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Bond Portfolio Management Bond taxonomy Bond valuation Yields and Term-structures Bond risk and Duration Bond Portfolio Strategies –Passive strategies –Active strategies –Protective strategies

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Bond = Long Term Debt from state, government or corporation-Contractual agreement Primary Financial markets Direct transfer Through an investment banking house Through a financial intermediary Secondary Financial markets Auction markets versus dealer markets (exchanges versus the OTC market) NYSE versus Nasdaq system: Differences are narrowing Bond issues…

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Bond taxonomy Bond = Long Term Debt from state, government or corporation-Contractual agreement (Default = bankruptcy) Face value or maturity value: Face amount; paid at maturity. Assume $1,000. Market value or proceed Coupon or payment: Stated as interest rate. Multiply by par value to get dollars of interest. Generally fixed. Maturity: Years until bond must be repaid. Declines. (Issue date: Date when bond was issued) Yield or discount rate: opportunity cost of capital, i.e., the rate that could be earned on alternative investments of equal risk. includes Default risk Risk that issuer will not make interest or principal payments

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Indenture Hard data: Term and amount of issue; date of issue and maturity Face value and Ask price Coupon and payment date Soft data: Collateral and seniority; covenants (on dividends, asset restriction and financing restrictions) Sinking fund: Provision to pay off a loan over its life rather than all at maturity.Similar to amortization on a term loan. Reduces risk to investor, shortens average maturity. Call provision and call premium :Issuer can refund if rates decline. That helps the issuer but hurts the investor. Therefore, borrowers are willing to pay more, and lenders require more, on callable bonds. Most bonds have a deferred call and a declining call premium.

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Rating

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What factors affect default risk and bond ratings? Financial performance –Debt ratio; TIE; Current ratios Provisions in the bond contract –Secured versus unsecured debt –Senior versus subordinated debt –Guarantee provisions –Sinking fund provisions –Debt maturity Other factors –Earnings stability –Regulatory environment –Potential product liability –Accounting policies

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Bankruptcy Two main chapters of Federal Bankruptcy Act: –Chapter 11, Reorganization –Chapter 7, Liquidation Typically, company wants Chapter 11, creditors may prefer Chapter 7. If company can’t meet its obligations, it files under Chapter 11. That stops creditors from foreclosing, taking assets, and shutting down the business. Company has 120 days to file a reorganization plan. –Court appoints a “trustee” to supervise reorganization. –Management usually stays in control. Company must demonstrate in its reorganization plan that it is “worth more alive than dead.” Various groups of creditors vote on the reorganization plan. If both the majority of the creditors and the judge approve, company “emerges” from bankruptcy with lower debts, reduced interest charges, and a chance for success. Otherwise, judge will order liquidation under Chapter 7.

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Liquidation If the company is liquidated, here’s the payment priority: 1.Secured creditors from sales of secured assets. 2.Trustee’s costs 3.Wages, subject to limits 4.Taxes 5.Unfunded pension liabilities 6.Unsecured creditors 7.Preferred stock 8.Common stock In a liquidation, unsecured creditors generally get zero. This makes them more willing to participate in reorganization even though their claims are greatly scaled back.

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Quotation

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Bond Valuation PV=Present value of payments+ Present value of face value Then, PV=PMT x PVIFA (n x m, R/m) + FV x PVIF (n x m, R/m) Calculator: FV I n PMT CPT PV Excel: Look at the functions PV, FV, PMT, Rate, NPER …………….. Payments Proceed Face Value

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Financial Asset Valuation applied to bonds PV= CF 1+k... + 1+k 1n 1 2 2 1 k n. 012n k CF 1 CF n CF 2 Value... ++ + PV=Present value of coupons + Present value of FV Then, intuitively PV=PMT x PVIFA+ FV/FVIF

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EXAMPLE 1: What’s the value of a 10- year, 10% coupon bond if k d = 10%? V kk B dd $100$1, 1 000 1 110... + $100 1 + k d 100 01210 10% 100 + 1,000 V = ?... = $90.91 +... + $38.55 + $385.54 = $1,000. ++ ++

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EXAMPLE 2: What would happen if inflation fell, and k d declined to 7%? 10 7 100 1000 NI/YR PV PMTFV -1,210.71 If coupon rate > k d, price rises above par, and bond sells at a premium. INPUTS OUTPUT

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M Bond Value ($) Years remaining to Maturity 1,372 1,211 1,000 837 775 3025 20 15 10 5 0 k d = 7%. k d = 13%. k d = 10%. A bond was issued 20 years ago and now has 10 years to maturity. What would happen to its value over time if I is 10%, 13%, or 7%?

