Morningstar Advisor - February/March 2010 - 24

Gray Matters Nailing Downside Risk By James X. Xiong A model called the Truncated Lévy Flight builds on Mandelbrot’s work to accurately capture the market’s fat tails. The financial crisis rekindled great interest in “fat-tailed” distributions. (See “Deju Vu All Over Again,” by Paul Kaplan, in the February/ March 2009 issue.) Investors discovered once again that the odds of experiencing significant losses are much greater than common models of asset returns suggest. Most models assume returns are “normally,” or Gaussian, distributed (Bachelier, 1900); when graphed, they look like a bell curve. The ends, or “tails,” of the bell curve are thin, meaning that outlier events— the market’s extreme gains and losses—should rarely occur. The historical record presents a different picture: a curve with tails that are fatter than standard models predict. For example, a normal distribution model assumes that an asset return that is three standard deviations below its mean (commonly called a threesigma event) has only a 0.13% probability of happening, or once every 1,000 return periods. From January 1926 to April 2009, however, the S&P 500 had a monthly mean return of 0.91% and a monthly standard deviation of 5.55%. A negative three-sigma event, therefore, means that the index would suffer a 15.74% monthly loss. In 83 years, the S&P 500 has suffered 10 monthly returns worse than that amount. The record implies that the probability of a three-sigma event is 1% rather than 0.13%, or eight times greater than an investor would expect from running a normal distribution model. A normal distribution fails to describe the fat tails of possible stock market returns. Enter Mandelbrot and Fama That these outlier events occur frequently isn’t exactly breaking news. Many academics have created statistical models to account for fat 24 Morningstar Advisor February/March 2010

Morningstar Advisor - February/March 2010

Table of Contents for the Digital Edition of Morningstar Advisor - February/March 2010

