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TERM PAPER:
Improvements of Long/Short Equity Screens With
Migration Tracking
Independent Study with Prof. Campbell Harvey
April 28th, 2004
Christoph Jacques
Fei (Felix) Xu
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1. Executive Summary:

In this paper we have developed and tested a few simple concepts to improve long/short
equity screening strategies by basing the selection of equities not only on the screen scores
derived from the current values of a stock with respect to a screen but on a blending of current
values with historic values (“migration tracking”). The underlying assumption is that past
volatility of stock scores is predictive of future volatility of stock scores and thereby contains
information that potentially helps to improve screen performance (Fig. 1).

We find that migration tracking can create significant value for screening strategies.

However, value creation depends on the style of the screen: Performance improvement is
better and more predictable for stable, low-turnover, slowly mean reverting value screens,
then for fast mean-reverting, high-turnover momentum screens.

For stable screens, incorporating information on past scores of up to 1/2 year back (3
rebalancing periods) seems to be optimal compared to selecting shorter historic time horizons.
For fast mean-reverting screens, the inclusion of only most recent information is
recommended.

More research needs to be performed on the conditions under which migration tracking
can be successful. In our research the performance of our base screens differed strongly
between the in-sample and out-of-sample period. In the same vein, the success of migration
tracking applied to the base screens differed markedly between in-sample and out-of-sample
periods.

We performed all test with FactSet’s Universal Screening and with the Alpha Tester
School. While FactSet is an excellent screening tool, one has to be very careful to get the
syntax correct – especially if portfolio decisions are being made on the screening. It is always
wise to conduct robustness checks to make sure that the code is doing what you think it is
doing.
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2. Introduction
a. Improving Long/Short equity screens with migration tracking
In this study we attempt to improve the performance of long/short equity screens by
incorporating historic information of stocks with regard to the screen in the equity selection
process. This is at odds with traditional stock screening techniques in which stocks are
selected according to their scores along the selected screens only at one given point in time.
These screens do not use information on the historical volatility of the stock with regard to the
achieved scores (“migration tracking”). We hope that by incorporating historical information
we can improve the performance of the screening strategies. Past high volatility of a stock is
believed to forecast future high volatility with regard to the score on a particular screening
dimension. Stocks with high past volatility should therefore get assigned lower scores with
respect to a screen. Additionally, we may be able to sort out stocks that appear only by
“accident” in the top and bottom fractile in the rebalancing period (e.g. through earnings
quality issues for screens based on accounting information), if they had consistently less
extreme scores in the past.
The potential cost of sorting stocks based on a entire time series of screening values is, that
there may be pronounced decreases in return spreads between the top and bottom fractile,
particularly for screens that exhibit fast mean reversion.
b. Levers of improvement
We envision that the performance of the long/short equity screens by adding migration
tracking can be improved via the following three mechanisms:

Decrease of turnover and transaction costs: If we achieve to identify stocks that
reliably score high on the screens over time, we will save transaction costs from
rebalancing our portfolio. For example, if under monthly rebalancing the total turnover of
stocks (sum of bottom and top quintile) is 50% we are faced with 600% portfolio turnover
annually. If we estimate 1% trading costs round trip (e.g. 20 cent per trade / $20 average
stock price), we lose 6% return to trading costs. If we could reduce the turnover by half by
incorporating estimates about future scores, we would be able to increase the alpha by 3%.
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
Increase in alpha: If we achieve to identify stocks at t=0 that will more reliably score
high on the screens in t=+1, we may be able to increase the alpha of the long/short
portfolio.

Decrease in volatility of Alpha (increase in Information Ratio): If past volatility of
stocks with regard to screen values contains information about future volatility, then
selecting only stocks with low historic volatility of screening scores could decrease the
volatility of the overall alpha, enhancing the information ratio.
c. Hypotheses and Research Design
We start with general hypotheses underlying this paper:
H1: Screen scores from historic rebalancings contain valuable information on a
stock’s future performance that can help us to improve Screening Strategy
Performance
H2: Screening strategy improvement via migration tracking improves screening
performance through three levers:

