Fear, Not Risk, Explains Asset Pricing
Rob Arnott
Edward F. McQuarrie
February 2025
Revised May 2025
Rob Arnott is founding chairman of Research Affiliates, and Edward F. McQuarrie is professor
emeritus at Santa Clara University.
Correspondence: arnott@rallc.com
The authors would like to acknowledge helpful impetus from Jonathan Treussard and to thank
William Bernstein, Ronald Blanken, Cam Harvey, David Hirshleifer, Stephen Foerster, Ken
Levy, Allan Roth, Hersh Shefrin, Robert Shiller, Richard Sylla, Meir Statman, Bryan Taylor, and
Jason Zweig for comments on the manuscript.
1
Abstract
Risk theory has dominated the asset pricing literature since the 1960s. We chronicle empirical
failures of conventional risk theory to explain the return on equities. Aversion to risk presumes
that investors are averse to both upside and downside risk. The former is contrary to human
nature, even if it makes the mathematics of finance relatively simple. We suggest a new
perspective that replaces aversion to variance with fear of missing out (FOMO, captured by a
preference for skew) and fear of loss (FOL, captured by an aversion to semivariance). In so
doing, we propose replacing risk theory with fear theory, in the hope of effecting a long-overdue
marriage of behavioral and neoclassical finance.
2
Risk-based explanations for excess returns, regardless of which risk measures are presumed to
matter, have largely failed in the task of explaining past returns. In what follows, risk refers to
variance. Our particular focus is whether risk has been priced accurately in the market. We probe
whether riskier assets have outperformed and whether any observed outperformance has been
proportional to the risk assumed.
We then explore how a theory based on fear can address the demonstrated shortcomings of
existing theoretical accounts centered on variance risk. Notably, many of the anomalies and
factors that transfixed the academic finance community in recent decades would have been
expected, indeed predicted, by a fear-based framework, in which fear of loss (FOL, an aversion
to semivariance) is paired with fear of missing out (FOMO, a preference for skew). We do not
offer tests for our hypothesis, nor have we explored the daunting mathematics of a model that
favors some risks and disfavors others. Rather, we are urging the finance community to consider
opening a door to a potentially superior path.
Risk as a Scientific Construct
A quarter century ago, David Hirshleifer (2001) imagined how finance theory might have
progressed differently back at the dawn of the modern era in the 1960s:
Picture a school of sociologists at the University of Chicago proposing the Deficient
Markets Hypothesis: that prices inaccurately reflect all available information. A brilliant
Stanford psychologist, call him Bill Blunte, invents the Deranged Anticipation and
Perception Model (or DAPM), in which proxies for market misvaluation are used to
predict security returns. Imagine the euphoria when researchers discovered that these
mispricing proxies (such as book/market, earnings/price, and past returns), and mood
indicators such as amount of sunlight, turned out to be strong predictors of future
returns. At this point, it would seem that the deficient markets hypothesis was the bestconfirmed theory in the social sciences.
Hirshleifer neatly turns on its head the vast body of research on anomalies (Harvey, Liu, and Zhu
2016; Hou, Xue, and Zhang 2020). The development of factors is itself evidence that market
beta, as embodied in the capital asset pricing model (CAPM), is an incomplete measure to link
risk and return. After all, these factors might never have been sought and developed, if market
beta alone sufficed to explain market returns, give or take random error. Even as the anomalies
3
have piled up and factors multiply like bacteria, risk theory has remained dominant. 1 How could
a theory that has been so repeatedly and uniformly contradicted by empirical data continue to be
held out to students and practitioners as the best scientific representation of investor behavior?
A brief detour into philosophy of science may help. 2 Many social scientists follow Karl Popper,
who held that practicing scientists develop bold conjectures in the form of a theory that makes
testable predictions. For example, it might be theorized that the expected performance of any
particular investment can be expressed in terms of its beta on a market factor, with that market
factor in turn representing the excess performance of the risk portfolio against an asset with zero
risk. Once theoretical assertions are formulated, scientific method requires that they be tested
against empirical data. If the data do not comport with what the theory predicts, then the theory
will be said to have been falsified, at which point scientists will eventually let it go and develop a
new conjecture.
Part of Popper’s appeal to empirical social scientists is precisely the idea that any theory that
cannot be falsified with data is not a scientific theory. It may be an interesting idea or an
appealing representation, but it isn’t science if it can’t be tested against data. Indeed, if a theory
cannot ever fail—if no pattern of results on some data set can ever be taken as a rejection of the
theory’s predictions—it is faith, not science. For a Popperian, the persistence of the CAPM,
despite overwhelming evidence of its empirical failure, poses a conundrum. Either CAPM
represents faith, not science, or falsification is not actually a useful account of how the social
sciences proceed. 3
Another philosopher familiar to readers of this journal shows a potential way out. According to
Thomas Kuhn, science is a matter of paradigms rather than directly testable unit theories.
Paradigms are born imperfect, beset by anomalies from the outset. Repeated falsifications
Factor proliferation, sharply criticized by John Cochrane (2011) in his AFA Presidential Address, in which he
coined the term “factor zoo,” came to a near standstill following the publication of “… and the Cross-Section of
Expected Returns” (Harvey, Liu, and Zhu 2016).
1
Here we expand on Arnott (2024) concerning both the nature of scientific method and the role of fear as a driver in
capital market returns.
2
An early reader/advisor of our paper observed that the durability of a variance-based model linking risk and return
may be because it is the “least worst” model available, hence better than nothing. We agree. We think the durability
of CAPM and its variants is also due to its elegant mathematical simplicity. We believe that “least worst” and
mathematical elegance are inadequate reasons to remain wedded to ideas that fare poorly in empirical testing. We
suggest a less passive response than simply rolling with it.
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steadily accrue, but no such falsification, nor any accumulation of same, can ever touch the
paradigm. A paradigm is remote from particular data sets in a way that a Popperian unit theory
can never be. Any reigning paradigm emerged for a reason: It does many things well, in the same
way that CAPM offers an elegant account of all possible investments in terms of a single
underlying concept—non-diversifiable risk or its absence.
Kuhn’s point was that a paradigm is never abandoned simply because it fails some test or series
of tests. Anomalies can accumulate indefinitely. A paradigm is only let go when a new, more
attractive one emerges. In that spirit, we propose the explanatory construct of fear. 4
Investments versus Investors
Sharpe’s (1964) seminal contribution was the introduction of the capital asset pricing model,
which postulates that expected risk is linearly related to expected return. Sharpe was trained in
operations research and naturally focused on quantifiable processes, not human subjectivity. The
very term “asset pricing” serves as a reminder that an asset gets priced based on its objective
characteristics relative to other assets, most notably, its exposure to risk. The market—or, more
accurately, the collective of human investors—simply pairs buyers with sellers, leading asset
prices to settle at a level that is expected to deliver a return consistent with the assets’ expected
risk. By changing the focus from investments to investors, we take the first small step in
reframing finance theory to recognize the centrality of fear. Fear is not an objective characteristic
of assets. Fear is a human response with the power to motivate and guide human action—in this
case the choice of what asset(s) to buy and how to allocate one’s buying (and implicitly, one’s
selling) across assets (Goetzmann, Kim, and Shiller 2024). A critic might correctly observe that
fear is difficult to quantify. This is clearly true, but the same can be said of risk aversion, for
which risk theory created the entirely non-objective gamma.
