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# Rethinking Risk And Diversification

Fortigent's Scott Welch looks at some of the academic and workplace approaches to portfolio construction and risk in the investment industry.

*“First, we make a guess. Then we compute the consequences of
the guess. Then we compare the consequences to experiment. If it
disagrees with [the] experiment, it’s wrong. In that simple
statement is the key to science. It doesn’t make any difference
how beautiful your guess is. It doesn’t make a difference how
smart you are, who made the guess, or what his name is. If [the
guess] disagrees with experiment, it’s wrong.”*

**Introduction**

When physicist Richard Feynman offered this observation on theory versus empirical reality, it is unlikely he was thinking about Modern Portfolio Theory. The market events of 2008 and early 2009, however, certainly raised questions of whether or not Modern Portfolio Theory (MPT) actually holds up in practice.

The wealth management industry was relatively slow in adopting Harry Markowitz’s notion of optimizing the trade-off between risk and return using diversification (he published his hypothesis in 1952). Since the 1980s, however, MPT has been the overwhelmingly accepted standard for building and managing investment portfolios.

For more than twenty years advisors and investors built portfolios based on a belief that risk could be minimized and successfully managed using appropriate diversification – an intelligent mix of stocks, bonds, cash, and real assets. And, for most of those twenty years, it worked – the markets experienced an unprecedented period of steadily rising equity prices (with a few hiccups along the way), low volatility, low and falling interest rates, easy access to credit, and general economic stability. For the most part, anyone who questioned the “truth” of MPT simply was ignored.

However, the events of 2008 and early 2009 – the collapse of the credit markets, the evaporation of liquidity, the skyrocketing increase in volatility, the lock-step correlations between asset classes, and the precipitous decline in global equity prices – dramatically challenged the “truth” of MPT.

“This wasn’t supposed to happen,” seemed to be the stunned reaction of the collective wealth management industry, followed quickly by cynics and opportunists shouting from the proverbial rooftops:

• The markets are NOT efficient!

• Diversification doesn’t work!

• MPT is DEAD!

• Buy and Hold is DEAD!

• "Stocks for the long run" is DEAD!

All of which, of course, led many investors to the natural conclusion of “The next time I see my financial advisor, he’s DEAD!” Naysayers claimed that MPT had failed, while its proponents and adherents claimed just as vigorously that markets were, in fact, hyper-efficient, and that what happened in 2008 was exactly what was supposed to happen – excessive risk taking was excessively punished. The only difference this time was the speed and severity of the market’s “reversion to the mean”.

The truth, as usual, probably lies somewhere in the middle. This article examines some of the underlying tenets of MPT that do not hold up well in reality – where experiment clearly disagrees with guess – and summarizes several of the new ways investors and advisors are thinking about risk, diversification, and intelligent portfolio construction. In many ways, it is a “back to the future” storyline, as wealth managers realize the danger of blind faith in the “science” of investing and rediscover the importance of common sense.

**Not so thoroughly modern portfolio theory**

Beginning with the investor, a quick comparison of the “experiment” of actual investor and market behavior to the underlying “guesses” of MPT reveals the potential pitfalls of strict adherence to the theory:

**MPT Assumption**

Investors behave “rationally”

• Investors seek to optimize their “utility function”

• Investors have uniform risk tolerances

• Mathematically, investors view risk symmetrically and in a “continuous” manner

• Expected return and standard deviation (“risk”) are sufficient to determine an investor’s

“optimal” portfolio

• Investors are primarily concerned with “end of horizon” results

**Investor reality**

Investors behave “irrationally”

• What is a utility function?

