Arbitrage Strategies for Fixed Income Portfolio Investment

1
Arbitrage and Hedging Strategies for
Fixed Income Portfolio Management
By
Win Udomrachtavanich,Ph.D., FRM
Kasikorn Asset Management
15 May 2007
2
Outline

• Fixed Income Arbitrage Strategies
• Fixed Income Hedging Strategies
• Fixed Income Investment in foreign markets

3
Arbitrage Strategies for Fixed Income
Investment
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Arbitrage Strategies for Fixed Income Portfolio

• Arbitrage ?
• The practice of taking advantage of a price
  differential between different instruments and/or
  markets
• Idea ? Buy low , Sell high ? use of Relative
  Valuation Analysis
• Example
• If the price of Microsoft stock on the NASDAQ is
  traded at 30 USD/share and its corresponding
  futures contract on the CME is traded at 2950
  USD/contract in which one contract will delivered
  100 shares of Microsoft. one can buy the less
  expensive instrument (Futures) and sell the more
  expensive (common stock). The differential is the
  arbitrage profit that arbitrageur would receive
  (0.5USD/Share).

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Arbitrage Strategies for Fixed Income Portfolio

• Relative Valuation Analysis
• Yield Spread Arbitrage (Cheap/Rich, OAS)
• Term Structure Arbitrage (Forward Rate and
  Arbitrage)
• Convertible Arbitrage
• On-the-run and Off-the-run Arbitrage
• Bond Swaps

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Relative Valuation Analysis

• Yield Spread Arbitrage ?
• Comparing spread of the bond over some benchmark
  to the required spread and determining whether
  the bond is overvalued or undervalued
  relative to the benchmark
• Complication
• Too many types of spread !!!
• Too many types of benchmark !!!

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Relative Valuation Analysis

• Types of spread
• Nominal Spread
• Zero Volatility Spread (Z-spread)
• Option-adjusted Spread (OAS)

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Relative Valuation Analysis

• Types of Benchmark
• Treasury Benchmark
• Bond Sector Benchmark (usually higher-rated bond
  within the same sector)
• Issuer-Specific Benchmark

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Relative Valuation Analysis

• Cheap/Rich
• Cheap / Undervalued
• ? spreads larger than required spread
• Rich / Overvalued
• ? spreads smaller than required spread
• Fair / Properly valued
• ? spreads equal to the required spread

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Relative Valuation Analysis

• Example
• A callable corporate ABC bond has nominal spread
  relative to treasury yield curve at 240 bps,
  Z-spread relative to Treasury spot curve at 200
  bps, OAS relative to Treasury spot curve at 180
  bps. If a comparable option-free XYZ bond in the
  market has Z-spread of 200 bps. Determine whether
  ABC bond is overvalued, undervalued, or properly
  valued relative to XYZ bond?
• Answer ABC is Overvalued relative to XYZ
• Strategy Long XYZ bond and short ABC bond

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Relative Valuation Analysis
This is OAS spread!!
Source Bloomberg
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Relative Valuation Analysis

• Forward Rate and Arbitrage
• Idea
• Current forward rate approximately reflects
  expectation on future rates
• Forward rate
• Example 1-year zero coupon bond yield is 6,
  2-year zero coupon bond yield is 8, then 1 year
  forward rate one year from now

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Relative Valuation Analysis

• Forward Curve and Spot Curve

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Relative Valuation Analysis

• Forward Rate and Arbitrage
• What if market expectation for 1f1 is 8, what is
  the implication?
• Yield of 2-year zero coupon bond falls to around
  7
• Or, Yield of 1-year zero coupon bond rises to
  around 8
• Or, combination of both.
• ? flattening yield curve
• Strategy
• Short 1-year bond and long 2-year bond for
  expected capital gain

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Relative Valuation Analysis

• Convertible Arbitrage
• involves purchasing a portfolio of convertible
  securities, generally convertible bonds, and
  hedging a portion of the equity risk by selling
  short the underlying common stock to make
  portfolio Delta-neutral
• Idea
• Convertible bond is sometime price inefficiently
  relative to underlying stock due to
• Lack of liquidity
• High Volatility in Interest rate
• market psychology

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Relative Valuation Analysis

• Example
• Convertible bond of ABC corporation is priced at
  850 with conversion ratio of 100. ABC common
  stock is currently traded at 9. What would be the
  profit from implementing convertible arbitrage
  strategy?
• Answer arbitrage profit would be 0.5 per share.
• What if price of ABC stock changes??