It is interesting to note how the theory of portfolio choice, developing in parallel, departed from
the path Sharpe took. Work by Merton, Samuelson, and others also made objective measures of
risk, such as standard deviation and covariance, central to investor decisions. However, in this
line of work, it was necessary to go beyond objective measures and add a subjective element,
The promise of brevity prevents any further development of these issues. Stove (2001) is a good place to start and
includes references to the relevant work of Popper, Kuhn, and others.
4
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risk aversion, quantified with the coefficient gamma (ℽ). Only by allowing gamma to vary (and
multiplying sigma by gamma) could the individual investor’s allocation to risky investments be
determined, as in the Merton share. 5
In that same vein, we present fear as a necessary supplement to objective measures of risk when
the task is to explain asset pricing. We make the case by applying a historical lens, tracking how
ineffective traditional objective measures of risk have been in explaining historical variations in
asset returns. The failure of risk and return to line up historically argues the need for some
additional explanatory factor, not unlike the introduction of gamma, to quantify subjective risk
aversion.
Continuing the parallel, we make fear the missing factor. Fear is aversion. But we disentangle the
human response of aversion from the specific target of “risk as variance.” Investors shun that
which they fear. In our telling, investors fear many things, but two types of fear matter above all
else: fear of missing out on outsize gains (skew) and fear of loss (semivariance). We argue that
FOMO is as real and potent as FOL in guiding investor action. Our thinking about FOMO and
skew has been influenced by Harvey and Siddique (2000). A standard utility framework (for
example, reliant on Constant Relative Risk Aversion utility, or CRRA), makes a tacit assumption
that risk aversion includes an aversion to both upside and downside risk. We believe that
aversion to upside risk is contrary to human nature. We often seek upside, but we do not shun it.
We suggest (but cannot prove) that FOMO and FOL largely subsume the risk aversion that
traditional risk theory seeks to model in a standard utility framework. Fear comes in many
flavors, but for investors, FOMO and FOL are the big two, not a symmetric aversion to variance.
In effect, we propose that an aversion to both upside and downside variance should be replaced
with a preference for upside risk and an aversion to downside risk. We believe that a preference
for skew replaces the tacit assumption that investors are averse to upside risk.
We are inviting the academic and practitioner finance communities to explore and develop an
entirely new mathematics of finance, to model aversion to semivariance and a preference for
skew, to replace the comparatively simple quadratic mathematics of aversion to variance. In
As we are only pointing to this literature, not contributing to it, no citations are offered. Rubinstein (2006) provides
a comprehensive intellectual history of these ideas. Haghani and White (2023) provides an accessible introduction to
the Merton share and kindred concepts from the utility literature.
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effect, we are inviting the finance community to move on from the brilliant and path-breaking
work of Markowitz and Sharpe after over 60 years and to recognize that aversion to variance
remains overly simplistic and thus cannot be used to model the asymmetric and sometimes
irrational human emotion of fear.
What about Sharpe’s non-diversifiable risk? Sharpe’s “beta” captures the non-diversifiable
variance, tacitly assuming that investors are averse to non-diversifiable risk and tolerant of
diversifiable risk. Our FOMO and FOL likewise have diversifiable and non-diversifiable
components. While it goes well beyond the scope of our paper, our fear framework might make a
parallel assumption that investors are averse to non-diversifiable semivariance (downside beta)
and have a preference for non-diversifiable positive skew (positive coskew). The mathematics of
FOMO and FOL will be far more daunting than the mathematics of CAPM and the standard
utility framework. While we do not explore that mathematics in this short paper, we think it will
be worth the effort for academe to begin the process.
A fear perspective is rooted in behavioral finance, especially with what has become known as
second-generation behavioral finance (Statman 2019, 2024). Decades of behavioral finance
scholarship have helped to shape our ideas (e.g., Kahneman and Tversky 1979; Shefrin 2002,
2008). We take from Prospect Theory the idea that for the human investor, gains and losses are
fundamentally different creatures which provoke quite distinct responses. 6 These two cannot be
placed on a single scale of utility that has a homogeneous slope throughout. Variance, which
treats upside deviations the same as downside deviations, thus provides a false representation of
how humans price assets. In our telling, fear appropriately distinguishes the prospect of gains
from the prospect of losses in a way that risk theory does not. Likewise, our account is consistent
with narrative economics (Shiller, 2017), which observes that people embrace and respond to
intuitively compelling stories and that these narratives spread quickly, drive crowd behavior, and
move markets. But as we show, our treatment of fear has distinctive elements.
The paper proceeds as follows: After summarizing the case for objective measures of risk as the
explanation for asset pricing, we examine the historical record of stock and bond returns,
6
Indeed, Prospect Theory serves as a direct challenge to risk aversion, as elegantly captured by gamma.
7
chronicling failure after failure of risk alone to explain returns. We then develop our new model
of fear, with its twin focus on FOMO and FOL, and draw out the practical implications.
Insights from History
A familiar folktale runs as follows: Late at night, a passerby encounters a man under a streetlamp
on his hand and knees peering around. Looking up, he asks, “Can you help me find my keys?”
After some minutes of fruitless searching, the passerby asks, “Are you sure you lost your keys
here?” The man replies, “No, I dropped them over in that dark alley, but the light is so much
better here.” 7
From a scientific standpoint, if it were possible to explain asset pricing purely in terms of
objective characteristics of assets (without any reference to a subjective element), such a solution
would be ideal. Risk, in the form of variance, can be measured with a great deal of precision.
With an exact estimate of risk, hypotheses about the relationship between risk and return, itself
measured with equal precision, can be formulated and tested.
But as noted above, the literature on portfolio choice could not make do without introducing a
subjective element: aversion to variance. It was not possible to explain why one investor could
rationally choose a 60/40 allocation and another a 40/60 allocation without invoking a variable
subjective element that came to be known as gamma, the coefficient of risk aversion.
And here is the crucial point: Because aversion is subjective, aversion to risk cannot be observed
or measured directly; it is typically “measured” by survey questions. We infer that one investor
has gamma of 2 and another has gamma of 3 by observing their choices. We discover that
scaling gamma as a single-digit integer makes the equations work and does a good job of
explaining how different portfolios can each be rationally chosen. It all looks easy but presumes
that investors know how averse they are to variance and that a questionnaire can give us an
accurate assessment of this aversion.
Fear theory attempts the same gambit in the explanation of asset pricing. We show that the
historical record is not consistent with an explanation solely in terms of the objective
The tale can be traced back at least 100 years in the US: https://quoteinvestigator.com/2013/04/11/better-light/.