• Investor risk tolerances differ widely as a function of objectives and of the beginning

level of wealth

• Investor risk tolerances change asymmetrically over time and frequently “jump”

discontinuously under different market conditions

• Investors are objectives-based and do not view upside and downside risk the same

• Investors are highly “path dependent” and sensitive to “within horizon” performance

Turning to the market, another quick comparison highlights the differences between theory and reality:

**MPT Assumption Market Reality**

• Investment returns are assumed to follow a statistical “normal” (bell curve) distribution

• Standard deviation (volatility) and correlation (the strength and directional relationship between asset classes) capture the “risk” of a portfolio

• Market behavior is efficient and can be accurately

modeled quantitatively

• Model inputs (expected return, standard deviation, and correlations) are static over time

**Market reality**

• Many investment returns exhibit skew (nonnormality) and/or kurtosis (“fat tails”, or extreme events)

• Portfolios have many types or risk – liquidity, counterparty, credit, leverage – that are not captured by portfolio statistical characteristics

• Extreme market behavior happens more frequently that statistically “possible” and, when it does occur, it causes compete model failure

• Model inputs can and do fluctuate wildly over time

Since all of the investor and market “realities” described above are, essentially, intuitive and not especially hard to understand, the begged question is, “How did we not see 2008 coming?” Enter Hyman Minsky. Minsky was a late-20th century economist who was not especially renowned or acclaimed in his own lifetime

(he died in 1996). His primary contribution to economic thought was his research into and explanation of financial crises, summarized in his working paper, “The Financial Instability Hypothesis”.iii In his own words, he believed, “Instability is an inherent and inescapable flaw of capitalism.”

Specifically, Minsky segmented borrowers into three categories:

1. Hedge borrowers, whose cash flow can cover both interest and principal on any debt incurred;

2. Speculative borrowers, whose cash flow can cover interest but not principal; and

3. Ponzi borrowers, whose cash flow cannot cover either interest or principal and who must rely on rising asset prices and increased borrowing to survive (sound familiar?).

Minsky’s theory states that in strong economic times the risk of failure is “forgotten”, leading to increased borrowing and a slow (but inevitable) “flow” from hedge borrowing through speculative borrowing and finally to Ponzi borrowing, at which point a market bubble has evolved that will soon, just as inevitably, pop. During periods of economic strength and “stability”, “within horizon” risk is forgotten or ignored and stability is extrapolated into perpetuity. This leads hedge borrowers to morph slowly into speculative borrowers and speculative borrowers to morph into Ponzi borrowers (liar-loans, anyone?) precariously balanced on a proverbial house of cards held together only by easy credit and rising asset values.

In other words, periods of market stability mask underlying high levels of market instability until a “Minsky Moment” occurs – a tipping point when the credit bubble pops, the leveraged house of cards collapses, and financial markets crater. It would be hard to find a more elegant or accurate description of the events leading up to and through 2008 and early 2009. It also helps to explain why so many investors did not see – or chose to ignore – the warning signals that preceded the recent market collapse – as a collective body we forgot that failure was an option.

We can segment the multitude of ways that academics and practitioners are responding to the now very visible cracks in MPT into three very broad approaches: (a) behavioral responses; (b) quantitative responses;

and (c) “rethink the problem” responses. Let us examine each of these in more detail.

**The Behavioral Responses**

**Post-Modern Portfolio Theory**

One of the more interesting challengers to MPT is the theory of Behavioral Finance. Simply put, Behavioral Finance is the study of why seemingly rational investors frequently make seemingly irrational decisions with respect to their money. While the theory has been under academic study since the 1960s, it is only within the past 5-10 years that investment professionals attempted to integrate the theory into actual investment practice.

The difficulty with the practical application of Behavioral Finance is that, because it is so closely tied to human emotion, conditioning, and biases, it can be very difficult to quantify in any meaningful way. Put differently, Behavioral Finance can be very effective in explaining why investors acted a certain way in the past, but it is very difficult to use that information to determine future behavior.