Increasing alpha

Reducing the variability of alpha

Reducing turnover and transaction cost
For which screens does migration-tracking work best? We test our propositions on two
screens: one value screen and one growth screen.
The value screen is the IBES one year forward consensus earnings forecast divided by
current month end price. Value screens tend to be relatively stable over time with less mean
reversion then growth screens, resulting in relatively low turnover (results will be further
discussed in section 4).
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The growth screen is the short-term earnings momentum, defined as (Current EPS – Previous
Quarter EPS)/Current Month-end Price. Growth screens tend to exhibit fast mean reversion
and therefore are expected to exhibit high portfolio turnover.
Given the initial hypotheses about the stability of growth vs. value screen we state the
following expectation:
H3: Growth screens should benefit more from migration tracking then value screens,
because the high turnover of growth screens offers more value creation opportunity
from decreasing turnover.
Which ways are there to incorporate historic information and which ones work best?
We see two primary way of how to take into account historic information: Looking at the
momentum of historic values leading up to now and looking at past volatility of scores. The
momentum argument implies that stocks that have exhibited a clear upward-trend with regard
to a screen over the last rebalancing periods are likely to continue to move upwards or
maintain high values and should therefore be assigned higher weights. The volatility
argument implies that stocks in the top/bottom fractile with high past score volatilities are less
reliable predictors for future performance then stocks with low historic volatility. This paper
focuses on exploring the volatility argument.
Caveat: It is worthwhile noting that we take the effectiveness of a screen, i.e. its correlation
between high screen scores and high returns as a given. If a highly volatile stock ends up in a
mid-field fractile and this fractile happens to yield the highest return in a given rebalancing
period, then there is an issue with the effectiveness of the screen: high fractiles are not reliably
correlated with high returns. In this paper we take the effectiveness of the screen as a given
and keep it constant - we merely analyze the improvement of the screens by amending the
selection process of stocks per screen.
Our methods to measure past volatility were restricted by the technical capabilities of FactSet
and our knowledge thereof. To measure past volatility we looked at two techniques: Averages
and Exponential Smoothing. The Average takes the arithmetic average of historic screen
scores over a specified period of time. The Exponential Smoothing Function gives more
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distant, historic screen values less weight over the specified period in time. For example,
selecting a parameter of 0.4 means that the screen score in t=-1 gets assigned a weight of 0.4,
the screen score in t=-2 gets assigned a weight of 0.4*0.4, etc. For the Exponential Smoothing
Function we experiment with weights of 0.4 and 0.8 in our study: 0.4 in order to test a
scenario where the value of historic information decreases quickly and 0.8 to test a scenario
where the value of historic information decreases less steeply, but is still discounted compared
to a simple average formula (implied weight of 1).
The underlying assumption is that stable high/low averages can only be achieved with low
volatility and therefore result in stable high/low fractile assignments (statement further
qualified in next paragraph).
H4: Exponential Smoothing techniques should lead to a better improvement of screens
then Averages, as more distant scores contain less relevant information.
Should we apply the Average/Exponential Smoothing function to the entire universe of
stocks or to the top and bottom fractile only? If we apply the averaging function to the
entire universe of stocks we may make currently weak stocks look strong. For example, if a
stock ranks in the midfield fractiles on current data, but has a stellar track record in past
rebalancing periods, using the average may bump the stock up into the top fractile to be
selected. The current average value of the stock for the screen may be due to mean reversion
setting, which would make us want to exclude this stock from our portfolio.
An alternative would be to sort the stocks on current performance first and then select from
the top and bottom quintile the 50% stocks with the highest/lowest historic values. This
technique makes sure that all selected stocks do well on current screen values.
H5: Applying migration tracking techniques to the top and bottom fractiles only after
having sorted them based on current value should yield better results then applying
migration tracking unconditionally to the entire universe of stocks.
Should we apply Averages and Exponential Smoothing to the primary values of the
stocks or to their fractile scores? This question requires a decision about the optimal data
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aggregation. If we use migration-tracking techniques based on primary values (e.g. the
FY1E/P value), we can extract a maximum amount of information from the data but we also
obtain the maximum amount of noise. Furthermore, we allow that outliers fully enter the
screening and sorting process. For example, if a stock scores mediocre in two periods but due
to some earnings quality or accounting issue displays some extraordinary values in a third
period, applying the average to the primary values could bump the stock back up into the
realm of top performing stocks.
Applying migration-tracking techniques based on the score values of stocks inhibits exactly
the inverse properties: Information is destroyed from sorting stocks into buckets first. Noise is
reduced, also. Outliers are taken care of somewhat because all stocks in the top/bottom
quintile get assigned the same score. How much information and noise is destroyed depends
on the number of fractiles we look at. In this paper we compare the performance of long/short
screens based on selecting the top/bottom deciles of screens (justification in section 3. on
Methodology).
H6: Under a top/bottom decile selection strategy, we believe that migration tracking
based on primary values works better then migration tracking based on screen scores,
as the benefits from higher information content of primary values outweighs the
negatives of overweighing outliers.
How long should we look back to include historic information and what is the right
rebalancing frequency?
For our study we used quarterly rebalancing frequency. Both, our value and our growth screen
are based on quarterly earnings numbers or expectations thereof. Pre-test showed us that
between earnings reporting dates, the IBES-forecasts for FY1E earnings change only
minimally, leading to value destruction from more frequent rebalancing as the information
content from changes between earnings reporting dates is low.
Given quarterly rebalancing, we experimented with including historic scores of up to 3
rebalancing periods back, which is equivalent to going ½ year back. Intuitively, we believe
that including information from prior 3 rebalancing periods will exceed the optimal time
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frame for many screening variables. The optimal historic time interval included in the
screening depends at least on two more factors: 1. The more short lived a screen is, i.e. the
faster it mean-reverts, the more value is destroyed from including long score histories in the
selection process 2. The optimal time interval to choose needs to be decided in connection
with the weight assigned to the information from each historic rebalancing. For example,
using a simple average of scores over the last three rebalancing periods may not be a good
idea (equal weight of each historic data point), but giving more distant data points
exponentially decreasing weights (Exponential Smoothing function with 0.4 weight) may still
yield some benefits. Our research design considers this interaction between the length of score
history included and the weights assigned to historic information by performing a complete
set of experiments on the matrix of both factors.
H7: We believe that under the chosen research set-up (quarterly rebalancing periods),
it is better to include only information on two rebalancing periods then to include
information on three rebalancing periods (all other things equal).
To test the questions and hypotheses above we have set up a research design that follows the
tree structure in Exhibit 1. For each end-node of the tree, results for a long/short portfolio are
recorded and measured in terms of key performance parameters (see next section).
3. Methodology
a. Sample period and Universe
We tested the propositions above with FactSet’s Universal Screening program and the Alphatester. Our in-sample period is 31/12/1988 to 31/12/1998. Our out-of-sample period is
31/12/1998 to 31/12/2003. Our universe was based on all North American stocks above
$100M market capitalization.
We checked the results of all proposed models based on a value weighted and an equal
weighted investment process. Most of the times, the equal weighted models yielded more
favorable results. However, in this paper we choose to focus only on the value weighted
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results: Firstly, an equal weighted selection process is not feasible for most portfolio
managers as it gives tremendous weight to small stocks. True results of an equal weighted
strategy would be distorted by liquidity constraints of small stocks. Secondly, some of the
more favorable results of the equal weighted selection process is due to loading up strongly
on other risk factors, such as size or beta.
b. Decile focus and Transaction Cost Assumptions
We recognize that some of the features in our research design would not be implemented by
portfolio managers in the “real world”, but are rather chosen to emphasize the mechanics and
the results of the migration tracking approach.

