Morningstar Advisor - April/May 2010 - 25

Exhibit 2 Smooth Approach As the area to the left of the red vertical line shows, the smooth scenario-based approach does a better job of estimating the probability of tail events than the mean-variance model.
Scenario-Based Distribution Lognormal Distribution

can be handled in a scenario-based model. For example, in scenarios that represent normal times, returns on different equity markets could be modeled as moving somewhat apart from each other while scenarios that represent global crises could model the markets as moving downward together.
Ultrasonic Statistical Technology

Finally, we make use of new technology. Because it could take thousands of scenarios to adequately model return distributions, a disadvantage of the scenario-based approach has been that it requires large amounts of data to be stored and processed. Even with the advances in computer hardware, the conventional approach of representing scenarios with large tables of explicit numbers remained problematic. That is, until recently. The phenomenal speed of computers has given rise to the field of probability management, an extension of data management to probability distributions rather than numbers. The key component of probability management is DIST—Savage’s Distribution String, which can encapsulate thousands of trials as a single data element. The use of Distribution Strings greatly saves on storage and speeds processing time—a Monte Carlo simulation consisting of thousands of trials can be performed on a personal computer in an instant. While not all asset-management organizations are prepared to create the Distribution Strings needed to drive the geometric-mean-CVaR optimization, some outside vendors, such as Morningstar’s Ibbotson Associates, can fulfill this role. Another facet of probability management is interactive simulation technology, which can run thousands of scenarios through a model before the sound of your finger leaving the Enter key reaches your ear. These supersonic models allow much deeper intuition into the sensitivities of portfolios and encourage users to interactively explore different portfolios, distributional assumptions, and potential “black swans.”

–90 –80 –70 –60 –50 –40 –30 –20 –10

0% 10

20

30

40

50

60

70

80

90

Annual returns of large-company stocks 1926–2008.

the 5th percentile of the return distribution. For example, as we mentioned, the 5th percentile of the distribution shown in Exhibit 2 is negative 25.8%, so its 5% VaR is 25.8%. This means there is a 5% chance of losing $2,850 or more on a $10,000 investment. CVaR, however, accounts for possible losses beyond VaR; it is the expected or average loss of capital should VaR be breached. Therefore, CVaR is always greater than VaR. The 5% CVaR for the distribution shown in Exhibit 2 is 35.8%, or $3,580, on a $10,000 investment.
Scenarios Versus Correlation

are related. In fact, the R-squared statistic of a simple linear regression model for two series of returns is equal to the square of the correlation coefficient. For many pairs of asset classes, however, a linear model misses the most important features of the relationship. For example, during normal times, non-U.S. equities are considered to be good diversifiers for U.S. equity investors. But during global crises, all major equity markets move down together. Furthermore, suppose that the returns on two asset-class indexes were highly correlated, but instead of including direct exposures to both in the model, one was replaced with an option on itself. Rather than having a linear relationship, we now have a nonlinear relationship that cannot be captured by a correlation coefficient. Fortunately, these sorts of nonlinear relationships between returns on different investments

Next, we model the distribution of returns differently. In mean-variance analysis, the covariation of the returns of each pair of asset classes is represented by a single number, the correlation coefficient. This is mathematically equivalent to assuming that a simple linear regression model is an adequate description of how the returns on the two asset classes

MorningstarAdvisor.com 25


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Morningstar Advisor - April/May 2010

Table of Contents for the Digital Edition of Morningstar Advisor - April/May 2010

