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

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

3. Yale School of Management Investment Problem Choice of securities Asset class choice Timing decision Forecasting

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

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

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

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

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

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

10. Yale School of Management The First Frontier Markowitz took stocks from the NYSE Mixed them with cash Created the first frontier

11. Yale School of Management 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. Yale School of Management A Universe of Assets

13. Yale School of Management 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. Yale School of Management Covariance Matrix

15. Yale School of Management

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. Yale School of Management 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. Yale School of Management 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. Yale School of Management Capital Market History 1926 - 1996

20. Yale School of Management Long-Term Performance

21. Yale School of Management Choosing the Optimal Portfolio Specifying investor risk aversion Specifying investor floor return

22. Yale School of Management 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. Yale School of Management The Optimal Portfolio 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

24. Yale School of Management 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. Yale School of Management CAPM and Expected Returns Only market exposure matters Higher  means higher expected return

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

27. Yale School of Management Risk Reduction by Adding Assets

28. Yale School of Management Systematic Risk Non-diversifiable risk Market Risk Beta Risk

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

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

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

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

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

35. Yale School of Management 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. Yale School of Management 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. Yale School of Management Liabilities in Mean - Variance Forecast future outflows Estimate statistical characteristics include as a negative return asset in model

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

39. Yale School of Management 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