For example, we select the top/bottom decile for our long/short strategy. 1. Most
managers would not follow this approach, as it produces high turnover. We select deciles
exactly for this reason to check whether we can significantly reduce this turn over
(favorable condition bias in research design). 2. We also use deciles to make certain
versions of our research design comparable: Our suggestion to apply migration tracking to
the top and bottom fractiles only after sorting on the current values requires some sort of
decile approach: We first sort into quintiles based on the current values of a screen and
then select the top/bottom 50% with the highest/lowest historic averages. This brings us
effectively to decile approach.

Transaction Cost Assumption: We follow Columbine Research in assuming 1%
round-trip transaction costs. This equates to joint buy and sell costs of $0.20 for an
average stock price of $20. We feel, the assumption is rather on the high end of the
spectrum, especially for big mutual funds, that may face almost no transaction cost if a
liquid internal market exists (potentially favorable condition bias in research design).
However, this assumption reflects an average of cost going long and costs going short in a
stock, the latter being much more expensive.
c. Definitions for Performance and Control Variables
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We look at the following performance metrics to compare the different migration tracking
screens against the benchmark without migration tracking (see Key Result Tables in Exhibit
2-5):
1. Quarterly Return Spread in %: Measures the quarterly return of the long portfolio
in the first decile minus the quarterly return of the short portfolio in the tenth decile.
2. Standard Deviation of Spread: Measures the standard deviation of the quarterly
Return Spreads over the rebalancing periods.
3. Quarterly Turnover in %: Measures the sum of the portfolio turnover (TO) for the
first decile and the portfolio turnover for the tenth decile.
TotalTOQuarterly  TOQuart.,1stDecile  TOQuart.,10thDecile
The percentage is measured as % of old stocks leaving the portfolio plus the % of new
stocks entering the portfolio. Therefore the maximum value of turnover is 400%.
Turnover is measured as value weighted turnover, i.e. if a stock with big market
capitalization and an accordingly high share in the top decile has to be removed from
one rebalancing period to the next, the turnover percentage for the decile of the stock
reflects its high share in the top decile.
4. Transaction Cost Adjusted Spread: Calculates the return spread between top decile
and bottom decile, where each return is adjusted for the turnover of the decile times
the estimated transaction costs (TC) divided by 2.
TC  
TC 

radjusted ,1stDecile  radjusted ,10thDecile   runadj .,1stD  TO1stD 
   runadj .,10thD  TO10thD 

