and the TIPS coupon is 1.5%×102,000 = 1530 • On the run issues are the most recently auctioned Treasury issues. • Off the run issues are older issues that have been replaced by a more recently auctioned issue. 22-59 100% Contribution Breeds Professionalism 100% R63: Overview of bond sectors and instruments Treasury Strips: zero coupon securities of various maturities.. • Coupon Strips: created from coupon payments stripped from the original security. • Principal Strips: bond (maturities of 20-30years) and note (maturities of 2.3.5 and 10 years) principal payment with the coupons stripped off. Example: Par:$100 million Coupon:10%, semiannual Maturity:10 years Principal: Coupon: Coupon: Coupon: Coupon: $100 million $5 million $5 million $5 million $5 million ... 0 0.5 1 1.5 Receipt in: 10 Zero-coupon securities created Maturity value: Maturity value: Maturity value: $5 million $5 million $5 million 0.5 10 coupon strips 1 principal strips 23-59 1 1.5 ... Maturity value: $100 million Maturity value: $5 million Maturity 10 100% Contribution Breeds Professionalism 100% R63: Overview of bond sectors and instruments Types and characteristics of securities issued by U.S. federal agencies Federal Agency Securities Federally Related Institutions TVA Government Sponsored Enterprises (GSEs) Ginnie Mae Freddie Mac Fannie Mae 房利美 Mortgage Passthrough Securities 24-59 Sallie Mae 房地美 CMOs 100% Contribution Breeds Professionalism 100% Asset Backed Securities R63: Overview of bond sectors and instruments Mortgage-Backed Securities Three types of cash flows from a mortgage: • Periodic interest • Scheduled repayments of principal • Principal repayments in excess of scheduled principal payments Mortgage passthrough securities抵押转手证券 MBS Collateralized mortgage obligations担保式抵押契约 Stripped mortgage-backed securities剥离抵押支持证券 • Mortgage passthrough securities: created when one or more holders of mortgages form a collection of mortgages and sell shares or participation certificates in the pool. • Collateralized Mortgage Obligations: created from mortgage passthrough certificates and referred as derivative mortgage-backed securities. • Stripped MBS: prepayment affect PO and IO differently. • If r↓, prepayment risk ↑, benefit to PO, not to IO. 25-59 100% Contribution Breeds Professionalism 100% 发行 基础 R63: Overview of bond sectors and instruments Mortgage-Backed Securities MBS MPS CMO • 将所有mortgage放入池 • 将所有mortgage放入池 子,按照等额的份额进 行分配,证券化过程中 完全平均切割 子,按照不同的风险等 级重新分配,然后卖给 风险偏好不同的投资者 Stripped MBS • 将所有mortgage放入池 子,按照IO与PO进行风 险在分配,PO的提前偿 付风险最低,而IO的提 前偿付风险最高 • Motivation for Creating CMO • Redistribute the prepayment risk inherent in mortgage passthrough securities. • Create securities with various maturity ranges. 26-59 100% Contribution Breeds Professionalism 100% R63: Overview of bond sectors and instruments Municipal bonds • Features: issued by state or local government, and other political subdivisions; often referred as tax-exempt or tax-free bonds. • GO (general obligation)/Tax-Backed Debt • Support by taxing power of local government • Almost no credit risk • Require voter approval • Types • Limited tax GO debt: a statutory limit on taxes that may be raised to pay off the obligation. • Unlimited tax GO debt: secured by the full faith and credit of the borrower ,backed by its unlimited taxing authority. (the more secure form) • Double barreled bonds: backed by the issuing authority's taxing power& additional resources. • Appropriation-backed obligations: states sometimes act as a back up source of funds for issuers during times of shortfall. (not legally binding) 27-59 100% Contribution Breeds Professionalism 100% R63: Overview of bond sectors and instruments Municipal bonds • Revenue Bonds • Supported only through revenues generated by projects. • Involve more risk, provide higher yield. • 现金流入依赖于项目的收入实现,因此风险较高 • Insured Bonds: • carry the guarantee of a third party to ensure the payments. • 第三方担保,往往适用于收入债券 • Pre-refunded Bonds: • treasury securities are purchased to ensure the payments. • Bonds that are pre-refunded have little or no credit risk and are likely to receive a rating of AAA • 先取得一笔保证金,相当于发行债券的额度,再进行发行 28-59 100% Contribution Breeds Professionalism 100% R63: Overview of bond sectors and instruments