The question, then, becomes whether there is a way of “bridging the gap” between MPT and Behavioral Finance. One attempt at this integration is Post-Modern Portfolio Theory (PMPT).iv PMPT begins by asking some fundamental and intuitive questions:

1. Is standard deviation an appropriate measure of risk?

2. Are returns really normal?

3. Do investors actually base their decisions solely on optimizing the risk/return utility?

PMPT then makes the following assumptions about actual investor behavior and actual investment performance:

1. Investors like upside risk but do not like downside risk, so use downside risk metrics to determine the

“risk” of the portfolio because that more accurately captures the way investors think about their money.

These downside metrics attempt to measure such intuitive risk factors as:

a. How often might the investor lose money?

b. When they lose, how much might they lose?

c. What is the maximum loss in any given time period?

d. When they do lose money, how long might it take to earn that money back?

2. Investors are “objectives-based” with respect to their portfolios. That is, they care less about the statistical expected return of the portfolio than about whether or not that portfolio will earn enough to meet personal investment objectives (e.g., be able to retire by a certain age, to generate enough cash flow to maintain or improve their lifestyle, or meet philanthropic or wealth transfer goals).

Further, PMPT recognizes that this so-called “Minimum Acceptable Return” (MAR) differs from investor to investor, and so does not assume a homogenous risk/return trade-off profile across all investors.

3. Actual investment returns are not assumed to be normally distributed around the mean, and various methods are employed (e.g., Monte Carlo simulation) to estimate the actual performance realized by the investor.

Back in the 1950s, when Harry Markowitz first envisioned what we now call MPT, he recognized that using standard deviation (or variance) was not the “best” way to measure portfolio risk – he preferred a “semivariance” approach that focused on downside risk (rather than viewing upside and downside risk symmetrically as standard deviation does). Given the computational abilities and speed of computers at that time, however, he opted to use far-easier-to-calculate standard deviation instead.

With today’s computer power, however, many investors are reconsidering this decision. An example of this is the “Sortino Ratio,” developed by Dr. Frank Sortino. The Sortino Ratio is a semivariance based risk metric that attempts to measure the downside risk-adjusted return, relative to a given investor’s MAR, of a specified investment. This can be contrasted with the more frequently used “Sharpe

Ratio”, which measures risk-adjusted return relative to the risk-free rate, and which uses standard deviation as the measure of risk. Dr. Sortino recently launched a blog site to encourage “open forum” dialogue and analysis on PMPT.v

Depending on the inputs used, PMPT can result in wildly different recommended portfolios than MPT for a given investor. Further, the assumptions of PMPT mean that each investor has his/her own “efficient frontier,” based on their specific downside risk tolerances and personal objectives-driven MAR. Put differently, a portfolio that is “efficient” from a PMPT perspective may look wildly “inefficient” when viewed through the lens of MPT.

It is important to note that PMPT has not been widely tested and is not widely accepted among many financial academics. Among the challenges of PMPT are the statistical implications of focusing only on downside risk, which may significantly reduce the amount of data included in the calculation (and, therefore, reduce the statistical significance of the outcome). In addition, there is little or no empirical evidence that downside risk metrics generated from historical data are any more accurate at forecasting future outcomes than traditional MPT metrics.

However, the analysis and research continues and PMPT will be refined and more widely employed as academics and practitioners alike seek better ways to build an “ecumenical” bridge between MPT and Behavioral Finance.

**A Purpose-Driven Investment Life**

A less quantitative, but still behaviorally oriented revision of MPT is the notion of “objectives-based” portfolio construction.vi The concept is to build client portfolios that target specific client or portfolio objectives (rather than the usual MPT approach of optimizing the risk/return trade-off of the overall portfolio – a statistical portfolio property that may or may not have any real meaning to the average investor).

**The Quantitative Responses**

Many quantitatively oriented academics and practitioners are less concerned with investor behavior than with improving the robustness of the inputs and models used to construct and manage portfolios. They look back over the history of the markets and see non-normal return distributions, extreme or “fat-tail” events that occur far more frequently than statistically suggested, and highly volatile asset class correlations that converge to +1 during market disruptions, and they believe the answer lies in applying new and better math to the problem.

