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Fixed Income Trading Strategies

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					Fixed Income Trading Strategies
Victor Haghani & Gerard Gennotte

General Characteristics
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Securities cash flows easy to replicate using other securities Term structure well explained by limited number of state variables But:
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Fixed costs are high (e.g. modelling, contractual framework, administration)  Size Price anomalies are small, volatility is low  Leverage

Leverage + fat tails Most non-fraud hedge fund (and IB) crises have involved fixed income trading strategies

Fixed Income Trading Strategies
Cash Flow “Arbitrage”  Term Structure  Higher Moment (Volatility)
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Cash Flow “Arbitrage”
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Instruments with negligible credit risk
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Government bonds
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Fixed rate Floating rate Inflation indexed

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Interest rate swaps Government guaranteed and other AAA+ issuers

Examples of Bond v Bond Trades
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Liquidity/ transactions costs Repo “specialness” Tax preference- coupon or regime Accounting preference Age Size

On the Run vs Off the Run Bond
On the run: 5% yield  Off the run 5.2% yield  Repo-reverse repo difference: 40bp  Specialness difference: 30bp  Duration: 7  Profit assuming 15% convergence in 3 months: Carry: (20-30-40)/4=-0.125% Convergence: 15% of 20bp x 7yr duration= 0.21% Total = 0.085% of par amount of trade “That is still a very big number”
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On the Run vs Off the Run Bond
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Return on capital:
Haircut: 1%, thus annual compound return on working capital: (1+0.085%/1%)^4-1= 39% very Nice!
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What are the issues?  What are the risks?
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On the Run vs Off the Run Bond
If the fund were fully invested in this strategy, leverage would be 100 to 1… Possibly more if haircuts were netted.  Stress test: on the run becomes more expensive by 20bp, loss is 1.4%  Thus: if fund restricted to have its working capital and its stress loss to be less than 40% of assets, then capital usage is 2.5*1.4%=3.5%, and the return becomes 10%.
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Interest Rate Swaps
What is LIBOR?  What is Govt Repo?  Fair pricing of Interest Rate Swaps
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Long term Repo-Libor Spread The arbitrage band
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LIBOR – Repo

 LIBOR - Reverse Repo

Basis Points (Govt bond yield - Swap Rate)
-180 -80 -60 -40 -160 -140 -120 -100 -20 0 20

2/28/1995 5/28/1995 8/28/1995 11/28/1995 2/28/1996 5/28/1996 8/28/1996 11/28/1996 2/28/1997 5/28/1997 8/28/1997 11/28/1997 2/28/1998 5/28/1998 8/28/1998 11/28/1998 2/28/1999 5/28/1999 8/28/1999 11/28/1999 2/28/2000 5/28/2000 8/28/2000 11/28/2000 2/28/2001 5/28/2001 8/28/2001
UKT 8 2021 JGB 2.2 12/20/07 FRTR 6 10/25/25 UST 6.625 5/15/07

Swap Spreads of G4 Govt Bonds

End Users of Interest Rate Swaps
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The original “Swap”
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Borrowers want floating rate liabilities and investors want fixed rate bonds High risk companies use to create long term liabilities from short term floating rate debt Banks and insurance companies fixed as synthetic assets Property investors use to create fixed rate mortgages U.S. mortgage agencies use as hedge of fixed rate mortgage portfolio

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Financial Institution ALM:
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Real Estate and other project finance:
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Governments to alter debt duration Hedging fixed rate issuance

What Drives Swap Spreads
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Historical regressions:
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Changes in Govt and high grade corporate bond issuance Slope of yield curve Change in short term rates Change in AA corporate spreads Bank credit crisis (Japan?)

Equilibrium when outside of Arbitrage Bands
Spread increases or decreases with duration  Return on capital example:
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10 year swap spread at 80bp Libor – Reverse Repo = 35bp Initial margin = 2% Stress loss = 60bp (5%) Risk capital  20% Carry  0.45%/20%= 2.25% excess return on capital To allocate risk capital, must believe in convergence of spread

Swap Spreads Today
10 years UK Gilts  Bund  JGB  US Treasury
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30bp 8 8 30

Inflation Linked Bonds
Recent rapid growth- UK (govt and corp), US, France, Italy, Sweden, Japan, Australia, New Zealand, Iceland  Complex and non-standard structures
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Indices Cash flows seasonality

Term Structure “Arbitrage”
Fundamental problem- bonds age and therefore cannot enforce convergence  Arb free models- many choices  Parsimony in factors  Mean reversion in residuals  Statistical vs structural approach- PCA  The model as a measurement tool not a forecasting tool  Model choice depends on application
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Simple 2-Factor TS Model
Level of yield curve  Slope of yield curve
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A Broader Set of Possible Term Structure Factors
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Overnight rate Near term trajectory of overnight rate
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Objective Speed of adjustment

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Long term expectation of short term rate Speed of convergence to long term expectation Risk premium Volatility

Fitting Term Structure Factors
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R0  Overnight rate Near term trajectory of overnight rate  R3month :  Objective  R1year  Speed of adjustment R10year  Long term expectation of short term rate R5year  Speed of convergence to long term expectation R30year  Risk premium Interest rate options Volatility and other distributional properties

Trading Strategies
In increasing order of speculativeness
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Betting on residuals
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Very narrow trades- 5-7-10-12-15 Not much margin
Government bond risk premium vs interest rate swap risk premium MFR- risk premium Japan- speed of convergence to long term rate

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Betting on inter-market factors
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Betting on factors
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Example 1: Japanese Yen Interest Rate Swap Rates Slow Convergence to Long Term Rate
Date 1 Year 2 Year 3 Year 4 Year 5 Year 7 Year 10 Year 15 Year 20 Year 30 Year 11-Jun-03 0.07% 0.09% 0.11% 0.15% 0.18% 0.27% 0.44% 0.70% 0.88% 1.09%

Example 2: UK Gilt Rates Low Risk Premium
Date 2-Year 3-Year 4-Year 5-Year 7-Year 8-Year 10-Year 15-Year 20-Year 30-Year 8-Feb-05 4.52% 4.50% 4.48% 4.46% 4.44% 4.43% 4.44% 4.40% 4.35% 4.25%

Fixed Income Volatility
Realized versus implied  Term Structure of Volatility  Skew  Smile  Caps vs swap options vs bond options  Spread options, barrier options, correlation etc.  Mortgage prepayment options
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Fixed Income Volatility: A Difficult Game
Many degrees of freedom  Supply-demand pressures  High transactions costs
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US Mortgages- Highly Complex and Very Large Market
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Description of market
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$3000BB of mortgage backed bonds FNMA/FHLMC own more than ½ of outstanding
Prepay efficiency Ramp up Burnout Dumbo Home equity Pool idiosyncrasies Yield curve

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Prepay Modeling
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Very big forecasting errors

Mortgage Derivatives
IO/PO  CMO tranching  Inverse floaters  ARMs
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Return on Capital in FI Trading Business
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Pre-fee post-trx costs Sharpe ratio of 1 How much risk?
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Capitalized such that a 5σ 1 month event results in a 10% loss

How much alpha?  σmonthly = 2%  σannual = 7%  1 x 7% = 7% gross alpha  7% gross alpha  4% net alpha Fees being 2% Mgmt Fees, 20% Incentive Fees (Sharpe ratio of 2  9% net alpha)
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