Corporate Debt Securities Corporate Bonds Secured Bonds Mortgage Debt 29-59 Unsecured Bonds (debentures) Medium-Term Notes (MTNs) Credit Enhanced Bonds Collateral Trust Bonds 100% Contribution Breeds Professionalism 100% Commercial Paper R63: Overview of bond sectors and instruments • Secured Debt: backed by the pledge of assets/collateral • Personal Property • Real Property • Financial Assets • Unsecured Debt: not backed by any pledge of specific collateral. • Referred to as debentures. • A general claim on any assets of the issuer that have not been pledged to secure other debt. • Credit Enhancements for Corporate Bonds • Third-Party Guarantees • Letters of Credit • Bond Insurance 30-59 Difference between Corporate bond and MTNs Corporate Bond MTNs (shelf registration) Be sold all at once Be sold over time On a firmcommitment basis On a best-efforts basis Single maturity and coupon rate Maturity and coupon rate ranges Not flexible More flexible, including many options 100% Contribution Breeds Professionalism 100% R63: Overview of bond sectors and instruments Structured Notes: • combine a typical bond or note with a derivative in order to reduce borrowing cost and avoid restriction. • Example:a bond with an equity swap:将利息收益盯住权益收益,适用于无法 • • • • • • 31-59 进行权益投资的投资者,相当于一个互换工具 Step-up notes: coupon rate increases over time Inverse floaters: coupon rate increases when the reference rate decreases Deleveraged floaters: coupon rate equals a fraction of the reference rate plus a constant margin Dual-indexed floaters:coupon rate is based on the difference between two reference rates Range notes: coupon rage equals the reference rate if the reference rate falls within a specified range, or zero if the reference rate falls outside that range Index amortizing notes: coupon rate is fixed but some principal is repaid before maturity, with the amount of principal prepaid based on the reference rate 100% Contribution Breeds Professionalism 100% R63: Overview of bond sectors and instruments Commercial Paper: • Short-term, unsecured debt instrument • Issued with maturities of 270 days or less • Issued as a pure discount security and makes a single payment equal to the face value at maturity • Directly-placed paper VS Dealer-placed paper Negotiable CDs • Permit the owner to sell the CD in the secondary market at any time • Have maturities ranging from days up to five years Bankers Acceptances • Essentially guarantees by a bank that a loan will be repaid • They are created as part of commercial transactions, especially international trade • The credit risk of a bankers acceptance is the risk that the initial borrower of the funds and the accepting bank will both fail to make the promised payment 32-59 100% Contribution Breeds Professionalism 100% R63: Overview of bond sectors and instruments Asset-Backed Securities • Financial assets are the underlying collateral for ABS. • ABS has credit risk. Special Purpose Vehicle • A corporate transfers assets to SPV for an ABS issue. (bankruptcy remove) • Motivation: Reduce Borrowing Cost & Higher Rating External Credit Enhancement • Corporate Guarantee: if the third-party guarantor downgrades, issuer will be downgrade even if the collateral is performing as expected. • Letter of Credit • Bond Insurance CDO • A debt instrument where the collateral for the promise to pay is an underlying pool of other debt obligations and even other CDOs. • Tranches of the CDO are created based on the seniority of the claims to the cash flows of the underlying assets. 33-59 100% Contribution Breeds Professionalism 100% R63: Overview of bond sectors and instruments Overview of Bond Sectors and Instruments (Brief Summary) Sovereign bonds central government Federally related institutions Semigovernment/ agency bonds Municipal bonds Corporate Debt Securities 34-59 Fixed-principal treasury securities Inflation-Indexed Treasuries Treasury Strips Debentures and discount notes MPS Government Sponsored Enterprises State and local governments MBS CMO Stripped mortgage-backed securities Tax-Backed Debt/GO Revenue Bonds Corporate Bonds Corporate MTNs Commercial Paper 100% Contribution Breeds Professionalism 100% R64: Understanding yield spreads Interest Rate Policy Tools • • • • Open