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Federal Reserve Bank of Chicago
Momentum Trading, Return Chasing,
and Predictable Crashes
Benjamin Chabot, Eric Ghysels, and
Ravi Jagannathan
November 2014
WP 2014-27
Momentum Trading, Return Chasing, and Predictable Crashes
Benjamin Chabot*
Eric Ghysels
Ravi Jagannathan
Abstract:
We combine self-collected historical data from 1867 to 1907 with CRSP data from 1926 to 2012,
to examine the risk and return over the past 140 years of one of the most popular mechanical
trading strategies — momentum. We find that momentum has earned abnormally high riskadjusted returns—a three factor alpha of 1 percent per month between 1927 and 2012 and 0.5
percent per month between 1867 and 1907 — both statistically significantly different from zero.
However, the momentum strategy also exposed investors to large losses (crashes) during both
periods. Momentum crashes were predictable - more likely when momentum recently performed
well (both eras), interest rates were relatively low (1867–1907), or momentum had recently
outperformed the stock market (CRSP era) — times when borrowing or attracting return
chasing “blind capital” would have been easier. Based on a stylized model and simulated
outcomes from a richer model, we argue that a money manager has an incentive to remain
invested in momentum even when the crash risk is known to be high when (1) he competes for
funds from return-chasing investors and (2) he is compensated via fees that are convex in the
amount of money managed and the return on that money.
JEL No. G1,G12,G14
Benjamin Chabot
Federal Reserve Bank of Chicago
ben.chabot@chi.frb.org
Ravi Jagannathan
Kellogg School of Management and NBER
rjaganna@northwestern.edu
Eric Ghysels
Department of Economics and Department of Finance
Kenan-Flagler Business School
University of North Carolina-Chapel Hill
and CEPR
eghysels@unc.edu
* The views expressed in this article are those of the author and do not necessarily reflect those of the Federal
Reserve Bank of Chicago or Federal Reserve System.
An increasing amount of capital is devoted to trading strategies that mechanically
construct portfolios to exploit market anomalies such as “value” or “momentum”. The latter
strategy — buying recent winners and selling recent losers— is one of the oldest stock-selection
strategies still in practice, presumably because of its continued profitability over the years.1 One
might have expected the profitability of the momentum strategy (momentum premium) to
disappear after it became well known in the early 1990s and attracted the attention and capital of
professional money managers. Indeed, the momentum premium seemed to have vanished around
the early 2000s, and yet reappeared in recent years. Such a simple yet resilient money making
strategy requires a new look.
By “new look” we mean (1) using an entirely new long historical data set and (2) using a
new model. We combine self-collected historical data with existing data to document the returns
to momentum investing in the CRSP-era United States and Victorian-era London. A consistently
applied momentum strategy generated abnormal returns across both periods. While the
momentum strategy has high historical average abnormal risk adjusted return (alpha), the
strategy is prone to periodic crashes. Thus, while investors could enjoy high abnormal average
returns by buying winners and selling losers, the momentum strategy exposed investors to large
losses with some regularity. It is tempting to argue that investors’ aversion to such large losses
may not be adequately captured by standard asset pricing models and the high historical alpha is
due to inadequate risk adjustment, and is compensation for exposure to such crash risk.
However, the hazards of these crashes vary in a predictable way across both eras.2 show that
times when momentum crashes are more likely is predictable during the CRSP era. We find that
1
To be more precise, at least since the time of David Ricardo, who advised, “cut short your losses, let your profits
run,” the strategy of holding winners and selling losers has been a favorite of stock market advisors. Ricardo’s
investment maxims—with which he made a fortune speculating on the London Stock Exchange—are quoted in
James Grant’s 1838 book The Great Metropolis, Vol II (p.58). Nineteenth and early twentieth century investment
manuals, such as The Ticker and Investment Digest and The Banker’s Magazine, often carried advice columns
recommending momentum strategies and stock guides, such as Walter Bagehot’s Investors Monthly Manual, Henry
Poor’s Poor’s Manual of Investments, Moody’s Manuals, and The Commercial and Financial Chronicle, all of
which included statistical information on stock highs and lows over various horizons for readers who wished to use
recent momentum to select stocks.
2
Earlier work by the authors, Chabot et al. (2009), showed that the Victorian era and CRSP era momentum
properties were very similar. This earlier work noted cycles in momentum profits but did not link returns to
momentum "crashes" or provide a model explaining crash intensities and estimates of an associated empirical hazard
model.
1
states when crashes are more likely had a common feature across the Victorian and CRSP era.3
We argue that crashes play an important role in sustaining momentum through limits to arbitrage
examined in Schleifer and Vishney (1997).
How can we rationalize such a persistent historical pattern across eras with arguably very
different equity trading environments? There were neither hedge funds during the Victorian era,
nor electronic trading, for example. What made momentum return patterns so similar? What
explains the persistence of momentum profits? Why does a strategy as simple as buy winners
and sell losers not become crowded with followers who bid away any abnormally high risk
adjusted returns? The fact that momentum strategies show so many similarities across two
different eras suggests that the underlying drivers have remained the same. That would be the
case if the high average abnormal returns were due to behavioral biases embedded into the way
most investors make decisions consistent with the stand taken in the behavioral finance literature.
But then, there are sophisticated professional investors who are not subject to such biases, and
they should be able drive away any persistent abnormal returns.
We argue that the persistent historical pattern across both eras is because sophisticated
investors who had the necessary skills to execute momentum strategies efficiently did not have
sufficient capital of their own, and had to rely on other people’s money. Indeed, the momentum
strategy does require significant trading and therefore requires skill in executing trades at
minimal cost. This separation of brains from capital can be overcome by professional managers
endowed with trading skills offering their services to investors with capital in exchange for a
percentage of the profits (in the latter part of the CRSP sample) or through leverage financed by
risky borrowings at suitable interest rates. By itself this does not explain why momentum profits
did not get eliminated. For a complete understanding we must look to an additional feature of
momentum returns – large crashes predictable occur at times when momentum is attractive to
return chasing capital.
If crash risk is hard wired into momentum returns, we should expect periodic rare crashes
in both the CRSP and Victorian era in the data to occur at similar times. This is what we find,
3
Daniel and Moskowitz (2014) document momentum crashes in several markets including commodities. Daniel,
Jagannathan and Kim (2012) find that call option on the market type features get embedded into momentum
strategy returns due to the way the momentum portfolios are formed, exposing momentum to potentially large
but rare losses (crashes).
2
there are periodic rare crashes in both periods and these momentum crashes can be predicted by
the same variables across both time periods. Crashes are more likely to occur during times when
managers who use other people's money would find it easier to attract blind capital. These are
also times when managers will not commit their own capital to momentum strategy but will still
commit other people's money - and those other people will still invest in momentum through
managers, knowing that this is the way managers behave. When crashes occur, return-chasing
blind capital is exposed to large losses, and that keeps blind capital away for a while. That may
explain momentum cycles, where we see momentum disappearing periodically, only to reappear
later. The periodic crashes are what keep momentum alive, supporting the “limits to arbitrage”
explanation of persistent anomalies of Shleifer and Visney (1997).
A number of papers have suggested a link between investor behavior and crash risk. For
example, DeLong et al. (1990) highlight that even without any incentive problems, rational
traders may front run positive feedback traders in the market, exacerbating later crashes. Hong
and Stein (1999) provide another model where the interactions between two groups of traders
can lead to price momentum and reversals. In the presence of incentive problems, Vayanos and
Woolley (2013) explicitly model momentum driven by professional managers.
To the best of our knowledge, however, the existing models do not feature the
periodically reoccurring moment cycles with the predictable time varying crash likelihood we
observe in the long historical sample. While we are not the first to notice cyclicality in
momentum returns, one of our contributions is to introduce a hazard model that successfully
captures the time-varying likelihood of momentum downturns.
Exploiting momentum involves the use of other people’s money either as a skilled
investor relying on leverage or as a professional financial intermediary who manages other
people’s money. If capital constraints prevent skilled investors from driving abnormal
momentum returns to zero, we hypothesize that a measure of capital scarcity should predict the
duration of momentum profit cycles. To test this formally, we introduce a new methodology
based on modeling profit duration dynamics as a function of the risk-free rate, the past stock
market return, and the past performance of the momentum strategy, which we interpret as a
proxy for the scarcity of capital available to skilled momentum traders. Consistent with models
of leverage-induced crashes, we find strong statistical evidence that our proxy for capital
available to momentum traders predicts sharp downturns in momentum profits.
3
After documenting the predictability of momentum crashes, we introduce a theoretical
model to illustrate why rational managers will commit other people’s money to momentum when
crashes are more likely - even when they will not commit their own capital. In fact, times when
large losses are likely are times when momentum has done better than the market and managers
will find it easy to attract the capital of return chasing investors, i.e., blind capital. That exposes
blind capital to crash losses. One consequence is also that other people’s money available to
sophisticated investors will be scarce following such crash losses, thereby letting momentum
alive.
For analytical tractability, the theoretical model is limited to three time periods, two
money managers and two market states. While this simplicity illuminates the money managers
decisions, the model lacks the rich dynamics of modern delegated finance. We therefore use
simulations to verify that the theoretical model explanation remain valid in richer economies
with many money managers, states of nature, and time periods. In addition, the investors in our
model perfectly understand the behavior of managers, and still choose to let them manage their
money. The simulated model—calibrated to mimic the aforementioned duration properties of
momentum cycles—explains the apparent paradox that even though large momentum losses are
predictable, sophisticated money managers may nonetheless choose to crowd into this strategy at
times of elevated risk. Our money managers are compensated by collecting fees equal to a small
percentage of assets under management and a larger percentage of profits above a high-water
mark. These managers compete with each other for the blind capital of return-chasing customers.
In our simulations calibrated with CRSP data, money managers who go to cash in periods of
elevated crash risk are less profitable on average than managers who remain invested in the
momentum strategy. While we do not model the behavior of momentum investors of the
Victorian era who relied on borrowed funds to invest in momentum strategies, we conjecture that
in light of the risk-shifting payoffs of margin loans, they too would have had little incentive to
exit when crash probabilities became high.
The paper is organized as follows. In Section 1 we introduce and describe the new data
and document the similarities between momentum profits in the Victorian and CRSP eras. Our
main results—that momentum profits exhibit predictable cycles: they stochastically vanish and
reemerge—are presented in Section 2. We characterize this stochastic periodicity using a hazard
model that successfully predicts transitions into momentum strategy bear markets as a function
4
of the recent relative attractiveness of the momentum strategy. In Section 3 we provide a possible
explanation for this phenomenon based on simulations of a stylized partial-equilibrium model
economy calibrated to the data. Section 4 concludes. Details about the unique data set can be
found in the Appendix.
1. Stock Price Momentum during CRSP and Victorian Eras: Abnormal Returns and
Cyclical Profits
There is a very large literature on momentum which we cannot possibly summarize. Most
relevant for our work are papers addressing momentum and limit to arbitrage issue. In particular,
when an anomaly exists but only a limited number of investors have both the capital and skill to
devote to a trading strategy designed to exploit it, they may not have enough collective resources
to drive the anomalous returns to zero. Typically, skilled investors will seek to expand their
profitable positions either through trading leverage (short positions funding long positions) or by
soliciting outside capital from less skilled investors. However, in theoretical models such as
Aiyagari and Gertler (1999), Gromb and Vayanos (2002), Geanakopolis (2003), Fostel and
Geanakopolis (2008), Brunnermeier and Pedersen (2009) and Kondor (2009) leverage
constraints can result in sudden reversals if idiosyncratic declines lower the value of collateral
and force correlated liquidations. Fear of forced liquidations limit the leverage arbitrageurs are
willing to employ and therefore the capital these arbitrageurs can devote to eliminating
anomalies. Moreover, when arbitrageurs raise equity from uninformed outside investors, poor
returns can result in contagious liquidations if outside investors interpret losses as evidence that
they have a low quality investment manager. In models such as Shleifer and Visney (1997), Liu
and Longstaff (2004), and Acharya et al. (2010) idiosyncratic volatility combines with the fear of
outside investor flight to prevent arbitrageurs from devoting sufficient capital to high alpha
investments.