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Relative Valuation Analysis

• Risks associated with Convertible Arbitrage
  Strategy
• Equities Risk
• Interest rate Risk
• Credit Risk
• Liquidity Risk
• Note
• Both prices of convertible bond and common stock
  could simultaneously move at different rate.
• ? Required Dynamic Delta Hedging
• ? Quite demanding and costly

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Relative Valuation Analysis

• On-the-run and Off-the-run
• On-the-run ? newest issued securities of a
  given series
• Off-the-run ? previously issued securities
• Idea On-the-run issues have the largest
  trading volume ? higher liquidity ? Less
  liquidity Risk ? lower required spread ?
  Disparity between On-the-run and Off-the-run
  yield
• Recall Disparity creates Arbitrage
  Opportunities

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Relative Valuation Analysis

• Spread b/w On-the-run and Off-the-run
• Spread Off-the-run yield On-the-run
  yield
• Example 10-year bonds On-the-run yield is
  3.85 and Off-the-run yield is 3.9, the spread
  is 5 bps
• See that price of On-the-run is more expensive
  than Off-the-run securities
• Usually, due to heavy arbitrage activities, yield
  converge to be very close as time pass

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Relative Valuation Analysis
Source Bloomberg
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Relative Valuation Analysis

• Sample of On-the-run and Off-the-run Yield Spread

Source Federal Reserve, Columbia University
Archive 2003
22
Bond Swaps

• In a bond swap, a portfolio manager exchanges an
  existing bond or set of bonds for a different
  issue
• Bond swaps are intended to
• Increase current income
• Increase yield to maturity
• Improve the potential for price appreciation with
  a decline in interest rates
• Establish losses to offset capital gains or
  taxable income

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Bond Swaps

• Types of Bond Swaps
• Substitution swaps / Yield Pick up swaps
• Intermarket or yield spread swaps
• Bond-rating swaps
• Quality swaps
• Rate anticipation swaps

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Substitution Swaps / Yield Pick up Swaps

• In a substitution swap, the investor exchanges
  one bond for another of similar risk and maturity
  to increase the current yield
• Strategy

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Substitution Swaps / Yield Pick up Swaps

• Example
• Selling a XXX bond with 8 coupon for par and
  buying a YYY bond with 8 coupon for 980
• Outcome immediate profit is pick up in the
  current yield by 16 basis points
• Note
• Profitable substitution swaps are inconsistent
  with market efficiency
• Obvious opportunities for substitution swaps are
  rare

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Intermarket or Yield Spread Swaps

• The intermarket or yield spread swap involves
  bonds that trade in different markets/sectors
• i.e., government versus corporate bonds
• Small differences in different markets can cause
  similar bonds to behave differently in response
  to changing market conditions

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Intermarket or Yield Spread Swaps

• In a flight to quality, investors become less
  willing to hold risky bonds
• As investors buy safe bonds and sell more risky
  bonds, the spread between their yields widens
• Flight to quality can be measured using the
  confidence index
• The ratio of the yield on AAA bonds to the yield
  on BBB bonds

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Bond-Rating Swaps

• A bond-rating swap is really a form of
  intermarket swap
• If an investor anticipates a change in the yield
  spread, he can swap bonds with different ratings
  to produce a capital gain with a minimal increase
  in risk

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Quality Swaps

• Strategy of buying bonds with high or low quality
  rating based on the expectation of a change in
  economic states.
• Strategy

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Rate Anticipation Swap

• In a rate anticipation swap, the investor swaps
  bonds with different interest rate risks in
  anticipation of interest rate changes/ Yield
  curve shifts.
• Strategy

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Long-Term Capital Management Case (LTCM)

• Background
• Found in 1994 by a group of ex Solomon Brothers
  Traders
• Joined by 2 prominent academia ? Merton and
  Scholes
• Average annualized return on the first several
  years was approximately 40
• Collapse in 1998, in which lost 4.6 billion in 4
  months
• Bailed-out orchestrated by FBNY along with other
  key major investment banks
• Officially liquidated in early 2000

