Paul D. Kaplan, Ph.D., CFA Quantitative Research Director, Morningstar Europe, Ltd.

Transcription

1 Building Portfolios in a Non-NormalNormal World Paul D. Kaplan, Ph.D., CFA Quantitative Research Director, Morningstar Europe, Ltd Morningstar, Inc. All rights reserved. <#>

2 We seem to have a once-in-a-lifetime crisis every three or four years. Leslie Rahl, Founder of Capital Market Risk Advisors Source: Christopher Wright, Tail Tales, CFA Institute Magazine, March/April 2007

3 The Black Turkey An event that is entirely consistent t with past data but that no one thought would happen Larry Siegel

4 A Flock of Turkeys Asset Class Time Period Peak to Trough Decline U.S. stocks (real total return) % U.S. stocks (DJIA, daily) % Long U.S. Treasury bond (real total return) % U.S. stocks % U.K. stocks (real total return) % Gold % Oil % Japan stocks % U.S. stocks (S&P) % U.S. stocks (NASDAQ) % U.S. stocks (S&P) % Nominal price return unless otherwise specified.

5 U.S. Stock Market History, 1871 April ,000 Crash of Dot Com Bubble Burst 1,000 Crash of 1987 Real Cumulativ ve Value 100 Postwar Bear Market Inflationary Bear Market of Great Depression 10 Panic of 1907 Auto Bubble Burst Year Source: 2011 Ibbotson Stocks, Bonds, Bills, and Inflation (SBBI) Classic Yearbook, Morningstar, Inc. Morningstar EnCorr. Goetzmann, William N., Roger G. Ibbotson, and Liang Peng, A New Historical Database for the NYSE 1815 to 1925: Performance and Predictability, Journal of Financial Markets, December Pierce, Phyllis S., ed., The Dow Jones Averages, , Homewood, IL: Dow Jones Irwin,

6 Cracks in the Bell Curve: U.S. Real Monthly Returns, January 1886 April 2011 Historical Frequency (Months) Lognormal Historical -30% -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% Monthly Return Source: 2011 Ibbotson Stocks, Bonds, Bills, and Inflation (SBBI) Classic Yearbook, Morningstar, Inc. Morningstar EnCorr. Goetzmann, William N., Roger G. Ibbotson, and Liang Peng, A New Historical Database for the NYSE 1815 to 1925: Performance and Predictability, Journal of Financial Markets, December Pierce, Phyllis S., ed., The Dow Jones Averages, , Homewood, IL: Dow Jones Irwin,

7 Covariation of Returns: Linear or Nonlinear? S&P 500 vs. EAFE, Monthly Total Returns: Jan Sep. 2010

8 Limitations of Mean-Variance Analysis Fat tails in returns not modeled Covariation of returns assumed linear, cannot handle optionality Single period investment horizon (arithmetic mean) Risk measured by volatility

9 Building A Better Optimizer Issue Markowitz 1.0 Markowitz 2.0 Return Distributions Return Covariation Investment Horizon Mean-Variance Framework (No fat tails) Correlation Matrix Linear Single Period Arithmetic Mean Scenarios+Smoothing (Fat tails possible) Scenarios+Smoothing Nonlinear (e.g. options) Can use Multiperiod Kelly Criterion Can use Geometric Mean Risk Measure Standard Deviation Can use Conditional Value at Risk and other risk measures

10 Markowitz 1.0 Inputs: Summary Statistics Correlation Asset Class Expected Return Standard Deviation A 5.00% 10.00% 00% B 10.00% 20.00% C 15.00% 30.00% D 13.00% 30.00%

11 Markowitz 2.0 Inputs: Scenarios % 40% 20% 0% 20% 40% 60% 80% 100% % 2 200% % 100% 1 50% % 50% 0% 50% 100% 150% 200% 250% 0% 60% 40% 20% 0% 20% 40% 60% 80% 50% 100% % 350% % 300% % 100% 0% 100% 200% 300% 400% 500% 250% 200% 150% 100% 50% 0% 60% 40% 20% 0% 50% 20% 40% 60% 80% 100% 250% 200% 150% 100% 50% 0% 100% 50% 0% 50% 50% 100% 150% 200% 250% 100% % 350% 350% % 300% 300% % 250% 250% 1 200% 200% 200% % 150% 150% % 100% 100% % 50% 50% % 100% 0% 100% 200% 300% 400% 500% 0% 60% 40% 20% 0% 50% 20% 40% 60% 80% 100% 0% 100% 50% 0% 50% 50% 100% 150% 200% 250% 100% 0% 100% 50% 0% 50% 50% 100% 150% 200% 250% 300% 350% 100%

12 Markowitz 1.0 Reward = 1-Period Return, Risk = Volatility 14% 12% Non-US Stocks 10% Expected Arithmetic Mean 8% 6% Mix 1 Mix 2 Non-US Bonds US Stocks 4% 2% US Bonds 0% 0% 5% 10% 15% 20% 25% 30% Standard Deviation

13 Value-at-Risk (VaR) VaR identifies the return at a specific point (e.g. 1 st or 5 th percentile) Worst 1 st Percentile 99% of all returns are better 1% of all returns are worse Worst 5 th Percentile 95% of all returns are better 5% of all returns are worse

14 Conditional Value-at-Risk (CVaR) CVaR identifies the probability weighted return of the entire tail Worst 5 th Percentile 95% of all returns are better 5% of all returns are worse

15 CVaR vs. VaR Notice that different return distributions can have the same VaRs, but different CVaRs Worst 5 th Percentile 95% of all returns are better 5% of all returns are worse

16 Markowitz 2.0: More Relevant Risk & Reward Measures Reward = Long-Term Return, Risk = How Bad is Bad 12% 10% Non-US Stocks ted Geometric Mea an Expect 8% 6% 4% Mix 1 Mix 2 Non-US Bonds US Stocks 2% US Bonds 0% 0% 5% 10% 15% 20% 25% 30% 35% Conditional Value at Risk

17 Mixes 1 & 2 Non-US Bonds US Stocks 34% 33% 37% 46% Mix 1 12% 3% 14% 21% Non-US Stocks US Bonds Mix 2

18 Modeling Fat Tails: Mix Lognormal Fat-Tailed % -40% -30% -20% -10% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 110% 120% Return

19 12% Markowitz 2.0: Fat Tails Modeled 10% Non-US Stocks Lognormal Exp pected Geometric Mean 8% 6% 4% Mixes Fat Tailed US Stocks Non-US Bonds 2% US Bonds 0% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% Conditional Value at Risk

20 Read More About These and Other Ideas in December The breadth and depth of the articles in this book suggest that Paul Kaplan has been thinking about markets for about as long as markets have existed. From the foreword

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