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Example 3 A bond has 5 years to maturity and a coupon rate of 10%. Interest rates are compounded semi-annually Joe thinks that such bond is expected (as of now) to return 12%, Cindy thinks it should yield 8%, and for Charles it must return 10%. What is the bond value for each individuals?

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Solution Variables: FV=1000; m=2; n=5 PMT=%C x FV/m=10% x 1000/2=$50 For Joe: PV=50 PVIFA(10,6%)+1000/FVIF(10,6%)=926.7 For Cindy: PV=50 PVIFA(10,4%)+1000/FVIF(10,4%)=1081.2 For Charles: PV=50 PVIFA(10,5%)+1000/FVIF(10,5%)=1000

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Then, At maturity, the value of any bond must equal its par value. The value of a premium bond would decrease to $1,000. The value of a discount bond would increase to $1,000. A par bond stays at $1,000 if k d remains constant.

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Bond Properties Par, Premium and Discount Bond prices and yield are inversely related Bond prices and maturity are inversely related Bond prices and coupon are positively related

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Yields Reinvestment rate=Yield Calculating yield: calculator or excel Approximation: Yield Components: Economic forces + issue characteristic “Nominal” Rate = Risk-free rate + Risk Real rate + Inflation + Risk

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EXAMPLE 4: Questions What is the assumption behind the YTM, when valuing bonds? How does “poor business performance” affect a corporate bond value?

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EXAMPLE 5: What’s the YTM on a 10- year, 9% annual coupon, $1,000 par value bond that sells for $887? 90 01910 k d =? 1,000 PV 1. PV 10 PV M 887 Find k d that “works”!...

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10 -887 90 1000 NI/YR PV PMTFV 10.91 V INT k M k B d N d N 11 1... + INT 1 + k d 887 90 1 1000 1 110 kk dd + 90 1+k d, Find k d + + + + + + + + INPUTS OUTPUT...

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Example 6: Find YTM if price were $1,134.20. 10 -1134.2 90 1000 NI/YR PV PMTFV 7.08 Sells at a premium. Because coupon = 9% > k d = 7.08%, bond’s value > par. Relationship between coupon rate and k d ? Relationship between price and k d ? Price at maturity? INPUTS OUTPUT

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Example 7: A 10-year, 10% semiannual coupon,$1,000 par value bond is selling for$1,135.90 with an 8% yield to maturity.It can be called after 5 years at $1,050. What’s the bond’s nominal yield to call (YTC)? Note: In general, if a bond sells at a premium, then coupon > k d, so a call is likely. Then, expect to earn: YTC on premium bonds.;YTM on par & discount bonds. 10 -1135.9 50 1050 N I/YR PV PMT FV 3.765 x 2 = 7.53% INPUTS OUTPUT

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Example 8 A bond yields 10%. It has 20 years to maturity and pays 6% coupon annually. 1) How much will you accumulate in 5 years if you reinvest your coupon at 2%? 2)What is the realized yield to maturity?

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Example 8 (continued) 1) find the future value of the coupons over 5 years and add the value of the bond 5 years from today: FV(Coupon): 60 pmt, 2 I, 5 n, Compute FV=312.24 Then get the PV(bond in 5 years: 60 pmt, 10 I, 15 n, 1000 FV, Compute PV=695.76 In sum, you will accumulate $1008 after 5 years

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Example 8 (continued) 2) Here, you know you will accumulate 1008 in 5 years. First, figure what you paid for the bond initially: 60 pmt, 10 I, 20 n, 1000 FV, Compute PV= 659.46 Then, if you invested 659.46 initially and received 1008 5 years later, then you must have returned: -659.46 PV, 5 n, 1008 FV, Compute i=8.9%

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How do you make money on a bond? Current yield = Capital gains yield = = YTM = + Annual coupon pmt Current price Change in price Beginning price Exp total return Exp Curr yld Exp cap gains yld

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EXAMPLE 9: Find current yield and capital gains yield for a 9%, 10-year bond when the bond sells for $887 and YTM = 10.91%. Current yield== 10.15%. $90 $887 YTM= Current yield + Capital gains yield. Cap gains yield = YTM - Current yield = 10.91% - 10.15% = 0.76%.

