# SEC Form 13F-HR: Statistical investigation of trading imbalances and
profitability analysis

Deborah Miori
University of Oxford
Oxford, United Kingdom
<EMAIL_ADDRESS>
&Mihai Cucuringu
University of Oxford
Oxford, United Kingdom
<EMAIL_ADDRESS>

###### Abstract

US Institutions with more than $\$100$ million assets under management must
disclose part of their long positions into the SEC Form 13F-HR on a quarterly
basis. We consider the number of variations in holdings between consecutive
reporting periods, and compute imbalances in buying versus selling behaviour
for the assets under consideration. A significant opportunity for profit
arises if an external investor is willing to trade contrarian to the 13F
filings imbalances. Indeed, imbalances capture the amount of information
already consumed in the market and the related trades tend to be inflated by
crowding and herding. Betting on a relatively short-term movement of prices
against the sign of imbalances results in a profitable strategy especially
when using a time horizon between 21 and 42 trading days (corresponding to 1-2
calendar months) after each financial quarter ends.

###### Contents

  1. 1 Introduction
  2. 2 Data
    1. 2.1 Form 13F-HR
    2. 2.2 Data pre-processing
    3. 2.3 Close-to-close price returns
  3. 3 Methodology
  4. 4 Preliminary analyses of imbalances
    1. 4.1 Considerations on threshold $N$
    2. 4.2 Price impact of imbalances on contemporaneous returns
  5. 5 Strategy construction and profitability
    1. 5.1 Vanilla strategy
    2. 5.2 Contrarian to Market Momentum and to Market Mean-Reversion strategy
    3. 5.3 Sector-specific investing
  6. 6 Conclusions
  7. A Price impact of imbalances over quarters
  8. B Cumulative PnL for the vanilla strategy
  9. C Evolution of the popularity of stocks within SIC sectors

##  1 Introduction

Diversification is a double-hedged sword in financial markets. It helps with
offsetting risks in quiet market times but significantly increases the
likelihood of being affected by financial contagion during periods of sudden
stress [1]. After the financial crisis of 2007-08, regulators strengthened
their control on systemically important institutions [2] and promoted higher
transparency of markets by increasing requirements on disclosures of holdings.
The behaviour and performance of banks and non-bank financial institutions
(such as mutual funds, pension funds, insurance companies, hedge funds, etc.)
has become an active area of research since then. Examples are the
investigation of corporate and Treasury bond funds in [3], [4], [5], of
insurance companies in [6], [7], and of hedge funds in [8], [9] and [10].
Interconnections between the returns of hedge funds, banks, brokers and
insurance companies are further analysed in [11] and [12], for the US and
European markets respectively. Many studies (e.g. [13], [14], [15], [16],
[17]) also address the importance of studying crowding, which is the tendency
of different investors to focus on a similar set of factors, strategies, or
securities. This happens both inside and across institutions’ categories, and
results in overlapping positions with generally lower returns but for hedge
funds.

The information contained in the Security and Exchanges Commission (SEC) Form
13F-HR can be of interest to any study spanning diverse agents’ classes, since
this filing publicly provides updates on the holdings of largest US
institutional investors on a quarterly basis. Despite being released with a
lag of $45$ calendar days after the financial quarter ends and reporting only
long positions, Form 13F allows insights on an extremely eclectic set of
market participants and has been published with satisfactory quality for at
least a decade. Seldom instances of research have been focusing on it so far,
likely due to difficulties in systematically accessing and pre-processing
these reports, which are singularly stored on a SEC platform and appear at
different times. An example is [18], which leverages on these filings to
forecast stock returns in mutual funds by trusting managers of companies that
demonstrated a track record of profitability in the past. Otherwise, [19]
shows that 13F filings are strongly used by plain copycat investors even if
this has little evidence of long-term benefits. The research in [20] relates
SEC Form 13F to SEC Form 10K, which must be filed annually by companies with
registered shares and provides a comprehensive summary of their financial
performance. As conceivable, the author finds that pessimism in Form 10K leads
to a decrease in related institutional holdings. Our study considers a
different investment approach from the above ones, and employs Form 13F data
to aggregate changes in investors’ positions, thus computing the flow of money
in and out of different assets.

Main contribution. We define a measure of trading imbalance for stocks, which
weights the strength of related buying versus selling behaviour between
consecutive reporting periods. In this way, we are able to investigate the
global view that our diverse set of institutional investors develops on each
stock. Our main contribution lies in the extraction of a statistically
significant signal from the imbalances computed via 13F filings, which
suggests that asset prices move in the opposite direction to their imbalance
sign at the end of each quarter.

Structure of the paper. Section 2 describes in detail the data used and the
pre-processing needed. Next, the methodology to compute imbalances and trading
signals is provided in Section 3. Preliminary considerations on imbalances and
their price impact on contemporaneous returns are presented in Section 4.
Section 5 shows our profits when betting contrarian to imbalances and it
describes experiments of conditioning positions on stocks’ past prices or to
the sector membership of each asset. Finally, Section 6 concludes our work
with some final remarks.