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Long-Term Capital Management Case (LTCM)

• Trading Strategies Involved
• Convertible Arbitrage
• On-the-run / Off-the-run Arbitrage
• Yield Curve Arbitrage
• Along with usage of Derivatives to enhance return

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Long-Term Capital Management Case (LTCM)

• Sample of On-the-run and Off-the-run Arbitrage
  practice by LTCM

Source Federal Reserve, Columbia University
Archive 2003
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Long-Term Capital Management Case (LTCM)

• Key Profit Generation
• Leverage ? some speculate that the number was gt
  1001
• Example
• LTCM bought 1 billion of Cheap off-the-run
  bond
• Short 1 billion of expensive on-the-run
• Off-the-run position is used as collateral for
  on-the-run
• Results is no money need to pay upfront.
• If everything works as planned (when on-the-run
  and off-the-run rates converge), profit would
  be 15 millions from this transaction

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Long-Term Capital Management Case (LTCM)

• Trigger of the fall
• Russian bond defaulted in 1997 ? Flight to
  Quality ? Spread rise between Emerging markets
  and US bonds, Spread rise between On-the-run
  and Off-the-run
• Multiply effect with Large position in
  derivatives for leverage ? Dooms Day solution !!!

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Hedging Strategies for Fixed Income Investment
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Hedging Strategies for Fixed Income Investment

• Portfolio Immunization
• Laddered Portfolio
• Derivatives and Hedging Strategies for Fixed
  Income Investment
• Bond Futures
• Option

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Portfolio Immunization

• If the average duration of a portfolio equals the
  investors desired holding period, the effect is
  to hold the investors total return constant
  regardless of whether interest rates rise or
  fall.
• In the absence of borrower default, the
  investors realized return can be no less than
  the return he has been promised by the borrower.

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Example Portfolio Immunization

• Assume we are interested in a 1,000 par value
  bond that will mature in two years.
• The bond has a coupon rate of 8 percent and pays
  80 in interest at the end of each year.
• Interest rates on comparable bonds are also at 8
  percent but may fall to as low as 6 percent or
  rise as high as 10 percent.

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Example Portfolio Immunization

• The buyer knows he will receive 1000 at
  maturity, but in the meantime he faces the
  uncertainty of having to reinvest the annual 80
  in interest earnings at 6, 8, or 10.

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Example Case 1

• Let interest rates fall to 6.
• The bond will earn 80 in interest payments for
  year one, 80 for year two, and 4.80 (80 x
  0.06) when the 80 interest income received the
  first year is reinvested at 6 during year 2.

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Example Case 1

• How much will the investor earn over the two
  years?
• First years interest earnings Second years
  interest earnings Interest earned reinvesting
  the first years interest earnings at 6 Par
  value of the bond at maturity.
• 80 80 4.80 1,000 1,164.80

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Example Case 2

• Let interest rates rise to 10.
• The bond will earn 80 in interest payments for
  year one, 80 for year two, and 8.00 (80 x
  0.10) when the 80 interest income received the
  first year is reinvested at 10 during year 2.

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Example Case 2

• How much will the investor earn over the two
  years?
• First years interest earnings Second years
  interest earnings Interest earned reinvesting
  the first years interest earnings at 10 Par
  value of the bond at maturity.
• 80 80 8 1,000 1,168.00

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Immunization and Duration

• The investors earnings could drop as low as
  1,164.80 or rise as high as 1,168.
• But, if the investor can find a bond whose
  duration matches his or her planned holding
  period, he or she can avoid this fluctuation in
  earnings.
• The bond will have a maturity that exceeds the
  investors holding period, but its duration will
  match it.

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Recall Example Case 1

• Let interest rates fall to 6.
• The bond will earn 80 in interest payments for
  year one, 80 for year two, and 4.80 (80 x
  0.06) when the 80 interest income received the
  first year is reinvested at 6 during year 2.
• But, the bonds market price will rise to
  1,001.60 due to the drop in interest rates.

