Top Down Investing Bottom-up Approach Top-Down Approach Choose under-valued securities Buying performance cheaply Top-Down Approach Build the ideal portfolio Structure portfolio to investor needs May have “expensive” & “cheap” stocks 5/3/2019

The Ideal Portfolio High return Low risk Inexpensive to manage 5/3/2019

Measures of Return Total return Geometric mean = growth After tax income and appreciation Geometric mean = growth [V(T) / V(o) ](1/T) - 1 5/3/2019

Measures of Risk Volatility Downside Risk Value-at-Risk 2 = variance: average squared deviation from historical mean Downside Risk semi-variance: average squared negative deviation from historical mean Value-at-Risk Minimum expected loss for a given horizon and probability level 5/3/2019

Measures of Expense Transactions Information acquisition Monitoring costs Probability of losing client 5/3/2019

Technology of Return and Risk Harry Markowitz , 1959 Reduced investment to two dimensions Showed that portfolio mix matters most Turned investing into statistics 5/3/2019

Mean and Standard Deviation Mean measures expected return Standard deviation measures investor risk Example: six asset classes 1970 - 1996 5/3/2019

Correlation: the Third Statistic Correlation and co-movement One asset “hedges” the other Two assets are better than one 5/3/2019

Gold and the Stock Market Correlation of -.3 since 1970 Hedged 70’s crash 5/3/2019

Gold in the Portfolio? 25% risk reduction 3/4 stocks, 1/4 gold Is gold dominated? 5/3/2019

The Efficient Frontier More assets move frontier Frontier is a continuous set of efficient portfolios Highest return for each level of risk 5/3/2019

The First Frontier Markowitz took stocks from the NYSE Mixed them with cash Created the first frontier 5/3/2019

Risk Reduction by Adding Assets 5/3/2019

International Equity Groups 5/3/2019

Risk and Return Inputs N Periods Geometric Arithmetic Standard Mean (%) Mean (%) Deviation (%) MSCI Automobiles Cap App 324.00 8.16 9.97 20.07 MSCI Banking Cap App 324.00 10.74 12.56 20.64 MSCI Chemicals Cap App 324.00 7.94 9.34 17.53 MSCI Energy Sources Cap App 324.00 9.18 10.84 19.33 MSCI Gold Mines Cap App 324.00 7.67 15.91 46.01 MSCI Telecomm Cap App 324.00 6.68 7.62 14.25 MSCI Textiles & Apparel Cap App 324.00 6.20 8.16 20.88 MSCI Transport - Airlines Cap App 324.00 7.40 10.25 25.51 MSCI Utilities - Elec&Gas Cap Ap. 324.00 5.97 7.03 15.29 5/3/2019

Capital Appreciation Indices 5/3/2019

Results 5/3/2019

Minimum Variance Portfolio 5/3/2019

Value at Risk How much do I expect to lose 1 in 20 times? E.G. VAR for a $100 million portfolio with a std. of 12% at the 1/20 confidence level is: VAR = $100m * 1.64 * 12% - 8% = 12% 5/3/2019

Value at Risk Minimum expected annual loss at a 95% confidence level for the lowest risk portfolio = -12% 5/3/2019

New Risk Technology VAR with simulations VAR with non-normal returns VAR with derivatives VAR with chaotic systems 5/3/2019

Systematic Risk Non-diversifiable risk Market risk Beta risk 5/3/2019

Portfolio Investors Diversify away most risk Demand return only for residual Have advantage over non-diversified investors Can bid more for risky assets Have less volatile portfolios 5/3/2019

Portfolio Investors’ Expected Returns Only market exposure matters Higher  means higher expected return 5/3/2019

Factor Models Assume price-setters are diversified Ignore diversifiable risk Expected return must compensate remaining risk “Factors” are risk sources 5/3/2019

Developing a Top-Down Portfolio Assess sensitivity of client to: inflation shocks interest rate shifts GDP shocks Tilt portfolio away from stocks matching firm sensitivity Capture factor exposure with minimum transactions costs 5/3/2019

Example Client is the pension fund of an international oil company defined benefits ability to contribute depends upon oil prices Exposure to oil shocks APT allows them to “hedge” oil shocks Analysis lets them tilt towards risks they care less about 5/3/2019

Measuring Beta Linear “Response” to Factor Returns Example: MSCI is about a 50% “hedge” of the S&P 500. Better Fit = Better Hedge 5/3/2019

Multi-Factor Models APT = Macro-economic risk factors BARRA = Security-specific risk factors Fama-French = Size and book to market ratio as risk 5/3/2019

Arbitrage Pricing Theory Chen, Roll and Ross factors are: Production risk Inflation shocks term structure shifts investor confidence Explanatory factors Fundamental economic forces drive stocks 5/3/2019

BARRA factor models Stock characteristics: No common factors Earnings Leverage Growth Sales No common factors model works to explain returns 5/3/2019

Fama and French Factors Size Small stocks have a premium Book to market A “distress” premium? These beat S&P beta 5/3/2019

Fma & French (1992) Results 5/3/2019

New Directions in Asset Pricing Statistical methods for identifying factors Style analysis Economic modeling of risk International Factors Diversity of markets Diversity of environments Diversity of historical experiences 5/3/2019