##  2 Data

###  2.1 Form 13F-HR

The SEC introduced Form 13F-HR (Holdings Report) to provide some publicly
available disclosure of institutions’ investments back in 1975. Following its
updated rules, the related managers need now to report long holdings via the
13F filings when handling US AUM $\geq\$100$ million. Institutional investment
managers can be part of investment advisers, banks, insurance companies,
broker-dealers, pension funds and corporations, etc. Therefore, non-financial
institutions are also included in this form. However, 13F disclosures are
required only quarterly, filed in number of shares, miss the short positions
and must be completed within 45 days after the financial quarter ends.
Institutions are also allowed to file amendments (Form 13F-HR/A) if they
mistakenly reported a position without any fees or alerts to follow, meaning
that the most valuable bets are often kept hidden for a longer time, and
deliberately disclosed with a delay, as [21] shows for hedge funds.

Every market participant filing this report is identified by a Central Index
Key (CIK). Investments pursued by different managers are identified by the
Other Manager integer number, while the division between actual portfolios
would be described in general by the SeriesID. Unfortunately, the latter
identifier is not required in 13F filings and therefore we cannot access this
most granular view. Assets that are compulsory to report are part of the SEC
Section 13(f) securities list, meaning that there is a bias towards US funds
and investments. The full list of securities covered includes $23,131$
securities as of Q4 2021 (fourth quarter of 2021). These are identified by the
US CUSIP number (Committee on Uniform Securities Identification Procedures)
and listed at https://www.sec.gov/divisions/investment/13flists.htm. Therein,
one can find equity securities that trade on an exchange, certain equity
options and warrants, shares of closed-end investment companies, and some
convertible debt securities. The shares of open-end investment companies are
instead not required.

US CUSIP codes are assigned with format AAAAAABBC, where AAAAAA represents the
company issuing the financial security, BB is the issue number used to denote
e.g. shares with/without voting rights, and C is the check digit. The
informative part for our purposes is the AAAAAA, which we denote as CUSIP6. As
an example, the AAPL stock has code 037833100, where 037833 is Apple, Inc.
Furthermore, 10 denotes Class A Shares and the final 0 is the check digit. It
is a convention to assign 10 as first issue number and increasing numbers
(20,30… or 11,12…) for subsequent securities.

###  2.2 Data pre-processing

We consider holdings disclosed via Form 13F-HR from 2013-06-30 to 2021-09-30,
where earlier quarters are not included due to low quality of reporting. We
also do not correct positions for which an amendment was later filed, in order
to investigate the trading signals directly available at the end of each
quarter. However, these are not fully actionable signals due to the 45-days
lag companies are allowed in their holdings’ disclosure deadline. Our 13F data
set shows long investments for $T=34$ points in time. For each quarter, the
number of samples is larger than $10^{6}$, where each occurrence represents an
agent holding a specific security of type shares at that point in time. The
Other Manager key is discarded, while the related number of shares held is
summed for each individual institution and security, for every period.
Similarly, we aggregate stocks information to CUSIP6 level. The full data
relate to $8,166$ unique CIKs, among which we see influential and diverse
institutions such as banks (e.g. Bank of America, Wells Fargo & Co), insurance
companies (e.g. American International Group, AXA), pension funds (e.g. Canada
Pension Plan Investment Board, Public sector pension investment board), hedge
funds (e.g. UBS O’Connor, Renaissance Technologies), market makers (e.g.
Cutler Group LP, Group One Trading)…

For each quarter ending at time $p$, we assume that we have all the related
13F filings immediately available, and build a holdings matrix $H_{p}=(F\times
A)_{p}$ where rows are investment institutions $f\in F$ and columns are assets
$a\in A$. Each cell is populated with the number of shares that $f$ is holding
of asset $a$ at the end of quarter $p$, or otherwise $0$. Then, we compute
differences in holdings between each two consecutive reporting periods and
consider a new set of $T-1$ matrices $D_{p}=H_{p}-H_{p-1},p=2,\ldots,T$.
Between $30-40\%$ of securities are in every case found to have the related
column fully populated with zeros. These are uncommon stocks chosen by only
one or two funds that keep the position over longer horizons of time. These
data amount to noise for our analyses and the related columns are thus
dropped, completing the pre-processing.

###  2.3 Close-to-close price returns

To investigate whether disclosures on holdings can provide profitable
investment signals, we download close-to-close adjusted daily returns for our
stocks from the Center for Research in Security Prices (CRSP) dataset from
Wharton Research Data Services (WRDS). The return of the S&P Composite Index
is also selected to be able to compute market-excess returns. We map our
CUSIP6 identifiers to tickers and obtain returns data for approximately
$5,000$ securities per each reporting period.