2  
2 

TC
 runadj .,1stD  runadj.,10thD 
TO1stQ  TO10thQ
2


Transaction costs are roundtrip transaction costs and are divided by two, because the
definition of turnover in the previous paragraph measures transaction costs as the sum
of one-way transaction cost.
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5. “Information Ratio”: Measures the quarterly return spread between top and bottom
decile (not adjusted for transaction costs) divided by the standard deviation of the
quarterly return spreads.
6. Transaction Cost adjusted Information Ratio: Measures the quarterly return spread
between top and bottom decile adjusted for turnover related transaction costs and
divided by the standard deviation of the quarterly return spread. This is a key ratio that
incorporates information on all levers of value creation from migration tracking:
Return spreads, spread volatility and turnover related costs. Migration tracking should
strive to improve this value.
While performing our experiments on migration tracking we control for two risk factors: Size
(Market Capitalization) and Beta. We want to make sure that increasing return spreads or
increasing spread volatility from migration tracking are not due to an increased load of size or
market risk.
Market Cap differential is defined as (Market CapTopDecile – Market CapBottomDecile)/Market
CapBottomDecile.
Beta Differential is defined as (BetaTopDecile – BetaBottomDecile)/BetaBottomDecile.
4. Results:
The following results are taken from the tables in Exhibits 2 to 5 (Illustrated in Fig 2). We
only reference the summary tables, as there are too many individual tables for all the
experiments involved. A complete overview of result tables can be found in the Excel file
delivered with the paper. In presenting results, we explicitly refer to the hypotheses stated
before.
In our tests we found evidence that migration tracking can improve long/short equity screens.
However, the effectiveness seems to be restricted to value screens with low turnover, high
stability and slow mean reversion.
4.1. Value Screen
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Standalone performance of the value screen: Our value screen is displays a relatively weak
performance in sample with a quarterly return spread of only 0.65%. Quarterly turnover is
relatively low at 109%. Taking into account transaction costs renders the return spread of this
screen almost indistinguishable from zero.
Out of sample the value screen displays excellent results of 6.44% quarterly return, indicating
the current return of value investing after the stock market bubble collapsed.
Improvements from migration tracking:
Hypothesis 1: The value screen can be improved with migration tracking in sample as well as
out sample. With two exceptions, all techniques to include historic values of screening scores
improved the Transaction Cost adjusted Information Ratio. Improvements in % were
strongest in sample, where the screen performs badly, with increases in the adjusted
information ratio ranging from 90-700% (departing from an admittedly low level, though).
Out of sample, improvements range from 1% to 25% only. However, it is remarkable that
almost all experiments lead to improvements. In addition, improving a screen that already
returns 24% per year by another 25% would be a veritable achievement.
Hypothesis 2: The sources of this improvement are mainly an improvement in the return
spread. We interpret this finding to mean that migration-tracking helps identifying stocks that
reliably score in the top and bottom fractiles, thereby removing outliers and improving the
effectiveness of a screen. Turnover is less of a factor in the value screen improvement:
Turnover decreases consistently during the in-sample period, but to a little extent (1%-11%)
so that the overall performance of the screen is not greatly enhanced from this lever. We do
see any evidence in the data that the standard deviation of quarterly return spreads is
significantly reduced.
Hypothesis 4: We did not find any evidence in-sample or out-of-sample that exponential
smoothing techniques outperform simple averages of past values.
Hypothesis 5: We did not find any indication, neither in-sample nor out-of-sample, that
migration tracking techniques focused on analyzing the history of stocks in the top/bottom
fractiles only work better then techniques looking at historic values of all stocks contained in
the equity universe.
Hypothesis 6: In-sample we saw some evidence that migration tracking based on primary
values does better then migration tracking based on scoring values. Out-of-sample, however,
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the opposite seems to be true. In conclusion, we do not feel confident to have found evidence
for our hypothesis.
Hypothesis 7: With respect to the optimal time period of historic data to include, results from
