Morningstar Advisor - August/September 2009 - 78

©2009 Morningstar. All rights reserved. The Morningstar name and logo are registered trademarks of Morningstar, Inc. The magazine of investing insights for independent-minded advisors Summer 2008 Spotlight Undiscovered Managers Summer 2008 Exhibit 2: Cracks in the Bell Standard risk models assume S&P 500 returns follow a bell-shaped distribution, even though the index has experienced more than 10 declines of at least –13%. Exhibit 3: It’s a Fat-Tailed World, After All A log-stable distribution does a good job of modeling the empirical returns of the S&P 500, especially at the center and the tails. Features 180 160 140 120 100 180 160 140 120 100 –29% 80 60 40 20 –29% –21% –13% –5% 3% 11% 19% –25% –21% –17% –13% 80 60 40 20 –29% –25% –21% –17% –13% 13 27% 35% 43% –29% –21% –13% –5% 3% 11% 19% 27% 35% 43% Histogram shows the frequency of monthly returns for the S&P 500 from January 1926 to November 2008. Histogram shows the frequency of monthly returns for the S&P 500 from January 1926 to November 2008. Spotlight: College Savings 32 Work Your Way Through College Planning The number of hurdles grows to reach such a simple goal: ﬁnancing a college education. 36 Sizing Up the Options We inspect the more popular college-savings vehicles and tally their pluses and minuses. 38 Best and Worst 529 CollegeSavings Plans Across the nation, many states clean up their messes, while others continue to offer bad plans. 42 A 529 Travel Guide Where to go to ﬁnd the best plans, and the states where you’ll ﬁnd the worst. 45 10 Tax-Smart Tips for College-Savings Planning Section 529 savings accounts need to be handled with care; otherwise, their tax beneﬁts could turn into tax nightmares. Morningstar Conversation 50 Global Dialogue With proﬁts falling and uncertainty spreading, T. Rowe Price manager Rob Gensler discusses his approach to investing in the world’s diverse markets. Undiscovered Managers 58 How Sequoia Cranks Out Good Returns Year after Year If you’re harboring doubts about Sequoia Fund’s reopening, cast them aside. It’s still a good mutual fund. 61 The Many Layers of David Winters A successful entrepreneur and world-class investor, Winters achieved both by taking an eclectic approach. With these standard models, the primary measure of risk is standard deviation. If returns follow a normal distribution, the chance that a return would be more than three standard deviations below average would be a trivial 0.135%. Since January 1926, we have 996 months of stock market data; 0.135% of 996 is 1.34—that is, there should be only one or two occurrences of such event. But the record of the stock market tells a different story. The monthly returns of the S&P 500 have been more than three standard deviations below average 10 times since 1926. In other words, the standard models assign meaninglessly small probabilities to extreme events that occur ﬁve to 10 times more than the models predict. We can illustrate the problem further by overlaying a lognormal model of returns over a histogram of monthly total returns on the S&P 500 (Exhibit 2). The model says that declines of more than negative 13% have almost no chance of happening—yet they have occurred at least 10 times since 1926. An Alternative Approach: Log-Stable Distributions Mandelbrot’s model to stock prices and obtained promising results. Until recently, however, the work of Mandelbrot and Fama had been largely ignored. In his dissertation, Fama assumed that the logarithm of stock returns followed a fat-tailed distribution called a “stable Paretian distribution,” or stable distribution. Hence, we refer to the resulting distribution of returns as a “log-stable distribution.” We can illustrate an example of Fama’s work by using the same S&P 500 histogram in our earlier exhibit but with a log-stable distribution curve overlaying it instead of a lognormal curve. The log-stable model (Exhibit 3) ﬁts the empirical distribution much closer than the lognormal both at the center and the tails. In particular, note the close match between the density curve and the histogram between negative 13% and negative 29%. The tails of a stable distribution are so fat that its variance is inﬁnite. In other words, the concepts of standard deviation and variance are not deﬁned for stable distributions. You might ﬁnd the idea of an inﬁnite variance counterintuitive, because it is possible to calculate a standard deviation for any ﬁnite set of data. However, the underlying mathematical distributions that we use to model asset returns assign probabilities over the range from negative inﬁnity to positive inﬁnity. Some distributions that cover this inﬁnite range assign so little probability out in the tails that variance can be deﬁned. These are “thin-tailed” distributions, the normal or bell-shaped distribution being the best-known example. Other distributions assign so much probability to the tails that variance is inﬁnite. Such is the case with stable distributions. The manner in which a stable distribution assigns probability to its tails is