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Portfolio%20 Construction%20and%20 Risk%20 Management%207 23 2010[1]

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  • 1. Portfolio Construction and Risk Management gConsider the portfolio selection model: whereQuantifying the inputs to the optimization is good discipline. 1
  • 2. Portfolio Construction and Risk Management g Risk Management Start with quantification of what you know (risk) S f f ( ) Prepare for what is not knowable (uncertainty) Challenge simplifying assumptions C f 1) Only care about the mean and variance of the probability di t ib ti of portfolio returns b bilit distribution f tf li t a) Ignore skewness (asymmetry) and kurtosis (fat tails) b) Event risk c) Market failure d) Government Intervention e) Investment horizon – liquidity demand versus provision 2
  • 3. Portfolio Construction and Risk Management g 2) Parameter Stationarity (or one period model) a) Regime Change b) Time variation characteristics (bonds) c) Cuspiness (securitized asset tranches) d) Dynamic interaction (liquidity->fundamentals- >liquidity => downward spiral e) Time-varying covariance structure (i.e., correlations Time varying increase during crisis periods) 3
  • 4. Portfolio Construction and Risk Management g Risk Management Approaches 1) Multi-Dimentional Risk Analysis (calculate sensitivity exposures to state variables) 2) Stress tests on each exposure 3) Value-in-Stress (multiple scenario analysis) 4) Value at Risk (VaR) is probabalistic a) ) Requires covariance matrix estimation q b) i.e., 95% VaR is L= –V x 1.645 x portfolio standard deviation . There is a 5% chance of loosing more than L. c) Distributional assumption for tail risk d) Parameter estimation i. Historical data (with or without forward looking adjustments) ii. Forward simulation e) Model the tail of the distribution 4
  • 5. Portfolio Construction and Risk Management g Dealing with the unknowable 1) Stop Loss (then what?) 2) Flight to quality hedges 3) Long/short strategies (no net market or macro-factor macro factor exposures) 4) L k Lock-ups 5) Portfolio Insurance 5
  • 6. Portfolio Construction and Risk Management g General Valuation Equation x1 x2 xN V0 = + + ...+ (1+ R1 ) (1+ R1 )(1+ R2 ) (1+ R1 )...(1+ RN ) For bonds, the cash flows in the numerator are expected coupons and principal payment(s) in each period. For common stock, N is infinity and the numerator contains stock expected cash flows to equity holders. The R s are the per period expected required rates of return to compensate investors for the riskiness of their respective cash flows. Risk Premi m is a function of priced risk factors and the sec rit ’s Premium f nction security’s sensitivity to those exposures. 6
  • 7. Portfolio Construction and Risk Management g 7
  • 8. Portfolio Construction and Risk Management g 8
  • 9. Pension Plan Asset-Liability Management2006 Pension Protection Act Requires underfunded plans to move toward a 100% funding level d f d d l d f d l l Provisions come into effect on a rolling schedule over several years 9
  • 10. Pension Plan Asset-Liability Management Provisions combined with market performance trends are affecting asset  allocations now 10
  • 11. Pension Plan Asset-Liability Management Major Factors Affecting Pension Plan Funding Status  Performance of assets Performance of assets Company contributions  Number of employees covered and cost per employee Discount  rates used to calculate the present value of  Discount rates used to calculate the present value of future obligations AA rated Long‐dated corporate bonds AA rated Long dated corporate bonds Average of AAA, AA, and A rated corporate bonds Note that the discount factors have fallen sharply during 2009 =>  Note that the discount factors have fallen sharply during 2009 => increase in PV of future obligations 11
  • 12. Pension Plan Asset-Liability Management Asset Allocation:  Select a portfolio that minimizes the standard deviation of the plan’s surplus 12
  • 13. Pension Plan Asset-Liability ManagementLiabilities rate of return series:Rate of change in the present value of future liabilities for the change in discount rates (AAA‐A corporate bond rates  g ( pprescribed by the 2006 pension protection act). The term structure of liabilities in this example is that of the The term structure of liabilities in this example is that of theaverage  pension plan.The riskiness of the plan’s liabilities in the time‐series of Th i ki f h l ’ li bili i i h i i freturns is defined by the time period selected. 13
  • 14. Pension Plan Asset-Liability Management Asset Allocation:  Select a portfolio that minimizes the standard deviation of the plan’s surplus 14