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The Sortino Framework for Constructing Portfolios
Focusing on Desired Target Return to Optimize Upside Potential Relative to Downside Risk
By Frank Sortino
Elsevier Science
Copyright © 2010 Elsevier Inc.
All right reserved. ISBN: 978-0-08-096168-2
Chapter One
The Big Picture Frank Sortino
Executive Summary
This chapter introduces the concepts of downside risk, upside potential, and DTR™-α, which are necessary to understand the chapters in the Applications section. In the interest of time, however, one could skip ahead to Chapter 5 without reviewing the in-depth background knowledge provided here. Most formulas and equations will be reserved for the Appendix.
Turning Points
The investment business is evolving slowly from a trade to a profession in much the same manner as the practice of medicine. The year 1876 was a turning point in medicine. Dr. Joseph Lister came to the first Centennial in America to debate the eminent Dr. Samuel Gross regarding whether surgeons should sterilize their equipment before an operation. A famous painting by Thomas Eakins shows Dr. Gross in action. The painting depicts surgical equipment lumped together in a couple of dirty trays and surgeons with bloody hands, wearing the same blood-splattered suits they had worn for many previous surgeries. Until recently, most people thought it was painted as a tribute to Dr. Gross. Many now believe Eakins was trying to point out the awful state of medicine in the United States.
At the Centennial debate, Lister called upon 30 years of evidence to support his case, beginning with Dr. Ignaz Semmelweis in 1847, who found that fewer pregnant women died of puerperal fever if doctors washed their hands after leaving the morgue and before they examined pregnant women. The germ theory of disease had not yet been discovered by Louis Pasteur, so Semmelweis didn't know why this happened. He suggested it might be due to something on their hands that could not be seen with the naked eye. Unfortunately, Semmelweis was made a laughing stock by his fellow physicians, eventually had a nervous breakdown, and died in a mental institution. His observations went against the current scientific opinion of the time, which blamed diseases on an imbalance of the basic "humours" in the body. It was also argued that, even if his findings were correct, it would be too inconvenient to wash one's hands each time before treating a pregnant woman. In addition, doctors were not eager to admit that they might have caused so many deaths. Pasteur later proved that indeed there was something called germs that could not be seen with the naked eye, and they could jump off the hands of surgeons and into open wounds to infect the patient.
During his presentation, Lister described an antisepsis he had invented to sterilize surgical equipment. He closed by citing a study of hospitals in Europe where surgeons washed their hands, wore surgical gowns, and sterilized their equipment, and there were 50% fewer deaths due to postoperative infections. The evidence was ignored, and Lister lost the debate. This was possibly due to the fact that the debate was held in America and Dr. Gross was president of the American Medical Association. Some physicians, however, chose to believe the evidence and went to Europe to learn what was then known about the science of medicine. Innovation takes time, though. Seventeen years later, in 1893, the Johns Hopkins University School of Medicine, the first in America to offer science courses, was founded.
After the debate, Lister was stuck with many gallons of antisepsis that he thought the attending physicians would want to purchase. By chance he met a promoter who suggested they water it down and sell it as a mouthwash that would make your breath "kissing sweet." You know it today as Listerine®. This sad tale (and others) is told in Thomas Kuhn's The Structure of Scientific Revolutions (1962, University of Chicago Press).
The year 1952 was the turning point in finance. That was the year Harry Markowitz quantified risk and presented a framework for evaluating the trade-off between risk and reward. Markowitz assumed that all investors had the same investment objective: to maximize the expected return for a given level of risk. Reward was measured as the mean from a bell-shaped (standard normal) distribution. A decade later, William Sharpe simplified the Markowitz model and presented the capital asset pricing model (CAPM) (see Figure 1.1), which assumes there exists a risk-free asset (Rf) and a market portfolio (M) that consists of every asset in the world in the proportion in which they exist in the world. In equilibrium, all assets would lie on the security market line (SML) and no one would be able to beat the market on a risk-adjusted basis. Therefore, everyone would want some linear combination of those two assets that lie on the SML in Figure 1.1. If someone was able to beat the market on a risk-adjusted basis, they would lie above the SML and have positive alpha (α). We assume the reader is familiar with the literature describing these two theories, which earned both of these scholars the Nobel Prize in Economics. Together, these theories are often referred to as modern portfolio theory (MPT).
MPT Criticism
Just as in medicine, it took about 20 years for these theories to be put into practice. Ron Surz, the author of Chapter 2, was with one of the first firms to market a service based on MPT, and he says several partners quit his firm rather than support this innovation. In academia, MPT led to a rift between traditional economists and professors who supported MPT. The latter eventually developed MBA programs outside the department of economics that are now essential elements in every graduate school of business in the world. CAPM allowed professors to explain to students how assets should be priced so that, on a risk-adjusted basis, all returns are equal. As the saying goes on Wall Street, "There ain't no free lunch." For a greater return, you need to take more risk.