Khandani and Lo (2007) and Mitchell et. al. (2007) document recent examples of shocks
that interact with leverage and capital constraints to generate forced liquidations and sudden
reversals in otherwise high return low systematic-risk strategies such as long-short quant funds
and convertible arbitrage funds. Ambastha and Ben Dor (2010) observed the same pattern for the
Long Barclays Alternatives Repliators, a particular hedge funds index clone. Hedge fund clones
5
rely on price momentum to some extent and Ben Dor, Jagannathan, Meier, and Xu (2011) find
that an index of six hedge fund clones exhibits the same pattern. Financial crises are times when
banks and other intermediaries withdraw funding that is otherwise available to arbitrageurs and
Daniel and Moskowitz (2014) document a similar breakdown in performance in momentum
strategies during the financial crisis. Elavia and Kim (2011) provide an explanation for a closely
related phenomenon based on how investors perceive risk and make decisions and Daniel,
Jagannathan and Kim (2012) make use of this pattern to identify hidden turbulent market
conditions when momentum crashes become more likely. More on point, Daniel and Moskowitz
(2014) document that infrequent crashes skew returns from momentum strategies across
numerous asset classes. These momentum crashes are the necessary ingredient to limit arbitrage
with other people’s money.
We revisit these issues with a new hand-collected data set of the London Stock
Exchange.4 Our data set consists of the closing prices, dividends, and shares outstanding of
1,808 stocks listed in London between 1866 and 1907. These data include virtually every
stock traded on the London Stock Exchange during this period. In some ways the Victorian
capital markets are an ideal laboratory to study momentum theories. The pre-WWI London Stock
Exchange had no capital gains tax distortions, and it was remarkably easy to retail investors to
short shares and form leveraged long–short portfolios.5
We consider two measures of returns from momentum strategies. The first is the return
an investor would receive from holding the Fama–French momentum factor portfolio.6 The
4
Pre-CRSP-era historical data have been used before to assess some of the salient empirical features of asset
returns. Schwert (1989) uses 1857–1986 U.S. stock return data to investigate the cause of stock volatility. Schwert
(1990) analyzes the relation between stock returns and real economic activity with 1889–1988 U.S. stock data.
Goetzmann (1993), Goetzmann, Ibbotson, and Peng (2001) and Annaert and Van Hyfte (2006) study long-term
predictability in London since 1695, the NYSE between 1815 to 1925, and the 19 th century Brussels stock exchange,
respectively.
5
The LSE used fortnightly clearing that minimized the costs of forming long–short portfolios. On the day before
settlement, the LSE clearing house ran a netting operation where shorts who did not want to deliver shares could be
matched with longs who did not wish to take delivery. Supply and demand was equated by the “contango” or
“backwardation” rate—the repo rate paid by longs and shorts to carry their position for another 14 days. Thus,
shorting involved none of the search frictions modeled in papers such as Duffie et al. (2002). See Rates of Interest
on Collateral Call Loans 66th 2nd session Congress Senate Doc 262 for a description of shorting on the Victorian
LSE and a comparison to practice on the NYSE.
6
The momentum factor portfolio is formed monthly by sorting stocks at time t into one of six value-weighted
portfolios formed on size and month t-12 to t-1 return. The six portfolios are the intersections of two portfolios
formed on size and three portfolios formed on prior return. The monthly size breakpoint is the median NYSE market
6
second, which we call the FF7030 portfolio, is computed from the Fama–French decile portfolios
formed monthly on momentum. The FF7030 portfolio is the return an investor would receive
from buying a value-weighted combination of the three Fama–French decile momentum
portfolios with prior returns above the 70th percentile and shorting a value-weighted combination
of the three portfolios with prior returns below the 30th percentile.7
Table 1 reports the average, standard deviation and skew of momentum portfolio returns
in the United States between 1927 and 2012 and London between 1867 and 1907. Momentum
strategies generated positive returns with remarkably similar Sharp ratios across both eras, but
the CRSP-era NYSE momentum portfolios generated higher average returns along with more
variance and skewness.
CRSP-era momentum is a well-known anomaly. The CRSP-era Fama–French momentum
factor and 7030 portfolio returns cannot be explained by their exposure to the Fama–French
market, small minus big (SMB), and the high book-to-market minus low book-to-market (HML)
risk factors. Were momentum returns always abnormal? Table 1 also reports the coefficients
from a regression of momentum portfolio returns on two three-factor models:
(
){
}
(
(
){
}
(
){
){
}
}
(
(
){
}
){
( )
}
( )
The first model (1) is the familiar Fama–French three-factor model, where the SMB size factor
and the HML value factor are both formed from double sorts that require accounting-book value.
Unfortunately, accounting data are either unavailable or unreliable for most stocks trading in
London before 1907. We therefore estimate a second three-factor model (2) with size and value
factors formed on variables observable in the pre-1907 London market. Our size factor (Size) is a
monthly small-minus-big portfolio formed by buying a value-weighted portfolio of all stocks
with a market value below the median and shorting a value-weighted portfolio of all stocks with
equity. The prior return breakpoints are the 30th and 70th percentiles. The momentum factor portfolio is the average
return on the two high prior return portfolios minus the average return on the two low prior return portfolios,
7
Fama–French portfolios are derived based on data from CRSP US Stock Database ©2013 Center for Research in
Security Prices (CRSP), The University of Chicago Booth School of Business.” Available online at
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.
7
a market value above the median. Our value factor (Divyield) is a monthly high-minus-low
portfolio formed on dividend yield. We form this value factor by sorting stocks each June based
on the same criteria that Fama and French use to construct portfolios formed on dividend yield.
Fama and French assign stocks to one of four portfolios based on dividend yield (no dividend,
bottom 30%, middle 40%, top 30%). Our high-minus-low dividend yield portfolio is the monthly
return on the top 30% of dividend-yielding stocks minus the return on the stocks that paid no
dividends.
Table 1 reports the regression coefficient from monthly time-series regressions of
momentum strategy returns on the factors in (1) and (2) for the CRSP-era United States and (2)
for the pre-1907 London stocks. The monthly CRSP-era momentum factor alpha is 101 basis
points in both specifications (1) and (2), and the monthly CRSP-era FF7030 alpha is 88 and 89
basis points, respectively. The similarity of alphas across specifications (1) and (2) reassure us
that our alternative size and value factors capture the risks spanned by the traditional Fama–
French SMB and HML factors.
The momentum strategy generated positive alpha in pre-1907 London as well. An
investor who held the Fama–French momentum factor or the FF7030 portfolio would have
enjoyed 28-day alphas of 52 and 49 basis points, respectively. The pre-1907 alphas are only 55%
as large as the CRSP-era alphas, but the momentum strategy generated strongly statistically
significant abnormal returns.
While the momentum strategy generated comparable Sharp ratios and statistically
significant alphas across both sample periods, the Victorian-era momentum returns were less
negatively skewed. Presumably, the limited role of delegated portfolio management during the
Victorian era diminished the crash risk due to contagious investor liquidations. However, the
ease with which Victorian retail investors could finance long–short positions in the stock lending
market suggests the risk of crashes due to binding leverage constraints discussed earlier
remained.
1.1 Dating Momentum Bull and Bear Markets
The momentum returns across both eras can be characterized by abnormally high returns
punctuated by occasional steep but predictable losses. To show this, we first date momentum bull
8
and bear markets via the Lunde and Timmermann (2004) algorithm. Bull (Bear) markets are
colloquially defined as a long-term upward (downward) trend in prices with inconsequential
interruptions. Lunde and Timmermann (2004) formalize this intuition with a dating algorithm,
which we briefly describe next.8
Assume time is measured at discrete intervals and the price of the portfolio of interest at
the end of time t is Pt. Let It be a bull market indicator equal to 1 if we are in the bull state at time
t and 0 otherwise. Let be a scalar defining the threshold of stock price movements that trigger
a switch from a bear to a bull market and 2 the threshold of stock price movements that trigger a
switch from a bull to a bear market. Suppose that at time t0 the portfolio is in a bull market at a
local maximum (It0 = 1). Set
, where
is the value of the portfolio at time t0. Let
max and min be stopping-time variables defined by
(
|
(
The
)
(
)
|
)
}
{
(
)
}
) is the first time the price crosses one of two barriers {
}. If
by setting
{
( )
(
, then we have a new local max. Update the current bull market state
equal to 1 when t is in the interval
to
and
and
continue with the new local max.
Conversely, if
, the price has declined by a sufficient amount to switch from
a bull to a bear market that has prevailed since t0. Set
to
and define
equal to 0 when t is in the interval
. If the starting point at t0 is a bear market, then the
stopping times are defined as
(
(
8
|
)
|
{
)
}
{
(
This description is taken from Lunde and Timmermann (2004, p. 254–255).
9
)
}
( )
This algorithm partitions the momentum return time series into bull or bear markets (i.e.,
or
for all t). We consider symmetric thresholds (
) for transitions between
bull and bear markets. There is no consensus on what the thresholds should be. Exceedingly
large thresholds will result in few transitions between bull and bear market states and are likely
to diminish the power of our hazard model analysis. On the other hand, if we set the thresholds
too small, we run the risk of labeling small fluctuations, which may be inconsequential to the
decision making of momentum traders. We weigh these trade-offs and decide to choose
symmetric 5% and 10% transition thresholds. We think these thresholds are large enough to
affect the behavior of momentum investors who often employ leverage and are therefore
sensitive to even small drawdowns while remaining small enough to generate a number of cycles
in the data.
Table 2 reports the frequency, duration, and average cumulative loss from momentum
strategy bear markets during both the CRSP and Pre-1907 eras. The CRSP-era momentum factor
and the FF7030 portfolios suffered bear market declines of at least 5% 63 and 68 times,
respectively, between 1927 and 2012. Bear markets of at least 5% occurred approximately every
15–16 months, and the average cumulative loss was 13.6% and 14.8%, respectively!
Given the absence of the delegated portfolio managers in the Pre-1907 era, we should
expect crashes to be less severe and less frequent. In fact, bear markets in momentum were both
less frequent and more benign before 1907. While the momentum factor and 7030 portfolios
suffered bear market declines of at least 5% every 16 or 15 months, respectively, during the
CRSP era, these same strategies suffered bear markets every 28 or 25 months during the pre1907 era. When bear markets did occur, both the speed and magnitude of declines were smaller.
The past 150 years illustrate that there is clearly more to momentum returns than
large alphas. Although the momentum strategy generated high abnormal returns on
average, the strategy has exposed momentum traders to brief but sharp declines. Cyclicality
is consistent with many behavioral and rational explanations of momentum. Cooper,
Gutierrez, and Hameed (2004) note that the theory of Daniel, Hirshleifer, and Subrahmanyam
(1997) predicts differences in momentum profits across states of the market. Momentum cycles
may also reflect changing risk over the business cycle. Chordia and Sivakumar (2002) show that
macroeconomic instruments commonly used for measuring macroeconomic conditions can
10
explain a large portion of momentum profits. Moskowitz, Ooi, and Pedersen (2012) find that
momentum across many markets is consistent with initial under-reaction and the trading
behavior of speculators, while Asness, Moskowitz, and Pedersen (2013) find that momentum
across many markets can be partially explained by liquidity and long-run consumption risks.
As noted in the Introduction, we are not the first to notice cyclicality in momentum
returns or the predictability of momentum crashes. One of our contributions is to introduce a
hazard model that successfully captures the time-varying likelihood of momentum downturns,
and examine the extent to which market conditions when momentum crashes become more
likely are the same during the Victorian and CRSP eras.
2. Predictable Momentum Cycles
If capital constraints prevent skilled investors from driving excess momentum returns to
zero, we speculate that a measure of capital scarcity should predict the duration of
momentum profit cycles. To test this formally, we introduce a new methodology based on
modeling profit duration dynamics as a function of the risk-free rate, the past stock market
return, and the past performance of the momentum strategy, which we interpret as a proxy
for the scarcity of capital available to skilled managers employing momentum strategies.
