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    Lecture 6

    Fixed-income investment strategies

    Module leader: Dr. Minh Nguyen

    NBS8336 Portfolio Management

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    The fundamentals

    This class

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    Outline

    After this lecture, you would be expected to perform the following tasks:

    • Explain bond passive investment strategies:

     – Bond indexing

     – Bond portfolio immunisation

    • Describe active strategies:

     – Riding the yield curve

     – On and Off-the-run arbitrage

     – Swap spread arbitrage

    • Further readings:

    Bodie, Kane & Marcus, Chapter 16

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    Fixed Income Fundamentals

    • Bond Price

    • Modified Duration

    • Duration and convexity approximation

    • Return: bond return,+ =  +possible coupon− 1 ≅

     − ഥ+(+ − )

      (1 )1

    T  CF t P t y t 

    *

    P D y 

    1   2

    *2

    P D y CX y  

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    Fixed income strategies

    • Passive bond portfolio managers track a

    benchmark portfolio or match liabilities

    • Active bond portfolio managers seek profits

    from their views about the evolution of

    interest rates and yield spreads

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    Passive Management

    • Two passive bond portfolio strategies:

    1.Indexing2.Immunization

    • Both strategies see market prices as beingcorrect, but the strategies have very different

    risks.

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    Objective:

    Track the returns of an index (‘indexing’ ) as closely as

    economically feasible or structure a portfolio to meet specific

    liabilities over time (‘liability funding’ )

    Rationale:

    Markets are assumed to be efficient enough that research

    cannot produce extra returns beyond its cost. Therefore a

    portfolio is run either to track a chosen benchmark index or to

    meet specific requirements over time whilst keeping expenses

    (management, transaction costs) to a minimum

    Bond indexing

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    Choosing a Bond Index

    There are broad based indices and specialist indices1. Broad based examples (all highly correlated, 98% annual)

     – Lehman Brothers Aggregate Index

     – Salomon Brothers Broad Investment Grade Bond Index

     – Merrill Lynch Domestic Market IndexEach contain more than 5000 issues, mostly from US issuers.All are investment grade and with medium to long termmaturities

    2. Specialized examples (still correlated, 90% annual) – Morgan Stanley actively traded (MBS) index

     – First Boston high yield index

     – DL&J High Yield Index

     –

    Ryan Labs Treasury Index

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    Immunization

    • Immunization is a way to control interest rate

    risk.

    • Widely used by pension funds, insurance

    companies, and banks.

    16-10

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    Immunization

    • Immunize a portfolio by matching the interest

    rate exposure of assets and liabilities.

     – This means: Match the duration of the assets and

    liabilities.

     – Price risk and reinvestment rate risk exactly cancel

    out.

    • Result: Value of assets will track the value ofliabilities whether rates rise or fall.

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    Immunization: an example•

    Suppose an insurance company must make a single paymentof £19,487 in 7 years

    • Suppose the current market interest rate is 10%. What is thepresent value of the obligation?

    • What is the present value of the obligation if interest rate isreduced by 50 basis points (i.e. 9.5%)?

    • The company wishes to fund the obligation using 3-year zero-coupon bonds. How can the manager immunize theobligation?

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    Immunization: an example

    1. Calculate the duration of the liability: as it is a single payment, theduration of the obligation is 7 years. PV of the liability = £19,487/1.107

    =£10,000

    2. Calculate the duration of the assets:

     – The duration of the zero coupon bonds = maturity = 3years

     – If w is the weight in zero bond. Match the duration of the asset and

    liability

    3w=7, thus w=7/3

     – As the PV of the obligation = £10,000 thus the manager needs to buy

    £23,333 (=7/3*10000) zero coupon bond4. If the interest rate “instantly” dropped to 9.5%, the PV of the liability =

    £10,323. Thus the obligation increase by £323.

    However, the PV of the zero coupon = 23333*1.103/1.0953=23,654,

    making a profit = 23,654-23333=£321. Thus offset the loss

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    Active Bond Strategies

    Objective:

    Take positions and rebalance positions actively to takeadvantage of differences between the consensus market view,as reflected in market equilibrium security prices, and the thefund manager’s view

    Rationale:

    Assumes that the fund manager has some better views ormakes better analyses than the average trader in the market,or has privileged access to some instruments that other

    agents find difficult to trade, or benefits from specialcircumstances (taxation, regulation, etc) that allow themanager to cover his management cost (research, systems,etc.) and still outperform his benchmark

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    Types of Active Strategies

