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JOURNAL OF INVESTMENT MANAGEMENT, Vol. 8, No. 1, (2010), pp. 1–17
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INSIGHTS
“Insights” features the thoughts and views of the top authorities from academia and the profession.
This section offers unique perspectives from the leading minds in investment management.
LESSONS ON INVESTMENT MANAGEMENT FROM THE
GLOBAL RECESSION AND BEAR MARKET∗
Frank J. Jones a,b
The current global recession and financial crisis have significantly affected virtually all investment
managers. The severity of the effects on investment management risk has induced many investment
managers to reconsider their investment approaches in terms of investment management risk. This
paper summarizes and evaluates many of the resulting “lessons learned” by the author from these
effects of the crisis. The perspective is that of a high net worth investor.
Some of the “lessons learned” by investors, however, are inappropriate responses to the investment
crisis and are refuted. These are, however, other responses investors should learn and consider using
prospectively. These responses include both modified responses to the financial crisis we have witnessed
and also new quantitative methodologies which have been developed to treat the investment problems
which have been encountered.
Among the issues considered are: (1) the utility of MPT; (2) the development process of contagion
and a quantitative response to contagion; (3) quantitative and qualitative rebalancing; (4) recent
evidence on the ERP (Equity Risk Premium) and the stock/bond allocation; (5) the paradigm of
extreme events (a.k.a. the “black swan”) and hedging extreme events; (6) the changing role of liquidity in investment management; (7) a consideration of risk tolerance in portfolio development and
others. Overall, the paper reviews both potential strategic and tactical responses with respect to these
issues to the recent severe financial crisis from the perspective of a high net worth investment advisor.
∗The
observations and conclusions, herein represent the
author’s only and not those of Private Ocean Wealth Management, LLC.
a Accounting and Finance Department, San Jose State University, USA.
b Chairman, Investment Committee, Private Ocean Wealth
Management, USA.
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1 Introduction
The current recession began in December 2007
and the S&P 500 peaked on October 9, 2007
(at 1,565.15). Since then the United States and the
world have experienced a global recession and bear
market.
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FRANK J. JONES
The recession and bear market have, however, been
quite unlike their predecessors. We have witnessed
the effects of several unprecedented experiences:
with respect to these issues with particular application to high-net worth individual investment
management.
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2 Lessons learned
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unprecedented leverage in the financial system;
extreme volatility in the stock market;
illiquidity and credit market impairment;
complexity and opacity of financial investments
and institutions;
ineffectiveness of the rating agencies in rating
financial investments;
applications of moral hazard;
applications of the agency effect;
extreme active and passive regulatory actions;
extreme consumer dissavings followed quickly by
significant savings (and the effect on the economy
of the “paradox of thrift”);
extreme risk aversion, which along with the
demand for liquidity, caused contagion and the
unified decline in most risky asset classes;
extreme systemic effects;
counterparty risk and its effect on the credit
markets;
the use of the Black Swan to interpret these
extreme changes; and
several other phenomenon.
The confluence of all these factors, and others, generated a “perfect storm” which led to the global
recession and market crisis.
Periods like these and the resulting very negative investment returns have prompted many
investment managers to reevaluate their investment
strategies. Some outcomes of these reevaluations
have been, in the author’s opinion, extreme and
wrong. Others have been moderate and productive. Some of these outcomes have been based
on market behavior and others based on recent
research findings. This paper summarizes what
the author has learned from these recent experiences, both market-oriented and research, and
an overview of his current investment approach
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2.1 The practice of Modern Portfolio Theory
(MPT)
The headline of the cover of the January, 2009
Journal of Financial Planning asks “Is Markowitz
Wrong?”1 Harry Markowitz, of course, fathered
Modern Portfolio Theory (MPT) in his 1952 article
and 1959 book.
Such questions about MPT are not new. They originated in two articles by William Jahnke (Journal
of Financial Planning, February 1997 and February 1999). MPT observes that over time, different
assets behave differently, that is their returns are
not perfectly correlated. Such assets provide diversification with the result that a diversified portfolio
exhibits less risk for a given return than a portfolio of perfectly correlated assets. Such portfolios are
often called Markowitz Efficient Frontiers (MEFs)
or simply Efficient Frontiers (EFs). These portfolios are calculated by mean–variance optimization
(MVO) techniques.
“Buy and Hold (B&H) investing” refers to any portfolio, whether efficient or otherwise determined,
which is held permanently. Warren Buffet is an
example of a B&H investor. EFs may be B&H portfolios or, on the other hand, may be rebalanced over
time.
A common type of investment management is to
specify a strategic (or policy) portfolio via MPT
and then to specify tactical bands around the strategic allocation for each asset and then to rebalance
back to the strategic allocation (or part of the way)
when the actual allocations go outside these bands
due to asset price changes. This is called Tactical
Asset Allocation (TAA) and is often accomplished
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LESSONS ON INVESTMENT MANAGEMENT FROM THE GLOBAL RECESSION
S&P 500
S&P Midcap 400
Russell 2000
MSCI EAFE
MSCI Emerging Markets
Barclay’s Aggregate Bond
CS First Boston High Yield Bond
Barclay’s Municipal Bond
Vanguard Long-Term Government Bond
Thirty-year Treasury Bond
−37.0%
−36.2%
−33.8%
−43.4%
−54.5%
5.2%
−26.2%
−2.5%
+22.5%
Over 44%
Figure 1 2008 security returns.
Source: Morningstar FundInvestor, January, 2009.
quantitatively. A more general form of TAA, usually non-quantitative, involves the asset allocators
shifting among assets based on their general views
of the markets. Such reallocations can approximate
market timing.
A major reason that the question “Is MPT Dead?”
is currently being asked is illustrated in Figure 1.
During 2008, the returns of most risky assets
were similar, that is all their correlation coefficients reverted to one. But high-quality bonds,
Treasuries and investment-grade corporate had positive returns. An alternative question about 2008
rather than “Is MPT Dead?” would be “Where were
the bonds?,” that is the portfolios were not fully
diversified.
The bases for the Jahnke criticism and many of the
current criticisms involve not the model itself but
data inputs into the model. Specifically, these data:
should be variables which apply to the future and
instead they are historical; do not consider valuations; and are changed only at the beginning of
the process and at rebalancing. These issues are
considered in the next section.
Finally, for those who want to eliminate MPT, with
what do they replace it? Two answers are frequently
given: market timing and TAA. With respect to
market timing, the case seems to be clear. The
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Hulbert Financial Digest regularly demonstrates the
futility of market timing.2 Coming after the almost
universally unexpected market crises of 2007–2009
gives the author little confidence that market timing could be accurate and could successfully replace
MPT.