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What four factors affect the cost of money? “Nominal” Rate=Risk-free rate + Risk Premium =Real rate + Inflation + Risk Premium Production opportunities Time preferences for consumption Risk Expected inflation k = k* + IP + DRP + LP + MRP. DRP= Default risk premium. LP= Liquidity premium. MRP= Maturity risk premium. Treasury: IP, MRP Corporate: IP, DRP, MRP, LP

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Term Structure of Interest Rates Relationship between term to maturity and yield to maturity for a sample of bonds at a fixed point of time. Referred to as the “yield curve.” Issues differ only in their maturities--Treasury instruments 3 shapes (Normal,Flat,Inverted) 3 underlying theories, relating to the different supply and demand pressures in different maturity sectors: –Expectation (expected to earn on successive investments in ST bonds during the term to maturity of a LT bond) –Liquidity (investors prefer the liquidity of ST bonds but will buy LT bonds if the yields are higher) –Market segmentation (yields curve reflects the investment policies of financial institutions who have different maturity preferences)

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Corporate yield curves are higher than for Treasury bond. However, corporate yield curves are not necessarily parallel to the Treasury curve. The spread between a corporate yield curve and the Treasury curve widens as the corporate bond rating decreases. 0 5 10 15 015101520 Years to maturity Interest Rate (%) 5.2% 5.9% 6.0% Treasury yield curve BB-Rated AAA-Rated

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U.S. Yield Curve Inverts Before Last Five Recessions (5-year Treasury bond - 3-month Treasury bill) % GDP Growth/ Yield Curve % Real annual GDP growth Yield curve ? Recession Correct 2 Recessions Correct Recession Correct Recession Correct Recession Correct Data though 12/20/00

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Bond Risks Interest rate risk dichotomy: –Price risk or price volatility –Reinvestment risk or “ending wealth” volatility If interest rates are expected to increase; bond price will decrease and ending wealth will increase. interest rates are expected to decrease; bond price will increase and ending wealth will decrease.

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Bond risk… As Coupon is greater, Price sensitivity to yield decreases. As Maturity gets greater, Price sensitivity to yield increases. A bond with high yield is less sensitive to a change in interests than a bond with low yield. Bond risk = Price risk and reinvestment risk Q: with an expected change interest rates, which bond would you pick?

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EXAMPLE 10: Effect of Maturity on Bond Price Volatility

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EXAMPLE 11: Effect of Coupon on Bond Price Volatility

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Some Trading Strategies… If market rates are expected to decline, bond prices will rise you want bonds with maximum price volatility. –Maximum price increase (capital gain) results from long term, low coupon bonds, low yield If market rates are expected to rise, bond prices will fall you want bonds with minimum price volatility. –Invest in short term, high coupon bonds to minimize price volatility and capital loss, high yield.

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EXAMPLE 12: Evidence of reinvestment risk (8% coupon, 25 years, 8% yield, semi-annual). How does the ending wealth change if interest rates increase by 1% ANS: ≈+15%)

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Price sensitivity and Duration Measures Duration: the weighted average time to full recovery of principal and interest payments.

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Characteristics of D D = term to maturity for a zero coupon bond. - D < term to maturity for a coupon bond - D as coupon - D as Term to maturity - D as YTM

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Duration Strategies (Dm) = Modified duration =Duration/(1+yield/m)…just a shortcut –Example 13: Given a bond that pays semi-annual coupons with a duration of 6 years and a yield of 8%, what will the percentage change in price be if market rates are expected to rise by 50 basis points? –ANSWER: P/P = 6/(1+8%/2) x.5% = 2.88% Some basic duration strategies: –If decline in rates is expected, buy a long duration bond. –If rates are expected to rise, buy a short duration bond. Some limitations on duration strategies: –Percent change estimates using modified duration are good only for small-yield changes. –Callable bonds

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Passive Bond Portfolio Strategies Buy-and-Hold Strategy Investor selection based on quality, coupon and maturity Match maturity with investment horizon Modified buy and hold Indexing Strategy Money managers can’t beat the market “If you can’t beat them, join them.” Difficulties: –Tracking error - difference between the portfolio’s return and the return for the index. –You must know characteristics and composition of the various indexes Indexes change over time.