Some accounts source it to the 13th century in the Near East. The wording here is our own.
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characteristic of risk. Fear enters the theoretical framework because risk theory does a mediocre
job of explaining the observed data on asset pricing. It is the dog that did not bark, the
unexplained perturbation in Neptune’s orbit. Whereas risk is one thing, human investors are
afraid of many things. Fear is also inconstant. What was scary yesterday may be desirable today,
and what seems safe today may be frightening tomorrow. FOMO (fear of missing out) is as real
and potent as FOL (fear of loss). 8
The light is surely better with risk, but the keys to asset pricing were lost in the dark alley of fear.
Asset Pricing in History
Under the risk theory of asset pricing, individual assets are priced to reflect their riskiness.
Goetzmann and Ibbotson (2006), in its summary of the equity premium literature, formulates the
risk hypothesis as follows: “The equity risk premium is commonly viewed as the extra return
needed to induce investors to risk their money in the stock market. Economic risk-taking must be
rewarded, or else no rational person would prefer a gamble over a sure thing.”
We note the imperative: “must be rewarded.” That implies an equity premium that is persistent
and well behaved, one that does not repeatedly surge to high levels nor regularly turn into a
deficit. The occasional brief divergence is to be expected because the relationship between risk
and reward is likely to be noisy when empirically observed—the theory concerns expected risk
and expected reward. But a repeated failure for expectations to be met calls into question whether
the relationship between risk and return is as lawful as supposed in the Goetzmann and Ibbotson
account.
This was the problem encountered by Mehra and Prescott (1985). The authors examined US
returns following the Civil War and calculated a reasonable range of risk coefficients for stock
market investors collectively. Taking the historically realized excess return on stocks as a proxy
for the ex ante equity risk premium, 9 they found this excess return to have been out of bounds for
FOMO has been a feature of investor behavior for a long time, with Isaac Newton and the South Sea Bubble a
classic instance. Newton got out with a good profit while the bubble was still inflating but could not bear to stay out
as the stock continued to rise, buying again just in time to lose a large sum when the bubble popped. See Foerster
(2025) for the full story and citations to early mentions of FOMO.
8
Use of historical excess returns as a good proxy for the equity risk premium has fallen out of favor, as described in
L. Siegel (2017). See Arnott and Bernstein (2002) for an early critique.
9
9
any of their estimates of the collective risk coefficient. In other words, the excess return on
stocks has been excessive. 10
If objective characteristics were sufficient to make predictions about return, then we would
expect an empirical link between average observed risks and average observed returns. In what
follows, we give multiple examples of how objective measures of risk fail to explain historical
observations. Sometimes, stocks have done too well, and at other times, not well at all (Shiller
1989). Fear provides an alternative explanation for the magnitude of the excess return realized
historically, namely FOMO.
Fear theory does not dispute that human investors are loss averse. FOL (fear of loss) motivates
many human investment decisions. But fear theory has a broader definition of loss, suggesting
that our fear is directionally sensitive: we fear loss and fear not earning a gain. FOMO (a missed
opportunity) may be just as aversive as FOL (an outright loss of principal), especially when a
bull market fosters boundless optimism. Again, human investors are afraid of many things. For
the human investor, it can be just as scary never to get anywhere as to lose some of what one
already has.
Fear theory is also entirely consonant with bubbles and crashes. Vernon Smith won his Nobel
Prize in part for empirically demonstrating that objectively irrational choices can create bubbles
and crashes, even in market settings in which all participants know that the price is above or
below its fair value. 11 A purely rational homo economicus does not exist.
Equity Returns over the Long Term
In this section, we build on the seminal insight of Mehra and Prescott (1985) and probe further
the expanded historical record that has become available since they wrote. Key to the risk
paradigm is the idea that risk is rewarded in proportion to the risk assumed. As the equity risk
premium literature has it, no rational investor would assume the expected risk of owning stocks
without some reasonable expectation of a commensurate reward.
Rubinstein (2006, pp. 323–24) identifies Mehra and Prescott as a key turning point in the assessment of risk
theory.
10
11
See Smith et al. (1988).
10
For a time, this element of the risk paradigm seemed to have empirical support. In the 1990s,
Jeremy Siegel (1994 and 2022) developed an extended historical record of stock and bond
performance, building on work by Ibbotson and Sinquefield (1976), Cowles (1939), Macaulay
(1938), and Smith and Cole (1935). At that point in the evolution of finance theory, documented
excess returns were believed to provide insight into the expected equity premium, an inherently
future-looking concept. 12 Siegel’s record, anchored in 1802, showed that stocks had relentlessly
outpaced bonds, and that this pattern had held for centuries, consistent with the simple facts that
the stockholders rank lower in the capital structure than bondholders and that a company’s stock
typically has more variance than its bonds.
The relative performance of stocks and bonds from 1802 through 2023 is shown in Figure 1,
variations of which are revisited later in this paper. 13 The impressive performance of stocks is
self-evident, enriching equity owners 45 millionfold (and over one millionfold net of inflation),
as long as they spent nothing, incurred no costs, and paid no taxes. The fact that bonds soundly
beat stocks for the first 60 years (even in Siegel’s inaugural 1994 edition of Stocks for the Long
Run) is all-too-easily overlooked.
As noted above, Laurence Siegel (2017) traces the demise of this notion and provides an overview of more recent
thinking about how the forward-looking equity premium might be estimated.
12
13
This the corrected record per McQuarrie (2024a, 2024b) as developed below.
11
Figure 1. Cumulative Growth of $100 Invested in Stocks and Bonds (1802–2023)
Note: Equity returns remapped as monthly, measured against McQuarrie (2024b) monthly government bond returns.
Source: McQuarrie (2024a) and (2024b).
Unremarked at the time was the subtle shift made in the baseline asset used in these long-term
historical accounts, relative to the pioneering effort of Ibbotson and Sinquefield (1976), which
used the 30-day Treasury bill. That instrument did not exist before 1929 (Garbade 2012) and thus
could not be used if the full two-century record of equity returns was to be examined. Siegel
substituted bonds with a maturity around 20 years, which allowed his series to be linked to the
later Ibbotson series for long government bonds. But with the 30-day Treasury bill set aside,
there was no longer a risk-free foil for equities. Long government bonds carry duration risk and
are necessarily volatile, except when held (and ignored) until maturity. Although there is
presumably no risk to nominal principal if a long Treasury bond is held to maturity, there is
12
substantial risk of a temporary loss of value at any point. 14 Of perhaps greater importance, given
that fiat currencies and inflation are joined at the hip, bonds can deliver a loss of purchasing
power over any span, short or long. 15
In some respects, the switch from bills to bonds improved the realism of historical tests of risk
theory. Rather than a comparison of risk with no risk, bonds offered a comparison of a lower-risk
asset with a (putatively) higher-risk asset. There was no longer a sure thing on offer, but only
two different risky choices.