The case for TAA is more complex. Using quantitative TAA to rebalance around an MPT-based
strategic portfolio is the preferable way to rebalance
a wealth portfolio. The width of the tactical bands
should be proportional to the asset’s risk and the
manager’s confidence in their tactical decisions (in
both cases, the greater the asset’s risk and the manager’s confidence, the wider the bands) and depends
on other variables as well (including the investor’s
risk tolerance, transaction costs, and correlations
among the assets).
TAA on a qualitative basis is also used to shift among
assets and asset classes. The difference between this
type of TAA and market timing, however, may be
small. Again, it seems presumptuous to implement
this type of strategy soon after the failures of 2007–
2009. TAA is considered again below.
With respect to diversifying assets, alternative assets
(private equity, hedge funds, real assets, commercial
real estate, commodities, and others) are used as
discussed below. They represent a swap of liquidity
for return and have been fairly unsuccessful during
the current crisis. They do, however, have a role
in a portfolio, and in most environments provide
diversification.
In equity portfolios, despite the fact that Figure 1
illustrates that international equities did not provide diversification to a U.S. stock portfolio during
2008, the author retains a “no home country bias” in
his global equity portfolio. During non-contagion
years, international equities provide modest diversification. Over a longer period of time, it will provide
diversification due to structural differences in economic growth rates among countries. The weight
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FRANK J. JONES
of U.S. equities in a global equity portfolio is now
approximately 45%.
The applications of the specific lessons learned
by the author on this topic are summarized
below.
– Use MPT to develop a policy (or strategic) portfolio. Consider the data as discussed in the next
section.
– Improve diversification (which is effective in
most environments) as follows:
• Include a moderate amount (10–20%) of
diversifying alternative assets (e.g., hedge
funds, private equity, commercial real estate,
and other real assets).
• Actively monitor new asset classes and asset
classes currently in the portfolio which provide
diversification.
Consider the current valuations of the new
assets (e.g., timberland may currently have
a high valuation).
– Rebalance quantitatively on the base of TAA with
specific bands, as discussed below.
2.2 Data inputs into MPT
This section evaluates the lessons which have been
learned about the data inputs into MPT. As indicated above, the use of irrelevant historical data is a
major reason for rejecting MPT. The correct way to
develop data for MPT is provided in the following
quotes from Markowitz.3
– Use historical data as initial and tentative benchmark data.
– Revise these data on the basis of judgment
and experience to provide expected or forwardlooking numbers. According to Markowitz
(1952):
• “The first stage starts with observations and
experience and ends with beliefs about the
future performance of available securities.”
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• “These procedures, I believe, should combine statistical techniques and the judgment
of practical men. My feeling is that the
statistical computations should be used to
arrive at a tentative set of µi and sij [returns
and variances-covariances]. Judgment should
then be used… on the basis of factors or
nuances not taken into account by the formal
computations.”
– Related to the second quote, current market valuations should be considered in the revisions.
Thus, valuation is an essential component of
the optimization process. Overvalued assets will,
thus, have smaller allocations.
– When the judgments of practical men and/or
valuations change, the input data, which are
expected values, in the optimization should also
change.
– Strategic re-optimizations should be conducted,
perhaps annually.
Overall, with regard to the MPT model and
the data inputs, the author believes that little
has been learned. The author believes, however, that the importance of data implementation
techniques should be appreciated. The importance of specifying the MPT inputs adds to the
responsibility of the portfolio managers relative to
mechanically using historical data. These ideal practices are consistent with the approach originally
proposed by Markowitz. Not all portfolio managers, however, have followed this approach. The
fault is, thus, with the portfolio managers, not
MPT.
2.3 Portfolio dynamics
2.3.1 Contagion
Contagion is a flight from risky assets to less risky
assets during times of significant market declines.
During contagion, correlations among the risky
assets will trend toward one, and the returns of
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LESSONS ON INVESTMENT MANAGEMENT FROM THE GLOBAL RECESSION
all risky assets will decline together. Contagion
should be anticipated, based on previous experiences, during periods of significant market declines.
Contagion occurred during the 1997 Thai baht crisis, again very severely in 2008 as shown in Figure 1,
and during other periods. Contagion is a common
criticism of MPT. Prepare for contagion events in
two ways.
(i) Portfolio allocation
To reduce the effects of contagion, increase the
allocation to Treasury and other high-grade bonds
as illustrated in Figure 1. This results in a more
liquid portfolio. This issue is discussed again
below.
Consider another approach based on recent
research.
(ii) Current quantitative methods—contagion
Chua et al. (2009) have found that the returns of
some asset pairs unify (move in the same direction)
during severe market declines and decouple (move
in opposite directions) during market increases, an
undesirable combination.4 Other asset pairs exhibit
the opposite and ideal combination. For example, while the relative value arbitrage strategy has
a downside correlation (when the U.S. stock market declines) with the U.S. stock market of 65.76
and an upside correlation (when the U.S. stock
market increases) of −30.78, an undesirable relationship. On the other hand, convertible arbitrage
has a −24.96 downside correlation and 6.69 upside
correlation with the U.S. stock market, an ideal
relationship. As a benchmark, world-ex U.S. equities have a 53.59 downside correlation, and −4.26
upside correlation with the U.S. stock market, a
mild form of contagion.
Chua et al. have developed a full-scale optimization
model for developing portfolios which are less subject to the negative influences of contagion by using
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selected asset pairs. The utilization of this model
should be explored.
2.3.2 Rebalancing
MPT is often called a “Buy and Hold (B&H)” strategy. It is not, however, necessarily a B&H strategy;
most applications of B&H involve portfolio rebalancing. The risks of B&H strategies, that is without
rebalancing, increase significantly over time. For
example, according to Ibbotson, a 50% stock/50%
bond portfolio formed in 1926 and rebalanced
would have still had a 50%/50% allocation by the
end of 2008 (obviously) with a standard deviation
of 11.5% over the period. Without rebalancing it
would have had a 95.7%/4.3% allocation at the end
of 2008 and a standard deviation of 16.0% over the
period, a much higher risk. Portfolio rebalancing
to a fixed mix is used to manage risk (and perhaps
increase return since it is a contrarian buy low/sell
high strategy).
As discussed above, the typical application of MPT
is to develop a policy (strategic) portfolio via MPT
and in addition rebalance via TAA when the tactical
bands are reached. Such rebalancing represents a
TAA strategy, usually quantitatively, relative to the
strategic portfolio.