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Active Bond Strategies Active management strategies » Interest Rate Anticipation (Valuation Analysis, Credit Analysis, Yield Spread Analysis, and Bond Swaps) Riskiest –If i is expected to increase, preserve capital –If i is expected to decrease, make capital gains Objectives are achieved by adjusting the portfolio’s duration (maturity). –Shorten duration if rates are expected to Play the Reinvestment advantage card and get Cash flow ASAP (liquidity) –Lengthen duration if rates are expected to Play the Interest rate card lower coupons and play on an increase in bond prices Q: What is the duration of a portfolio of bonds? A: The weighted average duration of each bond in a portfolio—I.e.,

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Matched Funding Techniques: Dedicated Portfolios What are they? Bond portfolio management technique used to service a specific set of liabilities Pure-Cash Matched Dedicated Portfolio Cash flows from all sources exactly match up in timing and size with the liability schedule. Can be achieved by buying a series of zero coupon Treasury securities. Total passive strategy Dedication with Reinvestment Cash flows don’t exactly match the liability schedule, also cash flows received earlier are reinvested at a relatively low interest rate. Advantages: (1) Allows for wider set of bonds to be considered; (2) Lower net cost of the portfolio; (3) Safety equivalent to with pure cash-matching. Potential problem: Early redemption

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Matched Funding Techniques: Immunization Strategies Immunization: Attempt to generate a specified rate of return regardless of what happens to market rates during an investment horizon. Immunization is a process intended to eliminate interest risk; it is achieved if the ending wealth of a bond portfolio is the same regardless of whether interest rates change Example 14: Assume a 6 year strategic asset allocation horizon and market rates on 6% coupon bonds is 6%. –Strategy one: Maturity (cash) Matching Strategy A manager has a portfolio of bonds with an average maturity of 6 years. The average coupon rate of the portfolio is 6%. –Strategy two: Duration Matching strategy=portfolio immunization A manager has a portfolio of bonds with an average maturity of 7 years. The average coupon rate of the portfolio is 6%. The average duration is about 6 years. –Q: What happens if interest rates increase or decrease suddenly by 1%

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Example 14…continued Interest rates unchanged or R=6% Strategy 1: FV=PMT x FVIFA + 1000=60 x 6.975 +1000=$1,418.5 Strategy 2: FV=PMT x FVIFA + PMT x PVIFA +1000/FVIF= =60 x 6.975 +60 x.943 + 1000/1.06=$1,418.5 Decrease of 1% or R=5% Strategy 1: FV=PMT x FVIFA + 1000=60 x 6.802 +1000=$1,408 Strategy 2: FV=PMT x FVIFA + PMT x PVIFA +1000/FVIF =60 x 6.802 +60 x.952 + 1000/1.05=$1,417.6 Increase of 1% or R=7% Strategy 1: FV=PMT x FVIFA + 1000=60 x 7.153 +1000=$1,429.2 Strategy 2: FV=PMT x FVIFA + PMT x PVIFA +1000/FVIF =60 x 7.153 +60 x.935 + 1000/1.07=$1,419.9 For strategy 2: At t=6 years, bonds have 1 year left of life!

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Conclusion: Applications: immunize the bond portion of your strategic allocation Immunize a future cash outflows (pension funds, insurance companies) Not as easy as it sounds (rebalancing, duration drift, unavailability…) Strategy 1Strategy 2 R=6%1,418.5 R=5%14081417.6 R=7%1429.21419.9 %change (-1%)-0.07%0% %change (+1%)0.08%0%

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Example 15: Questions You immunize a 4-year investment by purchasing a coupon bond with a duration of 4 years. If interest rates do not change, is your bond still immunized one year after? What if you purchased a 4-year zero coupon bond?

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Horizon matching combines cash matching and immunization to Provide protection against unequal interest rate changes –» Short term end is set up as a cash matching portfolio –» Longer term end is duration immunized –» Roll out occurs when the time horizon is pushed out one year further into the long term time horizon Contingent immunization allows for active portfolio management while assuring a minimal return by creating a Cushion spread ( difference between market rates and the minimum that investors are willing to accept.) Immunize a specific return; play with the cushion! Matched Funding Techniques: Horizon Matching and contingent immunization

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McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 16 Managing Bond Portfolios.

McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 16 Managing Bond Portfolios.

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