**Here is a brief summary of some of the more interesting
ideas being considered:**

• Market “Turbulence” Portfolio Optimization suggests that markets pass through periods of “quiescence” and “turbulence”. Additionally, these periods are both persistent and forecast-able. If true, then building and managing portfolios to incorporate these different turbulence regimes (rather than assuming static volatility and correlation conditions) results in more “true” diversification, less tail risk, and more consistent portfolio performance. Mark Kritzman at Windham Capital is a leading proponent of this theory, and he has published extensively on the subject.viii

• Extreme Value Theory (EVT) is the statistical analysis of results that deviate wildly from the norm, that is, the study of market behavior in the “fat tail” portion of the return distribution. EVT typically is used to study the risk of low-probability, high impact events, such as floods and mutational evolutionary events. Industry thought leaders such as Blake LeBaron believe that applying EVT to portfolio management leads to better understanding of both the likelihood and outcome of extreme market events, and thus drives more intelligent portfolio construction and risk management.

• Somewhat related to EVT are the uses of Value at Risk (VaR) and Conditional Value at Risk (CVaR). VaR is a statistical metric that measures the potential risk of loss within a portfolio over a specified time period.

In May 2009 at the IMCA Spring Development Conference in San Diego, one session explored some of the weaknesses of using VaR to measure portfolio risk, weaknesses driven primarily by VaR’s assumption of normal “bell curve” return distributions, which dramatically underestimates so-called “tail” or extreme event risk.

The presenter, Dr. William Shadwick, recommended using Conditional VaR (CVaR) instead. CVaR measures “extreme risk” or “the risk beyond VaR”ix. He further recommended using “Laplace” distribution curves rather than a normal distribution curves when measuring CVaR.

Laplace distribution curves have higher and narrower “peaks” at the mean and fatter “tails” than normal bell curves, and thus place a higher probability on tail events. The belief is that portfolios can be more robustly constructed and managed by (i) assuming a higher probability of tail events and (ii) focusing on what happens if those tail events occur.

• Fractals and Chaos Theory – Fractals are geometric shapes that are, regardless of scale, “selfsimilar” - no matter how macro or micro you look at any given shape, it exhibits the same geometric properties. The mathematical equations describing this property can be applied to any number of different phenomena.

Chaos theory analyzes systems that are highly sensitive to both initial conditions and subsequent small changes to those conditions (resulting in seemingly random evolution of the system).x

Mathematician Benoit Mandelbrot and quantitative practitioner Edgar Peters are two leading proponents of applying fractal analysis and chaos theory to investment management. They suggest these mathematical concepts result in pricing and market models that display discontinuity, path dependence, and wild randomness – in other words, a much close approximation to real market behavior.

What all of these quantitative responses have in common are the following observations / beliefs:

• Standard deviation and correlation analysis are backward looking, unstable over time, and represent an insufficient measure of actual portfolio risk;

• Assuming normal “bell curve” return distributions can be very dangerous;

• Traditional MPT metrics significantly underestimate actual market risk. The empirical evidence indicates that the chance of a market “blow up” is far greater than what is indicated by normal distribution assumptions;

• Market price movements are neither independent nor continuous, as assumed by MPT assumptions;

and

• A better understanding and modeling of actual market behavior, especially extreme market movements, leads to more robust portfolio construction and risk management.

Interestingly, and similar to the behavioral responses, the quantitative responses do not discard outright the underlying tenets of MPT (i.e., the benefits of diversification, the optimization of risk and return, etc.). Rather, the intent is to “tweak” the models to reflect more accurately the empirical reality of the market place.

**The “The Rethink the Problem” Responses**

**The Black Swan Response**

Nassim Taleb’s now ubiquitous notion of Black Swan Events posits that (i) markets are utterly unpredictable and (ii) truly disruptive events are far more likely to occur – and will have a far worse impact – than statistics suggest.