Recently, Kirtzman et al. (2009) have developed a
model for optimal rebalancing and have developed a
quadratic heuristic which is scalable to several hundred assets. This method provides results which are
very close to the superior dynamic programming
method which can, however, be scaled only to a
few assets. They also explore the use of derivatives
to minimize transactions costs. This model represents a significant improvement in rebalancing
techniques.5
The author’s conclusion is that tactical rebalancing
around the strategic portfolio with fixed portfolio composition bands (not at fixed times, which
is an inferior approach) should be employed and
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FRANK J. JONES
transacted on a purely quantitative basis (to avert
emotional market-timing decisions).
2.4 Asset allocation issues
2.4.1 Stock/bond allocation
A major asset allocation decision is the ideal
stock/bond mix, which relates to the magnitude
of the prospective equity risk premium (ERP). The
ERP is the incremental return for bearing equity
risk, that is the difference between expected stock
and bond returns. While expected returns should
be used to determine the relevant ERP, they are
unknown and so historical returns are usually used.
Obviously, the greater the ERP, the greater the allocation to equities in a stock/bond portfolio. The
common calculation of the risk premium is based on
Ibbotson data. From 1926–2008, large cap stocks
had a return of 11.7% and long-term U.S. Treasuries a return of 6.1%.6 Thus, the risk premium
over the last 82 years has been 5.6%. These data
are most likely the basis for the common belief that
stock returns have outperformed bond returns by
5% over the last several decades.
It is also commonly asserted that if stocks are
held long enough, perhaps 10 years, they will
outperform bonds. The level of the equity risk premium has been one of the most controversial topics
in finance (along, perhaps, with the efficient market hypothesis). Many skeptics believe that 5–6%
is an unreasonably high and unsustainable risk premium. Behavioral economists assert that it reflects
a very high degree of risk aversion by investors.
Recent stock market performance, however, particularly the bear markets of 2000–2002 and 2007–
2009 have provided sharply lower ERPs and have
challenged the above generalizations. As of June 30,
2009, U.S. stocks have underperformed long-term
Treasury bonds for the past 5, 10, 20, and 25 years,
that is there has been a negative ERP over these
periods.
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A recent article by Arnott focused on stock versus
bond returns. Among Arnott’s findings are7 :
– over the 1802–2009 time period, stocks underperformed bonds from 1803 to 1871 (68 years);
from 1929 to 1949 (20 years); and from 1968 to
2009 (41 years);
– these stock/bond data over the 1802–2009
period indicate a 2.5% equity risk premium; and
– based on recent data, over the last 10, 20, and
40 years, Treasury bonds have outperformed the
broad stock market.
While there may be some reservations with these
data, they unequivocally make one less comfortable with a large stock holding on a buy and hold
basis.
Ibbotson’s observation is that indeed stocks have
outperformed bonds over the last 40 years.8 But the
ERP has declined because even though stocks have
performed approximately the same as over the entire
1926–2008 period, bonds have performed better
over the last 40 years. Bonds have performed better
because bond yields were very high during the 1970s
due to inflation and have declined significantly since
1980. Such a significant continuing decline in bond
yields is extremely unlikely, if not impossible, given
the current low-bond yields. Thus, if stock returns
revert to their long-term levels, the ERP should
again increase.
The future level of the ERP is a very controversial
question. Will the recent (at least 25 years) relationship prevail and stocks continue to underperform
with an ERP of zero or negative? Or do we currently witness a great buying opportunity for stocks
as the long-run risk differential from 1926 to 2008
based on Ibbotson continues and the recent differential reverts to this previous level? These levels may
provide outer bands for the future. On a conceptual basis, however, it is reasonable to believe that
stocks will remain riskier than bonds and that the
equity risk premium will not be negative or zero.
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LESSONS ON INVESTMENT MANAGEMENT FROM THE GLOBAL RECESSION
The author believes the ERP will be in the 3–4%
range, again significantly above zero.
One lesson learned from the recent experience,
however, is that it is not a certainty that stocks will
outperform bonds over moderate periods of time,
for example 10 or 20 years.
At a minimum, this discussion induces an investor
to reconsider the stock and bond returns and
risk inputs they enter into their optimizer, which
determine their stock/bond mix. The author’s
view of the ERP is consistent with a somewhat
increased bond allocation. The value of high-quality
bonds during times of contagion, illiquidity, and
extreme events, as discussed below, supports this
view.
2.4.2 Tactical asset allocation
Extreme market moves, both up and down, have
increased interest in occasional significant asset reallocations between stocks and bonds based on a qualitative tactical asset allocation basis. Some investors
are reluctant to conduct reallocations because they
believe that the market is efficient. Others, however,
assert that occasionally the markets become significantly overvalued or undervalued and on these
occasions reallocations should be made.
Robert Shiller developed the concept that while
the markets are micro efficient, that is efficient
with respect to individual securities, they are macro
inefficient, that is, can become overvalued or undervalued with respect to broad asset classes. These
views do not represent a recent heresy. Consider
the following.
Paul Samuelson stated:
“Modern markets show considerable micro efficiency… In
no contradiction to the previous sentence, I had hypothesized
considerable macro inefficiency, in the sense of long waves in
the time series of aggregate indexes of security prices below
and above various definitions of fundamental values.”9
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Consistently,
“Jung and Shiller interpret their results as “confirming the
Samuelson dictum… There is no evidence of macro efficiency.” But the case for micro-efficiency—the Efficient
Market Hypothesis—emerges unscathed.”10
In retrospect, the stock market was overvalued during the tech stock bubble which ended in early
2000. But a common observation in this regard was
that bubbles become only evident while they burst,
not while they are ongoing. Investors want to stay
in the market as long as it is going up. Nevertheless,
attempts to respond to bubbles introduce the concepts of valuation and macro market inefficiency
into asset allocation analysis.
Jeremy Grantham has recently effectively emphasized the importance of responding to market
bubbles or overvaluations. Grantham reviewed
32 bubbles including the South Sea bubble, the
Japanese buildup to the Lost Decade of the 1990s
and the two recent U.S. stock market bubbles, and
asserts that they were all obvious. “And out of the
32, 32 have gone all the way back down—and
the average time to go back down is half a year
faster than they went up.”11 Grantham introduces
some behavioral explanations for investment managers’ reluctance to acknowledge bubbles: “Keynes
explained it all in 1936… ‘Never be wrong on
your own.’ The definition of a prudent banker is
to go bust with all of the other bankers—a perfect
demonstration of what we are seeing today.”12
Grantham also says with respect to the classic bubbles, “These are the things that matter (selling at
the top of a bubble). The rest of the time, show
up for work and keep your nose clean—but you
might want to cash in some career chips when you
see one of these things.”13 As a segue to Section 2.5
(Extreme Events) consider “And Mandelbrot wrote
that, ‘the whole world is missing the extraordinary
importance of a few outliers.’ ”14 Grantham is also
obviously very critical of the macro efficiency of the
market.