Fund managers find it easier to attract new assets when their past performanc e is
strong.9 Likewise, self-leveraged investors have more money to invest when their strategy
has performed well in the recent past. The past return of the momentum strategy is
therefore likely to contain information about how crowded the momentum trade i s. Money
crowding into the momentum strategy is likely to both reduce any future returns
attributable to slow moving capital and increase the probability that a negative shock will
result in a large decline as more leveraged investors are forced to liquida te and rush for the
exit.
If capital constraints do limit arbitrage, we would expect a measure of capital
scarcity to predict the duration of momentum profit cycles. We model the hazard of the
momentum strategy transitioning from a bull to a bear market and find strong evidence that
9
Agarwal, Daniel, and Naik (2009) and Fung, Hsieh, Naik, and Ramadorai (2008) have documented the AUM
Flow-Performance Relationship with individual hedge funds and funds of funds, respectively.
11
our proxy for capital available to momentum traders predicts momentum cycles.
2.1 The Discrete Time Hazard Model
We model the hazard of a transition from a momentum strategy bull market to a
bear market. We start with the assumption that the data are generated with a continuous
time process with a proportional hazard
(
( )
)
( )
( )
is the baseline Weibull hazard, where t is the age of the bull market and X
are covariates that shift the hazard relative to the baseline. The Weibull specification
allows for duration dependence in the baseline hazard. If > 1, the baseline hazard
increases as the bull market ages; if < 1, the baseline hazard decreased as the bull ages;
and if = 1, the baseline hazard becomes the exponential model with constant hazard.
When the data are generated by (5), Prentice and Gloeckler (1978) derive the
discrete time hazard with time-varying covariates. The probability that a bull market ends
at time t is Prt:
( )
(
where
Let
) ( )
is the Weibull baseline hazard.
be a dummy variable equal to 1 if the bull market ends at time t and 0
otherwise. The discrete time log-likelihood function is 10
∑
where
(
)
∑
(
)
( )
is the number of time periods at risk (the number of time periods in bull
markets).
We estimate (7) via maximum likelihood with three covariates in Xt. Our first
10
See Allison (1982)
12
covariate—the level of the time t risk-free rate—captures the opportunity cost of capital.
Our second and third covariates are the cumulative return on the momentum portfolio and
the value-weighted market portfolio from time (t-12) to (t-1)—which captures the
performance of the momentum strategy relative to the market over the past year .
2.2 Empirical Findings
The estimated hazard model coefficients are reported in Table 3. Holding the past
return on the market fixed, high past returns on the momentum strategy increase the odds
of the onset of a bear market in momentum in both the NYSE CRSP and Pre -1907 London
data. On the other hand, holding the past momentum return fixed, higher past returns on the
market lower the odds of entering a bear market in momentum during the CRSP era, but
increase the odds of entering a bear market in the Victorian era, and statistica lly
significantly so for the 7030 momentum strategy. Again, this is consistent with the
institutional differences across the two eras. In the Victorian era, when delegated portfolio
management was not in vogue, individual investors engaging in momentum trading
financed their positions by pledging their financial assets as collateral. An increase in the
level of the stock market would increase collateral values, thereby reducing the odds of
crashes induced by forced selling to meet collateral calls. In contrast, during the CRSP era,
when professional money management became more prevalent, superior past stock market
performance would decrease the relative attractiveness of investing in momentum
strategies to owners of money, especially return-chasing blind capital. Consequently,
momentum strategies were likely to be less crowded following superior stock market
performance. 11
High levels of the risk-free rate decreased the odds of a bear market in momentum
during the Victorian era but had no effect on bear market odds in the CRSP sample. Again,
this is consistent with institutional differences. In the Victorian era, absent the availability
of other peoples’ money, a momentum trader could only deploy large amounts of money
11
See Agarwal et al. (2009) and Fung et al. (2008) for the effect of relative performance on investment flows.
13
through margin borrowing. 12 An increase in the level of the risk-free rate raised the cost of
margin borrowing, which would make the momentum strategy funded by margin borrowing
less attractive and consequently less crowded.
The hazard models do an excellent job fitting the data. Momentum bear ma rkets can
be forecasted with surprising precision. Figure 1 plots the receiver-operating-characteristic
(ROC) curve for the full model estimated with the CRSP-era data and the Fama–French
momentum factor. 13 In our context, the hazard model generates a time-varying probability
of transitioning to a bear market. A money manager who wishes to avoid bear markets
could select a discrimination threshold above which he will exit momentum and move into
cash.
Partition the data sample into crash months (denoted by C) and no crash months
(denoted by NC). If a crash occurs while the money manager is in cash, the model has
correctly predicted that bear. Let c* denote the number of crash months that occur when the
manager is in cash. Define the true positive rate as
. Similarly, let nc* denote the number
of months when the manager is in cash and no crash occurs. Then the false positive rate
is
.
Consider an extremely careful manager who chooses a very low discrimination
threshold such that he is always in cash. All crashes will occur when this manager is in
cash, and consequently the true positive rate
equals 1. However, by choosing such a low
threshold, the manager will also be in cash every time a crash does not occur, and the false
positive rate
will also be 1. As the manager increases the discrimination threshold, both
the false positive and true positive rates will decline. The ROC curve plots the trade -off
between the true positive and false positive rates as the money manager varies the
discrimination threshold above which he will exit the momentum strategy.
The area under the ROC curve (AUC) is a summary statistic of the model’s goodness of
fit. A model that can successfully predict every transition from bull to bear with no false
12
It was exceptionally easy for a Victorian-era retail investor to lever long–short portfolios with margin loans. See
Chapter 17 in Duguid (1902) and Chiswell (1902, p. 11–18) for descriptions of the rules and practice of short selling
with margin on the London Stock Exchange.
13
The ROC curve is a common tool used in engineering, medicine, and machine learning for measuring the
accuracy of diagnostic models of rare events. See Swets (1988).
14
positives will have an AUC of 1, while a model with no ability to forecast will have an
AUC of .5.14 Our hazard model is estimated to fit within sample, so even if the underlying
data are generated from i.i.d. returns selected at random with no predictability, the
estimated AUC will be greater than .5. To evaluate the predictability in a time series of
data and a given model, one can bootstrap the AUC by generating data series via random
draws with no memory and fit the model to each draw to compute the distribution of AUCs
under the null of no predictability. Using this bootstrap procedure, we find that momentum
return bear markets are predictably different from random at the 1% significance level in
all specifications.
In addition to the probability of transitioning to a bear market increasing with past
momentum returns, the return to investing in momentum conditional on remaining in a bull
market also increases with past momentum return.
In Table 4 we select only the realized momentum strategy returns where the momentum
portfolio was purchased in a bull market (return realized at time t if t-1 is a bull state). We
partition this data into decile bins based on the percentile rank of momentu m strategy
returns from time (t-12) to (t-1). Therefore, the 1 st decile is the one-month return one would
receive if they invested in the momentum strategy when the average return of momentum
over the past year was in the lowest 10% of all bull market states, and the 10 th decile is the
one-month return one would receive if they invested in the momentum strategy when the
average return of momentum over the past year was in the highest 10% of all bull market
states.
Conditional on past momentum return deciles, Table 4 reports the probability of
transitioning to a bear market, the annualized sharp ratio of the one-month return, and the
one-month momentum strategy return conditional on remaining in a bull market or
transitioning to a bear market. In the CRSP era, the probability of transitioning to a bear
market increases dramatically and the sharp ratio for remaining invested in the momentum
strategy declines when the past year’s momentum strategy return enters the top decile.
14
For example, the ROC for the naïve model that each month assigns the same probability of transitioning from bull
to bear will have two points, (0,0) and (1,1) and the area under the line connecting these points will be .5 .
15
2.2 Profiting from Predictability: Managed Portfolios
As we noted earlier, it is well recognized in the literature that times when momentum
crashes are more likely is predictable in real time 15. What is interesting is that the hazard
model coefficients tell us that the probability of a momentum crash increases with the
performance of momentum over the past year (relative to the overall stock market) – during
the Victorian as well as the CRSP eras. In what follows we illustrate a simple rule that
exploits this predictability to manage the investment in the momentum strategy to improve
the Sharpe Ratio of the managed portfolio which confirms that momentum risk goes up
more than momentum return when momentum has done well in the past.
Define the recent relative performance of momentum at month t as the difference
between the return of the momentum strategy and the return on the market index over the
past K months:
(
percentile rank of
)
(
)
in the set of
. And define
as the
.
Consider a portfolio manager who constructs a managed portfolio that switches between
the momentum strategy and risk-free security by investing in momentum whenever
is below a predetermined
threshold and holds the risk-free asset
otherwise. For example, if the manager chooses K to equal 3 years (K=36) and sets the exit
threshold at the 90 th percentile, this manager’s realized return in month t+1 will equal the
is below the 90th percentile of all
return on the momentum strategy whenever
and the risk-free return otherwise. We chose K = 36 given the well
documented long run momentum reversal phenomenon where 36 months was chosen as
long run in several empirical studies. When K is set equal to 36, the portfolio management
rule does not always exit momentum, but only when the threshold is crossed.
Figure 2 plots the change in the CRSP-era Sharp Ratios of managed portfolios formed
by switching between the Fama-French momentum factor portfolio and the risk-free asset
at different thresholds of
and K=36 months. A manager who always invests
in momentum chooses a threshold of 100 and would have earned a Sharp Ratio of .66 from
1950-2012 and .45 from 1930-2012. A manager who exited momentum and switched to the
15
See Chabot et. al. (2009) Daniel and Moskowitz (2014), Daniel, Kim and Jagannathan (2012) and Baroso and
Santa Clara (2013).
16
risk free asset whenever
exceeded the 75 th percentile of all
over the
past 3 years would have enjoyed a higher Sharp Ratio of .83 between 1950-2012 and .65
between 1930-2012.
3. Why Money Managers Stay Invested when Crash Risk Is Elevated
The hazard model coefficients and areas under ROC curves imply that bear markets in
momentum can be forecasted based on the past performance of the momentum strategy. The
probability of a bear market in momentum increased significantly when the momentum strategy
has performed well over the past year. This is consistent with market folk wisdom. The
“crowded trade” is common jargon amongst practitioners for a strategy that performed well in
the past but has attracted so much money that it is now unprofitable and risky. Nonetheless, some
of the empirical evidence suggests that even skilled money managers may crowd into strategies
that have generated recent success.16
Why would skilled money managers not exit the momentum strategy when the
probability of a bear market is high? Two factors diminish the incentives for fund managers to
attempt to strategically enter and exit the momentum strategy. First, fund managers are often
compensated with incentive fees equal to a portion of profits above a high-water mark and solicit
funds from return-chasing investors. The momentum strategy is most likely to transition into a
bear market when past returns are high. This is exactly the time when a fund manager is most
able to attract more funds and likely to have a high proportion of his assets under management
above the high-water mark. The risk-shifting convex payout structure of incentive fees can
combine with the return-chasing behavior of future investors to provide incentives for fund
managers who have a finite horizon to remain in a crowded momentum strategy.17 Secondly, as
we discussed earlier, the return to investing in momentum conditional on remaining in a bull
market increases with past momentum return as well. Therefore, a manager who exited
16
See Pedersen (2009) for a theoretical overview and example of crowded trades and subsequent crashes. Fung et al.
(2008) document the performance–flow relationship in funds of hedge funds and find that capital inflows to funds
that have over-performed in the recent past attenuates the ability of past alpha-producing funds to continue to deliver
market-beating returns.
17
Many authors have claimed that the fee structure of hedge funds creates an incentive for excess risks. For
instance, see the models of Carpenter (2000) or Goetzmann, Ingersol, and Ross (2003).
17
momentum when past returns were high would avoid the risk of being invested in momentum
during a bear market but would also forgo abnormally high returns should the bull market in
momentum persist.
In the remainder of this section, we first illustrate the effects of the convex compensation
structure and return-chasing investors on rational fund managers’ behavior using a parsimonious
two-period game-theoretic model. We then, explore the profitability of various managers’
strategies in a richer setting via a simulation that reflects the conditional return dynamics
documented Table 4.
