BA453: Global Tactical Asset Allocation
Automated Model for Cross-Sectional Stock Selection
Looney Tunes Asset Management
Contents
1.Introduction and Objective
2.Model Design
3.Cross-Sectional Stock Selection
4.Model Flow
5.Database Layout
6.Problems encountered
7.In-sample test
8.Proposed future improvements
9.Conclusion
1.Introduction and Objective
The primary objective was to develop software capable of predicting returns for any number of assets based on the cross-sectional stock selection model and to develop a portfolio that optimized returns for a given level of risk.
Our second objective was to identify the intricacies and problems of building and running such a model. To test its ability it was run on 100 securities transacted on the South African Stock Exchange (JSE). The portfolio returns generated are benchmarked against the JSE All Share Index.
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2.Model Design
The program, written in Visual Basic code, allows the selection of any number of attributes in order to perform the cross-sectional regressions. Data are organized and stored in Microsoft Access for easier and more efficient manipulation. Data are parsed to Excel through a number of dynamic SQL queries. The results of each run of the model are stored in MS Access allowing further analysis.
The software leverages the built-in Excel Correlations function and matrix functions as well as the Solver add-in to perform portfolio optimization.
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3.Cross-Sectional Stock Selection
The model aims to select winners and losers from a cross section of securities. This is accomplished by regressing the returns of the assets at a given point in time against a set of lagged attributes:
rt = d0 + d1Ai1,t-1 + d2Ai2,t-1 + ….. + et
where Ai,t-1 is a lagged firm specific attribute
The shortcoming of this approach is that the slope coefficients change over time. This is due to the fact that sensitivity to the factors is firm specific. In order to cater for this it is necessary to adjust the factor to get rid of firm specific sensitivities. This is accomplished by regressing time series returns for each firm against the attributes.
The dynamic linear factor model assumes that the beta of security changes throughout time with changes in its structure, captured by a given number of attributes:
it = ci0+ ci1A1 + ci2A2 + …
If we substitute slopes in the original equation with a dynamic slopes we get:
ri,t = i + ci0Ft + ci1Ft Ai1,t-1 + ci2F tAi2,t-1 + ….. + eit
where Ft is the return of the market at time t
By capturing firm and attribute specific slopes we can create adjusted attributes:
A*1,t-1 = ci1A1,t-1
The resulting regression formulation is thus:
rt = d0 + d1A*i1,t-1 + d2A*i2,t-1 + ….. + et
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4.Model Flow
In a given run, the software goes through the following steps:
i)Run a time series regression on the return of each of the companies selected for the period of the sample. The independent variables are the market returns and lagged attributes interacted with the market returns.
ii)Capture and store the firm-specific coefficients (ci) for each attribute in the database.
iii)Retrieve the attribute values on a specific date and the firm-specific coefficients. Multiply values to obtain adjusted attributes (ci * Ai).
iv)Run a cross-sectional regression on the securities in the market using the lagged adjusted attributes and store the intercepts, coefficients and model statistics.
v)Use calculated coefficients to forecast each firm’s return for next period.
vi)Calculate the correlation between each security in the market using historical data retrieved from database. Store correlations in database.
vii)Calculate the standard deviation of each security using historical data retrieved from database.
viii)Generate variance-covariance matrix (on Excel worksheet) using the calculated correlation and standard deviation.
ix)Optimize the portfolio using the calculated expected returns and the variance-covariance matrix. Optimal weights are found for a chosen level of volatility using Excel Solver. Store the optimal portfolio security weights in the database.
x)In the case of an in-sample test, the entire procedure is automatically repeated through the specified in-sample period.
xi)Portfolio security weights for each period are matched to actual security performance to generate portfolio performance for each period.
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5.Database Layout
Figure 5.1 shows the database architecture used to support the software. The relational database structure provides full scalability. It provides the base for further analysis of results as well as other modeling techniques.
Figure 5.1 : Database architecture
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6.Problems encountered
The most important problem we faced had to do with the quality of the data. Most of the data series were incomplete, had errors or gaps. This problem has been dealt with by including an extensive rule base to capture and deal with data inconsistencies.
A second problem was the low explanatory power found for attributes in some firms. It is important to note that this is a mathematic tool and is not capable of making judgments on how sound the logic is behind choosing particular attribute sets that have explanatory power.
Linking the two problems discussed, the use of an incomplete set of data has a negative impact on the quality of the regressions and, therefore, the predictions. One must question how much of the low explanatory power of most of the attributes used is due to underlying economic reasons and how much just to poor data quality.
A final problem encountered, from an operational perspective, was the time required to run an in-sample test. This could be easily overcome by higher computing power and streamlined coding that did not leverage Excel’s functionality but rather ran as a stand alone application.
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7.In-sample test
A number of in-sample tests were performed. For the most part our regressions had R-squares of just 2%. This was disappointing and could partly be attributed to the incomplete data and limited attributes available.
The test used securities in the South African stock market and used the JSE-all-share index as a benchmark for portfolio performance. Portfolios were optimized using the historical volatility of the JSE-all-share index.
Due to the inconsistencies in some of the data, it is felt that it would be inaccurate to report the results of the model in-sample tests.
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8.Proposed future improvements
In the future, it would be better to use a more sophisticated methodology to address the volatility issue in the model such as GARCH, with the purpose of using a forecasted volatility instead of historical like we did.
Other potential area of development would be to add sorting and screening features to the program. The existing database infrastructure makes this added functionality easy to develop.
Finally, as pointed out earlier, the quality of the database used and the predictability power of the attributes chosen are critical for the success of the model. As with any mathematical tool, its true value is captured only by proper judgment and sound economical reasoning behind attribute selection.
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9.Conclusion
The model building exercise revealed many of the complications encountered in migrating theory into real practice. It showed however that modern computing provides the power to perform a level of calculation previously unattainable. The program helps make stock selection decisions on a consistent theoretically underpinned basis. Analysts however should always be used to override any selections made by the model as it is impossible to capture all information within a model.
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References
Eugene F. Fama and Kenneth R. French, 1992, "The Cross-Section of Expected Stock Returns" Journal of Finance 47, 427-465
Campbell R. Harvey, "Conditioning Variables and the Cross-Section of Stock Returns," with Wayne Ferson, Journal of Finance 1999, 54 1325-1360. (P57)
Kent Daniel and Sheridan Titman, 1997, "Evidence on the Characteristics of Cross-Sectional Variation in Stock Returns", Journal of Finance 52, 1-33.