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FRANK J. JONES
Grantham’s view is that assets experiencing a bubble should be “sold at the top.” Of course, this
view begs the question of what is the top. But the
MPT approach with quantitative rebalancing provides two other mechanisms to a bubble with the
same directional outcomes. Once valuation is introduced into the data inputs into MPT, the increased
valuation would reduce the allocation to the asset
experiencing the bubble. Second, the quantitative
TAA rebalancing would also reduce that allocation
of the asset when the price of the asset exceeded the
TAA bands. Thus, MPT with TAA rebalancing provides a more quantitative and perhaps more gradual
way to respond to bubbles, with the same effect of
reducing the allocation to the asset experiencing the
bubble. These mechanisms also tend to stabilize the
market due to selling before the highs.
An opposite approach to a developing bubble, however, could be that once it is accepted that the market
is macro inefficient, informed investors may decide
to ride the trend rather than fight it when the market
becomes overpriced. They, thus, become momentum investors and plan to exit the market before the
top. Such strategies tend to contribute to bubbles
and destabilize the markets rather than stabilize the
markets. Finding the top of the market, however, is
very difficult and risky.
The choice between assuming a mean reversion scenario or a momentum scenario influences whether
to use TAA or DAA (dynamic asset allocation)
for rebalancing. In addition, if using TAA, which
assumption is used influences the magnitude of
the rebalancing bands (the greater the momentum influence, the wider the bands). Consider the
following quote from Bhansali:
“Confusing mean-reversion, which works over cycles, with
momentum, which works over secular intervals, in such an
environment is a guarantee for loss of portfolio wealth. No
degree of timing and forecasting ability would mitigate getting this characteristic wrong, especially when the markets are
volatile.”15
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Overall, the author prefers the continuous and
quantitative application of MPT based on annual
returns. In addition, for rebalancing, the author
prefers a TAA strategy with fairly wide bands
executed on a quantitative basis (to avoid emotionbased, fear-greed decisions).
2.5 Extreme events
2.5.1 The basics
Most securities research and practice assumes that
security returns exhibit a Gaussian (normal) distribution around the mean return. According to
the normal distribution, for example, approximately 95% of the returns are within two standard
deviations (SDs) of the mean. The outlying 5%,
respectively, are called “tails.” It is the lower tails
(one-half of the above numbers) that provide the
probability of the extreme losses, which are of concern to investors. Considerable research, however,
has shown that the actual tails of stock returns
are greater than these normal distribution values
indicate. Statisticians call this property “leptokurtic;” others call it “fat tails” or extreme returns.
Another name, “black swan,” has become common.
Regardless of the name, extreme security returns are
much more frequent than the normal distribution
suggests.
Consider the following by Eugene Fama:
“Half of my 1964 Ph.D thesis is tests of market efficiency,
and the other half is a detailed examination of the distribution of stock returns. Mandelbrot is right. The distribution
is fat-tailed relative to the normal distribution. In other
words, extreme returns occur much more often than would
be expected if returns were normal. …For other applications,
however, the difference can be critical. Risk management by
financial institutions is a good example. …The normality
assumption is also likely to be a serious problem in various
kinds of derivatives, where lots of the price is due to the probability of extreme events. For example, news story accounts
suggest that AIG blew up because its risk model for credit
default swaps did not properly account for outlier events.”16
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LESSONS ON INVESTMENT MANAGEMENT FROM THE GLOBAL RECESSION
Outliers, unlikely events, or extreme events in the
financial markets have recently become the subject
of considerable interest.
The Black Swan by Nassim Nicholas Taleb on
extreme events has captured much of this interest. This subsection is based on Taleb’s book.17
Taleb, to describe the black swan effect, distinguishes between scalable and non-scalable probability distributions. In a scalable distribution, the
probabilities drop at a constant rate as values move
farther from the mean. In a non-scalable distribution (the Gaussian distribution is an example), the
probabilities decline at a progressively faster rate as
the values move farther from the mean. It is as if in
a non-scalable distribution the probabilities face a
headwind as the values move farther from the mean
and for a scalable distribution there is no headwind. Thus, outliers, or extreme events, are much
more likely with a scalable distribution than with a
non-scalable distribution.
Consider the example in Figure 2 for the European
wealth distribution.18 Three distributions are provided, two scalable (A and B) and one non-scalable
(C). Scalable distributions (called Mandelbrotian
after Benoit Mandelbrot) follow power laws. To
completely define the power law, the exponent,
called the power, must be specified, as illustrated in
this example. In the first scalable distribution, (A),
in Figure 2, the power is two, that is if wealth doubles, the odds decline by four (are one-fourth the
previous amount). In the second, (B), the power is
one, that is if wealth doubles, the odds decline by
two (are one-half the previous amount).
All three cases in Figure 2 begin with 1 out of
63 people having wealth greater than 1 MM .
In all three, of course, there is a decline in the
proportion that have progressively greater wealth.
In (C), however, the proportions decrease at a
progressively greater rate (called non-scalable), that
is there are very few extreme wealth holders. Only
1 in 16 × 1033 has wealth over 8 MM . These
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numbers are based on a non-scalable Gaussian
distribution.
In both (A) and (B), however, the proportions
decrease at a constant rate (are scalable):
– in (A) decreasing fourfold for every doubling of
wealth. This example has a power exponent of
two. So, only 1 in 4,000 has wealth over 8 MM
; and
– in (B) decreasing twofold for every doubling of
wealth. This example has a power exponent of
one. So, 1 in 500 has wealth over 8 MM .
So there are many more wealthy people in (B) than
in (A), that is a larger inequality of wealth.
In the scalable examples, there are many more very
wealthy people (extreme cases) than in the nonscalable example. And in the scalable examples,
there are more extreme cases the lower the power
exponent. Overall, the non-scalable Gaussian distribution has a much smaller tail than scalable
Mandelbrotian distributions. In the case of security
returns, a security whose returns have a scalable distribution have fatter tails, or more extreme values,
than with a Gaussian distribution.
For example, compare further the scalable (B)
and the non-scalable (C) distributions in Figure 2.