Market Operation (most commonly used) The Discount Rate Bank Reserve Requirements Verbal Persuasion: influence how bankers supply credit to business and consumers. Yield Curve and the Various Shapes of the Yield Curve • Types : Flat/Normal/Inverted/Humped • Features • Different shapes at different time. • The curves are climbing normally. • The curves of bonds with different terms move in the same direction. • Structure of Interest Rates Term/Risk/Liquidity 35-59 100% Contribution Breeds Professionalism 100% R64: Understanding yield spreads Basic theory of the term structure Theory Pure Expectation Shape under various scenarios ST rates expected to rise ⇒upward sloping upward sloping expected to fall ⇒ downward sloping rise then fall ⇒humped expected to remain constant ⇒flat downward sloping or flat, even upward Liquidity Preference Market Segmentation/ Preferred habitat 36-59 Can take any shape 100% Contribution Breeds Professionalism 100% R64: Understanding yield spreads Basic theory of the term structure Description Unbiased expectation theory Biased expectation theory 37-59 Pure expectation theory Liquidity theory Shapes The yield for a particular maturity is an average of short-term rates that are expected in the future. Upward slope: short-term rates are expected to rise Downward slope: short-term rates are expected to fall Flat yield: short-term rates are expected to remain the same In addition to expectations about future short-term rates, investors require a risk premium for holding longer term bonds. Upward slope: either rising expected future rates or rates remain/fall but liquidity premium is added Downward slope: short-term rates are expected to fall Investors and borrowers have No specific linkage among the Market preferences for different maturity yields at different maturities. segmentation ranges. The supply and demand for theory bonds determine equilibrium yields for the various maturity ranges. 100% Contribution Breeds Professionalism 100% R64: Understanding yield spreads spot rate & spread measures •Spot Rates: the appropriate discount rates for individual future payments. • Arbitrage-Free Treasury Spot Rates: the spot rates for different time periods that correctly value the cash flows from a Treasury bond. •Measuring Yield Spread Absolute yield spread = yield on the higher-yield bond — yield bond on the lower-yield bond absolute yield spread • Relative yield spread= yield on the benchmark bond • • sub ject bond yield Yield ratio= b enchmark bond yield The yield ratio is simply one plus the relative yield spread 38-59 100% Contribution Breeds Professionalism 100% R64: Understanding yield spreads • Credit (quality) Spread: the difference in yields between two issues that are similar in all respects except for credit rating. • During an expanding economy, credit spreads decline. • During economic contractions, credit spreads rise. • Flight to Quality: when investors anticipate an economic downturn, they often sell low-quality issues and buy high-quality issues. • How embedded option affect yield spreads • Yield spreads are higher for the callable/prepayment bond. • Yield spreads are lower for the putable/conversion bond. • How the liquidity or issue-size of a bond affects its yield spread • Bonds that have less liquidity have higher spreads to Treasuries • Liquidity is affected by the size of an issue. Larger issues normally have greater liquidity 39-59 100% Contribution Breeds Professionalism 100% R64: Understanding yield spreads • The after-tax yield on a taxable security can be calculated: after-tax yield = taxable yield ×(1 – marginal tax rate). • Taxable-equivalent yield is the yield a particular investor must earn on a taxable bond to have the same after-tax return they would receive from a particular tax-exempt issue. • Taxable-equivalent yield=tax-free yield/(1- marginal tax rate) • LIBOR is important to investors who borrow short-term • London Interbank Offered Rate • LIBOR is most important for short-term rates of one year or less • Benchmark or Reference Rate • Measure of funding cost for funded investors. 