##  3 Methodology

The set of matrices $D_{p}$ describes differences in the amount of shares of
stocks $a\in A$ held by institutions $f\in F$ between each consecutive periods
$p-1$ and $p$. Our goal is to leverage such increments for the construction of
a predictive signal for the assets in question. For each asset $a$, we proceed
by calculating the volume of shares $B_{p,a}^{vol},S_{p,a}^{vol}\geq 0$ that
are bought or sold by market participants, respectively. Similarly, we compute
the number of buying and selling trades, $B_{p,a}^{tr}$, respectively
$S_{p,a}^{tr}\geq 0$ for each stock, by counting the number of entries with
positive, respectively, negative sign.

We define an imbalance of allocations over asset $a$, between periods $p-1$
and $p$, by considering the normalised discrepancy in terms of volume

$I_{p,a,N}^{vol}=\frac{B_{p,a}^{vol}-S_{p,a}^{vol}}{B_{p,a}^{vol}+S_{p,a}^{vol}}\in[-1;+1],$
(1)

and define similarly the imbalance discrepancy in terms of trade counts

$I_{p,a,N}^{tr}=\frac{B_{p,a}^{tr}-S_{p,a}^{tr}}{B_{p,a}^{tr}+S_{p,a}^{tr}}\in[-1;+1].$
(2)

To increase the significance of our measure, we compute imbalances on
securities that have at least $N$ institutions active on them. Activity of
fund $f$ on stock $a$ is defined as having $D_{p}^{(f,a)}\neq 0$. In this way,
we avoid e.g. the unreliable case of having irrelevant strongest signals
$I_{p,a,1}^{vol,tr}=\pm 1$ associated to stocks being traded only by one
institution. Other normalisations could be considered for $I_{p,a,N}^{vol}$,
for example, by the total traded volume in the market over the same period.

As already mentioned, we assume that all data from Form 13F-HR are made public
at the end of the last day of the financial quarter. At this point in time, we
compute imbalances and employ them as signals to identify the set of assets to
invest in, starting from the following trading day. As a first vanilla
strategy that can leverage either $I^{vol}$ or $I^{tr}$, we simply go long
each asset for which $\textsc{sign}(I_{p,a,N}^{vol,tr})=+1$ and short the ones
with $\textsc{sign}(I_{p,a,N}^{vol,tr})=-1$. Moreover, we divide our imbalance
signals between quantiles ranks $qr_{i}$ for $i\in\\{1,2,3,4,5\\}$ defined as

$qr_{i}=\text{top }\frac{100}{i}\text{\% imbalances largest in magnitude},$

where we neglect imbalances equal to zero. This allows us to focus on the
strongest segments of our signals available and reinforces the $N$ threshold.

For each one of our strategies defined by the choices of $I^{vol,tr}$ and
$qr_{i}$, we consider future markout horizons of $m\in\\{5,10,21,42,63\\}$
trading days ahead of the end of each quarter $p$ (considering that there are
$21$ trading days on average in a month). The raw future return
$fret_{p,a}^{m,RAW}$ of an investment on asset $a$ is computed summing close-
to-close adjusted daily returns over the horizon of interest, and then we
define the future market-excess return $fret_{p,a}^{m,MER}$ as

$fret_{p,a}^{m,MER}=fret_{p,a}^{m,RAW}-fret_{p,SPY}^{m,RAW},$ (3)

where SPY is the S&P Composite Index ETF. Market excess returns allow us to
remain orthogonal to the market component and hedge our investments. The
related profit-and-loss ($PnL$) from our strategy amounts to

$PnL_{p,a}^{m,MER}=fret_{p,a}^{m,MER}\times\textsc{sign}(I_{p,a}).$ (4)

For clarity, we represent in the diagram in Fig. 1 our quantities and
timelines of interest.

Figure 1: Illustration of the timeline on which we extract imbalances and
compute future returns for each quarter $p$.

At each period $p$, we allocate capital uniformly (i.e. $\$\frac{1}{|A_{p}|}$)
to each one of the stocks $a\in A_{p}$ chosen by our strategy and to SPY. This
choice allows us to have comparable long-short portfolios in terms of capital
invested. A different weighting scheme can also be implemented, e.g. by
trading stocks proportionally to the magnitude of their imbalance. However,
this type of modification is redundant to the quantile approach and can lower
the expected profit. Thus, we decide to proceed with the uniform weighting
scheme, for simplicity.