Both have a 1 in 63 probability of a net worth
of 1 MM . If it was assumed the distribution
was Gaussian, there would be a 1 in 127,000 of
exceeding 2 MM. If the actual distribution was scalable with a power of one, the tail above 2 MM
would be much greater (1 in 125) than assumed
in the Gaussian distribution. Thus, if a Gaussian distribution was assumed and two or three
SDs used for the calculation and the actual distribution was a scalable distribution, the outcome
would be much less certain than the 95% or 99%
confidence intervals, respectively, would suggest.
One is given a false sense of confidence by assuming a Gaussian distribution in a scalable world.
Another application of this concept is setting the
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FRANK J. JONES
Wealth distributions
People with a net
worth higher than:
1 MM Euros ( )
2 MM
3 MM
4 MM
8 MM
16 MM
32 MM
320 MM
640 MM
Comment:
(A)
Scalable—moderate
inequities
(B)
Scalable—large
inequities
(C)
Non-scalable (Gaussian)
(small inequities)
1 in 62.5
1 in 250
—
1 in 1000
1 in 4000
1 in 16,000
1 in 64,000
1 in 1,280,000
—
When you double the
initial amount, you
decrease the incidence
fourfold (i.e., one-fourth
the incidence), no matter
what the initial level. No
headwind.
1 in 63
1 in 125
—
1 in 250
1 in 500
1 in 1000
1 in 2000
1 in 20,000
1 in 40,000
When you double the
initial amount, you
decrease the incidence
twofold (i.e., one-half
the incidence), no
matter what the initial
level. No headwind.
1 in 63
1 in 127,000
1 in 14 × 109
1 in 886 × 1015
1 in 16 × 1033
Non calculable
Speed of Decrease Remains Constant
Power (of Power Law)
Comment (Taleb)
Two
One
Extremistan—aggregate can be affected by a
single observation.
Face a headwind
Speed of Decrease Increases
—
Mediocristan—
dominated by the
mediocre; no single
observation can affect the
aggregate.
Figure 2 18
bands on a quantitative TAA rebalancing. These
bands should be wider for a security with a scalable distribution than with a Gaussian distribution.
Scalable distributions provide a conceptual framework for distributions other than the Gaussian
distribution and, thus, for understanding extreme
events.
The distributions of closed form distributions, such
as the Gaussian distribution and scalable distributions with specified exponents, have defined
JOURNAL OF INVESTMENT MANAGEMENT
tails. Simulations, however, such as Monte Carlo
simulations, can incorporate other tails. The Financial Engines financial planning tool assigns higher
probabilities to extreme events than the normal
distribution. Morningstar, in its asset allocation
software, offers clients a fat-tailed distribution as
an alternative to a normal distribution. In addition,
Moshe Milevsky of York University provides a calculation which Monte Carlo simulations can use
to show a retirement plan’s vulnerability to extreme
events.19
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LESSONS ON INVESTMENT MANAGEMENT FROM THE GLOBAL RECESSION
Taleb (2007) practices what he preaches and the
results are what would be expected. In a fund he
advises, over 90% of the assets are in cash or Treasuries. The remainder is in long deep OOM (outof-the-money) puts on stock indexes and stocks.
Such a strategy should deliver a series of mediocre
returns and an occasional great year. And it has. One
such fund was closed in 2004 after several years of
low returns associated with a period of low volatility. During 2008, however, the returns on others of
his funds were spectacular. In 2008, the returns on
versions of these funds were up in a range of plus
65–115%.20,21 Taleb asserts that he has been profitable only three times, the crash of 1987, the dot
com bust, and the current episode.
2.5.2 Hedging extreme events
Hedging is equivalent to buying insurance. A black
swan event is a catastrophic event. Thus, hedging
black swan events is equivalent to buying catastrophic insurance. Selling insurance is essentially
selling (a short) put option and buying insurance,
essentially buying (a long) put option. Thus, buying insurance against an unlikely black swan event
is essentially buying a long deep OOM put option.
In general, deep OOM options are cheap. So hedging black swan events should be cheap. Of course, if
a black swan event is imminent or underway, such
hedging will be much more expensive just as fire
insurance is very expensive if you can see the flames.
Standard options models, such as Black–Scholes,
do not assume fat tails (they are based on a
Gaussian distribution) and so deep OOM options
would be underpriced, a bargain for hedgers (buyers of options) if the environment was scalable.
But market makers of OTC options undoubtedly
increase the premiums of deep OOM options based
on assessments of extreme events because market
makers are usually on the short side and, thus, collect premiums. The same undoubtedly occurs for
exchange-traded options although the availability
FIRST QUARTER 2010
11
of long, deep OOM options are limited. The probabilities of extreme events are not easily calculable
and so the calculated option prices or hedging costs
cannot be very precise. It, thus, induces sellers of
options, to price their options based on the relevant
distribution. For example, it should be priced based
on a scalable distribution if it has a fat tail relative
to a normal distribution.
Consider three types of hedges of extreme events
suggested by Bhansali.22 The first would be to
develop a portfolio of short-term and/or long-term
Treasuries, since they gain during extreme events.
The “cost” of this hedge would be the difference in
the expected return of the overall portfolio and the
Treasury, an opportunity cost.
The second type is to buy OOM put options on a
portfolio of securities (such as on an ETF on the
world stock portfolio). The cost of this put is an
explicit cost. As with all types of insurance, the best
time to buy it is when it is not needed.
The third type of hedge is to invest in strategies that are negatively correlated to tail risk. The
CBOE Volatility Index (VIX) is a tail-risk indicator and there are options on the VIX. In addition,
managed futures strategies (including mutual funds
and ETFs) are positively correlated to the VIX.23
In general, trend-following strategies behave like a
long position in look-back straddles and so are, in
effect, long tail risk.24
In a long bear market, dynamic asset allocation
(DAA), also called portfolio insurance, might provide an effective hedge. Bhansali, however, appropriately does not engage in such hedging since it
requires liquidity to be available during a crisis. Liquidity typically disappears during crises as it did in
1987 and is discussed below.25
Bhansali (along with two PIMCO associates) implements these tail-risk hedging strategies in PIMCO’s
Global Multi-Asset mutual fund. Bhansali argues
that the often assumed “reverting to the mean”
JOURNAL OF INVESTMENT MANAGEMENT
12
FRANK J. JONES
strategies (in which TAA is appropriate) do not
always occur; but rather disorderly momentum
events frequently occur (as has been the case
recently), in which DAA is appropriate, as discussed
initially above. He observed that there have been
seven shocks occurring every 5–7 years over the last
30 years. According to Bhansali, “While the origins
of financial crises can be very hard to predict, they all
tend to have similar macro consequences. For macro
hedges to be successful, we do not need to correctly
predict exactly which tail events will happen. We
simply need to predict against the range of responses
to those events.26 For this reason, the fund employs
a permanent “just-in-case” risk strategy rather than
a tactically executed “just-in-time” risk strategy.