40-59 100% Contribution Breeds Professionalism 100% R65: Introduction to the Valuation of Debt Securities Bond Valuation Process • • The general procedure for valuing fixed-income securities is to take the present values of all the expected cash flows and add them up to get the value of the security. • Estimate the cash flows • Determinate the appropriate discount rate • Calculate the present value of the estimated cash flows Cash Flow is Difficult to Estimate Due to: • The principal stream is not known with certainty. Example: Bonds with Embedded Options. • The coupon payments are not known with certainty. Example: Floating-Rate Securities • The bond is convertible or exchangeable into another security. Example: Convertible Bonds 41-59 100% Contribution Breeds Professionalism 100% R65: Introduction to the Valuation of Debt Securities • Estimate the yield on a risky bond • Yield on a risky bond=yield on a default-free bond + risk premium • Bond values and bond yields are inversely related as showed in priceyield curve. n P= ∑ t =1 • 从右图可以看出,收益率变化幅度 不变时,收益率变低导致的债券价 格上升到幅度大于收益率变高导致 的债券价格下降的幅度 • 因为收益率曲线为上凹形状 • 该种形状有利于bondholder • 有利于bondholder的权利使得收益 率曲线上凹,有利于issuer的权利 使得收益率曲线下凹 42-59 100% Contribution Breeds Professionalism 100% Coupon t B + t n (1+r) (1+r) R65: Introduction to the Valuation of Debt Securities • 距离到期时间越近,债券 价格收敛于面值 • 到期收益率高于息票率, 折价发行;到期收益率低 于息票率,溢价发行 • 距离到期时间越近,债券 价值升降的速率越快 premium 1085.458 par 852.480 discount A premium bond (a 6% bond trading at YTM of 3%) A premium bond (a 6% bond trading at YTM of 6%) A premium bond (a 6% bond trading at YTM of 12%) Maturity Time to Maturity YTM=3% YTM=6% YTM=12% 3 years 1085.40 1000.00 852.48 2 years 1057.82 1000.00 896.05 1 year 1029.34 1000.00 945.00 0 1000.00 1000.00 1000.00 43-59 100% Contribution Breeds Professionalism 100% R65: Introduction to the Valuation of Debt Securities • the value of a zero-coupon bond bond value = maturity value (1 + i ) number of years×2 • Example: To find the value of a 8-year, $1000 face value zero-coupon bond with a yield to maturity of 8 percent. Answer: N=8×2=16; FV=1000; I/Y=8/2=4; PMT=0; CPT→PV=533.9038 Yield to maturity • A summary measure and is essentially an internal rate of return based on a bond’s cash flows and its market price Arbitrage-free valuation approach • Discount each cash flow using a discount rate specific to the maturity of each cash flow; • Compare the obtained present value to the market price to determine arbitrage opportunities; • STRIPS program helps to force the bond price toward equality with their arbitrage-free values. 44-59 100% Contribution Breeds Professionalism 100% R66: Yield measures, spot rates, and forward rates Sources of Return from Investing in a Bond •Periodic Coupon Interest Payments •Recovery of Principal & Capital Gain or Loss •Reinvestment Income Current yield is the simplest of all return measures •Current yield = annual cash coupon payment / bond price BEY(bond equivalent yield): semiannual-pay YTM Example: Consider a 20-year, $1000 par value bond, with a 6% coupon rate (semiannual payments ) with a full price of $802.07. Calculate the YTM PV=- 802.07, N= 20×2=40, FV= 1000, PMT = 60/2=30, CPT I/Y =4 4% is the semiannual discount rate, YTM=8% The yield to call is used to calculate the yield on callable bonds that are selling at a premium to par. Yield to call may be less than the yield to maturity 计算yield to call时,按照赎回时的价格作为终值 45-59 100% Contribution Breeds Professionalism 100% R66: Yield measures, spot rates, and forward rates Bond Selling at: Relationship Par coupon rate = current yield = yield to maturity Discount coupon rate<current yield<yield to maturity Premium coupon rate>current yield>yield to maturity • Yield to Worst: the worst yield outcome of any that are possible given the call provisions of the bond. • Yield to Refunding: is similar to YTC. Yield to refunding would use the call price, but the date is when refunding protection ends. • Cash Flow Yield: a monthly internal rate of return based on a presumed prepayment rate and the current market price of a mortgage-backed or assetbacked security. • The Limitation of Traditional Yield Measures • YTM can’t tell the compound rate of return that an investor will realize on the reinvested coupon payments . • YTC and YTP suffer from the same shortcomings. 