1、Fixed Income Portfolio ManagementProfessor Paul BolsterNortheastern UniversityBoston, Massachusetts USAFixed Income Portfolio Managemento What is fixed income?o Valuation of fixed income securitieso Sources of risk in fixed income portfolioso Passive, active, and other management strategiesWhat is f
2、ixed income?o “Fixed income” refers to all securities that provide (or promise to provide) contractual payments during their lifetime. Fixed income securities often make regular payments of interest.o Bonds, Notes, some money market instrumentso Some variable-interest instruments are classified as f
3、ixed incomeBonds Basic Featureso Contract: interest, par, maturityo Senior or Junior claim?o Collateral or Debentureo Sinking Fundo Call (or Put) featureo Conversion featureo Other types (floating rate, ZCB,)Bond Ratingso Assessment of creditworthinesso Issues are rated, not firmso Ratings agencieso
4、 Investment grade vs. Junko Ratings changes and valueBond Ratings S&P Outlineo Industry AnalysisnIndustry RisknMarket PositionnOperating Efficiencyo Management Evaluationo Financial AnalysisnEarnings ProtectionnFinancial Leverage and asset protectionnCash flow adequacynFinancial flexibilitynAccounti
5、ng qualityBond Ratingo Springfield debt downgraded to junk-bond status (Boston Globe, June 3, 2004)o “only 2 percent of cities nationwide are considered to be such a risky investment. The move by Standard & Poors puts Springfield in the company of such downtrodden economically burdened cities as Cam
6、den, N.J.; Troy, N.Y.; Cranston, R.I.; and Pittsburgh” One year transition matrixFromToAaaAaABaaBaBC&DAaa91.97.380.720000Aa1.191.37.10.30.200A0.12.691.25.30.60.20Baa00.25.487.95.50.80.2Bond Valuationo Present value!o Assume cash flows are known, adjust for risk in the required return (or Yield-to-Ma
7、turity)o Example:n ATT 6s 10 (as listed on the NY Bond Exch.)n Par value = $1,000; Matures: Oct. 15, 2011n Semiannual coupon=(6% of $1,000)/2=$30n Payments: April 15, October 15YTMBond Price = PV of Coupons + PV of Par5.14%1,050.03349.03701.005.64%1,020.58343.08677.516.14%992.13337.27654.866.64%964.
8、63331.61633.027.14%938.04326.08611.967.64%912.34320.69591.658.14%887.50315.43572.068.64%863.47310.30553.169.14%840.23305.29534.939.64%817.75300.41517.35Bond Valuation Exampleo Assumes valuation on October 15, 2004Bond Valuationo What is the Yield to Maturity (YTM)?n Assumes:o No defaulto Bond held t
9、o maturityo Coupons reinvested at the YTMn Its the “promised” yield based on current market valuen Contrast with alternatives:o Current Yieldo Yield to Callo Realized Yield (or Horizon Yield)Sources of risk in fixed income portfolioso Interest rate risknIf interest rates change, all bonds are affect
10、ednMore important for bonds with high credit ratingso Default risknIf the economy improves/worsens, all bonds are affectednMore important for bonds that are speculative in naturenCaptured by bond ratingInterest Rate Risk Bond Pricing Theorems1.Bond prices and yields vary inversely- recall example on
11、 previous slide2.Long term bonds are more sensitive to i-rate changes than short term bondsnex.ABCnCoupon ($)909090nFace Value1,000 1,000 1,000nMoodys RatingAaAaAanTerm-to-maturity5 yrs. 10 yrs. 15 yrs.nYTM9%10%11%nPrice1,000939856nLet yields decrease by 10% (8.1%, 9%, and 9.9% respectively). n nNew
12、 prices are:1,0361,000931n%Price change:3.6%6.6%8.8%Interest Rate Risk Bond Pricing Theorems3.Bond price sensitivity increases at a decreasing rate as maturity approachesex. See previous slide. The price change for B is 3% higher than A, but the price change for C is only 2.2% higher than B.4.Bond p
13、rices are more sensitive to a decline in i-rates than a rise in i-ratesnLet yields increase by 10% (9.9%, 11%, 12.1% respectively).nNew prices are:966882790n%Price changes:-3.4%-6.1%-7.7%nCompare these price changes with the ones resulting from a decline in i-rates provided above.Interest Rate Risk
14、Bond Pricing Theorems5.Low coupon bond prices are more sensitive to i-rate changes than high coupon bond pricesnex.ABnCoupon ($)60100nFace Value1,000 1,000nMoodys RatingAaAanTerm-to-maturity10 yrs. 10 yrs.nYTM12%12%nPrice661887nLet yields decrease to 11%.nNew prices are:706942n%price changes:6.7%6.2
15、%6.Prices are more sensitive when i-rates are low than when they are high.Durationo Maturity is imperfect measure of short term or long term nature of bondoneed to take into account effect of couponsocompute average: “effective maturity” o (Macaulay) duration: weighted average of cash-flow times, wi
16、th weight of date (t) proportional to cash-flow (CFt) present value:TtttTtttYTMCFYTMtCFD11)1()1(Example of Duration CalculationYear t CouponPV coupon t*PV200413028.8961664428.896166442004.523027.8329478355.66589567200533026.8088497780.426549322005.543025.82243284103.2897314200653024.87231057124.3615
17、5292006.563023.95714754143.7428852200773023.07565743161.5296022007.583022.22660126177.8128101200893021.40878565192.67907082008.5103020.62106111206.21061112009113019.86232047218.48552522009.5123019.13149727229.57796732010133018.42756432239.55833612010.5141030609.40060518531.608471Sum912.343947610493.