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Recall Example Case 1

• How much will the investor earn over the two
  years?
• First years interest earnings Second years
  interest earnings Interest earned reinvesting
  the first years interest earnings at 6 Market
  price of the bond at the end of the investors
  planned holding period.
• 80 80 4.80 1,001.60 1,166.40

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Recall Example Case 2

• Let interest rates rise to 10.
• The bond will earn 80 in interest payments for
  year one, 80 for year two, and 8.00 (80 x
  0.10) when the 80 interest income received the
  first year is reinvested at 10 during year 2.
• But, the bonds market price will fall to 998.40
  due to the rise in interest rates.

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Recall Example Case 2

• How much will the investor earn over the two
  years?
• First years interest earnings Second years
  interest earnings Interest earned reinvesting
  the first years interest earnings at 10 Par
  value of the bond at maturity.
• 80 80 8 998.40 1,166.40

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Portfolio Immunization

• The investor earns identical total earnings
  whether interest rates go up or down.
• With duration set equal to the buyers planned
  holding period, a fall (rise) in the reinvestment
  rate is completely offset by an increase (a
  decrease) in the bonds market price.
• Immunization using duration seems to work
  reasonably well because the largest single
  element found in most interest rate movements is
  a parallel change in all interest rates (explains
  about 80 of all interest rate movements over
  time).
• So, investors can achieve reasonably effective
  immunization by approximately matching the
  duration of their portfolios with their planned
  holding periods.

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Opportunity Cost and Portfolio Immunization

• Duration is not free. There is an opportunity
  cost.
• If the investor had simply bought a bond with a
  calendar maturity of two years and interest rates
  rose, he or she would have earned 1,168.
• The opportunity cost of immunization is a lower,
  but more stable, expected return.

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Limitation of Portfolio Immunization

• In reality it can be difficult to find a
  portfolio of securities whose average portfolio
  duration exactly matches the investors planned
  holding period.
• As the investor grows older, his planned holding
  period grows shorter, as does the average
  duration of his portfolio, but they may not
  decline at the same rate.
• Portfolio requires constant adjustments.

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Limitation of Portfolio Immunization

• Many bonds are callable so bondholders may find
  themselves with a sudden and unexpected change in
  their portfolios average duration.
• The future path of interest rates cannot be
  perfectly forecast therefore, immunization with
  duration cannot be perfect without the use of
  complicated models.

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Contingent Immunization

• Contingent Immunization is a mixed of both an
  active and passive strategy.
• Bond manager pursues an active bond strategy
  until an agreed-upon minimum rate is reached or
  safety margin approaches zero when that occurs
  the manager immunizes the position.

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Contingent Immunization

• Example
• Suppose an Investment Company offers a contingent
  immunization strategy for investors with HD 3.5
  years based on a current 4-year, 9 annual coupon
  bond trading at a YTM of 10 (assume flat YC at
  10). The bond has a duration of 3.5 years and
  an immunization rate of 10, in which assumes
  that minimum target rate is approximately 8.
• Strategy
• the investment will be immunized when the
  following case occurs
• The minimum target rate is reached 8
• The investments safety margin is zero

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Contingent Immunization

• Suppose the investment company has a client with
  1M to invest and HD 3.5 years.
• Clients Initial Safety Margin (SM)

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Contingent Immunization

• As part of its active strategy, suppose the
  investment company invest the clients funds in a
  10-year, 10 annual coupon bond trading at par.
• Scenario 1 One year later the YC shifts down to
  8
• Clients Safety Margin (SM)

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Contingent Immunization

• With a positive SM, the company could maintain
  its current investment, pursue a different active
  strategy, or it could immunized the position.
• If the company immunizes, it would liquidate the
  original 10-year bond and purchase a bond with HD
  2.5 years yielding 8 (assume flat YC at 8).
  If it did this, it would be able to provide the
  client with a 11.96 rate for the 3.5 year period

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Contingent Immunization

• Scenario 2 One year after investing in the
  10-year bond, the YC shifts up to 12.25.
• Clients Safety Margin (SM)

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Contingent Immunization

• With the SM approximately zero, the company would
  immunized the position.
• The company would liquidate the original 10-year
  bond and purchase a bond with HD 2.5 years,
  yielding 12.25 (assume flat YC at 12.25). For
  the 3.5 year period the rate would be the minimum
  target rate of 8