46-59 100% Contribution Breeds Professionalism 100% R66: Yield measures, spot rates, and forward rates Reinvestment Income N Required reinvestme nt income = purchase price × (1+Rmrt) - marturity value - coupon YTM的假设条件: • Bondholder持有至到期 • 期间所有现金流入均按照YTM进行再投资 现实中的限制: • 债券可能中途停止,赎回、提前偿付、回售等 • YTM for a coupon bond is theoretically correct only to the extent that the spot rate curve is flat • 现金流入再投资的收益率不确定 • 若再投资收益率低于YTM,则导致期间实现的收益率低于YTM • 若再投资收益率高于YTM,则导致期间实现的收益率高于YTM • Other things equal, a bond’s reinvestment risk will increase with: • Higher Coupons • Longer Maturities • 与影响利率风险的因素相反 47-59 100% Contribution Breeds Professionalism 100% R66: Yield measures, spot rates, and forward rates Bond Equivalent Yield • A Semiannual YTM or Semiannual-Pay YTM • 2×the Semiannual Discounted Rate • BEY of an annual-pay bond = [(1+annual YTM)1/2 -1] ×2 • convert semiannual to annual EAR=(1+BEY/2)2-1 Cash Flow Yield (CFY) • A monthly internal rate of return • Usually used for mortgage-backed securities and asset-backed securities • BEY = [(1+monthly CFY)6 -1] ×2 Example:Suppose that a corporation has a semiannual coupon bond trading in the United States with a YTM of 6.25%, and an annual coupon bond trading in Europe with a YTM = 6.3%. Which bond has the greater yield? BEY of an annual-pay bond = [(1+annual YTM)1/2 -1] ×2 将6.3%带入求解出BEY,与6.25%比较。 也可以6.25%对半进行年化,与6.3%比较 48-59 100% Contribution Breeds Professionalism 100% R66: Yield measures, spot rates, and forward rates Difference between the nominal spread, the zero-volatility spread and the optionadjusted spread •NS是线性的利差、ZS考虑了收益率曲线的形状 •OAS是剔除了期权因素的利差,反映不含权的债权同无风险利率债权之间的利差 Nominal spread Z-spread Description = Bond yield to maturity – yield on a comparable-maturity government treasury security C F1 C F2 Pm arket = + +... 1 2 (1+ R +N ) (1+ R +N ) C F1 C F2 Pm arket = + +... (1+ R 1 + Z )1 (1+ R 2 + Z ) 2 OAS=Z-spread – Option cost OAS 49-59 Pm arket = C F1 C F2 + +... '' (1+R 1 + O AS )1 (1+R ''2 + O AS ) 2 100% Contribution Breeds Professionalism 100% Character Use a single interest rate to discount each cash flow, so it ignores the shape of the spot yield curve Assume the interest rate volatility is zero. R66: Yield measures, spot rates, and forward rates The difference between the NS and the ZS • The steeper the benchmark spot rate curve, the greater the difference between the two spread measures. There is no difference between the NS and ZS when the spot yield curve is flat. If the spot yield curve is upward sloping, the ZS is larger than the nominal spread. The ZS is less than the NS when the spot yield curve is negatively sloped • The earlier bond principal is paid, the greater the difference between the two spread measures. For a given positively sloped yield curve, and amortizing security, such as an MBS, will have a greater difference between its ZS and NS than a coupon bond will Rate Rate Z-volatility spread Nominal spread Maturity 50-59 100% Contribution Breeds Professionalism 100% Maturity R66: Yield measures, spot rates, and forward rates The Option-adjusted spread • The option-adjusted spread is the spread to the Treasury spot rate curve that the bond would have if it were option-free. The OAS is the spread for non-option characteristics like credit risk, liquidity risk, and the interest risk • OAS相当于剔除了期权因素后,债券与无风险 Z-spread 债权(Treasury bond)之间的利差 • Z-spread – OAS = option cost in percent • 对issuer有利的权利,剔除权利后,投资者对 收益率的要求下降 • 对bondholder有利的权利,剔除权利后,投资 者对收益率的要求上升 • For embedded calls, option cost > 0: OAS < Z-spread • For embedded puts, option cost < 0: OAS > Z-spread 51-59 100% Contribution Breeds Professionalism 100% Callable bond Option risk Liquidity risk Credit risk OAS Interest risk Treasury (risk free) R66: Yield measures, spot rates, and forward rates Spot Rates, and Forward Rates • Forward Rates :borrowing/lending rate for a loan to be made at some future date. • Relationship Between Forward Rates and Spot Rates (1 + S T )T = (1 + 1 f 0 )(1 + 1 f1 ) K (1 + 1 f (T −1) ) • Valuation Using Forward Rates bond value = • • • • 52-59 CFn CF1 CF2 + +K (1 + 1 f 0 ) (1 + 1 f 0 )(1 + 1 f1 ) (1 + 1 f 0 )(1 + 1 f1 ) K (1 + 1 f n−1 ) 即期利率是指起点为零时点的利率 远期利率是指起点非零时点的利率 长期利率是指期限超过一年的利率 短期利率是指期限短于一年的利率 0 1 100% Contribution Breeds Professionalism 100% 2 3 R67: Introduction to measurement of interest rate risk Price Volatility Characteristics for option-free, callable, prepayable, and putable bonds when interest rates change • • 53-59 Price moves in the opposite direction from the change in yield; For a given change in yield, the percentage price increase is greater than the percentage price decrease. 