the in-sample period seem to suggest that the longer the time horizon the better. With respect
to the exponential smoothing technique, giving more weights to historic data is better then
giving less weight. However, out of sample, these last two findings on optimal time periods
and optimal weights cannot be confirmed.
In sum, we feel confident that stable, low volatility value screens can be improved with
almost all variations of migration tracking. Migration tracking mainly improves screen
performance by differentiating stably high performing stocks from temporary outliers.
Turnover reduction is not a significant lever of value creation for stable value screens. There
seems to be a slight indication that migration tracking based on primary values works better
then migration tracking based on scoring values. With respect to the other hypothesis we feel
uncomfortable drawing further inference from a contradictory data picture. We do not find
any significant changes in the control variables beta risk and market risk that could be an
intervening variable for explaining the improvements of screen performance. The exception is
the migration tracking based on the top and bottom quintiles only with primary values for the
in-sample period. In this version, the excess of beta in the top decile over the beta in the
bottom decile increases from an average 5% in the benchmark to about 15%.
4.2. Momentum Screen
Standalone performance of screen: The momentum screen shows consistently good results
in and out of sample with quarterly return spreads of around 4.5%. Given the quick mean
reversion of the screen, the transaction costs become a real issue with turnover numbers
beyond the 300% level per quarter
Improvements from migration tracking:
Hypothesis 1: Compared to the value screen, there is less evidence that the momentum screen
can be improved with migration tracking techniques. In sample, we do not see any
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improvements from migration tracking, but major deteriorations of screen performances
ranging from –5% to –70% in the transaction cost adjusted Information Ratio. Out of sample
we see some improvements in the range of 18% to 54% in the transaction cost adjusted
Information Ratio. However, these improvements are limited to certain techniques, discussed
later.
Hypothesis 2: We find that migration tracking significantly improves the turnover of our
momentum screen by 11% to 33%. However, the economic benefits from reduced transaction
costs are outweighed by a serious reduction in return spreads in-sample. In sample, we do not
find improvements in return spreads under any scenario. Decreases in spreads range between
–3% to –58%. Out of sample, we see clear improvements in return spreads for most
techniques also, leading to overall beneficial results.
The standard deviation of return spreads goes up slightly for almost all scenarios, contributing
to the performance deterioration under migration tracking.
Hypothesis 4: Although we do not achieve any performance improvement in-sample, it is
worthwhile noting, that exponential smoothing techniques seem to do better then average
based migration tracking. In-sample, the performance deterioration for the exponential
smoothing technique is smaller. Out-of-sample, the exponential smoothing technique on
average also sees to have a minimal advantage, although the picture here is not very
conclusive. We take these results to give and indication that likely only the most recent
history of screen values can be used to improve the screen performance, if at all. All other
things being equal, the exponential smoothing technique assigns less weight to historic
information then the average technique.
Hypothesis 5: For the Momentum Screen, migration tracking that takes into account historic
data for the top and bottom quintile only works better then migration tracking that sorts stocks
after calculating the historic averages for all stocks. In-sample, the top and bottom only
technique clearly produces the smallest losses from applying migration tracking. Out-ofsample, this technique also outperforms all other experiments, which are based on time series
scores of the entire security universe, except one.
Hypothesis 6: Regarding the question whether the use of primary values is superior to the use
of scores in doing migration tracking, we see inconclusive evidence for the momentum
screen. In sample, there is not evidence of superiority of one over the other. Out of sample,
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the picture is not much clearer. If primary values are used in conjunction with the exponential
smoothing technique, superior results seem to be achievable. However, we do not feel
confident enough in the representativeness of our experiments to derive any generalized
conclusion.
