Fixed Income Portfolio Management

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Fixed Income Portfolio Management

• Professor Paul Bolster
• Northeastern University
• Boston, Massachusetts USA

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Fixed Income Portfolio Management

• What is fixed income?
• Valuation of fixed income securities
• Sources of risk in fixed income portfolios
• Passive, active, and other management strategies

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What is fixed income?

• 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.
• Bonds, Notes, some money market instruments
• Some variable-interest instruments are classified
  as fixed income

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Bonds Basic Features

• Contract interest, par, maturity
• Senior or Junior claim?
• Collateral or Debenture
• Sinking Fund
• Call (or Put) feature
• Conversion feature
• Other types (floating rate, ZCB,)

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Bond Ratings

• Assessment of creditworthiness
• Issues are rated, not firms
• Ratings agencies
• Investment grade vs. Junk
• Ratings changes and value

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Bond Ratings SP Outline

• Industry Analysis
• Industry Risk
• Market Position
• Operating Efficiency
• Management Evaluation
• Financial Analysis
• Earnings Protection
• Financial Leverage and asset protection
• Cash flow adequacy
• Financial flexibility
• Accounting quality

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Bond Rating

• Springfield debt downgraded to junk-bond status
  (Boston Globe, June 3, 2004)
• only 2 percent of cities nationwide are
  considered to be such a risky investment. The
  move by Standard Poor's puts Springfield in the
  company of such downtrodden economically burdened
  cities as Camden, N.J. Troy, N.Y. Cranston,
  R.I. and Pittsburgh

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One year transition matrix

• From\To Aaa Aa A Baa Ba B CD
• Aaa 91.9 7.38 0.72 0 0 0 0
• Aa 1.1 91.3 7.1 0.3 0.2 0 0
• A 0.1 2.6 91.2 5.3 0.6 0.2 0
• Baa 0 0.2 5.4 87.9 5.5 0.8 0.2

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Bond Valuation

• Present value!
• Assume cash flows are known, adjust for risk in
  the required return (or Yield-to-Maturity)
• Example
• ATT 6s 10 (as listed on the NY Bond Exch.)
• Par value 1,000 Matures Oct. 15, 2011
• Semiannual coupon(6 of 1,000)/230
• Payments April 15, October 15

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Bond Valuation Example

• Assumes valuation on October 15, 2004

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Bond Valuation

• What is the Yield to Maturity (YTM)?
• Assumes
• No default
• Bond held to maturity
• Coupons reinvested at the YTM
• Its the promised yield based on current market
  value
• Contrast with alternatives
• Current Yield
• Yield to Call
• Realized Yield (or Horizon Yield)

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Sources of risk in fixed income portfolios

• Interest rate risk
• If interest rates change, all bonds are affected
• More important for bonds with high credit ratings
• Default risk
• If the economy improves/worsens, all bonds are
  affected
• More important for bonds that are speculative in
  nature
• Captured by bond rating

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Interest Rate Risk Bond Pricing Theorems

• Bond prices and yields vary inversely
• - recall example on previous slide
• Long term bonds are more sensitive to i-rate
  changes than short term bonds
• ex. A B C
• Coupon () 90 90 90
• Face Value 1,000 1,000 1,000
• Moody's Rating Aa Aa Aa
• Term-to-maturity 5 yrs. 10 yrs. 15 yrs.
• YTM 9 10 11
• Price 1,000 939 856
• Let yields decrease by 10 (8.1, 9, and 9.9
  respectively).
• New prices are 1,036 1,000 931
• Price change 3.6 6.6 8.8

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Interest Rate Risk Bond Pricing Theorems

• 3. Bond price sensitivity increases at a
  decreasing rate as maturity approaches
• ex. 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.
• Bond prices are more sensitive to a decline in
  i-rates than a rise in i-rates
• Let yields increase by 10 (9.9, 11, 12.1
  respectively).
• New prices are 966 882 790
• Price changes -3.4 -6.1 -7.7
• Compare these price changes with the ones
  resulting from a decline in i-rates provided
  above.

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Interest Rate Risk Bond Pricing Theorems

• Low coupon bond prices are more sensitive to
  i-rate changes than high coupon bond prices
• ex. A B
• Coupon () 60 100
• Face Value 1,000 1,000
• Moody's Rating Aa Aa
• Term-to-maturity 10 yrs. 10 yrs.
• YTM 12 12
• Price 661 887
• Let yields decrease to 11.
• New prices are 706 942
• price changes 6.7 6.2
• Prices are more sensitive when i-rates are low
  than when they are high.