We iterate the above investment procedure at the end of each financial
quarter, i.e. when we assume that we can see the newly released 13F filings.
Next, we compute summary statistics to judge the actual information provided
by imbalances and their effectiveness at different markouts. We compute the
$PnL$ for each period $p$ as

$PnL_{p}=\sum_{a}PnL_{p,a}^{m,MER}.$ (5)

The full performance of our strategy is given by adding each result in time,
i.e. $PnL_{tot}=\sum_{p=p_{i}}^{p_{f}}PnL_{p}$ where $p_{i,f}$ are the first
and last quarter with available imbalances’ data. We keep track of the profit-
per-trade ($PPT$) by computing

$PPT=\textsc{AVG}_{p}\Big{(}\frac{PnL_{p}}{|A_{p}|}\Big{)}$ (6)

for each configuration. This metric is useful to qualitatively compare the
profits after execution costs for each portfolio.

We also compute the Sharpe Ratio $S$ as

$S=\frac{\textsc{avg}_{p=p_{i}}^{p_{f}}(PnL_{p})}{\textsc{std}_{p=p_{i}}^{p_{f}}(PnL_{p})}\times\sqrt{4},$
(7)

to value the profit achieved by unit of risk taken. Since S is usually
reported annualised, we process it accordingly by considering that we are
investing once per quarter in each year. The work of [22], [23] and [24]
further highlight the importance of checking the significance of Sharpe Ratios
when back-testing a sample of hypothetical strategies. We implement the
methodology developed in [22] to compute a confidence level $C_{k}$ of the
performance of each one of our strategies $k\in K$. This is defined as

$C_{k}=Z\Big{[}\frac{(S_{k}-S_{0})\sqrt{L-1}}{\sqrt{1-\gamma_{3}S_{k}+(\gamma_{4}-1)S_{k}^{2}/4}}\Big{]},$
(8)

where $Z$ is the cumulative function of the standard Normal distribution,
$S_{k}$ the Sharpe Ratio of the specific strategy we are testing, $L$ its
sample length, $\gamma_{3}$ the skewness of the related returns distribution
and $\gamma_{4}$ its kurtosis. $|K|$ is the total number of strategies
developed and tested. Finally,

$S_{0}=\textsc{std}(\\{S_{k}\\})\Big{(}(1-\gamma)Z^{-1}[1-\frac{1}{|K|}]+\gamma
Z^{-1}[1-\frac{e^{-1}}{|K|}]\Big{)},$ (9)

is a term that deflates our Sharpe Ratio to account for selection bias and
overfitting due to multiple testing. The parameter $\gamma\sim 0.5772$ is the
Euler-Mascheroni constant.

##  4 Preliminary analyses of imbalances

###  4.1 Considerations on threshold $N$

Before investigating whether 13F imbalances carry a profitable signal, we
check the implications of choosing a different threshold $N$. For each period
$p$, we vary $N\in[0,500]$ with step size $=50$ and count the remaining number
of securities, i.e. how many assets have at least $N$ funds active on them at
that point in time. We also compute the related imbalances, following Eqs. 1
and 2. Figure 2(a) shows the number of remaining securities for different $N$
in Q3 of 2013, 2017 and 2021. This is a linear-log plot and the witnessed
linear relationship implies that we can approximate the number of surviving
securities via an exponential decay dependent on the threshold $N$. The shift
between the three temporal lines expresses the increase in active institutions
over the years, as intuitively expected from the expansion of markets, but
does not influence the shape of the relationship.

In Fig. 2(b), we decompose the above relationship between remaining securities
with positive or negative imbalance and compute the related ratio. We also
look at the evolution of this ratio in time in Figs. 3 and 4, for imbalances
computed in terms of volume or trades, respectively. We observe that there is
a predominance of buying (selling) behaviour with decreasing (increasing) $N$.
However, there is also a stable tendency of reversion towards the balanced
proportion. This is especially true for $I^{vol}$, while $I^{tr}$ shows a more
persistent bias in time. This difference is due to the two natures of the
quantities. While the former considers the actual amount of shares traded in
the market, but can include special strong long niche bets from highly
knowledgeable investors, the latter relates specifically to the number of
buying or selling trades and will strongly react to market conditions. We can
thus infer that investors tend to start or increase their common positions at
different points in time, but they will decrease or exit them more
synchronously. This result is again in agreement with intuition. Finally, the
oscillations of Fig. 3 can be related to liquidity injections or withdrawal.

For the purpose of our analysis, we will consider and compare imbalances
generated by $N\in\\{50,150,500\\}$. The case $N=150$ will be the least
unbalanced one in terms of sign proportions, but also $N=50$ does not divert
too strongly from equilibrium. These two options allow us to consider more
than $1,000$ or $3,000$ securities, respectively. We are also interested in
investigating the results of trading those securities on which investors are
most active on, and to this end, we further consider $N=500$. Due to the
biases witnessed, we also build a data set where we cross-sectionally demean
the signals from imbalances, in order to investigate the impact on the
performance of the strategy.

(a)

(b)

Figure 2: We vary the threshold $N$ on the x-axis and (a) look at how many
securities (i.e. number of imbalances) are left to possibly trade, (b) compute
the fraction of volume and trades imbalances with positive sign. Figure 3:
Evolution in time of the fraction of volume imbalances with positive sign for
different choice of threshold $N$. Figure 4: Evolution in time of the fraction
of trades imbalances with positive sign for different choice of threshold $N$.

