1. Global Portfolio Strategies Optimal Bank Loan Portfolio Hedging A Practitioners Perspective Randy Miller SAMSI Credit Risk Workshop October 31, 2005 Risk Expected Return Efficient Frontier Better Portfolios Current Portfolio

2. Global Portfolio Strategies 2 Desirable Performance through the Credit Cycle Time Earnings Path through Credit Cycle Active Lumpy Credit Portfolio Systematic Benchmark Evidence suggests underperformance in Region 2 is more important to PE Multiple than underperformance in Region 1 Region 1 Benchmark Underperformance Region 2 Benchmark Outperformance

3. Global Portfolio Strategies 3 An Interdependent Two Part Hedging Problem Hold to Maturity Loan Book and Mark-to-Market Credit Derivatives Book Objective Manage default and downgrade risk of credit risk concentrations Reduce earnings volatility through the credit cycle Improve portfolio efficiency Method Single name credit derivatives Size of Hedgeable Loan Book $100 billion notional 1500 names Key Questions How much? Priority? Objective Manage P&L volatility Method Single name credit derivatives Size of Long CDS Book $15 billion notional 300-500 names Key Questions Best Short CDS Hedge Portfolio Limited liquidity Limited price discovery Limited time series Hold to Maturity Loan Book Accrual Accounting Credit Derivatives Book Mark to Market Accounting CHALLENGES

4. Global Portfolio Strategies 4 $1,650 $1,700 $1,750 $1,800 $1,850 $1,900 $1,950 $2,000 $2,050 $700$900$1,100$1,300 An Optimal Benchmark to Guide HTM Portfolio Rebalancing Strategies Using Asset Allocation Approach to Address How Much? Priority? Current HTM Portfolio Minimum Risk Benchmark Dominated by Concentrated High Yield Portfolios Risk expressed as CVAR in USD mm Expected Total Credit Return In USD mm Minimum Risk Benchmark An efficient portfolio with respect to risk appetite and p&l aspirations A benchmark index to guide strategy and to track performance Minimum Risk Benchmark An efficient portfolio with respect to risk appetite and p&l aspirations A benchmark index to guide strategy and to track performance

5. Global Portfolio Strategies 5 A Scenario Based Optimization Model What Do We Optimize Against? Credit risk attributes (Merton Structural Model Framework) Default probabilities (Mark to Model valuation under the risk neutral measure) Loss Given Default Loan Equivalent Exposure Based on Usage Given Default Correlation structure based on KMV asset return factor model estimated over period 1988-2002 Expected credit migration based on bond migration data Expected benchmark portfolio performance meets business plan objectives Benchmark subject to selected prudential, and generally nonbinding, policy and business constraints Scenario based optimization model is implementation of Conditional Value at Risk (CVAR) approach discussed in Rockafellar, R.T. and Uryasev, S., Optimization of Conditional Value at Risk, mimeo, September 5, 1999; and in related papers Focus on CVAR as risk measure Addresses skewed credit return distribution Addresses risks of greatest concern to the bank CVAR Coherent Mathematically tractable and intuitive wrt decomposition and analysis of risk drivers

6. Global Portfolio Strategies 6 Two Stage Optimization Procedure Addressing the Optimal Portfolio Cherry-Picking Problem Stage 1 Segment by Industry and Debt Rating Simulate and Optimize Under Infinite Granularity Stage 2 Construct Replicating Portfolio Results Portfolio Performance Metrics Overweight/Underweight Names Risk and Return Contribution

7. Global Portfolio Strategies 7 Liquid and Nonliquid Risk Mitigation Opportunities March, 2005 ( millions $$ ) Total CommitmentExpected MTM P&LRisk (CVAR)Return/Risk RatioCountTotal Cmt $$Average Cmt $$ Benchmark123,4032841,1850.2405627,067483 Current Hold to Maturity (No CDS)114,2622841,3460.2116440,969640 Current HTM + Current CDS102,4792521,2020.2105833,800583 Current HTM + Liquid Bmk CDS97,1992581,0440.2475329,715561 Headline Risk (Cmt > $300mm) Risk Mitigation Performance Metrics Portfolio March, 2005 220 230 240 250 260 270 280 290 1,0251,0751,1251,1751,2251,2751,3251,3751,425 Risk - CVAR95 ($millions) MTM Return ($millions) Current HTM + Current CDS Current HTM + Liquid Bmk CDS Benchmark Current HTM Nonliquid Opportunity Current Risk Mitigation Impact Liquid CDS Opportunity

8. Global Portfolio Strategies 8 Hedging P&L Volatility in the Credit Derivatives Book Construct a Portfolio of Short CDS Positions Credit Derivatives Book Returns Long CDS – Short Credit Risk + - 65 th -80 th Percentile Manage Preserve Hedge Default Events Separately (How?) Deal with Cost of Carry Separately Minimize Shortfall Risk (What Percentile?) Minimize Tracking Error Position Size Limited by Willingness to Take on More Credit Exposure in a Name

9. Global Portfolio Strategies 9 Hedging Expected Performance Analysis Optimal short CDS portfolio constructed under tracking error minimization

10. Global Portfolio Strategies 10 Performance Trade-off Credit Derivatives versus Hold to Maturity Book