3.1 An Illustrative Model of Fund Managers’ Behavior
Why would a sophisticated money manager remain invested in momentum when the
probability of a large decline is high? In this section we present a parsimonious model that
illustrates how risk-shifting convex incentive fees and return-chasing investors can combine to
provide incentives for fund managers to remain invested in momentum even when the
probability of a crash is high.
The model consists of two time periods, two investors, and two fund managers who can
allocate funds between cash and the momentum strategy with the following return dynamics.
Returns:
Each period, the gross momentum return can take one of two values, Rup > 1 or Rdown < 1.
We model the predictability of momentum returns as a two-state Markov process where the
states are unobservable to investors but observed by skilled fund managers before making
investment decisions. The probability of Rup is pUG in the good state and pUB in the bad state with
pUG > pUB. The probability of transitioning between states is governed by a 2x2 Markov transition
matrix with the (i,j)th element i,j equal to the probability of transitioning from state i to state j.
Investors:
Each of the two investors has $1 of saving each period. Investors can allocate this saving
between cash with a risk-free unit gross return or deposit it with one or both fund managers who
can invest in the risky momentum strategy. In the first period, investors have no signal about the
managers’ skills and choose to divide all their period 1 savings equally between the two fund
managers. In period 2, investors’ return-chasing behavior manifests itself in two ways. First, any
18
investment in momentum will be allocated to the fund manager(s) who performed best in period
1. Second, investors allocate all of their period 2 savings to the best-performing fund manager(s)
if the momentum strategy generated positive returns in period 1 and a smaller amount (f<1) of
their period 2 savings to the fund managers if the momentum strategy generated negative returns
in period 1. We further assume that the flow f is sufficiently small such that (Rdown+f)*Rup<(1+f).
Investor behavior results in the following aggregate cash flows to fund managers based
on their period 1 performance. In period 1, $2 is split equally between the fund managers. If
momentum earns a positive return in period 1, an additional $2 is allocated to the fund manager
with the best period 1 performance or split equally if both managers enjoyed the same return in
period 1. If momentum earns a negative return in period 1, however, $2*f is allocated to the fund
manager with the best period 1 performance or split equally if both managers enjoyed the same
return in period 1.
The fund managers provide investors with access to the momentum strategy via the
following contract. Managers take deposits from investors in each period. For analytical
convenience, we only allow contracts where any money given to a manager is committed until
the end of period 2. At the end of period 2, managers subtract a management fee equal to a
proportion
of investment profits and return the remaining money to investors. Due to
our assumption that (Rdown+f)*Rup <(1+f), fees will be zero unless the managers’ returns are
weakly positive in both time periods.
Fund Managers’ Decisions:
Each period fund managers decide whether to invest their assets under management in
cash or the momentum strategy. The fund managers’ skills enable them to observe the state
before choosing how to allocate funds between momentum and cash. Managers are risk neutral
and maximize their expected management fee taking investors’ return-chasing behavior and the
strategy of the other manager as given. Let fee1 denote the management fee of the first fund
manager.
19
Period 2 Strategies:
There are 16 states of nature at the beginning of period 2. The states are characterized by
what each of the two managers choses (to invest in momentum or cash), the realization of the
period 1 return on momentum (up or down), and the state going into period 2 (good or bad)—
i.e., 24 = 16. Without loss of generality, consider the strategies available to manager 1 at the
beginning of period 2 in each of the 16 states. If manager 1 did not invest at the beginning of
period 1 (8 of the 16 states), investing at the beginning of period 2 dominates not investing. To
see this, note that when the manager does not invest at the beginning of period 2, he will get no
fees at the end of period 2. Investing gives positive fees with positive probability. So, for 8 of the
states the strategy is to invest regardless of what the other manager chooses to do. Suppose
manager 1 had invested in momentum at the beginning of period 1 and the return on momentum
was down (4 of the remaining 8 states). Given our assumption that (Rdown+f)*Rup <(1+f), the
manager will get no fees regardless of his period 2 investment decision. Suppose manager 1 had
invested in momentum at the beginning of period 1 and the return on momentum was up (the
remaining 4 states). Then manager 1 will have Rup + 1 or Rup+2 assets under management
depending upon manager 2’s investment decision at the beginning of period 1. Suppose the state
is bad at the beginning of period 2. Then manager 1 will always invest if [(Rup+1)Rup-2]*PUB >
(Rup-1) . We limit our parameter space to values of Rup and PUB such that [(Rup+1)Rup-2]*PUB >
(Rup-1). Since PUG > PUB, manger 1 will always choose to invest regardless of the state at the
beginning of period 2. To summarize, manager 1 will always invest in momentum at the
beginning of period 2. He will only be paid a fee if the momentum strategy has a high return Rup
in period 2. We have therefore shown that at the beginning of period 2, both managers will
remain invested in momentum.
Now consider the decision rule of manager 1 at the beginning of period 1. Given that the
optimal strategy during period 2 is to always invest in momentum, the expected management fee
conditional on the period 1 state and period 1 investment decision of manager 2 can be written as
follows.
20
Given: Bad State (st1 = bad) in period 1, Manager 2 holds cash in period 1.
Expected fee of Manager 1 to investing in momentum in period 1:
E[fee1 | mom,cash,st1 = bad] =
(
)
(
)
(8a)
Expected fee of Manager 1 to holding cash in period 1:
E[fee1 | cash,cash,st1 = bad] ={
) (
{[(
(
)]
)
(
)
(
) }
}.
(8b)
Given: Bad State (st1 = bad) in period 1, Manager 2 invests in momentum in period 1.
Expected fee of Manager 1 when investing in momentum in period 1:
E[fee1 | mom,mom,st1 = bad] =
(
)
(
)
(
) .
(8c)18
Expected fee of Manager 1 to holding cash in period 1:
E[fee1 | cash,mom,st1 = bad] = {
(
)]
(
(
)
) }
}.
{[(
)
(8d)
Given: Good State (st1 = good) in period 1, Manager 2 holds cash in period 1.
Expected fee of Manager 1 when investing in momentum in period 1:
(
E[fee1 | mom,cash,st1 = Good] =
)
(
) .
(8e)
Expected fee of Manager 1 when holding cash in period 1:
(
E[fee1 | cash,cash,st1 = Good] ={
{[(
) (
)]
)
(
)
18
(
}.
) }
(8f)
Note that (8c) implicitly assumes that the case where Rdown in period 1 is followed by Rup in period 2 yields zero
)
(
)
(
)
fees, which is only true if (
, or equivalently,
21
Given: Good State (st1 = good) in period 1, Manager 2 invests in momentum in period 1.
Expected fee of Manager 1 when investing in momentum in period 1:
(
E[fee1 | mom,mom,st1 = Good] =
)
(
)
(
)
}.
)
(8g)
Expected fee of Manager 1 when holding cash in period 1:
E[fee1 | cash,mom,st1 = Good] = {
) (
{[(
(
)]
(
) }
(8h)
We are interested in showing that for reasonable parameter values, an equilibrium with the
following properties exists: (A) If investors could directly invest in momentum after observing
the state, they would prefer to hold cash in the bad state. (B) Despite their ability to observe the
state, all fund managers choose to remain invested in momentum when period 1 is a bad state.
(C) Investors who use the steady state probabilities implied by the Markov transition probability
matrix to compute expected values prefer to allocate funds to managers rather than hold cash
even though they know that managers will always remain invested in momentum. In addition,
previously discussed parameter restrictions include (D)
(
(
)
and (E)
).
(
A) Implies
)
B) Implies (8a) >(8b) and (8c) >(8d), which also automatically ensures (8e)>(8f) and
(8g)>(8h)
C) Implies
|
|
Where:
is the row vector of steady-state probabilities that satisfy
for the
matrix of transition probabilities ;
and m is the money returned to an investor at the end of period 2, in excess of what was
invested;
22
|
]
[
) (
[(
[
[
)]
[
]
(
where
)]
]
|
]
) (
[(
) is the probability of drawing two up returns
conditional on the good state in period 1, and
are similarly defined.
For reasonable parameter values (Rup =1.02, Rdown =.75, PUG =.99, f =.5, and I,j =.5
for all i and j), Figure 4 plots manager 1’s profits as a function of his period 1 investment choice
and the crash probability (1-pUB) when the first period is a bad state and manager 2 holds cash.
The fund manager is indifferent between investing in momentum or holding cash at the breakeven value of PUB equal to .426. As long as the probability of a crash in the bad state is less than
(1-.426), manager 1 will prefer to respond to manager 2’s decision to hold cash in the bad state
by investing in momentum. It can be verified that manager 1 will prefer to respond to manager
2’s decision to be in momentum in the bad state by investing in momentum under these
conditions.
In Table 5, we confirm that all equilibrium conditions exist for a reasonable choice of a
10% crash probability in the bad state (i.e.,
,
,
,
). When
, and
and
,
for all i and j,
. Table 5 summarizes and confirms that all equilibrium conditions are met.
23
and
Table 5:
Equilibrium conditions of the 2-player game
Condition
Expression
Value
(
(A)
)
0.993<1
(
(B1) (8a)>(8b)
(
)
)
(
)
(
(B2) (8c)>(8d)
(
)
)
0.0103>0.0042
(
)
|
(C)
0.0137>0.0077
|
0.0045>0
(D)
0.90>0.33
(
)
(
(E)
)
0.765<0.99
3.2 Profit Simulations with CRSP-Era Data
The example above explains in a simple two-period, two-player game setting the
apparent paradox that even though large momentum losses are predictable, sophisticated money
managers may nonetheless crowd into the momentum strategy at times of elevated risk. The
actual dynamics of conditional momentum returns and predictable crashes and investor returnchasing behavior is too complex for a multiplayer, multi-period game. Instead, we use the CRSP
data to calibrate a simulation of the profits managers could expect to earn by following
momentum timing strategies when the number of time periods and competing funds are large.
Our simulations suggest that managers who aggressively remain invested in momentum even
when the likelihood of a crash is high outperform managers who attempt to time the momentum
strategy.
24
3.2.1 Fees and Assets under Management
Our simulations model the profits of money managers who are compensated by collecting
a monthly management fee equal to 2/12ths of a percent of assets under management and a
quarterly performance fee of 20% of profits above a high-water mark. These managers compete
with each other to manage the investment funds of return-chasing customers who reallocate their
investments each month by withdrawing 1% of assets under management (AUM) from the
managers in the bottom quartile of performance over the past year and invest an equal portion of
these funds with the managers in the top quartile of performance over the past year. In addition
to the monthly reallocation, investors devote new funds or withdraw existing funds from the
momentum strategy each month based on the relative performance of the momentum strategy.
We assume these new deposits or withdrawals are equal to 20% of the difference between the
return on the momentum strategy and the return on the value-weighted market portfolio over the
past year. Therefore, if the momentum strategy outperformed the market by 10% over the past
year, investors would invest new funds equal to 2% of existing assets under management.
Likewise, if the momentum strategy underperformed by 10%, investors would withdraw 2% of
assets under management. We assume new investment is divided equally amongst the funds in
the top quartile of performance over the past year and all funds are subject to withdrawals when
the momentum strategy underperforms.
These realistic assumptions—that funds have a fee structure of 2–20 with high-water
marks, and investors chase returns by depositing more money in top-performing funds when
their track record is good and withdrawing funds from underperforming funds and strategies—
create incentives for money managers to stay invested in the momentum strategy even when the
probability of a crash is high. The intuition is simple: the very time that crash risk is high is also
the time when a high proportion of AUM is likely to be above high-water marks and a large
inflow of new assets awaits any manager who outperforms his peers in the immediate future.
3.2.2 Simulated Returns
We simulate 25 years of returns to match the conditional returns and bear markettransition probabilities of the CRSP-era Fama–French momentum factor portfolio previously
25
reported in Table 4. Specifically, we simulate returns by drawing from an 11-state Markov chain,
with states 1–10 corresponding to the 10 bull market states in Table 4 and state 11 corresponding
to the bear markets. We calibrate the Markov transition matrix to match the sample transition
probabilities in the CRSP data.
