Portfolio Management I

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

16. 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

17. 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

18. 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

19. Capital Market History 1926 - 1996

20. Long-Term Performance

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

22. 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

23. 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

24. 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

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

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

27. Risk Reduction by Adding Assets

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

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

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

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

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

33. 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

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

35. 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

36. 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

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

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

39. 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