Hypothesis 7: With respect to the optimal time period of historic data to include, results from
the in-sample period seem to suggest that the shorter the time horizon the better. However,
out of sample, the evidence is inconclusive such that we feel uncomfortable making any
definite statements, although it makes intuitive sense, that for screens with fast mean
reversion, only the most recent historic information should be valuable.
In sum, we do not find a convincing pattern to improve our momentum screen by applying
migration tracking. In-sample, we do not manage to improve performance with any of out
propositions, while out-of-sample improvements can be achieved. As we do not have an
explanation for these contradicting findings, our confidence in the value of migration tracking
for momentum screens is not high.
We contribute our negative findings to the fact that for highly volatile screens with fast mean
reversion the loss of return spreads from looking at historic data clearly outweighs the
benefits of reduced portfolio turnover. If migration tracking creates value at all for momentum
screens, most likely only very recent historic information increases value by improving the
selection of stocks without sacrificing valuable momentum.
The two control variables market capitalization and beta show slight changes for the out-ofsample period, where migration tracking seems to have some successes: The beta of the
bottom decile increases relative to the beta of the top portfolio. In the same vein the market
capitalization of the bottom decile decreases relative to the top decile.
4.3. Summary
In this paper we have developed and explored a range of relatively easy concepts of migration
tracking. While we have found evidence that migration tracking can improve the performance
of long/short equity screens, the improvements strongly depend on the types of screens used.
Migration tracking seems to work best with value screens that slowly mean revert and are
- 16 -
relatively stable over time (Hypothesis 3). The main driver of improvement for the value
screen is the improvement of return spreads between the top and bottom decile, while the
reduction of turnover contributes little. For these types of screens, the longer time series
horizons chosen ( 3 quarters) seemed to work better then the short one (2 quarters) (Fig 3)
For fast mean-reverting momentum screens, there is significant danger that the incorporation
of historic information significantly reduces the return spread. Turnover is significantly
reduced, but the positive economic effects are not able to outweigh the negatives of
decreasing return spreads, should they occur. More research needs to be done under which
(market) conditions value screens and particularly momentum screens can benefit from
migration tracking. We have reason to believe, that in times when migration tracking works
for momentum screens, enriching the stock selection process with most recent historic scoring
information creates more value then enriching it with more distant historic information.
As the biggest drive of value creation seems to be the increase in return spreads between top
and bottom deciles, our results are not very sensitive to the transaction cost assumptions we
stated above.
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Figure 1
T(0)
Score of Stock A
buy / overweight
decison
Score of Stock B
sell / underweight decison
Decile 1
Decile 10
1
2
3
4
5
6
7
8
9
10
11
12
Periods (T)
Both Stock A and B appear in the top decile at T=0, the volatile path of stock B’s scores in
the past periods makes it less desirable to buy/overweight. At T=1, given the fact that both
have fallen out of the top decile, it is probably better to keep holding A, because it has higher
probability of returning to top decile next period.
- 18 -
Figure 2A
Impact of scoring adjustment on value and momentum screens
Spread vs. turnover
20%
-3.0%
-2.5%
-2.0%
-1.5%
-1.0%
-0.5%
0%
0.0%
0.5%
1.0%
1.5%
change in return spread
2.0%
-20%
-40%
"ideal"
Quadrant
-60%
-80%
-100%
In Sample FYIE
In Sample ChgESP
Out of Sample FY1E
Out Of Sample ChgEPS
change in turnover
We applied two (and three) periods Average function and exponential smoothing functions to
both value (FY1E / P) and momentum (ChgEPS) scores. Their impacts on top – bottom decile
return spread and turnover are shown here.
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Figure 2B
impact of score adjustment on value and momentum screens
Spread vs Sharpe ratio
0.2
"ideal"
Quadrant
0.1
-3.0%
-2.5%
-2.0%
-1.5%
-1.0%
-0.5%
0.0
0.0%
change in return spread
0.5%
1.0%
1.5%
2.0%
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6
in sample FY1E
in sample ChgEPS
out of sample FY1E
Out of sample ChgEPS
change in Sharpe Ratio
We applied two (and three) periods Average function and exponential smoothing functions to
both value (FY1E / P) and momentum (ChgEPS) scores. Their impacts on top – bottom decile