We form a time series of returns via the following algorithm:
1) Begin by selecting a bull market state at random, and draw one monthly momentum
and market return pair at random from the sample returns of the selected state.
2) Draw a state at random to transition to, where the probability of transitioning to the
next state is determined by the Markov transition matrix calibrated to the CRSP data.
3) If the draw results in another bull state, select a random momentum and market return
from the sample returns of the selected state and return to 2) to draw a new state.
4) If the draw is a bear state, select an entire sequence of momentum and market returns
from the 63 bear markets in the CRSP data (we choose the entire sequence to assure
that once one transitions to a bear market, the momentum strategy will lose at least
5%). Once the bear market is complete, draw a new bull state at random from the
Markov transition probabilities.
5) Let this process run for 100 years and select the last 25 years for analysis.
6) Repeat steps 1–5 5,000 times to generate 5000 times series of simulated returns.
3.2.3 Profits as a Function of Risk-Taking
We wish to show that in our simulations calibrated with CRSP data, money managers
who go to cash in periods of elevated crash risk are less profitable on average than managers
who remain invested in the momentum strategy. Of course, due to the tournament nature of
return-chasing investors, profits depend on the behavior of other fund managers.
We model the behavior of fund managers by assigning each a risk threshold based on the
past momentum return percentile beyond which they exit momentum and place their funds in
cash earning the risk-free rate. For example, a type 80 manager would invest in the momentum
strategy if the past year’s momentum return were at or below the 80th percentile of all 1-year
lagged returns, while a type 99 manager would not exit momentum until the 1-year lagged return
exceeded 99% of all sample returns.
26
The profits of a given type depend on the distribution of types he is competing against.
To summarize the riskiness of the distribution of types in a parsimonious manner, we assign a
proportion of managers to the 70–80 interval at random and a proportion (1-of managers to
the 90–100 interval at random. Thus, if alpha = .1, 10% of the managers will be conservative
types assigned a uniform random integer between 70 and 80, and 90% will be aggressive types
assigned a uniform random integer type between 90 and 100.
We run 5000 simulations of 100 competing fund managers who begin with the same
initial assets under management. Table 6 reports the average profits of managers as a proportion
of the average profit of the most aggressive, type-100 manager. The more aggressive managers
are more profitable on average. For example, in the economy where 90% of the managers are
conservative types (=.9), the conservative fund managers earn average profits that range from
27.7% to 68.2% of the profits of a manager who is always invested. The conservative fund
managers underperform by an even worse margin in an economy with more aggressive
competitors. In the economy where only 10% of the managers are conservative types (=.1), the
conservative fund managers earn meager average profits that range from 9.64% to 37.6% of the
profits of a manager who is always invested.
The aggressive type of fund manager earns higher average profits across all values of
alpha. These simulations suggest that a profit-maximizing manager who took other managers’
behavior, momentum returns, and crash probabilities as given would chose a very high threshold
of past return beyond which he would exit momentum and hold cash.
4. Conclusion
Using unique historical data on stock returns spanning 140 years, we examine the returns
on one of the most popular mechanical trading strategies—momentum. We confirm that
momentum investors have enjoyed large abnormal risk-adjusted returns. However, the strategy
also incurs infrequent but very large losses.
These losses are more likely to occur during periods when capital is easily available to
investors employing the momentum strategy with other people’s money. In Victorian London,
momentum investors could leverage via margin loans collateralized by the value of their
portfolio, and momentum crashes were more likely to occur following large momentum strategy
27
gains and periods of easy availability of margin leverage as evidenced by low interest rates. In
the CRSP era, when many momentum investors access other people’s money through active
funds established to invest in momentum, crashes are more likely to occur when the recent
performance of momentum has compared well with the overall stock market. These are times
when momentum fund managers are likely to find it easy to access the blind capital of returnchasing investors.
In light of the fact that momentum crashes are predictable, why do professional money
managers not take steps to avoid momentum crashes? The answer may lie in the fact that the
times when the hazard of momentum crashes is high are exactly the times when a momentum
fund manager will have a strong recent performance and find it easy to attract funds from returnchasing investors. We show that even sophisticated money managers may rationally crowd into
momentum strategies at these times of elevated risk. We argue based on both a stylized model
and simulated outcomes from a richer model that a money manager who competes for funds
from return-chasing investors and is compensated via fees that are convex in the amount of
money managed and the return on that money has an incentive to remain in a crowded
momentum trade even when the hazard of large losses is high.
What are the policy implications, if any? There is indeed a growing concern among
regulators and market participants that large inflows of capital into trading strategies—such as
momentum—may contribute to market fragility. Our findings suggest that regulators who wish
to monitor the buildup of crash risk in the financial sector should pay particular attention to
strategies that become crowded by inflows of blind capital following recent success. Those are
the times when the interests of even sophisticated money managers may start diverging from the
interests of those whose money they manage when it comes to deciding how much risk to take.
28
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31
Appendices
The London Stock Market Data: 1866–1907
The closing bid and ask prices were collected from the quotation list of The Money Market Review, a weekly
financial paper published in London between 1860 and 1908. Published on Saturdays, The Money Market Review
reprinted H.H. Wetenhall's official quotation list of the previous Friday's closing prices. These were the official
prices published by the Committee of the Stock Exchange under the name “Course of the Exchange.” The data were
sampled every 28 days, rather than the more traditional end-of-month observations, due to the newspaper’s weekly
publication schedule.
The official list was organized by industry and asset type. The list begins with British government debt, then
lists foreign government debt and British, Commonwealth, and foreign railroads, and concludes with commercial
securities organized by industry (banks, breweries, canals and docks, insurance, iron, coal and steel, gas, mining,
shipping, spinning, waterworks, tea, land, financial and investment trusts, and miscellaneous securities). The
Money Market Review's list is not complete. Some industries do not appear on certain dates, and, within
industries, individual stocks may have no price for one or more dates. When possible, we filled in the missing
price data with The Economist's “Stock Market Prices Current.” The Economist's price list included only the
largest and most active securities listed in London. Since its coverage was sparse, we only employ the Economist
to fill in data that were missing from The Money Market Review. If a section of the official list was omitted from
a given Money Market Review, we attempted to replace the missing data with quotes from the Economist.
The data set contains 610,421 bid and ask prices. To minimize entry time and assure quality, the data were
double entered by undergraduate research assistants. As a consequence of our data-entry strategy, a stock must
appear on the official list for at least one January before it is included in the data set.
The official lists did not differentiate between equity and debt. Today, one would assume that an economist and
trained historian would have no problem distinguishing a stock from a bond, but in the 19 th century the difference
between debt and equity was seldom obvious. The 19 th century English publications generally referred to both debt
and equity claims as “stocks.” A careful examination of the claims each class of shareholder enjoyed usually
allowed us to determine if a given security was a debt or equity claim. When selecting which securities to include in
our data set, we excluded all securities with fixed interest rates, a face value to be returned at a maturity date, or
other obvious characteristics of bonds.
In general, London securities were divided into the following types of asset classes: “stocks,” “shares,”
“ordinary,” “common,” “limited,” “deferred,” “preference,” “debenture” and “convertible” shares. Whether, the
name of the share corresponded to what a modern investor would consider equity depended upon the type of
company in question. We looked at each potential security and excluded every security with characteristics similar
to modern-day debt. “Common,” “limited,” and “ordinary” shares were almost always the residual claimants and
therefore correspond to modern-day equity. “Stock,” on the other hand, was the name given to 19 th century bonds!
“Preference,” “debenture,” and “convertible” shares were also excluded, while “deferred” shares generally referred
to debt offerings with one notable exception—the investment trusts. Many investment trusts issued only three types
of shares: “preference,” “debenture,” and “deferred.” Debenture and preference shares had a fixed dividend rate and
often had a maturity date when the nominal amount (face value) of the share would be returned. Deferred shares in
investment trusts, on the other hand, were generally the residual claimant to all income in excess of the debenture
and preference obligations. We include the deferred shares of investment trusts in our data, provided the trust has no
ordinary shares and the deferred shares satisfy our conditions of no maturity date and no cap on dividends.
32
For each January, a list of all securities was compiled, meeting our definition of equity. This list of security
names and copies of the subsequent year's quotation lists were distributed to research assistants. To eliminate typos,
each date was double entered by different research assistants and then compared. Therefore, to appear in the data set,
a stock had to appear on the official quotation list for at least one January.
In addition to the closing prices, we collected dividend payments and shares outstanding for each security.
These allowed us to compute market values and 28-day holding period returns that accurately reflect dividend
payments and stock splits. In total, the data set consists of 610,421 bid and ask prices and 39,090 dividend
19
payments. The dividend payments were collected from the security lists of The Investor's Monthly Manual. The
Investor's Monthly Manual (IMM) published the monthly closing price, shares outstanding, and last four dividends
of each security, listed on the London Stock Exchange. We use the IMM to collect dividend and share histories for
each security that appears in our data set. Like The Money Market Review, certain securities vanish from the IMM
and reappear at a later date without explanation.
Capital Calls and Returns
We use the price and dividend data to compute the 28-day holding period return for each consecutive price
observation. The 28-day holding period gross return is defined as (
)
where
and
are the
average of the bid and ask prices at time
and , respectively, and is the net dividend payments and capital
calls (if any) that occurred between time and
. Capital calls are a form of reverse dividend common to 19th
century stock exchanges.
Many 19th century companies issued shares with a nominal value known as the “amount.” The company typically
did not require the shareholders to pay for the entire share at the time of issue. Instead, shares were issued with a
“par” or “paid” value that was less than the nominal amount of the share. Dividends were based on the par value of
the share and not the nominal amount. For example, if a company with a £100 share with £50 paid announced a 10%
declared dividend, this would amount to £5 rather than £10.
The shareholder was legally obligated to pay the remaining capital (the difference between the nominal and paid
amount) at the whim of the company. Thus, the company could “call” upon its shareholders to pay for the remaining
value of their shares. This call was apparently binding, as the shares in many bankrupt companies with par values
less than nominal amounts traded at negative values when the implicit short put option embedded in the shares was
20
worth more than the company's equity. To compute holding period returns, we treat capital calls as a negative
dividend paid at the beginning of the holding period.
19
20
The IMM is available online at http://som.yale.edu/imm/html/index.shtml
We only include stocks with positive values in the analysis that follows.
33
Figure 1: ROC Curve
The figure displays the ROC curve from the full hazard model estimated with CRSP-era data to predict bear markets in the Fama–French momentum factor portfolio returns
34
Figure 2:
Sharp Ratios of CRSP-era Managed Portfolio:
Plot of the Sharp Ratios of managed portfolios formed by investing in the Fama-French momentum factor
portfolio whenever
is below a predetermined threshold and investing in the risk-free asset
otherwise.
is the percentile rank of
in the set of
(
)
(
)
and K is set equal to 36 months.
35
Figure 3: Number of Stocks in London Portfolios
This study makes use of a new data set of 1,808 stocks (equity) listed in London between 1866 and 1907. The plots display the
number of stocks, which decline to 985 in 1903 and 544 in 1904,due to a number of industries vanishing from the quotation list,
only to reappear in 1905.
36
Figure 4: Manager 1’s profits as a function of his period 1 investment
choice
Solving the game in section 3.1, the figure plots manager 1’s expected profits when the first period is a bad state and manager 2
holds cash, as a function of his period 1 investment choice (hold cash or invest in momentum) and the crash probability (1-pUB).
0.018
Invest in Momentum in Period 1
0.016
Hold Cash in Period 1
0.014
Poly. (Invest in Momentum in Period 1)
E[Profit]
0.012
Poly. (Hold Cash in Period 1)
0.01
0.008
0.006
0.004
0.002
0
0
0.2
0.4
0.6
PUB
37
0.8
1
Table 1:
Summary Statistics and Regression Results
Momentum
Portfolio:
CRSP FF
MOM
FACTOR
CRSP FF
MOM
FACTOR
CRSP FF
7030 MOM
PORT
CRSP FF
7030 MOM
PORT
London FF
MOM
FACTOR
London
7030 MOM
PORT
Sample Dates:
JUL1927DEC2012
JUL1927DEC2012
JUL1927DEC2012
JUL1927DEC2012
JUL1867DEC1907
JUL1867DEC1907
Monthly Returns1:
Mean
St.Dev.