Further, once these events take place, they are rationalized in hindsight by the market, as if they could/should have been anticipated (leading to a false belief that models can be improved to anticipate future Black Swan Events). Taleb’s ideas do not really open themselves up to modeling or mathematical treatment, since by definition the disruptive events are unpredictable and likely to have a larger impact than anticipated.

The practical implication for portfolio management, if Taleb is correct, is that “catastrophe insurance” or, conversely, “opportunity exploiters” (which may take the form of various financial products) should be standard components of any portfolio asset allocation.

**The “Unified Field Theory” Response**

Still other academics and practitioners are exploring completely different ways to think about the problem. Dr. Andrew Lo, for example, suggests an Adaptive Market Hypothesis that attempts to integrate MPT, behavioural finance, and evolutionary neurobiology.xi Dr. Lo’s hypothesis makes for fascinating reading, and there is a growing amount of research into examining the financial markets as a complex adaptive system (i.e., a system made up of myriad and multiply interconnected networks of relationships that “learn from experience” and evolve accordingly over time). To date, however, no practical applications exist.

**The Risk Factor Response**

More interesting, at least in terms of practical application, is the concept “deconstructing” asset classes into their underlying risk factors and then building portfolios diversified across these risk factors, rather than across asset classes.

If traditional asset classes are thought of simply as convenient “bundles” of underlying risk factors, this approach makes a great deal of intuitive sense. It also may explain why “traditional” diversification fails during times of market disruption – asset classes we believe have low correlation to one another really are exposed to similar sets of risk factors (equity markets, interest rates, etc.), and therefore react in similar ways to dramatic changes in those risk factors. Under this scenario, diversifying across risk factors should deliver better “true diversification” and more robust portfolio protection against extreme market movements.

Several large institutional investors are already applying a logical extension of this concept.xii Recognizing that traditional asset class diversification left many portfolios exposed to common underlying risk factors, these investors are broadening their asset class definitions (equities, bonds, real assets, etc.) and rethinking diversification along risk factor (and return driver) lines. The issue remains, of course, of correctly identifying these risk factors and how they may positively or negatively impact portfolio performance.

**The Qualitative Overlay Response**

Another, highly practical, response to the events of 2008 is simply to recognize that traditional MPT statistics (expected return, volatility, and correlations) represent necessary but insufficient measures of the true risk of an investment portfolio.

Additional steps to measure or address the true risk of a given portfolio might include:

“Time Diversification”

Bucketing portfolios with different target maturity dates and different investment policies

< 2 years (cash, tactical, principal protection, etc.)

2-10 years (strategic asset allocation)

>10 years (illiquid holdings)

Developing metrics for measuring and illustrating:

Portfolio liquidity (e.g., weighted average time to liquidate)

Portfolio / strategy leverage (both actual and implied through optionality)

Credit exposure (on both the asset and liability side)

Behavior of investment strategies under non-normal (extreme) market conditions (i.e., explanation of blow up risk)

Re-evaluate nomenclature and benchmarks

The “strategy formerly known as ‘Absolute Return’”

Should benchmarks be objectives-based rather than market index-based?

Remember Pascal’s Wager

Do not assume the probability of being wrong is the same as the consequence of being wrong

Adopting a very simple “explanation” rule of thumb

If you can’t explain an investment strategy to your client, don’t use it

If your client cannot explain an investment strategy back to you, do not allow them to invest.

**Concluding thoughts**

The empirical disconnect between market reality and many of the underlying assumptions of MPT is well known and has been understood “since inception”. Therefore, it is inaccurate to state, “MPT failed in 2008". It might be more accurate to state that, because of the Minsky-like stability of the capital markets for the past twenty years, many market practitioners inappropriately or sloppily applied MPT.