The hedges employed by this fund are those discussed above: purchasing short-term Eurodollar
futures or Treasuries; deep OOM options on credit
indexes; managed futures style strategies; or reducing portfolio risk when the market is not offering
attractive valuations. PIMCO estimates that the
cost of these tail-hedging strategies is approximately
25–50 basis points.27
There are several lessons learned from a consideration of extreme events. First, it is widely understood that extreme events may be more likely than
indicated by a Gaussian distribution. Second, it is
also now accepted that the stock market may be
described by a scalable Mandelbrotian distribution
rather than a Gaussian distribution. Thus, the market’s risk may exceed the investor’s risk tolerance
if the investor anticipates a Gaussian market and
realizes a Mandelbrotian market. This discrepancy
should be considered in constructing a portfolio
to be consistent with an investor’s risk tolerance.
Third, extreme events are likely to occur due to illiquidity, risk aversion, and leverage. Fourth, options
priced off an assumed Mandelbrotian distribution
will be more expensive than if priced off an assumed
Gaussian distribution. Finally, confidence intervals
for any investment decision will be inaccurately
JOURNAL OF INVESTMENT MANAGEMENT
small if a Gaussian distribution is assumed in a
non-scalable environment.
As discussed, tail risk can be hedged, either by incurring an actual cost by using options or an opportunity cost by modifying the portfolio. The author
prefers the latter approach, specifically an increase
in the Treasury portfolio, which, as discussed, also
has other advantages.
The author, however, is not as extreme in his
approach to extreme events as Taleb is in the
following comment:
“This implies the need to use the extreme event as a starting
point and not treat it as an exception to be pushed under the
rug.”28
After all, extreme events occur infrequently and a
portfolio manager has a portfolio to manage at all
times.
Other issues in preparing for extreme events
• Use CBOE Volatility Index (VIX) as a tail-risk
indicator.
• Consider tail-risk hedging strategies:
– Treasuries
♣ Use intermediate-term Treasuries; and
♣ Use TIPS for inflation protection also.
– Long deep OOM puts on global stock indexes;
and
– Use futures or options on VIX or managed
futures strategies.
• Since the return distributions of the securities
markets are leptokurtic relative to the Gaussian distribution, consider this deviation from
normality in:
– risk tolerance determinations for investor asset
allocation decisions;
– confidence intervals for significance conclusions; and
– rebalancing bands in quantitative TAA.
FIRST QUARTER 2010
LESSONS ON INVESTMENT MANAGEMENT FROM THE GLOBAL RECESSION
• Consider the costs of hedging (explicit and
opportunity):
– Hedging costs increase as need for and imminence of extreme crises increases (monitor the
VIX); and
– Employ a “just-in-case” rather than “just-intime” hedging strategy—market timing in this
regard is difficult, even with monitoring VIX.
2.6 Liquidity
During 2003–2006 short-term interest rates (as
measured by the Fed funds rate) and the volatility in the stock market (as measured by the VIX
index) were very low and liquidity was abundant.
Given this environment, many investors, particularly endowment funds, swapped liquidity for
return. As a result, the extreme events of 2007–
2009 created a liquidity crisis and the freezing of
the credit markets.
Liquidity is central to many of the recent phenomena. Illiquidity and risk aversion are the core causes
of extreme events and contagion. Liquidity and
extreme events are codependent (Hill, 2009).29
U.S. Treasuries are the core of United States—
and global—liquidity. The Treasury component of
Barclay’s Aggregate Bond Index (which represents
the taxable, investment-grade U.S. bond market) is
approximately 25%.
Very few investment managers have 25% of their
fixed income portfolios in Treasuries, thus having
swapped liquidity for return. Major Ivy League and
other universities developed portfolios significantly
skewed toward private equity, hedge funds, real
assets, commercial real estate, and commodities, as
shown in Figure 3, which essentially attempted to
capture the liquidity premium. This is commonly
called the “Yale model.”
David Swensen, head of the Yale endowment,
recently said “diversification isn’t going to help you
FIRST QUARTER 2010
13
Endowment Portfolios
Asset
Classes
Domestic
equity
Bonds
Foreign equity
Hedge Funds
Private equity
Real assetsa
Cash
Avg. Educ.
Harvard Yale Princeton Endowment
(%)
(%) (%)
(%)
11
10
7
22
11
22
18
13
26
−3
4
15
25
20
29
−4
2
12
24
29
23
2
12
20
22
9
14
2
Figure 3 30
a Real
Estate, timber, oil and gas.
Source: Bary, Andrew. “The Big Squeeze.” Barron’s, June
29, 2009, pp. 20–22.
in the midst of a financial crisis, or at least the type
of diversification that you see in institutional portfolios like Yale’s.” He added, “I’m not sure that the
crisis has caused us to conclude that we would do
things differently, but it certainly highlighted the
importance of liquidity.”31
The author’s conclusion is that investment managers should more closely manage their liquidity
positions to hedge periods of extreme events and
contagion and, thus, somewhat increase the portion of Treasuries in their bond portfolios to closer
to 25%. This shift will represent an opportunity
cost to their portfolios.
2.7 Role of independent research and due diligence
The episodes relating to the Bernard L. Madoff
funds and AAA Subprime Mortgage investments
demonstrated that investors cannot rely on the
advice of others, that is “caveat emptor.” In both
cases, the basic “smell test” should have been
enough. With the Madoff funds, the evidence
included: high and stable returns in a low and
JOURNAL OF INVESTMENT MANAGEMENT
14
FRANK J. JONES
volatile return environment; required options trading volume with an options strategy equal to the
entire options market volume; internal custody;
essentially internal accounting; internal reporting;
etc.
Without doing the math—which the rating agencies did not seem to do correctly—high returns from
combining subprime mortgages into AAA securities during a very weak housing market does not
seem realistic. The volume traded globally in such
securities was incredibly large.
The lesson here is for investors to be skeptical and
to apply their own reasoning (the “smell test”) and
research. Many astute investors did consider and
avoid both of these investments.
2.8 Risk tolerance (RT)
The RT of an individual or its institution represents
its capacity to bear risk. Ideally, RT is a metric which changes only with an investor’s personal
circumstances, not with the market levels.
One of the many ways to consider RT is to divide
it into three components. First is Capacity, which
is a measure of the investors’ financial capacity to
bear risk, which is its assets relative to its liabilities.