However, we and others have pointed out that the real world is more complex than the normative models hypothesized by Markowitz and Sharpe. Professor Eugene Fama observed that the market portfolio described in CAPM does not exist; therefore, whatever values one gets for alpha and beta, they are theoretically wrong. Furthermore, the returns-generating mechanism is more complex than a single index model can describe. At minimum, there is a size effect (large cap stocks behave differently than small cap stocks) and a style effect (value stocks behave differently than growth stocks).
Andrew Rudd, former CEO of Barra, started the company Advisor Software because he felt that many investors' investment objectives were concerned with a future payout, and "CAPM is inappropriate because it doesn't recognize the liability of future income needs."
Innovations to MPT
The purpose of this book is to present some evidence of further advancements in the young science of portfolio management. Like Lister, there is growing evidence that these advancements can improve the financial health of clients, but they have yet to become commonplace. We have a long way to go to reach the level of innovation of the medical profession. Indeed, portfolio management is still more of a trade than a profession. Figure 1.2 illustrates the work of some of the people who have made great contributions to our efforts to improve the science of portfolio management.
Peter Fishburn, while at the University of Pennsylvania, laid the foundation for a portfolio theory based on a target rate of return and offered mathematical proofs that the mean-variance model of Markowitz was a subset of his richer framework. We refer to Fishburn's target return as the Desired Target Return™ (DTR™). Fishburn developed the mathematical equations that we use to calculate downside risk (see the Appendix). This is the risk that returns will fall below the DTR line shown in Figure 1.2.
Bradley Efron at Stanford University developed a new statistical procedure for generating this picture of uncertainty based on what could have happened in the past, instead of relying only on what did happen. This is the equivalent of taking an x-ray of the risk and reward characteristics of a portfolio. Our research indicates that this is superior to any other statistical procedure we know, and this approach is explained in Chapter 3 by Bernardo Kuan.
Atchison and Brown at Cambridge University developed the three-parameter lognormal that describes the shape of this uncertainty picture. This was an important improvement over the original lognormal distribution in that it allowed for negative returns and skewness.
Finally, the field of behavioral finance developed the reward concept of upside potential. The way we calculate the potential to exceed the DTR combines into one number the probability of exceeding the DTR with an estimate of how far above it might be. It is a linear function that says 2% more than the DTR is twice as good as 1% excess, and 4% is twice as good as 2%. This conveys more information than the mean (µ) or the probability of exceeding the DTR. Figure 1.3 provides a highly simplified example for illustration purposes only. It omits the use of the bootstrap and other procedures shown in Figure 1.2 and explained in the Appendix that are used to actually calculate the upside potential ratio.
In Figure 1.3, both Fund 1 and Fund 2 have the same mean (10%) and the same chance of exceeding the DTR (60%). However, the potential for Fund 1 to exceed 8% is 2.4% (8%+2.4% = 12.4% potential return), as opposed to 2.3% for Fund 2. That may seem trivial until the upside potential is compared to the downside risk for an upside potential ratio. The upside potential ratio for Fund 1 is 3.8 (2.4/.63) as opposed to 2.4 for Fund 2. In other words, Fund 1 has 3.8 times more upside potential than downside risk. Fund 2 has 2.4 times more upside potential than downside risk. This highlights the importance of always considering the trade-off between risk and reward.
Sharpe [1988] then developed a returns-based style analyzer that enables us to identify the unique style of thousands of managers in a few seconds of computer time. Ron Surz will explain in Chapter 2 the importance of having the correct set of indexes to use this powerful tool in asset allocation models and manager performance measurement.
Hands-on Experience
In 2004, Sortino Investment Advisors (SIA) began managing the first model portfolio using all of the concepts mentioned in this book. In 2006, SIA began acting as a subadvisor to Fiserv Investment Services, Inc., so they could apply these concepts to five collective investment funds for 401(k) plans. In 2009, Hand Benefits & Trust (HB&T) entered into an agreement with SIA to offer this service for their 401(k) plans. David Hand will provide the background in Chapter 5 for how this service fits into the new Qualified Default Investment Alternative (QDIA) proposal of the Pension Protection Act of 2006.
If we did nothing more than describe risk and reward in terms that were more meaningful to people, that would be a valuable improvement. We plan to do more than that. We claim that this represents a substantial improvement in the way portfolios are constructed.
The essence of our approach is shown in Figure 1.4. We assume that the return needed to achieve most investment objectives can be estimated (the DTR). An example is the rate of return that discounts the future cash outflows from a retirement plan at retirement to the cash inflows prior to retirement.
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Excerpted from The Sortino Framework for Constructing Portfolios by Frank Sortino Copyright © 2010 by Elsevier Inc. . Excerpted by permission of Elsevier Science. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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