return spread and Sharpe ratio (Spread / volatility) are shown here.
- 20 -
Figure 3
Two priod adjustment vs. three-period adjustment
20%
-3.0%
-2.5%
-2.0%
-1.5%
-1.0%
-0.5%
0%
0.0%
change in spread
0.5%
1.0%
1.5%
2.0%
-20%
-40%
"ideal"
Quadrant
-60%
-80%
-100%
Two-period value screen
Two-period momentum screen
Three-period value screen
Three-period momentum screen
change in turnover
We applied two periods and three periods score adjustment to both value (FY1E / P) and
momentum (ChgEPS) scores. These adjustments include averaging and exponential
smoothing. Their impacts on top – bottom decile return spread turnover are shown here.
- 21 Exhibit 2: Migration Tracking for Value Screen in Sample 1988-1998
Performance Metrics
Time series based on entire security
Universe
Time series top &
bottom quintile
only
Value Screen FY1E/Mthl. P(0)
Benchmark
No Migration
Tracking
Quarterly
Return
Spread in %
StdDev of
Qrtly.
Spreads
Qrtly.
Turnover in
%
Control Metrics
Transact. Cost
"Information Transact. Cost Market Cap
Beta
Adj. Return
Ratio"
adjusted IR
Differential Differential
Spread
Return
Spread
Improvements vs. Benchmark in %
Transact. Cost
"Information Transact. Cost
Turnover
Adj. Return
Ratio"
adjusted IR
Spread
0.65%
7.9
109
0.11%
0.0008
0.0001
27%
5%
-
-
-
-
-
2 Reb. Periods
0.91%
8.2
105
0.38%
0.0011
0.0005
22%
2%
40%
-3%
261%
36%
250%
3 Reb. Periods
1.32%
7.9
97
0.84%
0.0017
0.0011
21%
-3%
103%
-11%
689%
105%
695%
2 Reb., 0.4 Weight
2 Reb., 0.8 Weight
3 Reb., 0.4 Weight
3 Reb., 0.8 Weight
1.03%
1.01%
1.05%
1.27%
8.2
8.2
8.1
7.9
109
105
105
98
0.49%
0.48%
0.52%
0.78%
0.0013
0.0012
0.0013
0.0016
0.0006
0.0006
0.0006
0.0010
25%
23%
26%
21%
6%
5%
6%
-1%
58%
55%
62%
95%
0%
-3%
-3%
-10%
360%
357%
394%
636%
54%
50%
58%
97%
346%
342%
384%
642%
2 Reb. Periods
0.47%
8.0
103
-0.05%
0.0006
-0.0001
25%
4%
-28%
-5%
-144%
-28%
-143%
3 Reb. Periods
1.32%
8.0
101
0.82%
0.0017
0.0010
23%
-4%
103%
-8%
670%
103%
668%
2 Reb., 0.4 Weight
2 Reb., 0.8 Weight
3 Reb., 0.4 Weight
3 Reb., 0.8 Weight
0.73%
0.75%
0.75%
1.30%
7.9
8.1
8.1
7.4
107
107
107
102
0.20%
0.21%
0.21%
0.79%
0.0009
0.0009
0.0009
0.0017
0.0003
0.0003
0.0003
0.0011
26%
27%
24%
23%
2%
8%
5%
3%
12%
15%
15%
100%
-2%
-1%
-1%
-6%
86%
101%
102%
646%
13%
13%
14%
113%
87%
96%
99%
695%
2 Reb. Periods
3 Reb. Periods
0.91%
1.34%
8.3
7.8
105
97
0.39%
0.86%
0.0011
0.0017
0.0005
0.0011
23%
22%
-16%
-20%
40%
106%
-4%
-11%
263%
708%
35%
110%
250%
722%
2 Reb., 0.4 Weight
2 Reb., 0.8 Weight
3 Reb., 0.4 Weight
3 Reb., 0.8 Weight
1.10%
0.88%
0.99%
1.28%
8.2
8.3
8.1
7.8
107
103
103
98
0.56%
0.36%
0.48%
0.79%
0.0013
0.0011
0.0012
0.0016
0.0007
0.0004
0.0006
0.0010
26%
24%
24%
22%
-13%
-14%
-12%
-20%
69%
35%
52%
97%
-1%
-5%
-6%
-10%
431%
242%
350%
644%
65%
30%
49%
99%
417%
228%
339%
653%
Quarterly
Return
Spread in %
StdDev of
Qrtly.
Spreads
Qrtly.
Turnover in
%
Hist. Average
1. Primary
Values
Exponential
Smoothing
Hist. Average
2. Scoring
Values
Exponential
Smoothing
Hist. Average
3. Primary
Values
Exponential
Smoothing
Exhibit 3: Migration Tracking for Value Screen out of Sample 1998-2003
Performance Metrics
Time series based on entire security
Universe
Time series top &
bottom quintile
only
Value Screen FY1E/Mthl. P(0)
Benchmark
No Migration
Tracking
Hist. Average
Primary
Values
Exponential
Smoothing
Hist. Average
Scoring
Values
Exponential
Smoothing
Hist. Average
Primary
Values
Exponential
Smoothing
Improvements vs. Benchmark in %
Control Metrics
Transact. Cost
"Information Transact. Cost Market Cap
Adj. Return
Ratio"
adjusted IR
Differential
Spread
Beta
Differential
Return
Spread
Turnover
Transact. Cost
"Information Transact. Cost
Adj. Return
Ratio"
adjusted IR
Spread
6.44%
22.3
113
5.87%
0.0029
0.0026
153%
-61%
-
-
-
-
-
2 Reb. Periods
3 Reb. Periods
6.54%
6.31%
22.0
22.6
115
106
5.97%
5.78%
0.0030
0.0028
0.0027
0.0026
147%
147%
-61%
-63%
2%
-2%
1%
-7%
2%
-2%
3%
-3%
3%
-3%
2 Reb., 0.4 Weight
2 Reb., 0.8 Weight
3 Reb., 0.4 Weight
3 Reb., 0.8 Weight
6.46%
6.60%
6.60%
6.47%
22.1
22.1
22.1
22.6
113
114
110
107
5.89%
6.03%
6.05%
5.94%
0.0029
0.0030
0.0030
0.0029
0.0027
0.0027
0.0027
0.0026
148%
149%
150%
154%
-61%
-61%
-61%
-63%
0%
2%
2%
0%
0%
0%
-3%
-6%
0%
3%
3%
1%
1%
4%
3%
-1%
1%
4%
4%
0%
2 Reb. Periods
3 Reb. Periods
7.89%
7.10%
22.4
21.8
119
109
7.30%
6.55%
0.0035
0.0033
0.0033
0.0030
137%
143%
-62%
-62%
23%
10%
5%
-4%
24%
12%
22%
13%
24%
14%
2 Reb., 0.4 Weight
2 Reb., 0.8 Weight
3 Reb., 0.4 Weight
3 Reb., 0.8 Weight
6.61%
7.02%
7.52%
7.39%
22.2
22.2
21.6
22.2
114
116
115
110
6.04%
6.44%
6.94%
6.84%
0.0030
0.0032
0.0035
0.0033
0.0027
0.0029
0.0032
0.0031
154%
146%
144%
143%
-62%
-62%
-61%
-62%
3%
9%
17%
15%
0%
2%
2%
-3%
3%
10%
18%
17%
3%
9%
21%
15%
3%
10%
22%
17%
2 Reb. Periods
3 Reb. Periods
6.95%
7.18%
23.1
22.6
114
108
6.38%
6.64%
0.0030
0.0032
0.0028
0.0029
145%
149%
-60%
-62%
8%
11%
1%
-5%
9%
13%
4%
10%
5%
12%
2 Reb., 0.4 Weight
2 Reb., 0.8 Weight
3 Reb., 0.4 Weight
3 Reb., 0.8 Weight