Risk theory tacitly posits that human investors have a fine sensitivity to variance such that
investors would demand a reliable excess return for the riskier of the two assets in any such
comparison. For example, the SBBI indicates that over the post-1926 period, long bonds and
stocks have had an annual standard deviation of about 10% and 20%, respectively. If the
precision of risk was causally efficacious, then one would expect stock performance to be about
twice as great as bond performance, in rough proportion to the difference in risk. That is roughly
the result reported in the Ibbotson SBBI, with annualized nominal returns near 5% and 10% for
bonds and stocks, respectively, and is also consistent with earlier editions of Siegel’s book,
which showed real annualized returns of 3.3% and 6.6%, respectively.
Unfortunately, neither of these neat findings has stood the test of time. The 19th century US
record compiled by Siegel was re-examined by McQuarrie (2024a). He found that Siegel’s
sources had underestimated bond returns following the Civil War and overestimated stock
returns, especially in the earliest decades, as a result of survivorship bias. Net, across the
expanded and corrected record, McQuarrie found recurrent equity deficits, with protracted
periods when stocks underperformed government bonds. In fact, US stocks had slightly
underperformed US long bonds over the entire 19th century. 16
In the Siegel and Ibbotson historical bond series, each long bond is held for a short period, sold at market, and
then replaced with another. Returns if held to maturity are not computed. It also bears mention that default risk,
while low, is not zero. The Civil War, World War I, or World War II could have turned out differently. And
monetizing government debt with inflation can be described as default by another name.
14
15
Inflation-linked bonds, or TIPS, ostensibly protect against real loss of purchasing power, but that is only if held to
maturity and if CPI is an accurate measure.
We should bear in mind that, by the economic standards of the 21st century, the US economy at the time was the
equivalent of an emerging economy today, with poorly diversified stock and bond markets. Indeed, from around
1840 until late in the century, railroads dominated the stock and corporate bond markets.
16
13
However, these initial results were subject to dispute, insofar as McQuarrie’s measure of bond
returns prior to 1926 had sometimes included corporate bonds as well as government bonds.
Given the additional idiosyncratic risks of corporate bonds, their inclusion undercuts the desired
comparison of a riskier asset with a less risky one. More recently, McQuarrie addressed that
objection by constructing a new measure of bond returns from 1793 that uses government bonds
exclusively and Treasury bonds whenever available (McQuarrie 2024b). Figure 2 plots the real
equity premium or deficit over rolling 10-year (120-month) spans from January 1793 to
December 2023 using that new government bond index and the McQuarrie (2024a) stock returns.
Equity deficits are observed again and again, both in recent years as well as in the 19th century.
Figure 3 shows that investors sometimes would have had to wait until their great-grandchildren
were fully grown before they would have received a cumulative profit from exhibiting a
preference for equities. It bears mention that these results are for the US, which has had among
the best long-term real stock market returns in the world (Jorion and Goetzmann 1999).
These results are not compatible with the hypothesis that risk, as measured by standard deviation,
provides an index of the rewards that investors demand to receive (i.e., that riskier assets are
priced to deliver higher returns when held for a long period). The precision with which risk can
be estimated proves to be a distraction, with its precise measurement not helping as far as
prediction is concerned.
Of course, a “risk premium” presumes risk, or uncertainty. Perhaps the 19th century was an
unfortunate draw from a deck with many cards. Arnott (2004) noted that a 5% risk premium,
which many academics and practitioners still hold to be reasonably normal, would mean that
stocks have a 95% likelihood of beating bonds over a 27-year horizon. With a risk premium of
2%, reasonably close to the norm identified in Arnott and Bernstein (2002), an investor would
need an investment horizon of nearly 150 years in order to have a 95% likelihood of a win. And,
with a 1% risk premium, Christopher Columbus would still be waiting for his 95% confidence
outcome. If one has to wait a century to validate a hypothesis empirically, it may be necessary to
find ways to improve or replace that hypothesis.
It is difficult to interpret a pattern like that seen in Figure 2 in terms of risk. Whatever the
meaning of the term “risk premium,” the risk of a long government bond is what it is; its
riskiness over time does not fluctuate in line with the chart. The bonds used were backed at every
14
point by the promise of the sovereign to pay and guaranteed by its taxing power. Likewise,
stocks had a higher standard deviation than bonds in the 19th century, just as they did in the 20th
century (although not always in a ratio of 2-to-1).
Figure 2. Realized Equity Premium vs. Long Bonds in Rolling 10-Year Spans (1803–2023)
Note: Equity returns remapped as monthly, measured against McQuarrie (2024b) monthly government bond returns.
Source: McQuarrie (2024a).
The realized excess return for stocks relative to long government bonds, as charted in Figure 2,
has been too volatile to represent a risk premium. At times, stocks have been extremely
rewarding, as in the 10 years ending mid-1959, when the realized excess return for stocks
relative to long bonds approached 2000 bps annually. At other times, as in the mid-2000s, the
Great Depression, or the half century before the Civil War, the rolling 10-year equity deficit has
been substantial, with an annualized rate ranging from minus 800 bps to 1,000 bps. Return
15
fluctuations this extreme, which were sustained for a decade or more, are difficult to square with
a rational assessment of risk (Shiller 1989). Of course, a realized excess return is not the same as
the risk premium that a rational investor might have reasonably expected at the beginning of one
of these bleak decades. The realized excess return can be inflated by better-than-expected results
for stocks or worse-than-expected results for bonds or can be degraded by the opposite.
Even more compelling, excess returns for stocks relative to long Treasury bonds can disappear
for shockingly long spans, as shown in Figure 3. The stock market investor in 1804 would have
had to wait 97 years before finally exceeding the cumulative returns for an investor in long
government bonds. Worse, the market crash of 1929–1933 would have pushed our long-term
stock market investor of 1804 behind bonds one last time after 129 years. Even Jeanne Calment,
who lived 122 years (a longer documented lifespan than any other person in history), would not
have lived long enough to have been lastingly ahead of bonds if she had been born in 1804 and
had begun investing at that time.
The gold arrows on Figure 3 draw attention to the fact that, absent a remarkable half century
(1950–1999), stocks beat bonds by a remarkably modest margin (roughly fourfold, or a bit under
1% per year) over the other 170 years covered in the graph. This remarkable half-century, which
helped inform today’s risk-centric view of asset pricing, was helped along by the dividend yield
of US stocks falling eightfold, from over 8% at the end of 1949 to just over 1% at the end of
1999. That’s an eightfold upward revaluation (4% per year) in the price/dividend ratio for the
S&P 500, matched by a fourfold revaluation (3% per year) in the CAPE (cyclically adjusted
price–earnings) ratio. Unless we believe that upward revaluations can persist indefinitely, this
span should not shape our future expectations.