18、84517Duration Calculation - ContinuedA. Sum of Time Weighted Cash Flows10493.84517B. Sum of PVs of Cash Flows (or Price) 912.3439476C. Macauleys Duration = A/B =11.50 semiannual periods5.75 yearsD. Modified Duration = C/(1+YTM/2) = 5.54 yearsInterpretation? The slope of the Price-Yield function is a
19、bout -5.54. Therefore, a 1% change in bond yield will produce approximately a 5.54% change in bond price. (Why approximately?)This version of duration assumes a flat term structure.ConvexityoDuration is a linear estimate of the bonds price-yield function at a specific point. (it is the first derivat
20、ive)oThe price-yield function is convex.oIn our example, convexity = 149.32TtttYTMCFttYTMPconvexity122)1 ().()1 (1Duration and Convexity: Assumptionso Derivation and application of duration and convexity assumes:n Term structure is flatn Shifts are paralleln Bonds have no imbedded optionso Relaxing
21、the last assumption:n How does a call option influence the price-yield relationship? n A put option? (Mortgage backed securities)Fixed Income Portfolio Management Strategieso Passive or Active?n Passive:o Not trying to “beat the market”o Attempts to control risk of the portfolioo Indexationo Immuniz
22、ationFixed Income Portfolio Management - Passiveo IndexationnBuild a portfolio that replicates an observable indexoHigh-grade: Salomon Brothers, Lehman BrothersoHigh-yield: Credit Suisse First BostonoProblems: Numerous index components, liquidity is low for many, bonds matureoSolution: Cell approach
23、oManager: How do you beat an index?oInvestor: How do you evaluate effectiveness?Fixed Income Portfolio Management - Passiveo ImmunizationnManage or protect portfolio value from changes in interest ratesnNet Worth ImmunizationoBanks frequently have short-term liabilities (deposits) and long-term asse
24、ts (loans).oAsset Duration Liability DurationoObjective is to minimize the inequalitynAdjustable rate contractsnResale of loans, such as mortgages, to a third partynUse interest rate futures or other derivativesFixed Income Portfolio Management - PassiveoTarget Date ImmunizationnObjective is to guar
25、antee a specific value at a specific point in time.nOften used to match an assets future value with a future liabilitynInterest rate risk can be divided into price risk and reinvestment rate risk. How are these risks related?nIf portfolio duration is equal to planned holding period, then the portfol
26、io is immunizedFixed Income Portfolio Management - Passiveo Example of ImmunizationnA pension fund has a fixed liability of $1 million due in 5 years. Two bonds are available to build a portfolio that matches the liabilitys durationnBond A: 9% coupon, 5 years to maturity, D = 4.26 yearsnBond B: 8% c
27、oupon, 8 years to maturity, D = 6.21 yearsnTo generate a portfolio with a duration of 5 years, we must determine WA and WB. YTMA = YTMB = 8%Since WB = 1 - WA , (WA )(DA ) + (1 - WA )(DB ) = H, where H is the holding period or duration of the liability.nSolving for WA , WA = (H - DB ) / (DA - DB ) .n
28、So the initial position should be 61.8% A and 38.2% B.Immunization Example - continuedoOne year passes, interest rates have fallen from 8% to 7%. DL = 4oDA = 3.54 DB = 5.62oDuration does not decline at the same rate as time to maturity! (Except for ZCBs)oAn immunization strategy is not purely passiv
29、e. Must periodically rebalance:oNew weights for A and B: 77.9%, 22.1%Fixed Income Portfolio Management - Activeo Active management presumes that the manager can generate a positive a (or provide a positive risk-adjusted return)o Swaps:nExchanging one bond for another in anticipation of a change in t
30、he relative prices of the bondsFixed Income Portfolio Management - Activeo Examples of bond swaps:nSubstitution swap: exchanging one bond for another to exploit pricing discrepanciesnIntermarket spread swap: yield spread between 2 market segments is too wide or too narrownRate anticipation swap: mov
31、e toward higher/lower D portfolio depending on i-rate forecastsnPure yield pickup swap: buy higher yield bonds and sell lower yield bonds (increase in risk)Fixed Income Portfolio Management - Activeo Riding the yield curve:nIf YC is upward sloping and expected to stay that way, buy and hold. As matu
32、rity declines, yields decline and contribute to capital gains.nEx:Buy 9-month t-bills with yield of 1.5% per quarteroPrice = $10,000/(1.015)3 = $9,563.17oHold for 6 months. If yields now at 0.75% per quarter, Price = $10,000/(1.0075) = $9,925.56oReturn = 1.88% per quarternWhat is the risk of this strategy?Fixed Income Portfolio Management Other issueso Barbelled or laddered?n Barbelled portfolio: buy a larger amount of ST and LT bonds with smaller allocation to middle maturitiesn Laddered portfolio: buy equal amounts across a range of maturitiesn Why is this a bet on interest rates?