6.90%
7.09%
6.79%
7.38%
22.6
22.6
22.4
23.1
113
114
111
108
6.33%
6.52%
6.23%
6.84%
0.0031
0.0031
0.0030
0.0032
0.0028
0.0029
0.0028
0.0030
146%
147%
148%
148%
-60%
-60%
-60%
-62%
7%
10%
5%
15%
0%
0%
-2%
-5%
8%
11%
6%
17%
6%
8%
5%
11%
6%
9%
6%
12%
- 22 Exhibit 4: Migration Tracking for Earnings Momentum Screen in Sample 1988-1998
Performance Metrics
Time series based on entire security
Universe
Time series top &
bottom quintile
only
Earnings Momentum (Mthl. EPS(0)-Mthl. EPS(-3))/Mthl. P(0)
Benchmark
No Migration
Tracking
Quarterly
Return
Spread in %
StdDev of
Qrtly.
Spreads
Improvements vs. Benchmark in %
Control Metrics
Qrtly.
Transact. Cost
Transact.
"Information
Market Cap
Turnover in Adj. Return
Cost
Ratio"
Differential
%
Spread
adjusted IR
Beta
Differential
Return
Spread
Turnover
Transact. Cost
"Information
Adj. Return
Ratio"
Spread
Transact.
Cost
adjusted IR
4.64%
5.4
321
3.04%
0.0085
0.0056
2%
-15%
-
-
-
-
-
2 Reb. Periods
2.90%
6.3
215
1.82%
0.0046
0.0029
2%
-14%
-38%
-33%
-40%
-46%
-48%
3 Reb. Periods
1.94%
6.1
229
0.80%
0.0032
0.0013
3%
-8%
-58%
-29%
-74%
-63%
-77%
2 Reb., 0.4 Weight
2 Reb., 0.8 Weight
3 Reb., 0.4 Weight
3 Reb., 0.8 Weight
4.12%
3.30%
3.64%
2.58%
6.2
6.3
6.6
6.2
252
218
234
214
2.86%
2.21%
2.47%
1.51%
0.0067
0.0052
0.0055
0.0042
0.0046
0.0035
0.0037
0.0025
0%
1%
2%
0%
-20%
-13%
-21%
-8%
-11%
-29%
-22%
-44%
-22%
-32%
-27%
-33%
-6%
-27%
-19%
-50%
-22%
-39%
-35%
-51%
-17%
-37%
-33%
-56%
2 Reb. Periods
2.58%
6.3
235
1.41%
0.0041
0.0022
-1%
24%
-44%
-27%
-54%
-52%
-60%
3 Reb. Periods
2.13%
5.8
235
0.95%
0.0037
0.0017
-8%
16%
-54%
-27%
-69%
-57%
-70%
2 Reb., 0.4 Weight
2 Reb., 0.8 Weight
3 Reb., 0.4 Weight
3 Reb., 0.8 Weight
3.44%
3.32%
3.29%
2.37%
6.4
6.3
6.3
5.7
250
236
230
229
2.19%
2.14%
2.14%
1.22%
0.0054
0.0053
0.0052
0.0042
0.0034
0.0034
0.0034
0.0021
-9%
-4%
-5%
-3%
37%
22%
21%
16%
-26%
-28%
-29%
-49%
-22%
-26%
-28%
-29%
-28%
-30%
-30%
-60%
-37%
-38%
-39%
-51%
-39%
-39%
-39%
-62%
2 Reb. Periods
3 Reb. Periods
4.30%
4.11%
6.1
6.0
266
255
2.97%
2.84%
0.0070
0.0069
0.0049
0.0047
1%
-2%
-21%
-9%
-7%
-11%
-17%
-21%
-2%
-7%
-18%
-20%
-13%
-15%
2 Reb., 0.4 Weight
2 Reb., 0.8 Weight
3 Reb., 0.4 Weight
3 Reb., 0.8 Weight
4.51%
4.33%
4.49%
4.33%
5.8
6.4
6.4
6.2
284
270
277
259
3.09%
2.98%
3.11%
3.03%
0.0077
0.0068
0.0071
0.0070
0.0053
0.0047
0.0049
0.0049
0%
1%
-1%
-2%
-19%
-21%
-22%
-14%
-3%
-7%
-3%
-7%
-11%
-16%
-14%
-19%
2%
-2%
2%
0%
-9%
-21%
-17%
-18%
-5%
-16%
-13%
-13%
Hist. Average
1. Primary
Values
Exponential
Smoothing
Hist. Average
2. Scoring
Values
Exponential
Smoothing
Hist. Average
3. Primary
Values
Exponential
Smoothing
Exhibit 5: Migration Tracking for Earnings Momentum Screen out of Sample 1998-2003
Performance Metrics
Time series based on entire security
Universe
Time Series top
& bottom quintile
only
Earnings Momentum (Mthl. EPS(0)-Mthl. EPS(-3))/Mthl. P(0)
Benchmark
Hist. Average
Primary
Values
Exponential
Smoothing
Hist. Average
Scoring
Values
Exponential
Smoothing
Hist. Average
Primary
Values
StdDev of
Qrtly.
Spreads
4.39%
6.6
329
2.74%
0.0066
0.0041
2 Reb. Periods
3 Reb. Periods
3.95%
3.53%
7.0
7.2
213
235
2.88%
2.35%
0.0057
0.0049
2 Reb., 0.4 Weight
2 Reb., 0.8 Weight
3 Reb., 0.4 Weight
3 Reb., 0.8 Weight
5.23%
4.48%
5.55%
3.23%
7.4
6.9
7.3
6.6
250
220
228
217
3.98%
3.38%
4.41%
2.15%
2 Reb. Periods
3 Reb. Periods
5.39%
2.64%
8.0
6.7
245
246
2 Reb., 0.4 Weight
2 Reb., 0.8 Weight
3 Reb., 0.4 Weight
3 Reb., 0.8 Weight
4.87%
4.94%
5.84%
2.92%
7.7
8.0
8.2
6.4
2 Reb. Periods
3 Reb. Periods
6.30%
5.94%
2 Reb., 0.4 Weight
2 Reb., 0.8 Weight
3 Reb., 0.4 Weight
3 Reb., 0.8 Weight
5.52%
6.23%
6.07%
6.10%
No Migration
Tracking
Exponential
Smoothing
Improvements vs. Benchmark in %
Control Metrics
Quarterly
Return
Spread in %
Qrtly.
Transact. Cost
Transact.
"Information
Market Cap
Turnover in Adj. Return
Cost
Ratio"
Differential
%
Spread
adjusted IR
Transact. Cost
"Information
Adj. Return
Ratio"
Spread
Transact.
Cost
adjusted IR
Beta
Differential
Returns
Spread
Turnover
0%
2%
-
-
-
-
-
0.0041
0.0033
4%
1%
-13%
-15%
-10%
-20%
-35%
-29%
5%
-14%
-14%
-26%
0%
-21%
0.0071
0.0065
0.0076
0.0049
0.0054
0.0049
0.0060
0.0032
3%
4%
5%
0%
-13%
-10%
-8%
-11%
19%
2%
26%
-26%
-24%
-33%
-31%
-34%
45%
23%
61%
-22%
8%
-2%
15%
-26%
31%
18%
46%
-22%
4.17%
1.41%
0.0068
0.0039
0.0052
0.0021
8%
-3%
-14%
-22%
23%
-40%
-26%
-25%
52%
-49%
2%
-41%
27%
-49%
251
248
240
235
3.62%
3.70%
4.64%
1.75%
0.0063
0.0062
0.0071
0.0046
0.0047
0.0046
0.0056
0.0027
4%
7%
2%
3%
-19%
-21%
-19%
-21%
11%
13%
33%
-33%
-24%
-25%
-27%
-29%
32%
35%
69%
-36%
-5%
-6%
7%
-31%
13%
12%
36%
-34%
8.4
7.5
279
268
4.90%
4.60%
0.0075
0.0079
0.0058
0.0061
15%
15%
-10%
-14%
44%
35%
-15%
-19%
79%
68%
13%
19%
41%
48%
6.8
8.2
8.0
7.5
292
282
288
270
4.06%
4.82%
4.63%
4.75%
0.0081
0.0076
0.0076
0.0082
0.0059
0.0059
0.0058
0.0064
7%
14%
8%
13%
-9%
-11%
-12%
-11%
26%
42%
38%
39%
-11%
-14%
-12%
-18%
48%
76%
69%
73%
22%
15%
14%
24%
44%
42%
39%
54%