###  4.2 Price impact of imbalances on contemporaneous returns

Before proceeding to the analysis of imbalances as a signal to forecast the
future returns of assets, we first aim to gain an understanding of the impact
of imbalances over contemporaneous returns. The goal is to extract insights
into the extent to which fund managers, which are entering into a position
over a given quarter, impact the price return of the asset over the same
quarter. We perform a linear regression of raw returns (and market-excess
returns) onto the related imbalances $I^{vol,tr}_{N}$ with
$N\in\\{50,150,500\\}$, at each quarter $p$. Quarterly returns are calculated
summing the adjusted close-to-close daily returns covering the three months
within each quarter, but these are first winsorized to control for the lowest
and highest $10\%$ of values, which could include noisy outliers. Finally, we
compute the $R^{2}$ of each regression resulting from the different
combination of variables and quarter $p$ considered.

In Table LABEL:table-impact, we report the average $R^{2}$ over the whole set
of periods $p$, i.e. $\forall p$, for each one of the above combinations. To
investigate periodical patterns, we also report the average $R^{2}$ aggregated
across each quarter (Q$1$, Q$2$, Q$3$ and Q$4$), over the years available in
the study. Imbalances computed over trade counts generally attain higher
average $R^{2}$ compared to the volume ones, and their magnitudes are
particularly enhanced for Q$2$ with $N=50$, and Q$3$ with $N=500$. One
possible explanation of the latter result is that major investors might act
very similarly in entering/exiting positions during Q$3$ following the yearly
Russell Index Rebalancing. All $R^{2}$ values are fairly low, which is
somewhat expected since we are dealing with noisy financial data, and are
considering long periods of $3$ months. Moreover, we have already mentioned
that fund managers tend to hide their best bets and file amendments to the 13F
filings later in time. Thus, the related market impact is also concealed.

The full view on the temporal evolution of $R^{2}$’s is shown in Figs. 13 and
14 of Appendix A, for raw returns and MERs respectively. For clarity, Fig. 5
depicts below the mentioned trend for the case of raw returns and $N=500$.
Surprisingly, imbalances computed in terms of trade counts show extreme spikes
in explanatory power with $R^{2}$ reaching $10-15\%$. The related quarters
could be interesting to examine in future work, but for now we proceed to the
investigation of imbalances as investment signals forecasting future returns.

Figure 5: For each quarter $p$, we report the $R^{2}$ from the regression of contemporaneous raw returns on $I^{vol,tr}_{N=500}$. Table 1: For each combination of return type and imbalances $I^{vol}_{N}$ and $I^{tr}_{N}$, we report the average $R^{2}$ in percentage of the related regressions over the whole set of periods $p$. To investigate periodical patterns, we also show the average $R^{2}$ calculated for each quarter (i.e. Q$1$, Q$2$, Q$3$, Q$4$) over the years Returns |  $\mathbf{N}$ |  $\mathbf{I^{vol,tr}}$ |  $\mathbf{R^{2}\%}$, $\mathbf{\forall p}$ |  $\mathbf{R^{2}\%}$, Q1 |  $\mathbf{R^{2}\%}$, Q2 |  $\mathbf{R^{2}\%}$, Q3 |  $\mathbf{R^{2}\%}$, Q4
---|---|---|---|---|---|---|---
Raw rets |  $500$ |  $I^{vol}$ |  $0.90$ |  $1.46$ |  $0.67$ |  $0.65$ |  $0.86$
Raw rets |  $500$ |  $I^{tr}$ |  $2.40$ |  $2.64$ |  $0.87$ |  $4.40$ |  $1.46$
Raw rets |  $150$ |  $I^{vol}$ |  $0.47$ |  $0.31$ |  $0.58$ |  $0.53$ |  $0.44$
Raw rets |  $150$ |  $I^{tr}$ |  $1.08$ |  $1.22$ |  $0.86$ |  $1.76$ |  $0.40$
Raw rets |  $50$ |  $I^{vol}$ |  $1.05$ |  $1.22$ |  $1.47$ |  $0.90$ |  $0.61$
Raw rets |  $50$ |  $I^{tr}$ |  $1.98$ |  $2.01$ |  $2.71$ |  $2.37$ |  $0.80$
MERs |  $500$ |  $I^{vol}$ |  $0.86$ |  $1.16$ |  $0.83$ |  $0.69$ |  $0.77$
MERs |  $500$ |  $I^{tr}$ |  $2.59$ |  $2.79$ |  $1.78$ |  $3.91$ |  $1.71$
MERs |  $150$ |  $I^{vol}$ |  $0.45$ |  $0.21$ |  $0.63$ |  $0.58$ |  $0.35$
MERs |  $150$ |  $I^{tr}$ |  $1.09$ |  $1.23$ |  $0.87$ |  $1.57$ |  $0.61$
MERs |  $50$ |  $I^{vol}$ |  $1.04$ |  $1.14$ |  $1.62$ |  $0.91$ |  $0.52$
MERs |  $50$ |  $I^{tr}$ |  $1.89$ |  $1.91$ |  $2.67$ |  $2.19$ |  $0.77$