Skewness
Ann. Sharp Ratio:
FF- 3 Factor Regression
α
β(mkt)
βSMB
βHML
0.0069
0.048
-3.03
0.0055
0.051
-2.89
0.003
0.0224
-1.55
0.0027
0.026
-1.39
0.50
0.37
0.48
0.37
0.0101
(0.001)***
-0.22
(0.027)***
-0.07
(0.043)*
-0.45
(0.039)***
βsize
N
0.0088
(0.001)***
-0.23
(0.029)***
-0.10
(0.047)**
-0.45
(0.042)***
-0.31
(0.031)***
-0.31
(0.033)***
βdivyield
R2
0.0101
(0.001)***
-0.34
(0.03)***
0.22
1026
0.22
1026
0.21
1026
1) CRSP returns are monthly. 1867-1907 returns are 28-day returns.
38
0.0089
(0.002)***
-0.36
(0.033)***
0.0052
(.001)***
-0.45
(0.071)***
0.0049
(.001)***
-0.35
(0.079)***
-0.33
(0.034)***
-0.34
(0.036)***
-0.10
(0.05)**
-0.11
(0.028)***
-0.32
(0.056)***
-0.17
(0.031)***
0.22
1026
.08
529
.12
529
Table 2:
Momentum Bear Markets
Momentum
Portfolio:
CRSP FF
MOM
FACTOR
Sample Dates:
JAN1927DEC2012
CRSP FF
7030
MOM
PORT
JAN1927DEC2012
63
3.7
< -5% Bear Markets *
# of bear markets
average duration
average cumlative
decline
<-10% Bear Markets *
# of bear markets
average duration
average cumlative
decline
Monthly observations
JAN1867DEC1907
London
7030
MOM
PORT
JAN1867DEC1907
68
4.9
19
7.3
21
7.9
13.6%
14.8%
10.2%
11.7%
30
5.6
36
7.4
7
16.7
9
14.7
20.6%
21.6%
15.8%
16.9%
1032
1032
548
548
London FF
MOM
FACTOR
* Bear markets are dated via the Lunde & Timmerman (2004) algorithm described in the text
<-5% bear markets are declines of 5% or greater and <-10% bear markets are declines of 10%
or greater.
39
Table 3:
Hazard Model Coefficients
Momentum Portfolio:
CRSP FF
MOM
FACTOR
CRSP FF
MOM
FACTOR
CRSP FF
MOM
FACTOR
CRSP FF
MOM
FACTOR
CRSP 7030
MOM
PORT
CRSP 7030
MOM
PORT
CRSP 7030
MOM
PORT
CRSP 7030
MOM
PORT
Sample Dates:
DEC1927DEC2012
APR1930DEC2012
DEC1927DEC2012
MAR1931DEC2012
DEC1927DEC2012
MAY1928DEC2012
DEC1927DEC2012
MAR1931DEC2012
Decline Necessary for
Bear Market
5%
5%
10%
10%
5%
5%
10%
10%
Hazard Model
Coefficients
Constant
ρ
Rft
RETmkt(t-12)-->(t-1)
RETmom(t-12)-->(t-1)
Goodness of Fit
LogLiK
AUC
# of Bear Markets
N (times at risk)
-8.52
(2.15)***
-2.48
(4.38)
-1.96
(0.58)***
2.50
(0.92)***
-3.52
(1.45)**
0.94
(0.12)
-2.69
(4.43)
-1.63
(0.64)**
2.70
(0.94)***
2.63
(6.21)
-1.81
(0.80)**
6.06
(1.39)***
-9.27
(2.42)***
1.10
(0.17)
3.28
(6.47)
-1.81
(0.92)**
6.4642
(1.56)***
-205.75
0.68***
-202.19
0.68***
-109.93
0.80***
63
788
62
763
30
852
-3.09
(1.41)**
-2.65
(3.22)
-1.71
(0.53)***
1.96
(0.76)**
-2.41
(1.18)**
0.92
(0.11)
-2.69
(5.20)
-1.69
(0.60)***
1.98
(0.73)***
1.76
(9.96)
-1.57
(1.22)
5.76
(1.57)***
-10.05
(2.27)***
0.85
(0.16)
-0.13
(17.09)
-0.71
(0.89)
7.18
(1.46)***
-105.99
0.80***
-212.29
0.65***
-209.37
0.66***
-125.21
0.76***
-117.98
0.77***
29
815
68
690
67
686
36
753
35
716
40
-2.50
(1.09)**
-8.02
(2.70)***
Table 3 cont.
Hazard Model Coefficients
DEC1867DEC1907
London
7030
MOM
PORT
DEC1867DEC1907
London
7030
MOM
PORT
DEC1867DEC1907
London
7030
MOM
PORT
DEC1867DEC1907
London
7030
MOM
PORT
DEC1867DEC1907
10%
5%
5%
10%
10%
-19.06
(5.39)***
-27.39
(7.93)***
-81.72
(26.02)***
6.91
(3.35)**
9.74
(2.47)***
-20.59
(5.58)***
0.69
(0.25)
-74.40
(27.32)***
6.83
(3.33)**
11.74
(3.01)***
-33.93
(31.51)
13.56
(4.53)***
8.693
(3.89)**
-27.60
(8.16)***
1.10
(0.51)
-29.99
(34.32)
13.57
(4.55)***
8.47
(4.05)**
London FF
Momentum Portfolio:
MOM
FACTOR
London FF
MOM
FACTOR
London FF
MOM
FACTOR
London FF
MOM
FACTOR
Sample Dates:
DEC1867DEC1907
DEC1867DEC1907
DEC1867DEC1907
Decline Necessary for
Bear Market
5%
5%
10%
Hazard Model
Coefficients
Constant
-12.6
(3.97)***
-21.63
(7.14)***
-57.61
(12.23)***
2.42
(2.82)
7.74
(1.97)***
-13.42
(9.23)
0.85
(0.23)
-53.32
(11.26)***
2.72
(6.03)
8.46
(3.31)**
-37.43
(9.55)***
7.62
(4.54)
9.26
(3.56)***
-21.12
(10.27)**
0.87
(0.53)
-41.84
(43.62)
7.39
(5.84)
9.53
(4.83)**
-63.94
0.78***
-63.75
0.788***
-28.71
0.77***
-28.68
0.78***
-64.48
0.79***
-63.72
0.80***
-33.99
0.76***
-33.97
0.75***
18
375
18
375
6
410
6
410
20
360
20
360
8
395
8
395
ρ
Rft
RETmkt(t-12)-->(t-1)
RETmom(t-12)-->(t-1)
Goodness of Fit
LogLiK
AUC
# of Bear Markets
N (times at risk)
41
Table 4:
Transition probabilities and conditional returns
CRSP
London
London
CRSP
MomFactor CRSP FF7030 momFactor
FF7030
MomFactor CRSP FF7030
Past 1-year
Return Decile
1
2
3
4
5
6
7
8
9
10
0.114
0.051
0.063
0.051
0.051
0.038
0.025
0.063
0.103
0.241
Prob of Transition to Bear
0.116
0.027
0.087
0.000
0.087
0.000
0.029
0.079
0.059
0.054
0.116
0.000
0.130
0.054
0.044
0.105
0.101
0.054
0.217
0.108
Past 1-year
Return Decile
1
2
3
4
5
6
7
8
9
10
0.017
0.022
0.014
0.014
0.015
0.016
0.016
0.014
0.023
0.039
E[R|bull]*
0.026
0.020
0.017
0.016
0.021
0.019
0.014
0.021
0.027
0.037
0.012
0.003
0.007
0.006
0.007
0.015
0.004
0.012
0.007
0.015
1
London
momFactor
London
FF7030
0.000
0.028
0.000
0.083
0.028
0.056
0.056
0.114
0.083
0.111
0.625
1.170
1.602
1.445
1.402
0.748
1.697
0.979
1.416
0.230
Annual Sharp Ratio
1.305
2.397
0.796
1.005
0.617
1.613
1.541
0.619
1.798
0.067
1.129
2.945
0.658
0.494
1.847
1.375
1.606
0.901
0.604
1.184
2.005
1.337
2.704
1.058
0.436
0.940
0.546
0.810
1.452
1.336
0.009
0.009
0.013
0.009
0.011
0.007
0.004
0.009
0.014
0.017
-0.072
-0.103
-0.033
-0.042
-0.054
-0.140
-0.047
-0.063
-0.047
-0.099
E[R|bear]**
-0.064
-0.077
-0.085
-0.053
-0.036
-0.045
-0.041
-0.057
-0.048
-0.079
NA
-0.025
NA
-0.028
-0.212
-0.025
-0.018
-0.026
-0.037
-0.040
1. Prob of transitioning to bear = the in-sample frequency of switching from a bull to bear market
* E[R|bull] = the in-sample average one month ahead return conditional on remaining in a bull market
** E[R|bear] = the in-sample average one month ahead return conditional on switching to a bear market
42
-0.007
NA
NA
-0.021
-0.116
NA
-0.021
-0.027
-0.036
-0.040
Table 6:
Average Profits by Fund Type as a Ratio of Type 100 profits
α = .1
α = .25
α = .5
α = .75
α = .9
Fund Types*
70
71
72
73
74
75
76
77
78
79
80
0.1014
0.0964
0.323
0.0986
0.2497
0.3137
0.376
0.1889
0.2507
0.3164
0.2579
0.0714
0.0655
0.015
0.0545
0.0504
0.0212
0.0147
0.0394
0.0518
0.026
0.0347
0.2753
0.2065
0.2516
0.237
0.2252
0.2281
0.2981
0.3339
0.3332
0.2806
0.3163
0.1237
0.1406
0.1428
0.1547
0.1418
0.1404
0.1828
0.1486
0.1636
0.177
0.2482
0.503
0.4223
0.5439
0.5092
0.4921
0.2772
0.3574
0.3421
0.4565
0.4757
0.6824
90
91
92
93
94
95
96
97
98
99
100
0.339
0.3158
0.37
0.2717
0.3555
0.3509
0.9373
0.7038
0.7999
1.349
1
0.066
0.0684
0.1196
0.0684
0.2626
0.8493
0.3723
0.5704
1.0011
1.3102
1
0.448
0.4314
0.5096
0.5228
0.6704
0.7123
0.7714
0.9502
0.8584
1.0362
1
0.5976
0.6936
0.9032
1.0395
1.0834
0.8687
0.9315
0.891
0.9504
1.0078
1
0.9934
0.7671
0.7662
1.1228
1.0729
1.2765
0.7778
1.7108
0.8761
1.4583
1
* A fund of type k holds cash if the past-year momentum return exceeds the k-th
percentile of all in-sample past year returns and otherwise follows the momentum strategy.
Each cell reports the average profit by fund types in the 5000 simulations as a
ratio of type 100 average profits.
each simulation has 100 funds with α proportion of the fund types drawn uniformly from
70-80 interval and (1-α) drawn uniformly from the 90-100 interval
43
Working Paper Series
A series of research studies on regional economic issues relating to the Seventh Federal
Reserve District, and on financial and economic topics.
Corporate Average Fuel Economy Standards and the Market for New Vehicles
Thomas Klier and Joshua Linn
WP-11-01
The Role of Securitization in Mortgage Renegotiation
Sumit Agarwal, Gene Amromin, Itzhak Ben-David, Souphala Chomsisengphet,
and Douglas D. Evanoff
WP-11-02
Market-Based Loss Mitigation Practices for Troubled Mortgages
Following the Financial Crisis
Sumit Agarwal, Gene Amromin, Itzhak Ben-David, Souphala Chomsisengphet,
and Douglas D. Evanoff
WP-11-03
Federal Reserve Policies and Financial Market Conditions During the Crisis
Scott A. Brave and Hesna Genay
WP-11-04
The Financial Labor Supply Accelerator
Jeffrey R. Campbell and Zvi Hercowitz
WP-11-05
Survival and long-run dynamics with heterogeneous beliefs under recursive preferences
Jaroslav Borovička
WP-11-06
A Leverage-based Model of Speculative Bubbles (Revised)
Gadi Barlevy
WP-11-07
Estimation of Panel Data Regression Models with Two-Sided Censoring or Truncation
Sule Alan, Bo E. Honoré, Luojia Hu, and Søren Leth–Petersen
WP-11-08
Fertility Transitions Along the Extensive and Intensive Margins
Daniel Aaronson, Fabian Lange, and Bhashkar Mazumder
WP-11-09
Black-White Differences in Intergenerational Economic Mobility in the US
Bhashkar Mazumder
WP-11-10
Can Standard Preferences Explain the Prices of Out-of-the-Money S&P 500 Put Options?