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Laddered Portfolio

• In a laddered strategy, the fixed-income dollars
  are distributed throughout the yield curve
• A laddered strategy eliminates the need to
  estimate interest rate changes
• For example, a 1 million portfolio invested in
  bond maturities from 1 to 25 years (see next
  slide)

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Laddered Portfolio
Par Value Held ( in Thousands)
Years Until Maturity
63
Laddered Portfolio

• In laddered portfolio, the principal proceeds
  from the matured bond will be reinvested at the
  longer end of the ladder, often at higher
  interest rate.
• Portfolio Return and rate scenarios
• Unchanged Rate ? return is stable and fairly
  closed to the highest yield in portfolio
• Rising Rate ? return drop at first and recover
  later from reinvest in longer term bonds at the
  lower cost
• Falling Rate ? return rise at first and drop
  later from reinvest in longer term bonds at the
  higher cost

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Laddered Portfolio
Source Thornburg Financial
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Derivatives in Fixed-Income Management

• Primary Usage
• Derivatives (i.e., Futures, Swap, and Option) can
  be used to modify portfolio risk and return
• Using derivative for asset allocation ? portable
  alpha??
• Adjusting allocations in the underlying assets
  can be very expensive
• Less costly to achieve a similar asset allocation
  exposure using derivatives, especially for
  temporary adjustments
• To control portfolio cash flows
• Hedging portfolio cash inflows and outflows
• Hedging instruments against risk factors, i.e.,
  interest rate risk
• Target duration Contribution of current bond
  portfolio contribution of the futures component

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Futures

• Treasury bond futures contract
• Typically used contract for risk management of
  fixed-income portfolios
• Deliver pre-specified T-bonds at the expiration
• Those that are delivered are the
  cheapest-to-deliver (CTD) that satisfies contract
• Most common usage ? Duration Hedging

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Futures

• Determining How Many Contracts to Trade to Hedge
  a portfolio position ? determine Hedge Ratio
• Hedge ratio
• Conversion factor
• Adjusts the CTD bond to 8 (required for
  delivery)
• Duration adjustment factor (DAF)
• Reflects the difference in interest rate risk
  between the CTD bond and the portfolio being
  hedged

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Futures

• Example
• Suppose there is a 6-month hedging horizon and a
  portfolio value of 100 million. Further assume
  that the matching instrument is T-bond futures
  contract, which is quoted at 105-09 with the
  contract size of 100,000. The duration of the
  portfolio is 10, and the duration of the futures
  contract is 12. What is the contract no. required
  to trade to completely hedge this portfolio
  against small changes in yield?
• Answer
• But because we long bonds, therefore to make the
  portfolio Duration-Neutral, the manager needs to
  short 792 contracts of T-bond futures

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Futures

• Using Futures in Passive Fixed-Income Portfolio
  Management
• Will use futures primarily to manage Cash flow
  assets and liabilities
• Will not use futures to actively adjust duration
  due to interest forecasts

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Futures

• Using Futures in Active Fixed-Income Portfolio
  Management
• Modifying systematic risk
• Changing the portfolio duration in light of
  interest rate forecasts
• Lengthen duration if rates are expected to fall
• Modifying unsystematic risk
• Opportunities are more limited here, but can
  adjust exposure to various sectors to take
  advantage of expected yield changes

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Futures

• Changing the Duration of a Corporate Bond
  Portfolio
• There are no corporate bond futures contracts, so
  strategies are based on using T-bond futures
• Corporate bond yields also impacted by changes in
  default risk, unlike T-bond yields
• T-bonds are a cross hedge instrument
• Differences could impact the number of contracts
  required to hedge a corporate bond portfolio

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Futures

• Modifying the Characteristics of an
  International Bond Portfolio
• Positions in foreign bonds are positions in both
  securities and currencies
• Futures and option contracts allow the portfolio
  manager to manage the risks of the currency and
  the security separately
• In a passive strategy, the manager can hedge the
  risk exposure
• In an active strategy, the manager can adjust the
  exposure to try to benefit from expected changes
  in exchange rates