Recent history also provides instructive examples. A stock market investor beginning in early
2000 would have had to wait 22 years to beat a long-bond investor. And a stock market investor
beginning in early 1969 would have been under water relative to long bonds for a decade and
briefly would have been behind the long bond investor yet again in 2009, a 40-year span with no
realized equity risk premium. The common denominator of these spans was a starting stock
market yield well below that of long bonds, ahead of the long deficit. That is also the current
circumstance for an investor today.
16
Figure 3. Cumulative Realized Equity Premium vs. Long Bonds, 1803 – 2023
Note: Equity returns remapped as monthly, measured against McQuarrie (2024b) monthly government bond returns.
Source: McQuarrie (2024a).
Observed fluctuations in the realized equity premium or deficit require an explanation in terms of
something much more volatile than objective measures of the risk present in stock and bond
assets. Fear is an appropriate response when investors face radical uncertainty rather than
probabilistic uncertainty, which can be readily quantified using a metric such as standard
deviation.
International Stocks
If US stocks in the 20th century have delivered too much excess return to be explained by their
incremental risk, international stocks appear to have delivered too little. Jorion and Goetzmann
17
(1999) were the first to point out how exceptional historical returns in the US stock market had
been relative to every other international market in their dataset. In a series of publications
beginning in 2002, research by Dimson, Marsh, and Staunton (2024, the latest version) has
widened the data collection lens further and captured returns on international bonds as well as
stocks back to 1900. In the process, the authors also found US returns to be well above average.
Research by Jorda et al. (2019) and Taylor (2024), which pushed the record back into the 19th
century, confirms the pattern: Equity investors in many other markets in many periods have fared
much worse than US equity investors in many periods.
More to the point, equity deficits, such as those seen in Figure 2, have been commonplace in
non-US markets. McQuarrie (2024a) examines long-term returns collected from 19 markets
around the world and finds that all 19 markets, without exception, experienced at least one 20year span during which stocks produced lower returns than did the government bonds available
to investors. 17 Indeed, in 18 of these 19 markets, at least one 30-year span occurred during which
stocks failed to outperform long-term bonds. The following examples give a flavor of the
magnitude of the equity deficits observed internationally:
•
In Norway, the equity deficit was 10.0% annualized for the 20 years ending in 1938; in New
Zealand, 6.2% for the 20 years through 2006. 18
•
Over the 30 years ending in 1932, the equity deficit in Sweden was 3.3%; for a 30-year
period in Spain, the deficit was 4.2% through 1915.
•
Over the 50 years through 2011, Italy and Japan saw an equity deficit of 3.0% and 1.4%,
respectively, despite tremendous economic growth for both countries.
We don’t reject the notion that each of these could be perfectly normal statistical phenomena,
hence unsurprising. We do think fear may be a path to a better and more useful model. And we
are uncomfortable with the widespread tacit assumption that an investor can reasonably expect to
realize an incremental reward for bearing risk as long as their investment horizon is “long term”
(often taken to mean 20, 10, or even 5 years).
17
Returns from Global Financial Data, courtesy of Bryan Taylor.
From Table 3 in McQuarrie (2024a). Annualized real returns for stocks and bonds were computed over the period
and then the bond return was subtracted from the stock return to produce the stated values. The values given here
were selected to include a range of nations and periods, with an emphasis on more recent occurrences, and are not
always the worst cases tabled.
18
18
A good scientific theory is universal in application. While a risk premium is an expected
incremental return as a reward for bearing expected incremental risk, we suggest that a positive
realized risk premium in one century and not another—or over scores of years in one country and
not another—invites legitimate skepticism as to whether the concept of a conventionally defined
expected risk premium was mere wishful thinking. The equity deficits that were repeatedly seen
during the 19th century in the US and during the 20th century outside the US suggest to us that
risk-based asset pricing is a weak theory. Consider that, for the rolling 10-year returns in Figure
2, spanning 220 years, the average realized equity risk premium can’t even muster a t-statistic of
2 (with Newey-West adjustment for overlapping spans). And a t-statistic of 2 would be the
expected pattern if the risk premium was modest or inconstant, providing only a partial
explanation of observed asset pricing. If a span of two centuries is inadequate to achieve
statistically significant support for a theory, then perhaps we should reexamine our theory.
Risky Factors
In retrospect, the discovery of size and value factors sounded the death knell for risk theory as
implemented in CAPM. This implication was not apparent at the time. The initial Fama and
French (1992) model, adding only two risk factors—size and value—to the market factor, could
have been taken as a minor adjustment to CAPM that did not disturb the theory’s foundations.
Most important scientific theories, to be tested empirically, require auxiliary hypotheses. The
postulation of size and value factors could reasonably have been seen as an effective rescue
mission.
But as two factors became a dozen—then scores, then hundreds—it became increasingly
untenable to suppose that risk theory required only a minor emendation to account for the asset
pricing phenomena visible in the data. As we show next, even the two additional factors are
problematic. Their empirical risk premia are not well supported by nearly a century of data.
When broken out by size and by the ratio of book value to price, these sources of incremental
risk subsequently delivered decremental excess returns. 19
It is important to note that revaluation alpha has been a key driver of the poor subsequent performance for the size
effect and value effect (Arnott et al. 2021).
19
19
This pattern is difficult to grasp when only long-period arithmetic means are examined.
Following a strategy akin to that used in Figure 2, we split the post-1926 record into three 33year spans and probe whether the relationship between factor return and factor risk has been as
expected and also stationary. Figure 4 examines risk and return over four different time spans
over the past century for four factor portfolios: large growth, large value, small growth, and
small value, as defined by Fama and French. A risk-based theory of factor returns would predict
that, subject to perhaps substantial variability, higher risk should deliver higher return. So, value
should beat growth in both large- and small-cap stocks and small-cap should beat large-cap in
both growth and value stocks.
Consider the red arrows. These arrows connect dots that show the risk and return over the first 33
calendar years (1926–1958) for the four portfolios: large growth and value and small growth and
value. 20 This was a time of elevated volatility (but not elevated returns!) relative to the other 33year spans, as it included the Great Depression and World War II. The solid arrow goes from the
risk and return of the large growth portfolio (delivering 9.6% annual return with 23.4% standard
deviation) to large value (11.4% return with 36.9% risk) to small value (13.2% and 42.4%).
Each step raises the risk level and delivers a higher return, as one would expect. The dashed red
arrow goes from large growth (again, 9.6% return with 23.4% risk) to small growth (9.7% annual
return with 31.8% risk), again ending on small value (13.2% return and 42.4% risk). Each step
again raises the risk level and delivers a higher return, exactly as risk theory would predict.
The blue lines span the next 33 years (1959–1991), essentially the time period that inspired
Eugene Fama and Ken French. 21 But the relationship is unreliable. The solid blue line first goes
up to the left, and the dashed line down to the right. Large value was less risky than large growth
over this span, while small growth delivered less return than large growth. A risk premium
inherently involves risk, so outliers are unsurprising. But two of the lines go the wrong direction.
