FFIEC Capital Markets Conference

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FFIEC Capital Markets Conference

• Portfolio Management
• and Theory
• Steve Mandel
• May 18-19, 2004

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Portfolio Management Tools
Nominal Yield/Risk Measures
Effective Yield/Risk Measures
Return Attribution
Security Level Portfolio Level Portfolio vs.
Liabilities
Scenario Analysis
Optimization
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Nominal Yield/Risk Measures

• Nominal Yield Measures
• Current Yield
• Yield (to Maturity, to Worst)
• Spread to Benchmark
• Spread to Yield Curve
• Nominal Risk Measures
• Years to Maturity (Average Life)
• Nominal Duration (Macaulay, Modified)
• Nominal Convexity

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Nominal Yield Measures

• Current Yield
• FHLB 4.25 11/15/2010
• Price (2/29/2004) 103.369
• Current Yield 4.111

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Nominal Yield Measures

• Yield to Maturity The discount rate at which
  the present value of the cash flows equals the
  full price of the bond.

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Yield to Maturity
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Nominal Yield Measures

• Spread to Benchmark - The difference between the
  yield of a security and the yield of a
  corresponding benchmark security stated in basis
  points (1 bp.01) The benchmark is typically an
  On-the-Run Treasury closest to the maturity of
  the security (or average life for an amortizing
  security)

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Nominal Yield Measures

• Spread to Benchmark (Continued)
• Benchmark Security US 5 2/15/2011
• Yield of Bond3.68
• Yield of Benchmark Security 3.47
• Spread to Benchmark 0.21 (21basis points)

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Nominal Yield Measures

• Spread to Yield Curve - The difference between a
  securitys yield and the interpolated point on
  the yield curve corresponding to the securitys
  average life, stated in basis points (1 bp.01)
• On-The-Run Treasury Curve
• Off-The-Run Treasury Model Curve
• Swap Curve

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Nominal Yield Measures

• Spread to On-the-Run Treasury Yield Curve
• Yield Curve On-The-Run Tsy (2/27/2004)
• Average Life of Security 6.71
• Interpolated Point on Yield Curve 3.302
• Yield of Security 3.678
• Spread to Yield Curve100x(3.68-3.30)38bp

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Yield Curves (2/27/2004)A -Treasury On-the-Run,
B - Treasury Off-the-Run
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Nominal Yield Measures

• Spread to Off-the-Run Treasury Yield Curve
• Yield Curve Off-The-Run Tsy (2/27/2004)
• Average Life of Security 6.71
• Interpolated Point on Yield Curve 3.442
• Yield of Security 3.678
• Spread to Yield Curve100x(3.68-3.44)24bp

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Yield Curves (2/27/2004)A -Tsy On-the-Run, B -
Tsy Off-the-Run, C - Swap
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Nominal Yield Measures

• Spread to Swap Yield Curve
• Yield Curve Swap (2/27/2004)
• Average Life of Security 6.71
• Interpolated Point on Yield Curve 3.820
• Yield of Security 3.678
• Spread to Yield Curve100x(3.68-3.82) -14bp

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Nominal Risk Measures

• Years to Maturity (Average Life) 6.71
• Macaulay Duration - Percentage change in Price
  for a percentage change in Yield.
• (Average life of PV of Cash Flows)

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Macaulay Duration
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Nominal Risk Measures

• Years to Maturity
• Macaulay Duration
• Modified Duration - Percentage change in Price
  for a 100 basis point change in Yield. The
  tangent (first derivative) of the price/yield
  curve for a given yield.
• Modified Duration 5.851/(13.678/200) 5.746

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Modified Duration
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Nominal Risk Measures

• Years to Maturity
• Macaulay Duration
• Modified Duration
• Nominal Convexity - measures the degree to which
  the price/yield curve of a security differs from
  the tangent at the current yield.

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Portfolio Management Tools
Nominal Yield/Risk Measures
Effective Yield/Risk Measures
Return Attribution
Security Level Portfolio Level Portfolio vs.
Liabilities
Scenario Analysis
Optimization
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Effective Yield/Risk Measures

• Effective Yield Measures
• OAS
• Yield Curve Margin
• Effective Risk Measures
• Effective Duration
• Partial Durations
• Effective Convexity
• Spread Duration
• Volatility Duration
• Prepay Duration

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Effective Yield Measures

• Option Adjusted Spread OAS
• A securitys spread (in basis points) over the
  yield curve, after adjusting for the probability
  of any optional calls, puts, or prepayments and
  assuming a volatility (or set of volatilities) of
  future yields.
• The spread over the yield curves forward rates
  (multiple rate paths are considered) that makes
  the present value of the cash flows equal to the
  full price.