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Option

• Use of call, put, or combinations
• Practical Fixed Income strategies using options
• Portfolio Insurance ? long bonds, long puts
• Covered Calls ? long bonds, short calls
• Buy-Writes ? long bonds, short calls to the same
  dealer at the time of long bonds
• Writing Puts ? short puts (naked position)

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International Fixed Income markets
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International Fixed Income markets

• Rational of International Fixed Income Investment
• Styles of International Bond Portfolio Management
• Return of International Bond portfolio and
  sources of return
• Currency Hedge Decision

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International Fixed Income markets

• Rationales
• Higher return than domestic products
• Broader diversification
• Speculate in FX markets

77
International Fixed Income markets
Source Merrill Lynch, as of 2005
78
International Fixed Income markets
79
International Fixed Income markets

• Styles of International Bond Portfolio Management
  
• Fundamental style ? economic cycle based
• Black-box approach ? Quant based
• Experienced traders ? experience and intuition to
  identify market opportunities ? Active approach
• Technicians/ Chartist ? technical analysis to
  timing buy and sell ? Trend Reader
• Benchmarkier ? pure passive approach

80
International Fixed Income markets

• Sample of available benchmarks
• JPMorgan Global Government Bond
• JPMorgan Government Bond EMU
• JPMorgan Emerging Markets Band Index Plus (EMBI)
• iBoxx Euro Overall
• iBoxx Euro Sovereigns
• iTraxx Asian Series
• etc.

81
International Fixed Income markets

• Benchmark Dilemma
• Bond inclusion difficulty
• Size of issuance small
• Credit rating limit varies
• Country weights
• Driven by country budget situation, e.g. Japan
• Market capitalization can change quickly between
  countries
• Duration between countries indices vary
  significantly
• Replicability
• Bid-ask spreads generally wide
• Certain issues see small turnover from buy and
  hold investor
• Total return approach, focus on alpha generation

82
International Fixed Income markets

• Return of International Bond portfolio and
  sources of return
• Total expected portfolio return in managers home
  currency e (ri)
• N number of countries whose bonds are in the
  portfolio
• W weight of country i s bonds in the portfolio
• ri expected bond return for country i s in
  local currency
• eH,i expected percentage change of the home
  currency with country is local currency ?
  currency return ? depreciation of home currency
  over period

83
International Fixed Income markets

• Example
• Suppose a U.S. portfolio manager invests in US
  treasury bonds with expected return at 4.5. He
  also diversifies his investment global to reduce
  volatility by investing in a Japanese Bond and a
  UK Gilt. Proportion of his investment in US
  Treasury, Japanese bond and UK Gilt is 801010.
  The expected return over the investment holding
  period of Japanese bond and UK gilt are 1.2 and
  5 respectively. If Japanese Yen depreciates
  against USD by 1 and UK sterling depreciates
  against USD by 0.5 over the investment period.
  What should be the expected return of his
  portfolio?
• Answer expected return 0.84.5
  0.1(1.2-1)0.1(5-0.5) 4.07
• He turns to be worse off with his global
  diversification strategy due to stronger USD
  against other currencies.
• Question to hedge or not to hedge???

84
International Fixed Income markets

• If hedged currency, it means buying forward
  contract and lock in rate
• Total expected portfolio return in managers home
  currency if hedged e (ri)
• N number of countries whose bonds are in the
  portfolio
• W weight of country i s bonds in the portfolio
• ri expected bond return for country i s in
  local currency
• fH,i forward rate discount or premium between
  the home currency and country i s local currency
  ?
• cH and ci are short-term interest rate in home
  and country i that matched maturity of forward
  rate.

85
International Fixed Income markets

• Other alternative strategies besides using
  forward contract
• Cross Hedging
• Idea long bond i, and hedged by long forward to
  deliver currency j against currency i ? close FX
  exposure in currency i and open FX exposure in
  currency j
• Return
• Proxy Hedging
• Idea long bond i, leave FX exposure in currency
  i and short position in currency j ? cheaper to
  hedged in currency j
• Return

86
International Fixed Income markets

• Other considerations
• Taxation
• Regulations and legal system
• Political stability
• Economic Stability
• Liquidity
• Etc.

87
QA