The most recent 33 years is best described as a mess. Large value and small growth both deliver
As our factor data span July of 1926 to June of 2024, these are two 32.5-year spans (July 1926 to the end of 1958
and January 1992 to mid-2024), with a 33-year span in the middle (1959–1991, inclusive). When we refer to these
spans as 33-year spans, we are referring to calendar years.
20
See Davis, Fama and French (2000) for the earlier period and Fama and French (2001) for a discussion of the
most recent period.
21
20
less return than large growth, and small value is less risky than small growth. Three of the four
lines are going in the wrong direction.
Finally, for the full span of years, nearly a century of market history, small growth delivers more
risk and less return than large growth. The prediction from a risk-based theory of factor returns is
straightforward. Unless 98 years is inadequate to expect a risk premium to play out in the
expected way, more risk should deliver more return, give or take some potentially substantial
uncertainty, so each of the lines should slope upward and to the right as we take on more risk.
This expectation reflects the fundamental thesis of risk theory: that investors demand higher
returns when asked to assume higher levels of portfolio risk and that market returns cannot be
augmented unless more risk is also assumed.
Figure 4. Returns and Risks for Small vs. Large and Value vs. Growth (1926–2024)
21
Three decades is a long time in the life of a mortal human investor. The failure of risk theory
goes beyond the specifics given in the figure: it is the same failure to be roughly stationary
across time shown in Figure 2. To repeat, CAPM is a well-formed scientific theory. Recall
George Box’s famous dictum that “all models are wrong, but some models are useful.” CAPM is
wrong—reward correlates only weakly, and at times not at all, with risk—but it has been useful.
CAPM posits a mathematical relationship between return and risk, describing the way homo
economicus would behave in a perfectly rational world. It was a bold conjecture in the spirit of
Popper.
Alas, this rational relationship between risk and return fails to hold universally. As shown in
Figure 2, it does not always hold for US equities, even over spans longer than our own too-brief
lifespans. It also does not always hold for equities across international markets. Figure 3 shows
that it is not stationary for size and value over long spans. The Fama–French attempt to fix the
risk premium (by adding additional dimensions to risk) has instead served to further undermine
the risk premium thesis.
Something else must explain the asset pricing visible in the historical record.
Perhaps more importantly, risk theory can surely be rescued from each of our demonstrations,
just as the pre-Copernican astronomy of Ptolemy could always be patched up by adding another
epicycle, thereby providing yet more evidence that the planets revolved around Earth. For a
scientist schooled in the tradition of Popper, such repeated rescues ultimately raise an
uncomfortable question: Can risk theory ever be falsified, by any accumulation of evidence? If
not, then its claim to be empirical science grows dubious. Or in the words of Haghani and White
(2023, pp. 291–292):
“In the natural sciences, if a model fails when brought into contact with
experimental evidence, the general procedure is to discard the model, not
proclaim the real world puzzling for failing to match the chalkboard.”
Fear as an Explanatory Construct
So far, we have cataloged how risk theory has failed to explain observed asset pricing. Historical
excess returns have been exceptionally high or low, and observed risk premia have been volatile
22
and non-stationary over periods exceeding a human lifespan. This does not invalidate risk-based
asset pricing, but when observed risk–reward relationships can be upside down for a century, it
surely calls for a rethink. As Kuhn argued, no amount of negative evidence can overthrow a
paradigm. There must be a replacement in view.
In this section, we consider specific advantages of fear as an explanation for asset pricing.
Fear Is Omnidirectional
Once loss of gain is accepted as loss and aversive per se, investor behavior becomes much, much
harder to predict in advance. Stocks that are oversized and overpriced (the 0–0 cell in the original
Fama–French three-factor model) may nonetheless be regarded as attractive purchases if the
investor fears missing out on still further price gains. This fear becomes palpable when a
narrative of revolutionary change takes hold (e.g., dot-coms, EVs, AI, and countless previous
examples). Stocks with low valuation multiples (value) and small market cap (size) may still be
shunned by investors who fear they are missing out on some seemingly low-risk sure thing. Fear
of missing out, while difficult to measure, is undeniable and is likely as potent as fear of losing
money. FOMO is a fundamental tenet of fear theory.
Fear Is Social
The late Charlie Munger once observed, “The world is not driven by greed. It’s driven by envy.”
FOMO is envy. FOMO is comparative as well as absolute. Fear of doing worse than one’s social
group is just as potent as (indeed, in sociology studies, even more potent than) fear of falling
short of some wealth target. 22 Meme stocks are a necessary occurrence within a fear framework.
Likewise, a great boom acquires a momentum of its own as more and more members of one’s
social group eagerly report their outsized gains. If fear is social, there must be periodic events
such as the dot.com boom of the late 1990s, the Nifty Fifty of the early 1970s, and the closedend fund mania of 1929. 23 These are all instances of social contagion (Shiller 2015). Were the
22
See Bonaparte and Fabozzi (2025) for a discussion of FOMO outside of an investing context.
Closed-end funds were all the rage in 1929, being marketed as a sure thing based on the expertise of the stock
operators who launched them. Prior to the Investment Companies Act of 1940, an individual investor could buy on
margin a closed-end fund that had bought on margin other closed-end funds, which themselves had bought on
margin stocks or still other funds. Rapid gains were booked for a time in early 1929. The disastrous results of that
pyramiding were a primary stimulus for the Act of 1940, which outlawed the practice.
23
23
historical record instead to show a near absence of such market events, rather than their
recurrence, that would count against the theory that investors are fearful social beings.
Fear Is Arational
Fear is a powerful emotion. Sometimes emotional decisions produce the same outcome as a
rational choice, sometimes not. Backpackers who hear a rattle just ahead may—both rationally
and fearfully—freeze in their tracks. A charging grizzly may (irrationally and fearfully) prompt
the same reaction. Metaphorically, the correlation between emotion and reason is zero. Fear is an
independent ground from which investor behavior can be predicted. A fear-based theory of asset
pricing does not dismiss the homo economicus assumption that investors can behave rationally.
Recall that in the context of portfolio choice, it is rational for the risk-averse investor to allocate
less to the risk portfolio. But the aversion that drives that rational choice is not itself rational. It is
fear.
There Can Be No Fear-Free Asset
Whether or not there is a risk-free asset, there can be no fear-free asset. There are so many things
to fear when investing, even something as seemingly benign as cash. Nothing is safe. Anything
can be scary. Fluctuations in the target and intensity of fear help to explain the historical record.
The omni-directional character of fear implies that cash can be scary too. Where risk theory has
an anchor in the form of a supposed risk-free asset, which ostensibly provides a return without
risk, fear theory has no such anchor. Fear veers wildly in all directions.