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Option Adjusted Spread (OAS)

• Bonds Without Embedded Options OAS is not
  dependent on volatility and will be close to
  nominal spread (small difference due to the shape
  of the yield curve). OAS depends on Price and
  Yield Curve
• Bonds With Embedded Options OAS will depend on
  Price, Yield Curve and the volatility assumption.
  For callable bonds and mortgages the higher the
  volatility assumption the lower the OAS.

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Effective Yield Measures

• Yield Curve Margin OAS assuming a zero
  volatility. The spread over the yield curves
  forward rates that makes the present value of the
  cash flows equal to the full price.
• Option Cost Yield Curve Margin OAS

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Effective Risk Measures

• Effective Duration
• A measure of the sensitivity (percent change) of
  the Full Price of a security to a (100 bp)
  parallel shift of the Yield Curve.
• Utilized to measure a securitys price
  sensitivity to a change in the general level of
  interest rates.

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Effective Duration Calculation
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Effective Risk Measures

• Effective Duration
• Partial Duration - A measure of the sensitivity
  (percent change) of the full price of a security
  to a move in a single key rate point of the
  Yield Curve.
• Utilized to measure a securitys sensitivity to
  a particular reshaping of the Yield Curve

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Partial Duration Calculation

• Partial Duration (5Year)

YC Point Partial Duration
1 .337
2 .174
3 .300
5 .548
10 .738
20 .347
30 -.053
Total 2.39
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Effective Risk Measures

• Effective Duration
• Partial Duration
• Effective Convexity - measures the degree to
  which the price/parallel-shift curve of a
  security differs from the tangent at the current
  curve.
• A measure of the sensitivity of the Effective
  Duration of a security to a parallel shift of the
  Yield Curve so as to measure the sensitivity of
  price to large rate moves.

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Effective Convexity

• Positive Convexity implies P/Y curve is above
  tangent.
• Effective Duration goes up as rates come down.
• P/Y curve gets steeper as rates come down.
• Negative convexity implies P/Y curve falls below
  tangent.
• Effective Duration goes down as rates come down.
• P/Y curve flattens as rates come down.

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Effective Convexity Calculation
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Effective Risk Measures

• Effective Duration
• Partial Duration
• Effective Convexity
• Volatility Duration - A measure of the
  sensitivity (percent change) of the full price of
  a security to changes in Volatility.

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Term Structure of Volatilities
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Volatility Durations
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Effective Risk Measures

• Effective Duration
• Partial Duration
• Effective Convexity
• Volatility Duration
• Pre Pay Duration - The sensitivity of a
  (mortgage) securitys full price to changes in
  Prepayment Rates

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Prepay Durations
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Portfolio Management Tools
Nominal Yield/Risk Measures
Effective Yield/Risk Measures
Return Attribution
Security Level Portfolio Level Portfolio vs.
Liabilities
Scenario Analysis
Optimization
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Portfolio Risk Measures

• The Portfolio Risk Measures are analogous to the
  Security Measures in that they are measures of
  the sensitivity (percent change) of a Portfolios
  Market Value to various market changes.
• They are calculated by taking a Market Weighted
  Average of the Individual Security Risk Measures.

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Portfolio Risk Measures

• Effective Duration - A measure of the sensitivity
  (percent change) of the Market Value of a
  Portfolio to a parallel shift in the Yield Curve.
• The Market Weighted Average of the individual
  securities Effective Durations

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Portfolio Effective Duration

• Market Weighted Average of Individual Security
  Effective Durations 3.93
• or
• Percent MV Change (/- 25 bp) on Portfolio

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Portfolio Risk Measures

• Effective Duration
• Partial Durations - Measure the sensitivity of a
  Portfolios Market Value to reshapings of the
  Yield Curves
• Market Weighted Average of Individual Security
  Partial Durations

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Portfolio vs Benchmark/Liability Risk Measures

• Measures of the of the sensitivity of the ROR
  difference between the Portfolio and Benchmark
  (or Liabilities) to various market changes

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Portfolio Management Tools
Nominal Yield/Risk Measures
Effective Yield/Risk Measures
Return Attribution
Security Level Portfolio Level Portfolio vs.
Liabilities
Scenario Analysis
Optimization
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Scenario Analysis

• Framework for evaluating the combined effect of
  Yield and Risk Measures for a range of
  assumptions.
• Nominal Return Rate of Return on a security
  assuming it was purchased on a certain begin
  (settlement) date and sold on a certain horizon
  date. The return calculation takes into account
  the settlement full price, the horizon full
  price, intermediate cash flows from the security
  (coupon plus any principal payments) plus
  reinvestment of any intermediate cash flow
  payment to the horizon date.