Luca Benzoni, Pierre Collin-Dufresne, and Robert S. Goldstein
WP-11-11
Business Networks, Production Chains, and Productivity:
A Theory of Input-Output Architecture
Ezra Oberfield
WP-11-12
Equilibrium Bank Runs Revisited
Ed Nosal
WP-11-13
Are Covered Bonds a Substitute for Mortgage-Backed Securities?
Santiago Carbó-Valverde, Richard J. Rosen, and Francisco Rodríguez-Fernández
WP-11-14
The Cost of Banking Panics in an Age before “Too Big to Fail”
Benjamin Chabot
WP-11-15
1
Working Paper Series (continued)
Import Protection, Business Cycles, and Exchange Rates:
Evidence from the Great Recession
Chad P. Bown and Meredith A. Crowley
WP-11-16
Examining Macroeconomic Models through the Lens of Asset Pricing
Jaroslav Borovička and Lars Peter Hansen
WP-12-01
The Chicago Fed DSGE Model
Scott A. Brave, Jeffrey R. Campbell, Jonas D.M. Fisher, and Alejandro Justiniano
WP-12-02
Macroeconomic Effects of Federal Reserve Forward Guidance
Jeffrey R. Campbell, Charles L. Evans, Jonas D.M. Fisher, and Alejandro Justiniano
WP-12-03
Modeling Credit Contagion via the Updating of Fragile Beliefs
Luca Benzoni, Pierre Collin-Dufresne, Robert S. Goldstein, and Jean Helwege
WP-12-04
Signaling Effects of Monetary Policy
Leonardo Melosi
WP-12-05
Empirical Research on Sovereign Debt and Default
Michael Tomz and Mark L. J. Wright
WP-12-06
Credit Risk and Disaster Risk
François Gourio
WP-12-07
From the Horse’s Mouth: How do Investor Expectations of Risk and Return
Vary with Economic Conditions?
Gene Amromin and Steven A. Sharpe
WP-12-08
Using Vehicle Taxes To Reduce Carbon Dioxide Emissions Rates of
New Passenger Vehicles: Evidence from France, Germany, and Sweden
Thomas Klier and Joshua Linn
WP-12-09
Spending Responses to State Sales Tax Holidays
Sumit Agarwal and Leslie McGranahan
WP-12-10
Micro Data and Macro Technology
Ezra Oberfield and Devesh Raval
WP-12-11
The Effect of Disability Insurance Receipt on Labor Supply: A Dynamic Analysis
Eric French and Jae Song
WP-12-12
Medicaid Insurance in Old Age
Mariacristina De Nardi, Eric French, and John Bailey Jones
WP-12-13
Fetal Origins and Parental Responses
Douglas Almond and Bhashkar Mazumder
WP-12-14
2
Working Paper Series (continued)
Repos, Fire Sales, and Bankruptcy Policy
Gaetano Antinolfi, Francesca Carapella, Charles Kahn, Antoine Martin,
David Mills, and Ed Nosal
WP-12-15
Speculative Runs on Interest Rate Pegs
The Frictionless Case
Marco Bassetto and Christopher Phelan
WP-12-16
Institutions, the Cost of Capital, and Long-Run Economic Growth:
Evidence from the 19th Century Capital Market
Ron Alquist and Ben Chabot
WP-12-17
Emerging Economies, Trade Policy, and Macroeconomic Shocks
Chad P. Bown and Meredith A. Crowley
WP-12-18
The Urban Density Premium across Establishments
R. Jason Faberman and Matthew Freedman
WP-13-01
Why Do Borrowers Make Mortgage Refinancing Mistakes?
Sumit Agarwal, Richard J. Rosen, and Vincent Yao
WP-13-02
Bank Panics, Government Guarantees, and the Long-Run Size of the Financial Sector:
Evidence from Free-Banking America
Benjamin Chabot and Charles C. Moul
WP-13-03
Fiscal Consequences of Paying Interest on Reserves
Marco Bassetto and Todd Messer
WP-13-04
Properties of the Vacancy Statistic in the Discrete Circle Covering Problem
Gadi Barlevy and H. N. Nagaraja
WP-13-05
Credit Crunches and Credit Allocation in a Model of Entrepreneurship
Marco Bassetto, Marco Cagetti, and Mariacristina De Nardi
WP-13-06
Financial Incentives and Educational Investment:
The Impact of Performance-Based Scholarships on Student Time Use
Lisa Barrow and Cecilia Elena Rouse
WP-13-07
The Global Welfare Impact of China: Trade Integration and Technological Change
Julian di Giovanni, Andrei A. Levchenko, and Jing Zhang
WP-13-08
Structural Change in an Open Economy
Timothy Uy, Kei-Mu Yi, and Jing Zhang
WP-13-09
The Global Labor Market Impact of Emerging Giants: a Quantitative Assessment
Andrei A. Levchenko and Jing Zhang
WP-13-10
3
Working Paper Series (continued)
Size-Dependent Regulations, Firm Size Distribution, and Reallocation
François Gourio and Nicolas Roys
WP-13-11
Modeling the Evolution of Expectations and Uncertainty in General Equilibrium
Francesco Bianchi and Leonardo Melosi
WP-13-12
Rushing into American Dream? House Prices, Timing of Homeownership,
and Adjustment of Consumer Credit
Sumit Agarwal, Luojia Hu, and Xing Huang
WP-13-13
The Earned Income Tax Credit and Food Consumption Patterns
Leslie McGranahan and Diane W. Schanzenbach
WP-13-14
Agglomeration in the European automobile supplier industry
Thomas Klier and Dan McMillen
WP-13-15
Human Capital and Long-Run Labor Income Risk
Luca Benzoni and Olena Chyruk
WP-13-16
The Effects of the Saving and Banking Glut on the U.S. Economy
Alejandro Justiniano, Giorgio E. Primiceri, and Andrea Tambalotti
WP-13-17
A Portfolio-Balance Approach to the Nominal Term Structure
Thomas B. King
WP-13-18
Gross Migration, Housing and Urban Population Dynamics
Morris A. Davis, Jonas D.M. Fisher, and Marcelo Veracierto
WP-13-19
Very Simple Markov-Perfect Industry Dynamics
Jaap H. Abbring, Jeffrey R. Campbell, Jan Tilly, and Nan Yang
WP-13-20
Bubbles and Leverage: A Simple and Unified Approach
Robert Barsky and Theodore Bogusz
WP-13-21
The scarcity value of Treasury collateral:
Repo market effects of security-specific supply and demand factors
Stefania D'Amico, Roger Fan, and Yuriy Kitsul
Gambling for Dollars: Strategic Hedge Fund Manager Investment
Dan Bernhardt and Ed Nosal
Cash-in-the-Market Pricing in a Model with Money and
Over-the-Counter Financial Markets
Fabrizio Mattesini and Ed Nosal
An Interview with Neil Wallace
David Altig and Ed Nosal
WP-13-22
WP-13-23
WP-13-24
WP-13-25
4
Working Paper Series (continued)
Firm Dynamics and the Minimum Wage: A Putty-Clay Approach
Daniel Aaronson, Eric French, and Isaac Sorkin
Policy Intervention in Debt Renegotiation:
Evidence from the Home Affordable Modification Program
Sumit Agarwal, Gene Amromin, Itzhak Ben-David, Souphala Chomsisengphet,
Tomasz Piskorski, and Amit Seru
WP-13-26
WP-13-27
The Effects of the Massachusetts Health Reform on Financial Distress
Bhashkar Mazumder and Sarah Miller
WP-14-01
Can Intangible Capital Explain Cyclical Movements in the Labor Wedge?
François Gourio and Leena Rudanko
WP-14-02
Early Public Banks
William Roberds and François R. Velde
WP-14-03
Mandatory Disclosure and Financial Contagion
Fernando Alvarez and Gadi Barlevy
WP-14-04
The Stock of External Sovereign Debt: Can We Take the Data at ‘Face Value’?
Daniel A. Dias, Christine Richmond, and Mark L. J. Wright
WP-14-05
Interpreting the Pari Passu Clause in Sovereign Bond Contracts:
It’s All Hebrew (and Aramaic) to Me
Mark L. J. Wright
WP-14-06
AIG in Hindsight
Robert McDonald and Anna Paulson
WP-14-07
On the Structural Interpretation of the Smets-Wouters “Risk Premium” Shock
Jonas D.M. Fisher
WP-14-08
Human Capital Risk, Contract Enforcement, and the Macroeconomy
Tom Krebs, Moritz Kuhn, and Mark L. J. Wright
WP-14-09
Adverse Selection, Risk Sharing and Business Cycles
Marcelo Veracierto
WP-14-10
Core and ‘Crust’: Consumer Prices and the Term Structure of Interest Rates
Andrea Ajello, Luca Benzoni, and Olena Chyruk
WP-14-11
The Evolution of Comparative Advantage: Measurement and Implications
Andrei A. Levchenko and Jing Zhang
WP-14-12
5
Working Paper Series (continued)
Saving Europe?: The Unpleasant Arithmetic of Fiscal Austerity in Integrated Economies
Enrique G. Mendoza, Linda L. Tesar, and Jing Zhang
WP-14-13
Liquidity Traps and Monetary Policy: Managing a Credit Crunch
Francisco Buera and Juan Pablo Nicolini
WP-14-14
Quantitative Easing in Joseph’s Egypt with Keynesian Producers
Jeffrey R. Campbell
WP-14-15
Constrained Discretion and Central Bank Transparency
Francesco Bianchi and Leonardo Melosi
WP-14-16
Escaping the Great Recession
Francesco Bianchi and Leonardo Melosi
WP-14-17
More on Middlemen: Equilibrium Entry and Efficiency in Intermediated Markets
Ed Nosal, Yuet-Yee Wong, and Randall Wright
WP-14-18
Preventing Bank Runs
David Andolfatto, Ed Nosal, and Bruno Sultanum
WP-14-19
The Impact of Chicago’s Small High School Initiative
Lisa Barrow, Diane Whitmore Schanzenbach, and Amy Claessens
WP-14-20
Credit Supply and the Housing Boom
Alejandro Justiniano, Giorgio E. Primiceri, and Andrea Tambalotti
WP-14-21
The Effect of Vehicle Fuel Economy Standards on Technology Adoption
Thomas Klier and Joshua Linn
WP-14-22
What Drives Bank Funding Spreads?
Thomas B. King and Kurt F. Lewis
WP-14-23
Inflation Uncertainty and Disagreement in Bond Risk Premia
Stefania D’Amico and Athanasios Orphanides
WP-14-24
Access to Refinancing and Mortgage Interest Rates:
HARPing on the Importance of Competition
Gene Amromin and Caitlin Kearns
WP-14-25
Private Takings
Alessandro Marchesiani and Ed Nosal
WP-14-26
Momentum Trading, Return Chasing, and Predictable Crashes
Benjamin Chabot, Eric Ghysels, and Ravi Jagannathan
WP-14-27
6
Working Paper Series
A series of research studies on regional economic issues relating to the Seventh Federal
Reserve District, and on financial and economic topics.
