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Portfolio Management I

Portfolio Management I. William N. Goetzmann Yale School of Management,1997. Overview. Risk and return technology Optimization Past performance of asset classes Betas and factor models. Investment Problem. Choice of securities Asset class choice Timing decision Forecasting.

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Portfolio Management I

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  1. Portfolio Management I William N. Goetzmann Yale School of Management,1997

  2. Overview • Risk and return technology • Optimization • Past performance of asset classes • Betas and factor models

  3. Investment Problem • Choice of securities • Asset class choice • Timing decision • Forecasting

  4. Technology of Return and Risk • Harry Markowitz , 1959 • Reduced investment to two dimensions • Showed that portfolio mix matters most • Turned investing into statistics

  5. Mean and Standard Deviation • Mean measures expected return • Standard deviation measures investor risk • Example: six asset classes 1970 - 1996

  6. Correlation: the Third Statistic • Correlation and co-movement • One asset “hedges” the other • Two assets are better than one

  7. Gold and the Stock Market • Correlation of -.3 since 1970 • Hedged 70’s crash

  8. Gold in the Portfolio? • 25% risk reduction • 3/4 stocks, 1/4 gold • Is gold dominated?

  9. The Efficient Frontier • More assets move frontier • Frontier is a continuous set of efficient portfolios • Highest return for each level of risk

  10. The First Frontier • Markowitz took stocks from the NYSE • Mixed them with cash • Created the first frontier

  11. Applying Portfolio Theory • Select a Universe of Assets • Forecast Risk, Return and Correlation • Input to an Optimizer • Calculate Portfolio with Highest Mean For Each Level of Standard Deviation

  12. A Universe of Assets

  13. Historical Statistical Inputs • N Periods Geometric Arithmetic Standard • Mean (%) Mean (%) Deviation • BZW Extended Equity TR 22.00 16.39 17.36 15.24 • BZW Interm Cap TR 22.00 16.74 17.78 15.92 • BZW Micro Cap TR 22.00 19.22 21.34 22.47 • BZW Small Cap TR 22.00 18.93 20.31 18.28 • LB Corp TR 24.00 9.33 9.81 10.60 • LB Gvt TR 24.00 9.10 9.31 6.99 • LB Mortgage TR 21.00 9.96 10.39 10.32 • MSCI EAFE TR 27.00 12.89 15.00 22.52 • Wilshire Large Growth TR 19.00 16.18 17.25 16.39 • Wilshire Large Value TR 19.00 16.67 17.27 12.02 • S&P 500 Cap App 27.00 8.03 9.20 15.66 • S&P 500 TR 27.00 12.28 13.47 16.14

  14. Covariance Matrix

  15. Shifts in the Frontier • New assets shift frontier left • High correlations make frontier shallow • Different time periods change the inputs • Small changes have big effects • More assets than time periods create a false “riskless” portfolio • Constraining weights to be positive can flatten the frontier

  16. How Well Does it Work? • Short time periods give poor inputs • The risky end of the frontier is poorly estimated • The minimum variance portfolio is well estimated

  17. Optimizer Fixes • Extreme correlations are adjusted to the average, “shrinkage” • Extreme weights are decreased • Maximum holdings in any asset class specified. • Means are estimated by equilibrium models • Applications focus on broad asset classes

  18. Capital Market History 1926 - 1996

  19. Long-Term Performance

  20. Choosing the Optimal Portfolio • Specifying investor risk aversion • Specifying investor floor return

  21. Investor Choice With Floor • Choose a desired target “floor” of 4% return. • Select portfolio that minimizes chance of falling below that floor • Point given by tangent line

  22. Position 20 BZW Extended Equity TR 0.00 BZW Interm Cap TR 0.00 BZW Micro Cap T 0.00 BZW Small Cap TR 11.47 LB Corp TR 0.00 LB Gvt TR 10.13 LB Mortgage TR 18.18 MSCI EAFE TR 5.70 Wilshire Large Growth 0.00 Wilshire Large Value 54.51 S&P 500 TR 0.00 Exp Return 15.43 Std Dev 9.98 Yield 0.00 Threshold 3.92 Prob 87.57 Sharpe Risk 17.30 The Optimal Portfolio

  23. Quest for the Tangency Portfolio • All investor will choose a mix between T-bills and tangency portfolio • CAPM argues that tangency portfolio is the market portfolio

  24. CAPM and Expected Returns • Only market exposure matters • Higher  means higher expected return

  25. Betas and Factor Models • Assume price-setters are diversified • Ignore diversifiable risk • Expected return must compensate remaining risk • “Factors” are risk sources

  26. Risk Reduction by Adding Assets

  27. Systematic Risk • Non-diversifiable risk • Market Risk • Beta Risk

  28. Measuring Beta • Linear “Response” to Factor Returns • Example: MSCI is about a 50% “hedge” of the S&P 500. • Better Fit = Better Hedge

  29. Three Multi-Factor Models • APT = Macro-economic risk factors • BARRA = Security-specific risk factors • Fama-French = Size and B/M as risk

  30. Multi-Factor Model Applications • Tailor-made institutional portfolios • Risk-arbitrage • Analysis of sensitivity to macro-shocks • Cost-of-capital estimates

  31. Customizing a Portfolio • Assess sensitivity of client to: • inflation shocks • interest rate shifts • GDP shocks • Tilt portfolio away from stocks matching firm sensitivity

  32. Risk Arbitrage • Measure ’s on risk sources for securities • Estimate expected returns • Find under-valued (or overvalued) securities • Use ’s to create “market neutral” position • long in undervalued security • short in portfolio matching risk profile

  33. Sensitivity Analysis • Estimate  of investment portfolio • weighted average ’s of components • Estimate NAV change for 1% shocks in underlying risk factors

  34. Cost of Capital Estimates • Cost of capital is expected return • Linear factor model •  is the factor “loading” • Each factor has a risk premium • expected return sums up loadings times premia

  35. Liability Management • Optimization with liabilities and assets • Liabilities are forecast negative flows • Liabilities have risk, return and correlation • They will fit into the mean-variance framework

  36. Liabilities in Mean - Variance • Forecast future outflows • Estimate statistical characteristics • include as a negative return asset in model

  37. Optimizing With Liabilities • Result gives the frontier with liabilities as well as assets • Investor chooses portfolio with risk of not meeting liability obligations

  38. Conclusion • Modern Portfolio Theory • Statistical basis for choice • Optimizer reduces problem to 2 dimensions •  models based on portfolio investors • Applications • Asset/liability management • Custom portfolios • Active investing • Cost of capital

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