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Duration

• Maturity is imperfect measure of short term or
  long term nature of bond
• need to take into account effect of coupons
• compute average effective maturity
• (Macaulay) duration weighted average of
  cash-flow times, with weight of date (t)
  proportional to cash-flow (CFt) present value

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Example of Duration Calculation
Year t Coupon PV coupon tPV 2004 1 30 28.89
616644 28.89616644 2004.5 2 30 27.83294783 55.6658
9567 2005 3 30 26.80884977 80.42654932 2005.5 4 30
25.82243284 103.2897314 2006 5 30 24.87231057 124
.3615529 2006.5 6 30 23.95714754 143.7428852 2007
7 30 23.07565743 161.529602 2007.5 8 30 22.2266012
6 177.8128101 2008 9 30 21.40878565 192.6790708 20
08.5 10 30 20.62106111 206.2106111 2009 11 30 19.8
6232047 218.4855252 2009.5 12 30 19.13149727 229.5
779673 2010 13 30 18.42756432 239.5583361 2010.5 1
4 1030 609.4006051 8531.608471 Sum 912.3439476
10493.84517
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Duration Calculation - Continued

• A. Sum of Time Weighted Cash Flows 10493.84517
• B. Sum of PVs of Cash Flows (or
  Price) 912.3439476
• C. Macauleys Duration A/B 11.50 semiannual
  periods
• 5.75 years
• D. Modified Duration C/(1YTM/2) 5.54 years
• Interpretation? The slope of the Price-Yield
  function is about -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.

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Convexity

• Duration is a linear estimate of the bonds
  price-yield function at a specific point. (it is
  the first derivative)
• The price-yield function is convex.
• In our example, convexity 149.32

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Duration and Convexity Assumptions

• Derivation and application of duration and
  convexity assumes
• Term structure is flat
• Shifts are parallel
• Bonds have no imbedded options
• Relaxing the last assumption
• How does a call option influence the price-yield
  relationship?
• A put option? (Mortgage backed securities)

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Fixed Income Portfolio Management Strategies

• Passive or Active?
• Passive
• Not trying to beat the market
• Attempts to control risk of the portfolio
• Indexation
• Immunization

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Fixed Income Portfolio Management - Passive

• Indexation
• Build a portfolio that replicates an observable
  index
• High-grade Salomon Brothers, Lehman Brothers
• High-yield Credit Suisse First Boston
• Problems Numerous index components, liquidity
  is low for many, bonds mature
• Solution Cell approach
• Manager How do you beat an index?
• Investor How do you evaluate effectiveness?

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Fixed Income Portfolio Management - Passive

• Immunization
• Manage or protect portfolio value from changes in
  interest rates
• Net Worth Immunization
• Banks frequently have short-term liabilities
  (deposits) and long-term assets (loans).
• Asset Duration gt Liability Duration
• Objective is to minimize the inequality
• Adjustable rate contracts
• Resale of loans, such as mortgages, to a third
  party
• Use interest rate futures or other derivatives

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Fixed Income Portfolio Management - Passive

• Target Date Immunization
• Objective is to guarantee a specific value at a
  specific point in time.
• Often used to match an assets future value with
  a future liability
• Interest rate risk can be divided into price risk
  and reinvestment rate risk. How are these risks
  related?
• If portfolio duration is equal to planned holding
  period, then the portfolio is immunized

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Fixed Income Portfolio Management - Passive

• Example of Immunization
• A 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
  duration
• Bond A 9 coupon, 5 years to maturity, D 4.26
  years
• Bond B 8 coupon, 8 years to maturity, D 6.21
  years
• To generate a portfolio with a duration of 5
  years, we must determine WA and WB. YTMA YTMB
  8Since WB 1 - WA , (WA )(DA ) (1 - WA
  )(DB ) H, where H is the holding period or
  duration of the liability.
• Solving for WA , WA (H - DB ) / (DA - DB ) .
• So the initial position should be 61.8 A and
  38.2 B.

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Immunization Example - continued

• One year passes, interest rates have fallen from
  8 to 7. DL 4
• DA 3.54 DB 5.62
• Duration does not decline at the same rate as
  time to maturity! (Except for ZCBs)
• An immunization strategy is not purely passive.
  Must periodically rebalance
• New weights for A and B 77.9, 22.1

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Fixed Income Portfolio Management - Active

• Active management presumes that the manager can
  generate a positive a (or provide a positive
  risk-adjusted return)
• Swaps
• Exchanging one bond for another in anticipation
  of a change in the relative prices of the bonds

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Fixed Income Portfolio Management - Active

• Examples of bond swaps
• Substitution swap exchanging one bond for
  another to exploit pricing discrepancies
• Intermarket spread swap yield spread between 2
  market segments is too wide or too narrow
• Rate anticipation swap move toward higher/lower
  D portfolio depending on i-rate forecasts
• Pure yield pickup swap buy higher yield bonds
  and sell lower yield bonds (increase in risk)

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Fixed Income Portfolio Management - Active

• Riding the yield curve
• If YC is upward sloping and expected to stay that
  way, buy and hold. As maturity declines, yields
  decline and contribute to capital gains.
• Ex Buy 9-month t-bills with yield of 1.5 per
  quarter
• Price 10,000/(1.015)3 9,563.17
• Hold for 6 months. If yields now at 0.75 per
  quarter, Price 10,000/(1.0075) 9,925.56
• Return 1.88 per quarter
• What is the risk of this strategy?

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Fixed Income Portfolio Management Other issues

• Barbelled or laddered?
• Barbelled portfolio buy a larger amount of ST
  and LT bonds with smaller allocation to middle
  maturities
• Laddered portfolio buy equal amounts across a
  range of maturities
• Why is this a bet on interest rates?