##  5 Strategy construction and profitability

###  5.1 Vanilla strategy

Imbalances in volumes and trades are computed for $N\in\\{50,150,500\\}$,
following the methodology described in Section 3 without de-meaning at first.
We invest on horizons of $m\in\\{5,10,21,42,63\\}$ trading days and compute
the cumulative PnL from future MERs. The full set of results are reported in
Figs. 15, 16, 17 in Appendix B, while here we show the performance on the $42$
trading days horizon in Fig. 6. The striking feature, which is common to all
the simulations and for which Fig. 6 acts as a representative, is that trading
on the sign of imbalances generally leads to negative PnL for market excess
returns. Therefore, we proceed to compute the $PPT$ and $PnL$ of each strategy
but by trading $-1\times\textsc{sign}(I^{vol,tr})$ as the signal, i.e. betting
against the imbalances. The results are shown in Fig. 7, and in Fig. 8 we
report the significance levels of the Sharpe Ratios at less than $0.05$. For
ease of visualisation, strategies that did not pass the significance test are
reported with precise zero-value. We observe that no strategy has significant
Sharpe Ratio when $N=500$ and thus, we run all experiments also with de-
meaning the signals from imbalances. However, no significance arises at
$N=500$ and the performances and significance at $N=50,150$ are negatively
affected. We conclude that de-meaning is not suitable on 13F filings
imbalances.

From a pure investment purpose, we compare Sharpe Ratios and average PPT of
the strategies passing the significance test. It is indeed meaningful to look
at the profit-per-trade to have a qualitative view of performances when we
consider costs of executions from rebalancing. Our vanilla strategy achieves a
highly desirable Sharpe Ratio $S>1$ if we trade against trade imbalances on a
horizon of $21$ trading days, for $N=50$ and quantiles $qr_{4},qr_{5}$.
Otherwise, we can achieve good $PPT$ and $S>0.8$ if we trade against volume
imbalances on a longer horizon of $42$ days again for $N=50$. This result is
in line with our intuition. Trade imbalances are more suitable to show
crowding and over-heating of trades and indeed are our best performing signal.
Regarding the timeline, 13F filings are fully made public within 45 calendar
days after each financial quarter ends, making copycat investors start trading
the positions and indeed further fading our contrarian strategy performance.

Figure 6: Cumulative PnL from MERs on a horizon of $2$ months when trading the
sign of imbalances with $N=150$.

(a) $N=500$, average PPT

(b) $N=500$, Sharpe Ratio

(c) $N=150$, average PPT

(d) $N=150$, Sharpe Ratio

(e) $N=50$, average PPT

(f) $N=50$, Sharpe Ratio

Figure 7: Average $PPT$ and Sharpe Ratio statistics on our contrarian vanilla
strategy for $I^{vol,tr}$. The different colors relate to the different
quantile ranks as highlighted in the legend.

(a) $N=500$, vanilla strategy on volume imbalances

(b) $N=500$, vanilla strategy on trade imbalances

(c) $N=150$, vanilla strategy on volume imbalances

(d) $N=150$, vanilla strategy on trade imbalances

(e) $N=50$, vanilla strategy on volume imbalances

(f) $N=50$, vanilla strategy on trade imbalances

Figure 8: Results when testing the significance levels of our Sharpe Ratios.
Strategies rejected by the test are reported with precise zero-value for ease
of visualisation. In each heatmap, the x-axis is the horizon of the strategy
and the y-axis is the quantile rank used for trading.

###  5.2 Contrarian to Market Momentum and to Market Mean-Reversion strategy

To assess whether we can further enhance the profit achieved by our
strategies, we condition the imbalances that we trade according to the past
performance of the related security. We now hold positions for horizons of
$10,21,42$-trading days but further considering whether the MER of each
security was positive or negative over the past $10,21,42$ days. We define our
strategies being:

  * •

contrarian to market momentum (CMM) if we trade contrarian to imbalances that
have positive (negative) sign while the related securities showed past
positive (negative) performance,

  * •

contrarian to market mean-reversion (CMR) if we trade contrarian to imbalances
that have positive (negative) sign while the related securities showed past
negative (positive) performance.