Nevertheless, we did learn – or relearn – many invaluable lessons from the events of 2008. Among them:

• Uncertainty is NOT the same thing as risk;

• Portfolios are more risky than indicated by traditional MPT metrics;

• Most portfolios are more risky than investors can tolerate in the event really bad things actually happen;

• The real menace is not “known risk”;

• We do not need to “throw the MPT baby out with the 2008 market collapse bathwater”; and

• We do not need to wait for an academic or theoretical breakthrough to improve our portfolio and risk management capabilities.

In rethinking the problem, there are several intuitive, non-quantitative steps we can take to manage more effectively the real risk in our investment portfolios:

• Acknowledge the impacts of market globalization and shared underlying risk factors and use broader strategy definitions when building a “diversified” portfolio, for example:

o Equities

o Fixed Income

o Real Assets

o Volatility

o Momentum

• Build portfolios based on personal liquidity constraints, not pre-specified “time horizons”.

• Take less “known risk” in the portfolio to offset the “unknown risks” that almost certainly exist.

Some final observations: The highly quantitative responses to the events of 2008 are fascinating to consider, and perhaps they truly will lead to better portfolio management techniques. In May 2009, for example, a large financial institution announced it was switching from VaR-based to CVaR-based asset allocation and risk management models.xiii

It is interesting to note, however, that in the IMCA Spring Development conference session cited above, Dr. Shadwick’s analysis suggested that CVaR, while improving upon VaR, continued to underestimate both the probability and magnitude of tail events. This begs the question of, “Is this a case of simply being wrong more precisely?”

One root cause of the meltdown in 2008 was – perhaps counter-intuitively – the increased sophistication of quantitative risk models. As an industry, we seemed to believe that the increased elegance and sophistication of our risk models meant we were actually doing a better job of measuring and managing risk. This, in turn, made us confident to take on more risk than ever before (40:1 leverage, anyone?).

We were wrong.

Can we improve the risk/return profile of client portfolios without throwing out our existing models and/or learning higher mathematics? 2008 certainly reminded us that MPT and Mean Variance Optimization do not capture all the risk in an investment portfolio. Furthermore, we re-realized in a very nasty way the fact that correlations are not static and, in particular, increase during times of market distress. Finally, many investors learned, the hard way, that risks like counterparty risk and liquidity risk are very real, but are not quantified or captured with MPT risk statistics.

**We can learn from these experiences and recognize some
fundamental truths about our investment portfolios:**

1. They are susceptible to greater risk than what is captured by traditional MPT statistics; and

2. Most investor’s willingness / actual ability to stomach risk are probably much lower than they believe it to be (i.e., the behavioral finance concept of Prospect Theory).

Conclusion: Build more conservative portfolios – that is, take less “known risk” in order to mitigate some of the “unknown risk” we know is there. What might more conservative portfolios look like?

• More broadly defined asset classes;

• More fixed income;

• More alternatives (based on personal liquidity requirements); and

• An increased focus on portfolio liquidity.

These are exactly the same results the large financial institution espoused when it announced its adoption of CVaR-based portfolios, and not a mathematical calculation in sight.

Perhaps “Modern Portfolio Theory” does not really need more and/or better “theory”. Perhaps all it needs is a heavier dose of investor common sense and Modern Portfolio “Reality”.

**Suggested further reading**

1. “The Mismeasurement of Risk”, by Mark Kritzman and Don Rich, Financial Analysts Journal,

May/June 2002, pp. 91-99.

2. “Diversification and Risk Management: What Volatility Tells Us”, by Paul Goldwhite, The Journal of

Investing, Fall 2009, pp. 40-48.

3. “How To Kill a Black Swan: Risk and Asset Allocation in Crises”, by Remy Briand and David Owyong,

Journal of Indices, July/August 2009, pp. 10-17.

4. “Ponzi Nation”, by Edward Chancellor, Institutional Investor, February 2007

(http://www.iimagazine.com/article.aspx?articleID=1234345).