100% Contribution Breeds Professionalism 100% R67: Introduction to measurement of interest rate risk • High yield →unlikely call, → positive convexity • Yield decline → may call the bond →negative convexity 54-59 • price/yield relationship will be more convex when yield increase 100% Contribution Breeds Professionalism 100% R67: Introduction to measurement of interest rate risk Effective duration • Price change in response to rising rates is smaller than the price change in response to falling rates for option-free bonds effective duration = bond price when yields fall - bond price whe yield rise 2 × initial price × change in yield in decimal form V - -V + 2V0( Δy) • For bonds with no embedded options, modified duration and effective duration will be equal or very nearly equal • Percentage change in bond price = effective duration ×change in yield in percent 55-59 Effects of bond characteristics on duration: • Lower coupon means higher duration. • Longer maturity means higher duration. • Lower market yield means higher duration. 100% Contribution Breeds Professionalism 100% R67: Introduction to measurement of interest rate risk Macaulay duration • 按照现金流现值为权重的加权平均到期时间 麦考利久期= PV(CFt) ∑ P ×t t • 麦考利与修正久期只适合衡 量不含权债券的利率风险 Modified duration • Modified duration takes the current YTM into account Modified duration = Macaulay duration 1 + p eriodic market yield Interpreting duration • Duration is the slope of the price-yield curve at the bond’s current YTM • Duration is a weighted average of the time until each cash flow will be received • Duration is the approximate percentage change in price for a 1% change in yield 56-59 100% Contribution Breeds Professionalism 100% R67: Introduction to measurement of interest rate risk Portfolio duration • Portfolio duration = w1D1+ w2D2 + ……+wnDn • Limitations: the yields may not change equally on all the bond in the portfolio • Duration is a good measure of the sensitivity of portfolio value to parallel changes in the yield curve Convexity • A measure of the curvature of the price-yield curve • The more curved the price-yield relation is, the worse our duration-based estimates of bond price changes in response to changes in yield are 57-59 100% Contribution Breeds Professionalism 100% R67: Introduction to measurement of interest rate risk A bond’s percentage price change based on duration and convexity • Percentage change in price = duration effect + convexity effect {[- duration [ × ( Δy) ]+ convexity } × ( Δ y) 2 × 100 • The convexity adjustment is always positive when convexity is positive • For a callable bond, convexity can be negative at low yields. • When convexity is negative, the convexity adjustment to the durationonly based estimate of the percentage price change will be negative for both yield increases and yield decreases Effective convexity • Effective convexity take into account changes in cash flows due to embedded options, while modified convexity does not 58-59 100% Contribution Breeds Professionalism 100% R67: Introduction to measurement of interest rate risk The price value of a basis point (PVBP) • PVBP is the dollar change in the price/value of a bond or a portfolio when the yield changes by one basis point, or 0.01% Impact of yield volatility on the interest rate risk of a bond • Consider a Treasury bond with a duration of 7 and a similar single-B rated corporate bond with a duration of 5. Based on duration alone, we would say that the Treasury bond has more interest rate risk. If, however, the volatility of the market yield on the corporate bond is sufficiently greater than the volatility of the market yield on the Treasury bond, the corporate bond can have greater price volatility due to yield changes than the Treasury bond • It is important to combine a bond’s duration with its yield volatility in assessing its interest rate risk 59-59 100% Contribution Breeds Professionalism 100% ...
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