Morningstar Advisor - April/May 2010
Contents
New On MorningstarAdvisor.com
Contributors
Letter from the Editor
Our Job: Building Better Investors
What’s Your Biggest Long-term Concern for the Economy?
An Early Start
Women’s Work
Investment Briefs
Markowitz 2.0
Asset Allocation Is King
A Decade of Riskier Assets ...
... but with plenty of Silver Linings
Be Prepared
Facing up to the Economy’s Problems
Levelheaded
Surviving on Conviction
Four Picks for the Present
Pharmaceutical Firms Get the Urge to Merge
Funds That Look Cheaper Than the Market
Finding Dividend Leaders
Mutual Fund Analyst Picks
50 Most Popular ETFs
Undervalued Stocks with Wide Moats
VAs: Assets Rise as New Sales Slip
New at Morningstar
When You Wish Upon a Star
Morningstar Advisor - April/May 2010 - Morningstar Advisor - April/May 2010
Morningstar Advisor - April/May 2010 - Cover2
Morningstar Advisor - April/May 2010 - 1
Morningstar Advisor - April/May 2010 - 2
Morningstar Advisor - April/May 2010 - Contents
Morningstar Advisor - April/May 2010 - 4
Morningstar Advisor - April/May 2010 - 5
Morningstar Advisor - April/May 2010 - New On MorningstarAdvisor.com
Morningstar Advisor - April/May 2010 - 7
Morningstar Advisor - April/May 2010 - Contributors
Morningstar Advisor - April/May 2010 - Letter from the Editor
Morningstar Advisor - April/May 2010 - 10
Morningstar Advisor - April/May 2010 - Our Job: Building Better Investors
Morningstar Advisor - April/May 2010 - 12
Morningstar Advisor - April/May 2010 - 13
Morningstar Advisor - April/May 2010 - What’s Your Biggest Long-term Concern for the Economy?
Morningstar Advisor - April/May 2010 - 15
Morningstar Advisor - April/May 2010 - An Early Start
Morningstar Advisor - April/May 2010 - 17
Morningstar Advisor - April/May 2010 - Women’s Work
Morningstar Advisor - April/May 2010 - 19
Morningstar Advisor - April/May 2010 - Investment Briefs
Morningstar Advisor - April/May 2010 - 21
Morningstar Advisor - April/May 2010 - Markowitz 2.0
Morningstar Advisor - April/May 2010 - 23
Morningstar Advisor - April/May 2010 - 24
Morningstar Advisor - April/May 2010 - 25
Morningstar Advisor - April/May 2010 - 26
Morningstar Advisor - April/May 2010 - 27
Morningstar Advisor - April/May 2010 - Asset Allocation Is King
Morningstar Advisor - April/May 2010 - 29
Morningstar Advisor - April/May 2010 - 30
Morningstar Advisor - April/May 2010 - 31
Morningstar Advisor - April/May 2010 - 32
Morningstar Advisor - April/May 2010 - 33
Morningstar Advisor - April/May 2010 - A Decade of Riskier Assets ...
Morningstar Advisor - April/May 2010 - ... but with plenty of Silver Linings
Morningstar Advisor - April/May 2010 - 36
Morningstar Advisor - April/May 2010 - Be Prepared
Morningstar Advisor - April/May 2010 - 38
Morningstar Advisor - April/May 2010 - 39
Morningstar Advisor - April/May 2010 - 40
Morningstar Advisor - April/May 2010 - 41
Morningstar Advisor - April/May 2010 - 42
Morningstar Advisor - April/May 2010 - 43
Morningstar Advisor - April/May 2010 - Facing up to the Economy’s Problems
Morningstar Advisor - April/May 2010 - 45
Morningstar Advisor - April/May 2010 - 46
Morningstar Advisor - April/May 2010 - 47
Morningstar Advisor - April/May 2010 - 48
Morningstar Advisor - April/May 2010 - 49
Morningstar Advisor - April/May 2010 - Levelheaded
Morningstar Advisor - April/May 2010 - 51
Morningstar Advisor - April/May 2010 - 52
Morningstar Advisor - April/May 2010 - 53
Morningstar Advisor - April/May 2010 - Surviving on Conviction
Morningstar Advisor - April/May 2010 - 55
Morningstar Advisor - April/May 2010 - 56
Morningstar Advisor - April/May 2010 - 57
Morningstar Advisor - April/May 2010 - Four Picks for the Present
Morningstar Advisor - April/May 2010 - 59
Morningstar Advisor - April/May 2010 - 60
Morningstar Advisor - April/May 2010 - Pharmaceutical Firms Get the Urge to Merge
Morningstar Advisor - April/May 2010 - 62
Morningstar Advisor - April/May 2010 - 63
Morningstar Advisor - April/May 2010 - Funds That Look Cheaper Than the Market
Morningstar Advisor - April/May 2010 - 65
Morningstar Advisor - April/May 2010 - Finding Dividend Leaders
Morningstar Advisor - April/May 2010 - 67
Morningstar Advisor - April/May 2010 - Mutual Fund Analyst Picks
Morningstar Advisor - April/May 2010 - 69
Morningstar Advisor - April/May 2010 - 70
Morningstar Advisor - April/May 2010 - 71
Morningstar Advisor - April/May 2010 - 50 Most Popular ETFs
Morningstar Advisor - April/May 2010 - 73
Morningstar Advisor - April/May 2010 - Undervalued Stocks with Wide Moats
Morningstar Advisor - April/May 2010 - 75
Morningstar Advisor - April/May 2010 - VAs: Assets Rise as New Sales Slip
Morningstar Advisor - April/May 2010 - 77
Morningstar Advisor - April/May 2010 - 78
Morningstar Advisor - April/May 2010 - New at Morningstar
Morningstar Advisor - April/May 2010 - When You Wish Upon a Star
Morningstar Advisor - April/May 2010 - Cover3
Morningstar Advisor - April/May 2010 - Cover4
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