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Scenario Analysis

• Security FHLB 4.25 11/15/2010
• Settlement Date 2/29/2004
• Horizon Date 2/28/2005
• Yield Curve Assumption No Change
• Pricing Assumption Constant Spread to Yield Curve

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Rolling Yield

• Scenario Return calculation assuming that at the
  horizon the security will have the same spread
  (nominal or OAS) to the yield curve as the
  beginning spread. For a positive yield curve
  assuming Rolling Yield decreases the horizon
  yield and increases the expected return.

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Rolling Yield CalculationConstant Nominal Spread
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Rolling Yield CalculationConstant Nominal Spread

• Beginning
• Price of Security 103.366
• Yield of Security 3.678
• Interpolated Yield Curve 3.442
• Nominal Spread to Curve .236
• Horizon
• Interpolated Yield Curve 3.165
• Nominal Spread to Curve .236
• Yield of Security 3.401
• Price of Security 104.362

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Return Calculation

• Beg Full Price 103.366 1.334 104.700
• Hor Full Price 104.362 1.216 105.578
• Coupon 2.231 2.125 4.356
• Reinv .022

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Rolling Yield Constant Nominal Spread
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Rolling Yield CalculationConstant OAS

• For a bond without embedded options assuming
  constant nominal spread produces results similar
  to those produced by the more accurate constant
  OAS method.

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Rolling Yield Constant OAS
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Rolling Yield CalculationConstant OAS

• For a bond without embedded options assuming
  constant nominal spread produces results similar
  to those produced by the more accurate constant
  OAS method.
• For a bond with embedded options such as callable
  bonds and mortgage backed securities using
  constant OAS produces significantly different and
  more accurate results especially for large yield
  curve shifts.

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Rolling Yield Constant CPR Nominal Spread
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Rolling Yield Constant CPR Nominal Spread
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Rolling Yield - Model Prepay Projections
Constant OAS
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Portfolio Management Tools
Nominal Yield/Risk Measures
Effective Yield/Risk Measures
Return Attribution
Security Level Portfolio Level Portfolio vs.
Liabilities
Scenario Analysis
Optimization
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Scenario AnalysisParallel Shifts 3 Months
Horizon
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Pct ROR for Assets vs LiabilitiesParallel Shifts
3 Months Horizon
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Principal Component Scenarios

• Statistically likely re-shapings of the Yield
  Curve derived through analysis of 15 years of
  monthly movements in the Off-The-Run Treasury
  Yield Curve.
• These scenarios model 95 of observed movements
  in the Yield Curve. That is 95 of the monthly
  movements can be represented as a linear
  combination of the Principal Component Scenarios.

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Principal Components Scenarios
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Principal ComponentsCombination Scenarios
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Scenario Analysis Principal Comp Comb Scenarios-
3 Month Horizon
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Pct ROR for Assets vs LiabilitiesPrinc Component
Scenarios 3 Months Horizon
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Portfolio Management Tools
Nominal Yield/Risk Measures
Effective Yield/Risk Measures
Return Attribution
Security Level Portfolio Level Portfolio vs
Liabilities
Scenario Analysis
Optimization
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Portfolio Optimization

• A methodology utilizing mathematical procedures
  such as Linear Programming to optimize portfolios
  given
• Universe of available securities
• A Portfolio Objective
• Series of Portfolio Constraints

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Portfolio OptimizationDuration Target Example

• Universe All Securities in Citigroup Treasury
  Index
• Objective Maximize Average Yield
• Constraints
• Average Duration 5
• Total Market Value 50mm

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Portfolio Optimization Tips

• Remember optimizer is just a very powerful (but
  dumb) tool which can quickly evaluate all
  possible combinations to identify the optimal
  solution.
• The solution is only as good as the formulation
  of objective and constraints.
• Since the objective was to max YTM the optimizer
  incorrectly selected a callable bond trading to
  call.

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Portfolio Optimization Tips

• The number of securities in the optimal portfolio
  are equal to the number of binding constraints.
• To increase the number of securities in a
  portfolio add more constraints such as per issue
  limits.
• As you add more (binding) constraints the value
  of the objective function gets marginally worse.

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Portfolio Optimization Cash Matching Example 1

• Universe All non callable securities in
  Citigroup Treasury Index
• Objective Minimize Cost
• Constraints - Cash Match Liability Schedule

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Optimization Tips

• Minimum Cost for cash matching liabilities can be
  reduced by marginally increasing risk
• Increasing reinvestment rate assumption
• Lowering quality of portfolio (agencies,
  corporates etc., control risk with issue/sector
  limits)
• Allowing callable bonds and mortgages (control
  risk by imposing a series of scenario dependent
  cash flow constraints).