very close to what is known as “power law.” When a distribution of a loss follows a power law, a plot of logarithm of the magnitude of loss (x) versus the logarithm of the probability of the loss turning out to be x or worse is a downward-sloping straight line. Therefore, while the probability of loss decreases with the magnitude of loss, it does so gradually. In Exhibit 4, we plot the magnitude of loss versus the logarithm of the probability of Exhibit 4 Power Law Tails: Unlike a normal distribution, a stable distribution approaches the straight line of a power law, indicating that it has “fat tails.” In (Prob[X<x]) 2 Investors Should Mind Their Tails By Lawrence Jones The market experiences more shocks than investors think. PIMCO’s Vineer Bhansali thinks he has a way to guard against these events. Power Law Stable In the early 1960s, Benoit Mandelbrot, a mathematician teaching economics at the University of Chicago, was advising a doctoral student named Eugene Fama. Mandelbrot had developed a statistical model for percentage changes in the price of cotton that had “fat tails.” That is, the model assigned nontrivial probabilities to large percentage changes. In his doctoral dissertation, Fama applied –2 –6 Normal –4.5 –4.0 –3.5 –3.0 –2.5 –2.0 –1.5 –1.0 In (|x|) Like many great ideas, this one came together unexpectedly at a meeting between old colleagues. The story of the development of PIMCO’s tail-risk hedging strategy began as a casual chat between two highly respected scholars of ﬁnance: Vineer Bhansali and Mohamed El-Erian. Bhansali, head of PIMCO’s 14-person analytics team, was in Boston delivering a conference paper. El-Erian, who had worked at PIMCO, was president and CEO of Harvard Management Co., the ﬁrm charged with managing Harvard University’s endowment. Bhansali met up with his former colleague to discuss a novel hedging approach he was developing at PIMCO. As it turned out, El-Erian was doing something similar at Harvard. The approach, called “tail-risk hedging,” aims to protect portfolios that deploy the strategy from rare and systemic shocks. Popularly referred to as “black swans,” these events can greatly damage investor results. They are the dramatic losses that appear on the far left end—the “tail”—of the probability distribution curve of investment returns. Their chances of happening are supposed to be minute, but some in ﬁnance and economics believe that the shocks occur more frequently than commonly thought, and people are developing ways to hedge against the risks posed by these shocks. Bhansali ﬁrst implemented tail-risk hedging several years ago in a hedge-fund-like strategy he was running at PIMCO for an insurance company. The client became more interested in how Bhansali was hedging away the portfolio’s tail risk than in the overall hedge fund. The The College Savings Landscape: Choices are plentiful, as are the challenges. 5 For an account of the work of Mandelbrot and Fama during this period, see Benoit Mandelbrot and Richard L. Hudson, The (Mis)Behavior of Markets, New York: Basic Books, 2004. 6 The idea of using fat-tailed distributions to model asset returns is starting to gain some traction. FinAnalytica was founded to provide investment analysis and portfolio construction software based on Mandelbrot and Fama’s work. Morningstar added distribution charts and forecasting models based on it to Morningstar EnCorr. 7 Strictly speaking, the assumption is that the logarithm of one plus the return in decimal form follows a stable Paretian distribution. 8 This chart can be produced in Morningstar EnCorr Analyzer using the log-stable feature. 9 That is the probability distribution of one plus the return on an asset return in decimal form. The lowest possible return on an unleveled position in an asset is negative 100%, which is negative 1 in decimal form. Adding one we get 0. The logarithm of 0 is –∞. 30 Morningstar Advisor February/March 2009 MorningstarAdvisor.com 31 54 Morningstar Advisor April/May 2009 Morningstar Conversation Spotlight Undiscovered Managers Morningstar Conversation Be Careful What You Fish For In the wrong hands, leverage can drag down returns in a hurry. Get Rid of the Dead Weight By Lawrence Jones Greenspring Comes to the Rescue By Laura Lallos In this section: 32 36 Where Leverage Lurks Guide to Finding Hidden Risks How Leveraged ETFs Compound the Misery Eric Jacobson Eric Jacobson Paul Justice Rooted in Buffett, Going for Growth By Kunal Kapoor Let failures occur, Bob Rodriguez and Jeffrey Gundlach say. Only then can a fundamentally transformed economy prosper. Although 2008 was a brutal year for many segments of the ﬁxed-income markets, to bond managers Jeffrey Gundlach, who runs TCW Total Return Bond TGLMX, and Bob Rodriguez, who runs FPA New Income FPNIX (both Morningstar Fund Analyst Picks), it was a chance to shine. Both managers have long maintained among the most sober of assessments of the credit

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Morningstar Advisor - August/September 2009

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