5. “A New Approach to Tail Risk”, by Ana Cascon and William Shadwick, Journal of Investment Consulting,

Summer 2009, pp. 33-48.

6. “Ideas and Innovation Across Multiple Disciplines: A Discussion with Nobel Laureate Harry M. Markowitz,

PhD”, The Masters Series, Journal of Investment Consulting, Summer 2009, pp. 6-16.

7. “CalPERS Eyes Risk, Liquidity n Asset Review”, By Arleen Jacobius, Pension & Investments, March

23, 2009;

http://www.pionline.com/apps/pbcs.dll/article?AID=/20090323/PRINTSUB/303239971/1031/TOC

8. “Survey: Few Measure Counterparty Risk”, by Gregory Crawford, Pension & Investments, April 6,

2009;

http://www.pionline.com/apps/pbcs.dll/article?AID=/20090406/PRINTSUB/304069977/1031/TOC

9. “Does Your Portfolio Have Bad Breath?”, by Ed Peters, First Quadrant Perspective, December 2008

(http://www.firstquadrant.com/downloads/0812_Does_Your_Portfolio_Have_Bad_Breadth.pdf).

10. “Modern Tactical Asset Allocation”, by Harindra de Silva, CFA Institute Conference Proceedings, December

2006, pp. 1-10.

11. “A Brief History of Downside Risk Measure”, by David Nawrocki, Journal of Investing, Fall 1999, pp.

9-25.

12. “Alpha and Beta in an Exposure-Based Framework”, by Pranay Gupta and Jan Straatman, ABP

Working Paper Series, July 17, 2005 (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=765064).

13. “Skill Based Investment Management,” by Pranay Gupta and Jan Straatman, ABP Working Paper

Series, June 7, 2005 (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=737103).

14. “Portfolio of Risk Premia: A New Approach”, by Remy Briand, Frank Nielsen, and Dan Stefek, MSCI

Barra Research Insights, January 2009

(http://www.mscibarra.com/resources/pdfs/research/RI_Risk_Premia.pdf).

15. “Emphasizing Low-Correlated Assets; The Volatility of Correlation”, by William J. Coaker, Journal of

Financial Planning, September 2007, pp. 52-70.

16. The (Mis)behavior of Markets, by Benoit Mandelbrot, Basic Books (Cambridge, MA), 1994

17. “Steps in Applying Extreme Value Theory to Finance: A Review,” by Younes Bensalah, Bank of Canada

Working Paper, November 2000 (http://ideas.repec.org/p/bca/bocawp/00-20.html).

18. Extreme Value Theory and Fat Tails in Equity Risk,” by Blake LeBaron and Ripiruta Samanta, Working

Paper, November 2005 (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=873656).

19. Fractal Market Analysis: Applying Chaos Theory to Investment & Economics, by Edgar Peters, Wiley

(New York), January 1994.

20. “Beyond Markowitz: A Comprehensive Wealth Allocation Framework for Individual Investors”, by

Ashvin Chhabra, The Journal of Wealth Management, Spring 2005, pp. 8-34.

21. “The Legacy of Modern Portfolio Theory”, by Frank Fabozzi, Frank Gupta, and Harry Markowitz, The

Journal of Investing, Fall 2002, pp. 7-22.

**END NOTES**

iRichard Feynman, American physicist and Nobel Prize winner in Physics (1965), as quoted by David Nawrocki in “A Brief History of

Downside Risk Measures”, Journal of Investing, Fall 1999, pp. 9‐25. (Also available here:

http://www56.homepage.villanova.edu/david.nawrocki/Brief%20History%20of%20Downside%20Risk%20‐%20Nawrocki.pdf).

ii Or, “she’s DEAD” – it was an equal opportunity market disaster.

iii “The Financial Instability Hypothesis”, by Hyman Minsky, Working Paper #74, prepared for The Handbook of Radical Political