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Portfolio Optimization Cash Matching Example 2

• Universe Treasury, Agency, and Mortgage
  securities from the Citigroup BIG Index
• Objective Minimize Cost
• Constraints - Cash Match Liabilities for each of
  7 Principal Component Scenarios.

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Portfolio OptimizationImmunization Example

• Universe All non callable securities in
  Citigroup Treasury Index
• Objective Maximize IRR of Portfolio
• Constraints
• Market Value PV of Liabilities at estimated IRR
  of Portfolio
• Duration of Portfolio Duration of Liabilities
  at estimated IRR rate
• Iterate until IRR of Portfolio equals estimated
  IRR

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Portfolio OptimizationContingent Immunization
Example

• Add a buffer of additional Market Value to the
  portfolio beyond the minimum required for an
  immunized portfolio.
• Use that buffer for additional flexibility to
  tilt the duration of the portfolio away from the
  duration of the liabilities so as to maximize
  return per market view of manager.
• Impose constraints to insure that in the event of
  adverse market moves there is sufficient
  remaining Market Value to immunize.

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Portfolio Optimization Assets vs Liabilities

• Optimize Assets
• Optimize Liabilities
• Optimize Assets and Liabilities Simultaneously
  (Dual Optimization)

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Portfolio Management Tools
Nominal Yield/Risk Measures
Effective Yield/Risk Measures
Return Attribution
Security Level Portfolio Level Portfolio vs
Liabilities
Scenario Analysis
Optimization
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Return Attribution

• Return Attribution dissects the return of fixed
  income securities, trades, portfolios, indices
  and other benchmarks such as liability
  portfolios.
• The goal is to explain returns by decomposing
  the total return of each security into components
  corresponding to the effect of various market
  changes such as yield curve movement, volatility
  changes, sector spread changes etc.

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The Yield BookReturn Attribution Model

• 3 Steps To Portfolio Management Process
• Select Duration and Yield Curve Exposure
• Select Sector Weights
• Select Specific Issues

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The Yield BookReturn Attribution Model

• Create a Matched Treasury Portfolio for each
  Security
• Run a series of Scenario Analysis type RORs for
  the MTP and for the security. Each scenario
  analysis run introduces one new market factor.
• Capture the return due to each factor by dividing
  its ROR by the prior ROR

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Return Attribution Example

• Bank Assets Vs. Bank Liabilities
• Month of March 2004
• Assume constant OAS on Commercial Loans and Bank
  Liabilities

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Total Return without Attribution Bank Assets vs
Bank Liabilities
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Individual Security Return Attribution Non-Callabl
e Bond
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Individual Security Return Attribution Mortgage
Backed Security
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Individual Security Return Attribution Mortgage
Backed Security further detail
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Return Attribution Portfolio Vs. Benchmark
(Liabilities)
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Portfolio Management Tools
Nominal Yield/Risk Measures
Effective Yield/Risk Measures
Return Attribution
Security Level Portfolio Level Portfolio vs
Liabilities
Scenario Analysis
Optimization
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Combining Scenario Analysis, Optimization and
Return Attribution

• Use Scenario Analysis and Portfolio Optimization
  to Rebalance Assets to better match the return
  profile of the liabilities.
• Use Return Attribution to analyze results.

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Scenario Returns - Assets vs Liabilities
Principal Component Scenarios
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Portfolio Optimization

• Constraints
• Trade Only Treasury, Agency, Mortgage Securities
• ROR of Assets must be greater than ROR of
  Liabilities across all Principal Component
  Scenarios
• Max 10mm per issue
• Objective - Minimize Transactions

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Return Attribution Major Components

• Yield Curve Effects
• Sector Weighting Effects
• Issue Selection Effect
• Sample Bank Investment Portfolio vs
• Treasury, Agency and Mortgage components of
  Citigroup BIGINDEX

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Sector Weighting Effect

• Measures the effect of sector under-weighting
  /over-weighting decisions
• For each sector calculated by
• (Weight of Sector in Portfolio) -
• (Weight of Sector in Index) multiplied
  by
• (Spread Advantage of Sector in Index) -
• (Spread Advantage of Entire Index)
• Example Treasury Sector
• .1976 - .3307x-.007 - (-.040)
  -.1331x.033
• 
  -.004

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Issue Selection Effect

• Measures the effect of security selection within
  each sector
• For each sector calculated by
• Weight of Sector in Portfolio multiplied by
  
• (Spread Advantage of Sector in Portfolio) -
• (Spread Advantage of Sector in Index)
• Example Agency Sector
• .3940 x -.224 (-.026) .3940 x (-.198)
  -.078