Figure 9 shows the Sharpe Ratios following $I^{vol,tr}$ for the $5$ quantile
ranks, while Figs. 10 and 11 report the related significance levels for CMM
and CMR performances respectively. Interestingly, we mainly see that high and
significant Sharpe Ratios are achieved when trading contrarian to trade
imbalances on a horizon of $21$ days for $N=50$ for both CMM and CMR
strategies. We would have expected a stronger positive relationship between
imbalances and past market returns that would have further hint to the over-
heating of a trade. However, this result suggests possible independence of the
performance of imbalances to past prices, but further analysis is needed for
more reliable conclusions in this direction.

(a) $N=500$, CMM

(b) $N=500$, CMR

(c) $N=150$, CMM

(d) $N=150$, CMR

(e) $N=50$, CMM

(f) $N=50$, CMR

Figure 9: Sharpe Ratios achieved for our Contrarian to Market Momentum
imbalances (CMM) and Contrarian to Market Mean-Reversion imbalances (CMR)
strategies.

(a) $N=500$, CMM strategy on volume imbalances

(b) $N=500$, CMM strategy on trade imbalances

(c) $N=150$, CMM strategy on volume imbalances

(d) $N=150$, CMM strategy on trade imbalances

(e) $N=50$, CMM strategy on volume imbalances

(f) $N=50$, CMM strategy on trade imbalances

Figure 10: Significance level tests of our CMM Sharpe Ratios. Strategies
rejected by the test are reported with precise zero-value for ease of
visualisation. In each heatmap, the x-axis is the horizon of the strategy, and
the y-axis is the quantile rank used for trading.

(a) $N=500$, CMR strategy on volume imbalances

(b) $N=500$, CMR strategy on trade imbalances

(c) $N=150$, CMR strategy on volume imbalances

(d) $N=150$, CMR strategy on trade imbalances

(e) $N=50$, CMR strategy on volume imbalances

(f) $N=50$, CMR strategy on trade imbalances

Figure 11: Significance level tests of our CMR Sharpe Ratios. Strategies
rejected by the test are reported with precise zero-value for ease of
visualisation. In each heatmap, the x-axis is the horizon of the strategy, and
the y-axis is the quantile rank used for trading.

###  5.3 Sector-specific investing

We perform one final experiment and project imbalances of stocks onto sector
memberships, using data from Wharton Research Data Services providing SIC
(Standard Industrial Classification) Major Group for a set of securities. This
is a code that classifies stocks into $10$ sectors and its details can be
found on the SIC website itself at https://siccode.com/page/structure-of-sic-
codes. Table LABEL:table-sectors provides a summary of the number of
securities for which we have an imbalance and a SIC code, and assigns to each
category a short label that we will use in our plots. We then run our
contrarian vanilla strategy on each group for horizons of $21,42,63$-trading
days (i.e. $1,2,3$ months). We require only $N=50$, since a few sectors have
already a limited number of securities to possibly trade. The resultant Sharpe
Ratios are shown in Fig. 12, where each subfigure relates to a different
quantile. We also compute the related significance levels, but conclude that
we can accept only medium performances, while the most profitable ones are
rejected by the test.

We conclude that the major information that Form 13F carries is a suggestion
to go contrarian to what imbalances reveal. Further conditioning is not able
to uncover any stronger signals that could further enhance profits. However,
we think that there is one further view to investigate that we will address in
the future. This is the connection between average number (popularity) of
active funds on the securities of a sector and the related growth and
expectation of further inflows. We plot a few initial trends in Fig. 18 of
Appendix C to intuitively show our thoughts. Once we manage to increase the
proportion of securities for which we have available imbalances, returns and
SIC data, then we could monitor variations in the popularity of stocks within
sectors to identify signals of changes in inflows, and leverage them to
achieve stronger profits.

Table 2: SIC sectors on which we investigate the performance of our contrarian vanilla strategy. We report the number of securities for which we have available a SIC code for each sector (denominator in the right column), along with the number of them for which we have also imbalances and returns data (numerator) SIC CATEGORY |  LABEL |  No. SECURITIES
---|---|---
Agriculture, Forestry, Fishing |  agric |  $5/16$
Mining |  mining |  $98/352$
Construction |  constr |  $20/56$
Manufacturing |  manuf |  $521/1227$
Transportation & Public Utilities |  transp |  $161/441$
Wholesale Trade |  wholesale |  $70/149$
Retail Trade |  retail |  $71/194$
Finance Insurance, Real Estate |  fin-ins-RE |  $796/5136$
Services |  services |  $153/597$
Public Administration |  pubAdm |  $75/2897$

Figure 12: Sharpe Ratios achieved by our contrarian vanilla strategy when
restricting the trading to the different sectors. We use a threshold $N=50$
and test horizons of $m\in\\{21,42,63\\}$ trading days.