Morningstar Advisor - February/March 2010
Contents
New on MorningstarAdvisor.com
Letter from the Editor
Contributors
How has the Downturn Affected Your View of Global Investing?
Consistently Good
Taking Aim at Sacred Cows
Investment Briefs
Nailing Downside Risk
World Class
Map of International Moats
The Global View from Abroad
Crafting a Global Investing Strategy
Asset-Allocation Heavyweights Square Off
A World of Flexibility
Stay-at-Home Globetrotter
Four Picks for the Present
Making Money on Overseas Calls
Foreign Stocks: Think Selection, not 'Spice'
Your Foreign-and World-Stock Headquarters
Mutual Fund Analyst Picks
50 Most Popular ETFs
Undervalued Stocks with Wide Moats
VAs: Assets Rise as New Sales Slip
New at Morningstar
Skin in the Game
Morningstar Advisor - February/March 2010 - Morningstar Advisor - February/March 2010
Morningstar Advisor - February/March 2010 - Cover2
Morningstar Advisor - February/March 2010 - 1
Morningstar Advisor - February/March 2010 - 2
Morningstar Advisor - February/March 2010 - Contents
Morningstar Advisor - February/March 2010 - 4
Morningstar Advisor - February/March 2010 - 5
Morningstar Advisor - February/March 2010 - New on MorningstarAdvisor.com
Morningstar Advisor - February/March 2010 - 7
Morningstar Advisor - February/March 2010 - 8
Morningstar Advisor - February/March 2010 - Letter from the Editor
Morningstar Advisor - February/March 2010 - 10
Morningstar Advisor - February/March 2010 - Contributors
Morningstar Advisor - February/March 2010 - 12
Morningstar Advisor - February/March 2010 - 13
Morningstar Advisor - February/March 2010 - How has the Downturn Affected Your View of Global Investing?
Morningstar Advisor - February/March 2010 - 15
Morningstar Advisor - February/March 2010 - Consistently Good
Morningstar Advisor - February/March 2010 - 17
Morningstar Advisor - February/March 2010 - Taking Aim at Sacred Cows
Morningstar Advisor - February/March 2010 - 19
Morningstar Advisor - February/March 2010 - Investment Briefs
Morningstar Advisor - February/March 2010 - 21
Morningstar Advisor - February/March 2010 - 22
Morningstar Advisor - February/March 2010 - 23
Morningstar Advisor - February/March 2010 - Nailing Downside Risk
Morningstar Advisor - February/March 2010 - 25
Morningstar Advisor - February/March 2010 - 26
Morningstar Advisor - February/March 2010 - 27
Morningstar Advisor - February/March 2010 - 28
Morningstar Advisor - February/March 2010 - 29
Morningstar Advisor - February/March 2010 - 30
Morningstar Advisor - February/March 2010 - 31
Morningstar Advisor - February/March 2010 - World Class
Morningstar Advisor - February/March 2010 - 33
Morningstar Advisor - February/March 2010 - Map of International Moats
Morningstar Advisor - February/March 2010 - 34A
Morningstar Advisor - February/March 2010 - 34B
Morningstar Advisor - February/March 2010 - The Global View from Abroad
Morningstar Advisor - February/March 2010 - 36
Morningstar Advisor - February/March 2010 - 37
Morningstar Advisor - February/March 2010 - 38
Morningstar Advisor - February/March 2010 - 39
Morningstar Advisor - February/March 2010 - Crafting a Global Investing Strategy
Morningstar Advisor - February/March 2010 - 41
Morningstar Advisor - February/March 2010 - 42
Morningstar Advisor - February/March 2010 - Asset-Allocation Heavyweights Square Off
Morningstar Advisor - February/March 2010 - 44
Morningstar Advisor - February/March 2010 - 45
Morningstar Advisor - February/March 2010 - 46
Morningstar Advisor - February/March 2010 - 47
Morningstar Advisor - February/March 2010 - 48
Morningstar Advisor - February/March 2010 - 49
Morningstar Advisor - February/March 2010 - A World of Flexibility
Morningstar Advisor - February/March 2010 - 51
Morningstar Advisor - February/March 2010 - 52
Morningstar Advisor - February/March 2010 - 53
Morningstar Advisor - February/March 2010 - Stay-at-Home Globetrotter
Morningstar Advisor - February/March 2010 - 55
Morningstar Advisor - February/March 2010 - 56
Morningstar Advisor - February/March 2010 - 57
Morningstar Advisor - February/March 2010 - Four Picks for the Present
Morningstar Advisor - February/March 2010 - 59
Morningstar Advisor - February/March 2010 - 60
Morningstar Advisor - February/March 2010 - Making Money on Overseas Calls
Morningstar Advisor - February/March 2010 - 62
Morningstar Advisor - February/March 2010 - 63
Morningstar Advisor - February/March 2010 - Foreign Stocks: Think Selection, not 'Spice'
Morningstar Advisor - February/March 2010 - 65
Morningstar Advisor - February/March 2010 - Your Foreign-and World-Stock Headquarters
Morningstar Advisor - February/March 2010 - 67
Morningstar Advisor - February/March 2010 - Mutual Fund Analyst Picks
Morningstar Advisor - February/March 2010 - 69
Morningstar Advisor - February/March 2010 - 70
Morningstar Advisor - February/March 2010 - 71
Morningstar Advisor - February/March 2010 - 50 Most Popular ETFs
Morningstar Advisor - February/March 2010 - 73
Morningstar Advisor - February/March 2010 - Undervalued Stocks with Wide Moats
Morningstar Advisor - February/March 2010 - 75
Morningstar Advisor - February/March 2010 - VAs: Assets Rise as New Sales Slip
Morningstar Advisor - February/March 2010 - 77
Morningstar Advisor - February/March 2010 - 78
Morningstar Advisor - February/March 2010 - New at Morningstar
Morningstar Advisor - February/March 2010 - Skin in the Game
Morningstar Advisor - February/March 2010 - Cover3
Morningstar Advisor - February/March 2010 - Cover4
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