Economy, edited by Philip Arestis and Malcolm Sawyer, Edward Elgar: Aldershot, 1993. (http://www.levy.org/pubs/wp74.pdf).

iv See, for example, “Post‐Modern Portfolio Theory,” by Greg Kasten and Pete Swisher, Journal of Financial Planning,

September 2005, (http://www.fpanet.org/journal/articles/2005_Issues/jfp0905‐art7.cfm).

v See: http://pmpt.wordpress.com/.

vi A quantitative variation on this theme is applying to individual investors the institutional investing concept of “Liability‐Driven Investing”,

or LDI. With institutional LDI, the future liabilities of the investor (pension fund, endowment, defined benefit plan, etc.) are

forecast and a portfolio is built that attempts to minimize the risk that the portfolio will not be able to meet its future funding obligations.

Any surplus portfolio assets not required to “immunize” future liabilities can then be invested more aggressively to grow the

overall portfolio value. This concept is now being applied to individual investor portfolios: future obligations or “liabilities” (retirement

funding, education expenses, weddings or other “target date” events, etc.) are forecasted and portfolios are then constructed

to fund those liabilities, with any excess portfolio assets invested more aggressively for dynastic wealth or end‐of‐life charitable purposes.

vii Others, especially Ashvin Chhabra and Jean Brunel, recommend optimizing each sub‐portfolio and then “rolling up” the subportfolios

into an optimized overall portfolio. Since the author’s suggestion is that the primary value of the exercise is optical – presenting

the recommended portfolio in investor‐centric ways – optimizing at the overall portfolio level is sufficient.

viii See, for example, “Optimal Portfolios in Good Times and Bad”, by George Chow, Eric Jacquier, Mark Kritzman, and Kenneth Lowry,

Financial Analysts Journal, May/June 1999, pp. 65‐73

(http://www.windhamcapital.com/eerm/documents/optimal_portfolios_in_good_times_and_bad.pdf).

ix For a more detailed analysis of this topic, see “A New Approach to Tail Risk”, by Ana Cascon and William Shadwick, The Journal of

Investment Consulting, Summer 2009, pp. 33‐48.

x The apocryphal example is the “butterfly effect”, which suggests that a butterfly flapping its wings in one part of the world leads to

a series of events resulting in hurricanes in another part of the world.

xi “The Adaptive Market Hypothesis”, by Andrew Lo, The Journal of Portfolio Management, June 2004, pp. 15‐29. Also available

here: http://web.mit.edu/alo/www/.

xii See, for example:

1. “New Model Portfolio Lifts Indiana Foundation”, by Whitney Kvasager, FundFire, December 1, 2008

(http://fundfire.com/articles/20081201/model_portfolio_lifts_indiana_foundation).

2. “Experts Urge Broad Asset Silos for Pensions”, by Whitney Kvasager, FundFire, June 5, 2009

(http://fundfire.com/articles/20090605/experts_urge_broad_asset_silos_pensions).

3. “Endowments, Foundations Broaden Asset Silos”, by Whitney Kvasager, FundFire, September 25, 2008

(http://fundfire.com/articles/20080925/endowments_foundations_broaden_asset_silos).

4. “Macro Factors Take Central Role in Asset Allocation Following the Market Turmoil”, by Christine Williamson, Pension &

Investments,

(http://www.pionline.com/apps/pbcs.dll/article?AID=/20090810/PRINTSUB/308109971&crit=christine%20williamson).

5. “Consultant FEG Retools Asset Allocation Model”, by Jay Cooper, FundFire,

(http://fundfire.com/articles/20090319/consultant_retools_asset_allocation_model).

xiii “JPMorgan Dumps Tradition”, by Joel Chernoff, Pension & Investments, May 4, 2009

(http://www.pionline.com/apps/pbcs.dll/article?AID=/20090504/PRINTSUB/305049982/1031/TOC).