Corporate Average Fuel Economy Standards and the Market for New Vehicles
Thomas Klier and Joshua Linn
WP-11-01
The Role of Securitization in Mortgage Renegotiation
Sumit Agarwal, Gene Amromin, Itzhak Ben-David, Souphala Chomsisengphet,
and Douglas D. Evanoff
WP-11-02
Market-Based Loss Mitigation Practices for Troubled Mortgages
Following the Financial Crisis
Sumit Agarwal, Gene Amromin, Itzhak Ben-David, Souphala Chomsisengphet,
and Douglas D. Evanoff
WP-11-03
Federal Reserve Policies and Financial Market Conditions During the Crisis
Scott A. Brave and Hesna Genay
WP-11-04
The Financial Labor Supply Accelerator
Jeffrey R. Campbell and Zvi Hercowitz
WP-11-05
Survival and long-run dynamics with heterogeneous beliefs under recursive preferences
Jaroslav Borovička
WP-11-06
A Leverage-based Model of Speculative Bubbles (Revised)
Gadi Barlevy
WP-11-07
Estimation of Panel Data Regression Models with Two-Sided Censoring or Truncation
Sule Alan, Bo E. Honoré, Luojia Hu, and Søren Leth–Petersen
WP-11-08
Fertility Transitions Along the Extensive and Intensive Margins
Daniel Aaronson, Fabian Lange, and Bhashkar Mazumder
WP-11-09
Black-White Differences in Intergenerational Economic Mobility in the US
Bhashkar Mazumder
WP-11-10
Can Standard Preferences Explain the Prices of Out-of-the-Money S&P 500 Put Options?
Luca Benzoni, Pierre Collin-Dufresne, and Robert S. Goldstein
WP-11-11
Business Networks, Production Chains, and Productivity:
A Theory of Input-Output Architecture
Ezra Oberfield
WP-11-12
Equilibrium Bank Runs Revisited
Ed Nosal
WP-11-13
Are Covered Bonds a Substitute for Mortgage-Backed Securities?
Santiago Carbó-Valverde, Richard J. Rosen, and Francisco Rodríguez-Fernández
WP-11-14
The Cost of Banking Panics in an Age before “Too Big to Fail”
Benjamin Chabot
WP-11-15
1
Working Paper Series (continued)
Import Protection, Business Cycles, and Exchange Rates:
Evidence from the Great Recession
Chad P. Bown and Meredith A. Crowley
WP-11-16
Examining Macroeconomic Models through the Lens of Asset Pricing
Jaroslav Borovička and Lars Peter Hansen
WP-12-01
The Chicago Fed DSGE Model
Scott A. Brave, Jeffrey R. Campbell, Jonas D.M. Fisher, and Alejandro Justiniano
WP-12-02
Macroeconomic Effects of Federal Reserve Forward Guidance
Jeffrey R. Campbell, Charles L. Evans, Jonas D.M. Fisher, and Alejandro Justiniano
WP-12-03
Modeling Credit Contagion via the Updating of Fragile Beliefs
Luca Benzoni, Pierre Collin-Dufresne, Robert S. Goldstein, and Jean Helwege
WP-12-04
Signaling Effects of Monetary Policy
Leonardo Melosi
WP-12-05
Empirical Research on Sovereign Debt and Default
Michael Tomz and Mark L. J. Wright
WP-12-06
Credit Risk and Disaster Risk
François Gourio
WP-12-07
From the Horse’s Mouth: How do Investor Expectations of Risk and Return
Vary with Economic Conditions?
Gene Amromin and Steven A. Sharpe
WP-12-08
Using Vehicle Taxes To Reduce Carbon Dioxide Emissions Rates of
New Passenger Vehicles: Evidence from France, Germany, and Sweden
Thomas Klier and Joshua Linn
WP-12-09
Spending Responses to State Sales Tax Holidays
Sumit Agarwal and Leslie McGranahan
WP-12-10
Micro Data and Macro Technology
Ezra Oberfield and Devesh Raval
WP-12-11
The Effect of Disability Insurance Receipt on Labor Supply: A Dynamic Analysis
Eric French and Jae Song
WP-12-12
Medicaid Insurance in Old Age
Mariacristina De Nardi, Eric French, and John Bailey Jones
WP-12-13
Fetal Origins and Parental Responses
Douglas Almond and Bhashkar Mazumder
WP-12-14
2
Working Paper Series (continued)
Repos, Fire Sales, and Bankruptcy Policy
Gaetano Antinolfi, Francesca Carapella, Charles Kahn, Antoine Martin,
David Mills, and Ed Nosal
WP-12-15
Speculative Runs on Interest Rate Pegs
The Frictionless Case
Marco Bassetto and Christopher Phelan
WP-12-16
Institutions, the Cost of Capital, and Long-Run Economic Growth:
Evidence from the 19th Century Capital Market
Ron Alquist and Ben Chabot
WP-12-17
Emerging Economies, Trade Policy, and Macroeconomic Shocks
Chad P. Bown and Meredith A. Crowley
WP-12-18
The Urban Density Premium across Establishments
R. Jason Faberman and Matthew Freedman
WP-13-01
Why Do Borrowers Make Mortgage Refinancing Mistakes?
Sumit Agarwal, Richard J. Rosen, and Vincent Yao
WP-13-02
Bank Panics, Government Guarantees, and the Long-Run Size of the Financial Sector:
Evidence from Free-Banking America
Benjamin Chabot and Charles C. Moul
WP-13-03
Fiscal Consequences of Paying Interest on Reserves
Marco Bassetto and Todd Messer
WP-13-04
Properties of the Vacancy Statistic in the Discrete Circle Covering Problem
Gadi Barlevy and H. N. Nagaraja
WP-13-05
Credit Crunches and Credit Allocation in a Model of Entrepreneurship
Marco Bassetto, Marco Cagetti, and Mariacristina De Nardi
WP-13-06
Financial Incentives and Educational Investment:
The Impact of Performance-Based Scholarships on Student Time Use
Lisa Barrow and Cecilia Elena Rouse
WP-13-07
The Global Welfare Impact of China: Trade Integration and Technological Change
Julian di Giovanni, Andrei A. Levchenko, and Jing Zhang
WP-13-08
Structural Change in an Open Economy
Timothy Uy, Kei-Mu Yi, and Jing Zhang
WP-13-09
The Global Labor Market Impact of Emerging Giants: a Quantitative Assessment
Andrei A. Levchenko and Jing Zhang
WP-13-10
3
Working Paper Series (continued)
Size-Dependent Regulations, Firm Size Distribution, and Reallocation
François Gourio and Nicolas Roys
WP-13-11
Modeling the Evolution of Expectations and Uncertainty in General Equilibrium
Francesco Bianchi and Leonardo Melosi
WP-13-12
Rushing into American Dream? House Prices, Timing of Homeownership,
and Adjustment of Consumer Credit
Sumit Agarwal, Luojia Hu, and Xing Huang
WP-13-13
The Earned Income Tax Credit and Food Consumption Patterns
Leslie McGranahan and Diane W. Schanzenbach
WP-13-14
Agglomeration in the European automobile supplier industry
Thomas Klier and Dan McMillen
WP-13-15
Human Capital and Long-Run Labor Income Risk
Luca Benzoni and Olena Chyruk
WP-13-16
The Effects of the Saving and Banking Glut on the U.S. Economy
Alejandro Justiniano, Giorgio E. Primiceri, and Andrea Tambalotti
WP-13-17
A Portfolio-Balance Approach to the Nominal Term Structure
Thomas B. King
WP-13-18
Gross Migration, Housing and Urban Population Dynamics
Morris A. Davis, Jonas D.M. Fisher, and Marcelo Veracierto
WP-13-19
Very Simple Markov-Perfect Industry Dynamics
Jaap H. Abbring, Jeffrey R. Campbell, Jan Tilly, and Nan Yang
WP-13-20
Bubbles and Leverage: A Simple and Unified Approach
Robert Barsky and Theodore Bogusz
WP-13-21
The scarcity value of Treasury collateral:
Repo market effects of security-specific supply and demand factors
Stefania D'Amico, Roger Fan, and Yuriy Kitsul
Gambling for Dollars: Strategic Hedge Fund Manager Investment
Dan Bernhardt and Ed Nosal
Cash-in-the-Market Pricing in a Model with Money and
Over-the-Counter Financial Markets
Fabrizio Mattesini and Ed Nosal
An Interview with Neil Wallace
David Altig and Ed Nosal
WP-13-22
WP-13-23
WP-13-24
WP-13-25
4
Working Paper Series (continued)
Firm Dynamics and the Minimum Wage: A Putty-Clay Approach
Daniel Aaronson, Eric French, and Isaac Sorkin
Policy Intervention in Debt Renegotiation:
Evidence from the Home Affordable Modification Program
Sumit Agarwal, Gene Amromin, Itzhak Ben-David, Souphala Chomsisengphet,
Tomasz Piskorski, and Amit Seru
WP-13-26
WP-13-27
The Effects of the Massachusetts Health Reform on Financial Distress
Bhashkar Mazumder and Sarah Miller
WP-14-01
Can Intangible Capital Explain Cyclical Movements in the Labor Wedge?
François Gourio and Leena Rudanko
WP-14-02
Early Public Banks
William Roberds and François R. Velde
WP-14-03
Mandatory Disclosure and Financial Contagion
Fernando Alvarez and Gadi Barlevy
WP-14-04
The Stock of External Sovereign Debt: Can We Take the Data at ‘Face Value’?
Daniel A. Dias, Christine Richmond, and Mark L. J. Wright
WP-14-05
Interpreting the Pari Passu Clause in Sovereign Bond Contracts:
It’s All Hebrew (and Aramaic) to Me
Mark L. J. Wright
WP-14-06
AIG in Hindsight
Robert McDonald and Anna Paulson
WP-14-07
On the Structural Interpretation of the Smets-Wouters “Risk Premium” Shock
Jonas D.M. Fisher
WP-14-08
Human Capital Risk, Contract Enforcement, and the Macroeconomy
Tom Krebs, Moritz Kuhn, and Mark L. J. Wright
WP-14-09
Adverse Selection, Risk Sharing and Business Cycles
Marcelo Veracierto
WP-14-10
Core and ‘Crust’: Consumer Prices and the Term Structure of Interest Rates
Andrea Ajello, Luca Benzoni, and Olena Chyruk
WP-14-11
The Evolution of Comparative Advantage: Measurement and Implications
Andrei A. Levchenko and Jing Zhang
WP-14-12
5
Working Paper Series (continued)
Saving Europe?: The Unpleasant Arithmetic of Fiscal Austerity in Integrated Economies
Enrique G. Mendoza, Linda L. Tesar, and Jing Zhang
WP-14-13
Liquidity Traps and Monetary Policy: Managing a Credit Crunch
Francisco Buera and Juan Pablo Nicolini
WP-14-14
Quantitative Easing in Joseph’s Egypt with Keynesian Producers
Jeffrey R. Campbell
WP-14-15
Constrained Discretion and Central Bank Transparency
Francesco Bianchi and Leonardo Melosi
WP-14-16
Escaping the Great Recession
Francesco Bianchi and Leonardo Melosi
WP-14-17
More on Middlemen: Equilibrium Entry and Efficiency in Intermediated Markets
Ed Nosal, Yuet-Yee Wong, and Randall Wright
WP-14-18
Preventing Bank Runs
David Andolfatto, Ed Nosal, and Bruno Sultanum
WP-14-19
The Impact of Chicago’s Small High School Initiative
Lisa Barrow, Diane Whitmore Schanzenbach, and Amy Claessens
WP-14-20
Credit Supply and the Housing Boom
Alejandro Justiniano, Giorgio E. Primiceri, and Andrea Tambalotti
WP-14-21
The Effect of Vehicle Fuel Economy Standards on Technology Adoption
Thomas Klier and Joshua Linn
WP-14-22
What Drives Bank Funding Spreads?
Thomas B. King and Kurt F. Lewis
WP-14-23
Inflation Uncertainty and Disagreement in Bond Risk Premia
Stefania D’Amico and Athanasios Orphanides
WP-14-24
Access to Refinancing and Mortgage Interest Rates:
HARPing on the Importance of Competition
Gene Amromin and Caitlin Kearns
WP-14-25
Private Takings
Alessandro Marchesiani and Ed Nosal
WP-14-26
Momentum Trading, Return Chasing, and Predictable Crashes
Benjamin Chabot, Eric Ghysels, and Ravi Jagannathan
WP-14-27
6
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