Sometimes risk is quantified in a different way: not as variance but as risk of loss. However, only
within the narrowest frame of reference can cash be said to have no risk of loss. “Cash” typically
refers to the 30- or 90-day Treasury bill, which serves as a proxy for the risk-free rate in
calculations of the Sharpe ratio and tests of CAPM. In 1964, when Sharpe wrote, cash would not
have seemed scary at all, returning 3.6%, roughly the same as in preceding years. In recent
decades, when the return on cash fell—first below the rate of inflation then to the so-called zero
bound (and beyond in much of the developed world)—the risks of holding cash became
apparent.
24
“Risk free” is well-known to be a myth in the real world. No asset offers a standard deviation of
zero over multiple investment horizons or a guarantee of any positive return, let alone any gains
net of inflation.
By the 1960s, theorists must have forgotten (or chosen to ignore) that in 1946, the real return on
cash had been a negative 15.1%. And no theorist in the 1960s could have envisioned the two
decades following 1999, when the real return on cash was negative in 70% of those years. But
almost every investor in 2025 will recall the negative real return received on cash in 2021 and
2022, which cost investors over 10% of their purchasing power in two short years.
At this point in the debate, TIPS are sometimes brought up as a remedy for the limits of cash.
Some have argued that the equity risk premium should be measured against long TIPS (Arnott
2001, 2024), as both stocks and TIPS offer real returns with some measure of inflation
passthrough. 24 But it is important to recall that the real yield on shorter TIPS was negative after
2011 and again after 2020. 25 TIPS became a risky asset at that point, guaranteeing a real loss in
purchasing power if held to maturity. Scary indeed.
As a final historical case in point, consider the example of investors who became so fearful of
stocks in August 1929 that they sold everything and put it all in cash for the next two decades.
Through August 1949, stocks earned a pathetic real return of 5 basis points per year, with the
highest volatility of the past 220 years. But, cash lost money in real terms, as inflation ran 1.84%
per year. Not even superlative market timing—avoiding the crash and one of worst periods of US
stock performance—could extract an excess return from cash relative to stocks.
Even if cash is perceived as risk free, it certainly can still be scary. Fearful investors are
emotional and fickle. Sometimes, investors are afraid of not getting their principal back and
favor bonds or cash: FOL rules. At other times, the prospect of earning almost nothing drives
That said, we are not aware of any implementation of CAPM that subtracts the 30-day (or 30-year) TIPS yield
from the market return.
24
The FRED database maintained by the St. Louis branch of the Federal Reserve publishes Constant Maturity yield
series for 5-year and other TIPS maturities.
25
25
investors (over and over) out of cash and into stocks: FOMO rules. And as Figure 2 shows,
investors can switch from one fear to the other and back again with considerable rapidity.
Measurement of Fear
The coefficient of risk aversion (gamma) applies at the level of individual portfolio choice. We
need a measurement approach to fear that applies to investors collectively so that it can explain
observed asset pricing. A strictly objective measure of risk as standard deviation has failed that
test, as we demonstrated using historical data. The failure of risk was twofold: stock returns from
time to time have been larger than risk theory could reasonably justify, and the equity premium
from time to time has been a deficit. Neither (measured over a multi-decade investment horizon)
is consistent with a stationary pricing process in which returns are a direct function of risk.
Where the standard model needs a cross-individual measure of subjective risk aversion, gamma,
in order to reflect investor behavior, a fear-based model needs a time-varying measure of
subjective aversion to loss and to missing out, which we suggest as the two dominant human
fears that drive investment behavior, rather than simple risk aversion. Perhaps we might call it
upsilon, tacitly acknowledging humankind’s embrace of upside risk. It might be calculated as:
υt = [FOMOt * skew] minus [FOLt * semivariance],
where
•
FOMO and FOL, in strict parallel with gamma, take positive integer values and most
values observed in the field are expected to fall in the single digits,
•
skew and semivariance are placed on a common scale,
•
the expectation is that FOMO and FOL are time-varying,
•
and the further expectation is that FOMO ≠ FOL.
Restated in plain English, our proposed coefficient of aversion says investors collectively always
fear missing out and always fear losing it. Fear is an omnipresent feature of capital markets;
property is precarity. What varies is which kind of fear dominates at the moment.
26
When FOMO waxes, more weight is placed on a right skew in asset returns, and when FOL
waxes, more weight is placed on semivariance (drawdown risk). For investors collectively,
FOMO and FOL fluctuate over time and relative to one another. Consistent with the efficient
market hypothesis (EMH), this fluctuation is not predictable in advance but can only be
ascertained retrospectively.
Skew and semivariance are objective features of historical return series, but the time horizon
over which investors take these measurements is uncertain. Some investors will measure over the
trailing 20 years, others over the trailing 20 months, and so forth.
For any given asset class, sometimes FOMO exceeds FOL. When it does, upsilon takes a
positive value and returns in excess of risk predictions will be observed in the asset class.
Conversely, when FOL exceeds FOMO, greater weight is placed on semivariance and, ceteris
paribus, upsilon takes a negative sign, with riskier assets observed to underperform less risky
assets, as with the equity deficits observed historically.
With four inputs, all of which can vary over time, upsilon itself can vary through a wide range,
sufficient to retrodict the non-stationary pattern of historical equity returns observed in Figure 2.
We note the strict parallel with gamma, the coefficient of risk aversion, a subjective element
combined with objectively measurable variance to explain portfolio choice. Our formulation
argues that it is not enough to measure the objective properties of skew and semivariance;
FOMO and FOL are necessary as well.
Now that we have pointed to what investors fear—missing out on skewness and the more
traditional fear of drawdowns—it seems likely that existing measures of sentiment can be
adapted to capture this dual focus (e.g., Baker and Wurgler 2006). 26 The goal will be a
measurement of FOMO and FOL that does not depend on surveying individual investors, most
of whom are too small to affect asset pricing and who may lack introspection into their state of
fear. Rather, measurement of upsilon must reflect what is going on with investors collectively at
that juncture. The development of large language models, which can analyze vast quantities of
The Citibank measure of Panic versus Euphoria is another example of a sentiment measure that might be adapted
(Vrba 2011).
26
27
text (as on social media) in almost real time, holds promise in this regard. We can imagine an
ongoing scraping of text posted on the web that is scored for sentiment 27 to produce a daily
measure of upsilon for an asset class, focused on whether it is positive or negative.
Our goal in this paper was to lay the foundation for such future research by articulating the dual
focus of fear and the central role played by fear responses in shaping asset pricing.
Practical Implications
We propose a two-dimensional fear (FOMO and FOL), and we propose to discard variance, the
traditional measure of risk, as the central driver of asset pricing. Each of these endeavors has its
own implications.
Regarding the concept of risk as variance, this paper may serve as a corrective. Too many
advisors and analysts have come to see risk assets (equity investments) as offering a reliable
incremental return over fixed income and other low-risk assets for investors patient enough to
weather a market cycle with its inevitable bouts of disappointment. This tendency was
accentuated for those who found the “stocks for the long run” thesis of Siegel (2022) compelling.