This component can be determined from data and
is quantitative. It is also typically quite stable. The
second component is Attitude, which includes characteristics such as ability to stay invested in a down
market; and what their expected payoff would need
to be to make an even bet. Attitude is subjective
but is also quite stable. The third component is Perception, which refers to the individual’s knowledge
of and view of the markets. Is the market likely to
decline soon and are they planning to liquidate their
portfolio if it does? Perception is subjective and is
subject to behavioral limitations such as overconfidence; anchoring; recency; familiarity of data; etc.
Unlike Capacity and Attitude, Perception may be
quite variable and tends to be high when the market
JOURNAL OF INVESTMENT MANAGEMENT
is high and low when the market is low.32 This tends
to cause emotionally-based buying at the top and
selling at the bottom which leads to investment
underperformance. Dalbar data demonstrate that
investors in a fund consistently underperform the
fund itself due to bad market timing, as discussed
above.
Consider the following result.
Similarly, Grable notes that prior research indicated that risk
tolerance was fixed, but more research questions that axiom.
He conducted a study several years ago that found that a person’s risk tolerance lags the stock market by about two weeks.
“So if the market is up today then drops dramatically, and I
come back and measure the same person using the same scale,
risk tolerance will actually decline. Are we influenced by the
environment? Definitely.”33 (McCathy, 2009)
Such emotional buy high/sell low behavior was
common during the latter part of the market decline
from October 9, 2007 until March 9, 2009, when
many investors liquidated their stocks just before
the market bottom. Financial advisors undoubtedly
spent more time with clients providing emotional
counseling than discussing asset allocation during
this period. Fundamentally, RT should change only
for strategic reasons (called “inflection points”) such
as losing a job, receiving an inheritance, etc., and
not follow the market according to a fear-greed
investment cycle.
Consider two other comments about RT. First, an
investor’s RT, particularly their Attitude and Perception, may be investigated via simulated stress
tests. Second, high volatility in the markets, perhaps as measured by VIX, may make the risk of the
investor’s portfolio exceed their RT. The portfolio’s
volatility could be, perhaps temporarily, reduced by
shifting moderately from stocks to bonds, perhaps
with derivatives to conserve execution costs.
What important lessons are learned in this regard?
First, develop a portfolio whose risk is consistent
with your own risk tolerance after considering the
possibility of extreme events. Second, recognize our
FIRST QUARTER 2010
LESSONS ON INVESTMENT MANAGEMENT FROM THE GLOBAL RECESSION
natural emotionally-based buy high/sell low inclinations and how counterproductive they can be.
Then resist these natural but negative inclinations
either alone or with external advice.
2.9 Quantitative models and qualitative
approaches
2.9.1 Discussion
The recent crisis has also provoked the author to
reconsider the relative values of quantitative models
versus qualitative thinking. Quantitative modeling
requires a correct model, relevant data, and even,
as we have seen, the correct distributions of input
data.
Martin Leibowitz uses the expression “dragon risks”
(“taken from ancient mythology in which people
believed that the earth was flat and feared that
‘there be dragons’ in the spaces beyond”) to refer to
“beyond-model” risks—risks whose precise nature
and structure are unknown.34 Some analysts insert
“T.B.D.” at the ends of their probability distributions to indicate that “there be dragons” in these
tails.
A good example of overall risk management and
a qualitative input is recounted in Nocera.35 During December, 2006 Goldman Sachs’ risk models
signaled a problem in their mortgage-backed securities (MBS) activities for several days in a row. As a
result, David Viniar, their CFO, convened a meeting at which they concluded that they should reduce
their MBS portfolio. As a result, during the summer
of 2007, Goldman avoided the losses experienced
by many other investment and commercial banks.
Nocera queries whether this was an example of the
futility of risk modeling or its utility? “Or did it suggest that the individuals at Goldman acted wisely
by putting their models aside and making ‘decisions on more subjective degrees of belief about
an uncertain future,’ as Peter L. Bernstein said in
‘Against the Gods?’ ”36 As Nocera concludes, “It
FIRST QUARTER 2010
15
wasn’t just the math that helped Goldman sidestep
the early decline of mortgage-backed instruments.
But it wasn’t just judgment either. It was both. The
problem on Wall Street at the end of the housing
bubble is that all judgment was cast aside. The math
alone was never going to be enough.”37 Model risk
is likely to be much greater when the input variables
have scalable rather than non-scalable distribution.
In this spirit, consider the observations from three
noted investment professionals on a subjective,
qualitative approach.
2.9.2 Observations by three investment
professionals
A. Peter L. Bernstein38
“In 1970, Mr. Bernstein wrote: “We simply do not know what
the future holds.” Over the ensuing decades, he returned again
and again to that phrase in his speeches, articles and books,
because he felt it captured the central truth about investing.
Asked in 2004 to name the most important lesson he had to
unlearn, he said: “That I knew what the future held, that you
can figure this thing out. I’ve become increasingly humble
about it over time and comfortable with that. You have to
understand that being wrong is part of the investing process.”
In 1974, as Wall Street was suffering its worst market decline
since 1929, Mr. Bernstein cofounded the Journal of Portfolio
Management to improve risk management with insights from
academic research.
His introduction to the maiden issue reads as if it were written
yesterday: ‘How could so many have failed to see that all the
known parameters were bursting apart? …It was precisely our
massive inputs and intimate intercommunication that made
it impossible for most of us to get to the exits before it was
too late.”’
B. Mark Kritzman39
“Our goal is not to develop active trading strategies; therefore,
we do not try to predict regime shifts. Instead we focus on
strategic asset allocation and argue that portfolios should be
modeled after airplanes; which is to withstand turbulence
whenever it arises because it is usually unpredictable. Strategic investors, such as pension plans, are just like airline pilots:
their goal is not to predict the unpredictable, but they want
their portfolio to weather the storms.”
JOURNAL OF INVESTMENT MANAGEMENT
16
FRANK J. JONES
C. William Sharpe40
Sharpe is concerned that too many practitioners—and a large
number of the business school professors from whom they
learned their trade—tend to forget that all asset pricing models are about expectations. And how in the world can you
measure expectations, which are a look forward, not backward? You cannot just look at history and deduce much about
what expectations have been—or will be. The whole matter
revolves around the future. Therefore, the historical data on
which we all depend so heavily may be useless for asset pricing:
As we never know with certainty what the future holds, all we
have to rely on is a sense of the probabilities of future events.
“You are just reduced to a religious statement,” Sharpe concludes. “I have been around long enough to see empirical
results that seem to be really solid until you try a different
country or different statistical method or different time period.