##  6 Conclusions

This study investigates the hidden information that is disclosed within the
SEC Form 13F-HR. We leverage on the concept of imbalance in buying vs. selling
behaviour and show that a significant opportunity for profit arises if an
external investor is willing to trade contrarian to these 13F filings
imbalances. At first glance, the reliability of our signals might be thought
to increase with the number of active funds $N$ on a security. However, the
risk is to invest in very liquid stocks without real opportunities for profit
as shown by the lack of significance of our Sharpe Ratios for $N=500$. On the
other hand, we find that a threshold of $N=50$ provides a good trade-off
between reliability of the imbalance signals and variety of the remaining
stocks to possibly trade. Our simplest contrarian vanilla strategy achieves a
desirable Sharpe Ratio $S\sim 1$ that is significant at the $0.05$ level when
trading quantiles $qr_{4},qr_{5}$ of $I^{tr}$. These two options also show
higher average $PPT$. Our imbalances capture the amount of information already
consumed in the market and can be inflated by herding despite the very
eclectic set of institutions considered. The strongest imbalances point to
overheated trades, for which we expect a reversion of prices against the sign
of imbalances, which is also confirmed by our results. The highest
profitability is achieved when following trade imbalances, since they better
depict crowding in the market. We conclude that the optimal holding horizon is
around $21$ trading days. This agrees with the fact that plain copycat
investors become active around $45$ calendar days after the financial quarter
ends.

For future investigations, an interesting direction to explore concerns the
effect of correcting reports with their amendments (Form 13F-HR/A) prior to
running the analyses, and compare the results. We expect the signals to be
affected in a tangible way, but it is not trivial to establish this in
advance. However, it is very likely that we will gain stronger insights into
the extent to which fund managers, which are entering into a position over a
given quarter, impact the price return of the asset over the same quarter.

Yet another direction worth pursuing concerns the investigation of network
effects in terms of the cross-impact of the imbalance associated to a given
asset, in either the contemporaneous or future return of another asset, in the
spirit of the recent work in [25]. On a longer timescale, we also plan to
pursue the described investment analyses on N-PORT holdings reports, once more
history is available. At the beginning of October 2016, the SEC introduced the
form N-PORT to modernise portfolio reporting of both assets and liabilities of
Registered Investment Companies and exchange-traded funds (ETFs) organised as
unit investment trusts. This form became compulsory in May 2019 and provides a
further level of market transparency and holdings details, with potentially
valuable information to analyse.

## Acknowledgements

Deborah Miori’s research was supported by the EPSRC CDT in Mathematics of
Random Systems (EPSRC Grant EP/S023925/1).

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##  Appendix A Price impact of imbalances over quarters

We regress contemporaneous raw returns (raw rets) and market-excess returns
(MERs) on imbalances to weight the impact of fund managers’ new allocations on
the price returns of the related assets over each quarter $p$. We consider
both $I^{vol}$ and $I^{tr}$, and $N\in\\{50,150,500\\}$. For each point in
time, we compute the $R^{2}$ of the related regression and plot it as
percentage in Figs. 13 and 14, for raw rets and MERs respectively.

As highlighted in Section 4.2, imbalances computed in terms of trade counts
show higher explanatory power for asset returns, especially in Q$3$s.
Moreover, it is interesting to see here how this measure has spikes in $R^{2}$
reaching $10-15\%$, despite our data being extremely noisy and addressing very
long periods of $3$ months at each iteration.

Figure 13: For each quarter $p$, we report the $R^{2}$ from the regression of
contemporaneous raw returns on $I^{vol,tr}$ for $N\in\\{50,150,500\\}$.

Figure 14: For each quarter $p$, we report the $R^{2}$ from the regression of
contemporaneous MERs on $I^{vol,tr}$ for $N\in\\{50,150,500\\}$.

##  Appendix B Cumulative PnL for the vanilla strategy

We compute time series of the cumulative PnL gained while trading the plain
imbalance signal, i.e. buying (selling) stocks if the related imbalance is
positive (negative). Figures 15, 16 and 17 show the results for minimum number
of active funds $N\in\\{50,150,500\\}$ required on each security. In each
case, we plot the performance for quantile ranks $qr_{i}$ with
$i\in\\{1,2,3,4,5\\}$ and horizons of $m\in\\{5,10,21,42,63\\}$ trading days.
We also divide between trading $I^{vol}$ versus $I^{tr}$. The results agree
that a general opportunity for profit arises if the investor is willing to
trade contrarian to imbalances from 13F filings.

Figure 15: Time series of cumulative PnL when trading imbalances applying the
threshold $N=50$.

Figure 16: Time series of cumulative PnL when trading imbalances applying the
threshold $N=150$.

Figure 17: Time series of cumulative PnL when trading imbalances applying
threshold the $N=500$.

##  Appendix C Evolution of the popularity of stocks within SIC sectors

For each period $p$ and SIC sector, we compute the average number of active
funds $N$ on the related stocks. Figure 18 shows this evolution of popularity
of sectors across time and compares it to the cumulative average MER of
holding the related stocks.

Figure 18: Evolution of the average popularity of stocks within sectors and
related overall performance.