Advisors need merely counsel clients to stay the course to achieve an equity premium of perhaps
300 to 500 basis points. On this reading, rational investors demand extra return for bearing risk,
and that demand has been reliably met, provided the holding period is long. Short-term hiccups
are to be expected, but not over scores of years, let alone a century.
The dangers of that expectation are shown by our historical analyses, which use the corrections
to US data of McQuarrie (2024a) and the expanded international datasets of Dimson et al.
(2024), Jorda et al. (2019), and Taylor (2023), refinements that were not available when Siegel
first wrote his bestseller. Stocks can underperform risk-free” assets and lower-risk assets over a
human life-span, let alone any shorter span that an investor might find useful.
More generally, we question variance as a good predictor of asset pricing. We put the focus
instead on semivariance and positive skew as inputs to investor behavior. However, we do not
presume that a new rule for predicting return, using these objective measures alone, would
suffice. We insist on the subjective element, as risk theory already does with its reliance on a
27
The ability to extract sentiment from text is a core feature of LLMs.
28
quantitative estimate of gamma. Fear of missing out on positive skew and fear of semivariance
(loss) both vary over time, across assets, and across individuals. Asset pricing is net of the
perceived skewness of the asset, weighted by the fear of missing out on that reward, minus the
perceived probability of loss, weighted by the strength of the fear of loss.
If what investors fear is not volatility, but loss, then portfolio design needs to shift away from the
orthodox approach that developed out of modern portfolio theory (MPT), in which a portfolio of
bonds is blended with a portfolio of stocks, taking advantage of their often-light correlation with
one another, with the explicit goal of reducing variance. The terrible bond bear market of 2022
exposed the peril of this approach. The great bond bull market of 1981–2021 had lulled investors
into the complacent belief that the semivariance of a Treasury bond fund was effectively zero.
By shifting the focus from the second moment to semivariance, we lay a foundation for a return
to Tobin’s two-fund theory. Restated, the investor first chooses an asset with little or no
semivariance, in proportion to their fear of loss, and places the rest of their funds in a position to
harvest skew, again in proportion to their fear of missing out. With a fiat currency, and its
associated risk of inflation and monetizing of debt, a TIPS ladder, not a bond fund, is needed to
approach zero semivariance. Under EMH, the best way to harvest skew is to own the market
portfolio of risk assets, because there is no way to select individual stocks in advance that will
show the highest skew. 28 Analysts and money managers are free to make the attempt; the proof
is in the pudding.
The fear framework may lend itself better than risk theory does to today’s questionnaire
approach—for an interesting reason. Measuring an investor’s risk aversion is likely to be wildly
inaccurate, because most investors will dislike downside risk and crave upside risk. Thus, trying
to fit this schizophrenic view of risk (loving some risks and hating others) into a single measure
of risk aversion was always doomed to fail. A questionnaire approach, flawed as it is, can be
regeared accordingly. Measured separately, perceptions of positive skew and semivariance of a
portfolio of available assets may be accurate and may be a better input for determining the
relative strength of an investor’s FOMO versus FOL.
28
Bessembinder (2018) highlights the impossibility.
29
Fear Theory in Context of Prior Work
We are hardly the first to propose alternative theoretical frameworks. Inspired in part by the
overlooked work of Kraus and Litzenberger (1976) and Rubenstein (1973), Harvey and Siddique
(2000) posits a taste for the third moment of the distribution (skewness). FOMO is one reason
that investors might seek positive skew. Kraus and Litzenberger are, in a very real sense, the
intellectual fathers and Harvey and Siddique the godfathers to our suggestion that FOMO and
FOL are the dominant emotional drivers for investor behavior.
Nor are we the first to nominate fear as for the key emotion driving investor behavior. Fear and
other emotions have deep roots in the literature on behavioral finance (Shefrin 2002, Zweig
2010, Hirschleifer 2015) and experimental finance (Smith et al. 1988). Nevertheless, our
approach has some distinctive elements, which we attempt to summarize here.
First and foremost, we do not call into question EMH, even though we challenge the assumption
that investors are rational. For the purposes of this paper, we don’t have a dog in that hunt. While
we do not assert that markets are efficient, neither do we assert that they are not. As noted above,
fear is arational, and the inconstancy and unpredictable focus of investors’ fear supports key
elements of EMH.
Second, we do not focus on fear as a specific emotion traceable to the amygdala. Fear serves in
our framework as a four-letter word for aversion: we avoid what we fear. In terms of an objective
function, fear points us to what must be minimized. To minimize disutility is no less rational than
to maximize utility. Our contribution is to develop the centrality of fear in explaining observed
investment outcomes. A key element is the contention that FOMO is as real and potent as FOL in
guiding investor action. With this pair in hand, it is no longer necessary to speak of greed and
fear or the emotional investor or a supposed failure to be rational; the explanation is fear, all the
way.
Third, our evidentiary base is distinctive within the broad panoply of theoretical studies of
investor behavior. We focus strictly on historical outcomes and examine data that was not
available decades ago when risk theory first gained prominence. We show how risk theory fails
to retrodict asset prices when confronted with the new and more complete historical record,
30
which now extends much further across time and markets than when Mehra and Prescott (1985)
was written.
Conclusion
Risk theory has compiled a mixed record of success and failure, with too much of the latter to
hold onto its place as the singular (even dominant) driver of capital markets returns. Risk theory
delineates rational investment choice under the bright light of math but ignores the messiness of
human emotion and fails to withstand the muddy rockslide of history. It is time to seek
alternative drivers of capital market returns.
We do not advocate discarding objective measures of risk from being included among several
contributing factors that influence capital market returns and help in framing return expectations.
Fear is a superset of risk. Investors have asymmetric aversion to risk, fearing both loss and
missed opportunity for gain. Once it is recognized that risk alone has empirically been a poor
explanation for asset returns, fear emerges as a more powerful concept, both in explaining socalled premia and in shaping return expectations.
We recognize that no single paper can overturn a paradigm or shift the focus of an entire
discipline. Our hope is that a careful chronicle of the historical failures of risk theory in the realm
of asset pricing combined with an outline of how fear could provide an alternative explanatory
construct might launch a conversation that leads to future advances. Perhaps the hypothesis of
punctuated equilibrium in evolution (Eldridge and Gould 1972), which posits long periods of
stasis “punctuated” by periods of rapid change, can be applied to modern finance as well. With
MPT, CAPM, and EMH all arriving in the 1950s and 1960s, this burst of innovation laid a
foundation for the next 60 years of finance theory and practice—a period of normal science as
Kuhn calls it. Initially, these ideas were bold conjectures that made falsifiable predictions in the
spirit of Popper.
Now, after decades, it is folly to continue to ignore this record of failure, dismissing each new
inconsistency with empirical data as it appears or seeking new workarounds to explain each
inconsistency. The time has come to question the claim that risk theory represents the frontier of
31
empirical science. By incorporating fear into accounts of asset pricing we can build on existing
foundations to construct a more robust investment science.
32
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