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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

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.

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%.

• 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).

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 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 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 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 Alpha-tester. 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 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

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.

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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.

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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.

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

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, 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 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-of-sample, 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, 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-of-sample 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 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.

Figure 1

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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.

Figure 2A

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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.

Figure 2B

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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.

Figure 3

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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.

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