    Active strategies are based on views about one or several of thefollowing factors:

    1. Changes in level of interest rates

    • Stable yield Yield curve ride

    •Shift up or down of all ratesmarket-timing (shorteningand lengthening of duration)

    2. Changes in shape of the discount curve

    3. Changes in yield spreads (e.g. Corporate – Treasury yields)

    NB: For these strategies it is important to design portfolios that willbenefit if the expected change takes place but will be largely immuneto other changes

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    Term Structure of Interest

    maturity

    YTM

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    Yield to Maturity (YTM)

    maturity

    YTM

    YTM = internal rate of return if you hold the bond to maturity

    Yield as carry:

    Simple carry = return if the yield on this bond stays the same = YTM × holding period

    Yield on this bond

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    Riding the Yield Curve

    • Riding the yield curve is a technique that fixed-income portfolio

    managers traditionally use in order to enhance returns.

    • When the yield curve is upward sloping and is supposed to remain

    unchanged, it enables an investor to earn a higher rate of return bypurchasing fixed-income securities with maturities longer than the

    desired holding period, and selling them to profit from falling bond

    yields as maturities decrease over time.

    • We give below an example of riding the yield curve.

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    Riding the Yield Curve

    • We consider at time t = 0 the following zero-coupon curve and five bonds

    with the same $1,000,000 nominal value and a 6% annual coupon rate.

    The prices of these bonds are given at time t = 0 and 1 year later at time t

    = 1, assuming that the zero-coupon yield curve has remained stable (see

    table below).

    • What happens if the portfolio manager buys the 5-year bond at time 0 and

    sell it one year later?

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    Riding the Yield Curve• A portfolio manager who has $1,020,770 cash at disposal for 1 year buys 1

    unit of the 5-year bond at a market price of 102.077%, and sells it 1 year

    later at a price of 102.848%. The total return, denoted by TR, of the buy-

    and-sell strategy is given by the following formula:

    • Over the same period, the 1-year investment (i.e. 1-year zero coupon)

    would generate a return of 3.9%. Thus the surplus profit = 2.7333%

    • Of course, the calculation is based on the assumption that future interest

    rates are unchanged. If rates had risen, then the investment would havereturned less than 6.633% and might even have returned a loss

    • Reciprocally, the steeper the curve’s slope at the outset, the lower the

    interest rates when the position is liquidated, and the higher the return on

    the strategy.

    102.848 6Return 1 6.633%

    102.077

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    Fixed Income Arbitrage

    • Relative value among fixed-income securities toexploit price differences

    • Examples

     –On-the-run vs. off-the-run Treasuries

     – Swap spreads

     – Others: Mortgage trades, volatility trades, etc.

    Trading on fixed income arbitrage is like picking up

    nickels in front of a steamroller 

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    On-the-Run vs. Off-the-Run

    • On-the-run Treasuries:

     – New issued securities

     – Most liquid, i.e. easy to buy and sell at low

    transaction costs – Easy to fund: special repo rate

    • Off-the-run Treasuries

     – Old securities

     – Worse market and funding liquidity

     – As a result, often cheaper

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    On-the-Run vs. Off-the-Run

    • Typical trade:

     – Buy the “cheap” off -the-run Treasury

     – Sell short the “expensive” on-the-run

    • Reversing the trade:

     – Short the off-the-run, long to on-the-run

     – Betting that their yield-spread will widen is the

    near term

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    Time Series of On-the-Run vs. Off-the-

    Run Spread

    Spread of on-the-run vs. off-the-run 10-year U.S.

    Treasuries:

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    Swap Spreads

    •Swap spread – The difference between the YTM on the Treasury and the fixed

    rate of the comparable maturity swap

    SS = YTMswap – YTMTreasury 

    • If the swap spread will narrow in the near/medium termthen: – long swap, short Treasury

    • If the swap spread will be wider in the near/medium termthen: – sell swap, buy Treasury

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    Swap and Treasury Curves: October

    2004

    30

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    Swap and Treasury Curves: September

    28, 2006

    31

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    Swap and Treasury Curves: October 2,

    2008

    32

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    Swap and Treasury Curves: October 5,

    2010

    33

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    Summary

    • Fixed income strategies can be classified as passive and activestrategies

    • Passive strategies do not involve any views about the

    evolution of the interest rates. Passive managers simply tracka benchmark portfolio or match their investments with theirliabilities

    Active managers aim to generate higher returns from theirviews. Strategies such as riding the yield curve, off/on-the-runtrading and swap spreads are examples of active bondstrategies