Maybe that’s why Fisher Black said you should put your trust
only in logic and theory and forget about statistical empirical
results.”
These comments emphasize the uncertainty of
esteemed finance professionals. They are reminiscent of a comment by Charles Darwin in response
to a question about the correlation between intelligence and self-confidence: Darwin said that yes,
there is a correlation between intelligence and
self-confidence; unfortunately, it’s negative.
wealth management activity. The costs of learning
these lessons have been high. Ideally the benefits
will be even higher.
Notes
1
2
3
4
5
6
7
8
9
10
11
2.9.3 Lessons learned
The author’s lessons learned on this topic are:
– Incorporate both quantitative and qualitative
considerations in your analysis; and
– Be Humble—you may have missed something
(“TBD”).
12
13
14
15
3 Overview
This paper has reviewed what the author has learned
from the recent economic and financial crisis and
recent relevant research. In some cases, the author
has also dismissed what have others erroneously
learned. From these lessons, the author has developed specific portfolio management precepts which
are appropriate to the high-net worth individual
JOURNAL OF INVESTMENT MANAGEMENT
16
17
18
19
Journal of Financial Planning, January, 2009, cover,
pp. 20–26.
The Hulbert Financial Digest, May 2008, p. 1. “They
[Investors] become converts to buy-and-hold near market tops, for example, just when the market is about to
turn down and it is easier to beat a buy-and-hold through
market timing. And by the same token, they become
believers in market timing at market bottoms, which is
when they almost certainly would do better by sticking
with a buy-and-hold approach.”
Eversky, Harold, pp. 33–34.
David Chua, Mark Kritzman, and Sebastian Page, “The
Myth of Diversification,” Journal of Portfolio Management,
March 16, 2009.
Kritzman, Mark, Simon Myrgren, and Sebastian Page,
“Optimal Rebalancing: A Scalable Solution,” Journal of
Investment Management, First Quarter, 2009, pp. 9–19.
Ibbotson SBBI Classic Yearbook, Morningstar, p. 32.
Arnott, Robert, “Bonds: Why Bother?”
Ibbotson, Roger, and Peng Chen. “Are Bonds Going to
Outperform Stocks Over the Long Run? Not Likely.”
Peter L. Bernstein, Capital Ideas Evolving, 2007, p. 73.
ibid, p. 73.
Grantham, Mayo, and Van Otteloo’s Jeremy Grantham,
“This Crash Should Have Surprised No One. Great
Crashes Follow Asset Bubbles.” Outstanding Investor
Digest, , March 17, 2009, pp. 1 and 45–55.
ibid, p. 53.
ibid, p. 52.
ibid, p. 55.
Bhansali, Vineer. “Market Crises—Can the Physics
of Phase Transitions and Symmetry Breaking Tell Us
Anything Useful?” p. 9. This article provides an insightful
model which unifies these financial concepts via a model
based on physics.
Fama/French Forum; Q&A: Confidence of the Bell
Curve, March 18, 2009; www.dimensional.com/FamaFrench.
Taleb, Nassim Nicholas. The Black Swan. Random House,
2007.
This example is from The Black Swan, Taleb, pp. 232–233.
“Odds-On Imperfection: Monte Carlo Simulation,”
Eleanor Laise, Wall Street Journal, May 2–3, 2009, p. B1.
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LESSONS ON INVESTMENT MANAGEMENT FROM THE GLOBAL RECESSION
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
“October Pain was Black Swan’ Gain,” Scott Peterson,
Wall Street Journal, November 3, 2008, p. C1.
“The Oracle of Doom,” Robert Langreth, Forbes, February 2, 2009.
Bhansali, Vineer, “Tail Risk Management.” Journal of
Portfolio Management, 2008, pp. 68–75.
ibid, p. 70.
Fung, William, and David Hsieh, “The Risk of Hedge
Fund Strategies: Theory and Evidence from Trend Followers.” The Review of Financial Studies, Vol. 14, No. 2,
2001, pp. 313–341.
Hill, Joanne and Frank J. Jones, Financial Analyst’s Journal,
pp. 29–38.
Morningstar Advisor (4/1/09), p. 3.
ibid, p. 3.
The Black Swan, Nassim Nicholas Taleb, p. xxviii.
Hill, Joanne M. “Liquidity Leverage, and Horizon Uncertainty: Exploring Tail Risk in Investment Management,”
Journal of Portfolio Management, forthcoming.
Bary, Andrew. “The Big Squeeze,” Barron’s, June 29,
2009.
ibid, p. 22.
Kitces, Michael. The Kitces Report, September, 2008.
McCarthy, “Time for Another Look at Client Risk
Tolerance,” Journal of Financial Planning, February, 2009.
Bernstein (2007), pp. 209–210.
“Risk Management—Were the Measures Used to Evaluate
Wall Street Trades Flawed?,” Joe Nocera, New York Times
Magazine, January 4, 2009.
ibid, p. 27.
ibid, p. 50.
Jason Zweig, “Peter L. Bernstein, 1929–2009,” Wall Street
Journal, June 13–14, 2009, p. A14.
Chua, David, Mark Kritzman, and Sebastian Page, “The
Myth of Diversification,” March 16, 2009, Journal of
Portfolio Management, forthcoming.
Capital Ideas Evolving, Peter L. Bernstein, John Wiley &
Sons, Inc., 2007, p. 94.
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Bary, A. (2009). “The Big Squeeze,” Barrons June 29, 20–23.
Bernstein, P. L. (2007). Capital Ideas Evolving, John Wiley &
Sons, Inc.
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FRANK J. JONES
Markowitz, H. (1959). Portfolio Selection: Efficient Diversification of Investments, 2nd ed., New York: Wiley &
Sons.
McCarthy (ed). (2009). “Time for Another Look at Client
Risk Tolerance?” Journal of Financial Planning February,
18–24.
Nocera, J. (2009). “Risk Management,” New York Times
Magazine, 26ff.
Swensen, D. (2009). Pioneering Portfolio Management: An
Unconventional Approach to Institutional Investment. The
Free Press.
Taleb, N.N. (2007). The Black Swan, Random House.
JOURNAL OF INVESTMENT MANAGEMENT
Keywords: Black swan, buy and hold, contagion,
dragon risk, efficient market hypothesis, endowment portfolio, equity risk premium, extreme
events, hedging extreme events, leptokurtic, liquidity, modern portfolio theory, rebalancing, risk tolerance, scalable/nonscalable distributions, tactical
asset allocation, volatility index (VIX).
FIRST QUARTER 2010