Finance 453: Global Asset Allocation and Stock Selection
Final Project
Informing the Choice of Fractile Usage in Factor-Based Stock Screening
The Optimizers
Maria Fernandez
David Marcus
Matthew Meares
Hiren Patel
Hong Wan
Objective
We hoped to study the trade-offs (risk-return) in factor-based screening by varying portfolio size.
Introduction
Although fractiles are used as the standard method for choosing portfolio size, this decision seems to often be an afterthought in strategy formulation. For example, FactSet offers limited default selections for fractile choice of only 4, 5, and 10. However, the actual number of stocks utilized to carry out a factor-based screening is based not only on number of fractiles but also the size of the universe. Therefore, the implications for portfolio formation may be very different when applying the same number of fractiles to a universe of 500 stocks versus a universe of 2,000 securities. We were curious if it is possible to determine that an optimal number of securities (and thus universe divided by fractiles) may exist for factor-based screening models.
The chart below[1] highlights the well documented diminishing impact on portfolio standard deviation of adding more securities. As the number of securities reaches 40, the standard deviation of the portfolio becomes asymptotic at the market risk, essentially diversifying away the unsystematic risk of all of a portfolio’s securities.
Since factor-based ranking models expect that, with some error, return will decrease with the ranking of that factor, adding in additional securities decreases the expected return of a portfolio. We, therefore, suspect that there is a limit to the diversification benefit of larger portfolios. If so, we suspect that it should be possible to find a diminishing Sharpe ratio (risk-adjusted return) within factor-based ranking models over larger portfolio sizes. This will be the main focus of our research. Trading costs are a further issue that we expect will impact the performance of varying size portfolios non-uniformly, as we expect there to be some relationship between portfolio turnover and size. We will touch on this point briefly in the conclusion of this paper.
Methodology
Screening factors
We take a look at several factors that might be interesting to portfolio management. After initial screening process ( large cap), the following factors show a nice trend line between fractile and return.
- Average Volume
- Average Volume 500
- Cash price
- Dividend yield
- IBES mean
- IBES SUE
- ROA
- Total return
- Total return 500
Based on the shape of the curve across fractiles, the slope and R square of the trend line, we pick the five factors to further investigate: IBES Sue, IBES Mean, Dividend Yield, Cash Price and Average Volume.
Factors Analysis
- IBES Sue
a. Long Plot
If we long the first fractile, the sharp ratio indicates that the optimal number of companies per fractile is around 25. Further diversification is suboptimal.
b. Short Plot
If we short the last fractile, the sharp ratio across different number of fractiled doesn’t indicate a strong trend.
c. Long-short plot
If we long the first fractile and short the last fractile, there is a smooth trend line across different numbers of fractiles. It indicates that with at least 50 companies per fractile, the diversification doesn’t make a significant impact on the performance.
d. Maximum of one month loss
The curve of the last fratile of maximum of one-moth loss is smooth across different number of fractiles. In this scenario, diversification has less impact upon the performance of last fractile. However, it is interesting to observe that long-short strategy beats the performance of the first fractile when the number of fractiles is between 15 and 30. It indicates that certain level of diversification benefits long-short strategy.
e. Maximum of one month gain
For the last fractile, the curve of the maximum of one-month gain is smooth across different number of fractiles. It indicates that the diversification doesn’t have significant impact on the maximum of one-month gain. We also observe that for the first fractile, the less diversification increases the maximum of one-month gain. The long-short strategy is optimal across fractiles.
f. Number of losing periods, percentage of losing money, percentage of time making money, number of periods making money
Number of losing periods Percentage of losing money
Percentage of time making money Number of periods of making money
The smooth curves of the number of losing periods, the percentage of losing money, the percentage of time making money and the number of periods of making money indicate that diversification doesn’t have a significant impact on these performance criteria.
g. Consecutive losing periods
For the last fractile, the diversification seems to make sense. When the number of fratile increases above 20, the consecutive losing periods increase significantly. For the first fractile, the diversification seems doesn’t have significant impact across fractiles. The long-short strategy seems to smooth out the curve significantly. The curve looks smooth across different number of fractiles. In other words, diversification seems not having significant impact in long short strategy.
h. Maximum consecutive loss
There is a clear trend for the first fractile and the last fractile, indicating that the diversification reduces maximum consecutive losses. However, the long-short strategy is more or less mixed. We are not clear if the diversification improve the maximum consecutive loss in long-short strategy.
- IBES Mean
a. Long Plot:
If we long the first fractile, the sharp ratio indicates that the optimal number of fractile is 50. More or less diversification is suboptimal. The shape of the sharp ratio indicates that as long as 25 companies per fractile, further diversification won’t have significant impact.
b. Short Plot:
If we short the last fractile, the signal of diversification is a little bit mixed. It seems that the number of fractile less than 15 makes some significance.
c. Long-Short Plot
If we long the first fractile and short the last fractile, we found that the when the number of companies is above 50, the diversification doesn’t make a significant impact.
c. Maximum of one-month loss
It seems that the diversification in general reduced the maximum of one-month loss. However, it is interesting to observe that the first fractile is underperformed compared to the last fractile when the portfolio is more diversified ( the number of fractiles is less than 8 ).
d. Maximum of one-month gain
For the last fractile, the diversification doesn’t improve the maximum monthly gain. However, the less diversification, especially when the number of fractiles is more than 6, the monthly gain increases almost linearly with the number of fractiles.
f. Number of losing, periods, percentage of time losing money, percentage of time making money, number of periods of making money
Number of losing periods Percentage of losing Money
Number of periods making money Percentage of time making money
The curves of the number of losing periods, percentage of losing money, number of periods of making money, percentage of time making money are smooth. It indicates that diversification doesn’t make have a significant impact on these performance criteria.
g. Maximum consecutive periods
It seems that if there is enough diversification, the first fractile has a shorter maximum consecutive period than the long-short strategy. The long short strategy is optimal in a less diversified scenario, for example, when the number of fractiles is between 20 and 25. .
h. Maximum consecutive losses
For the first fractile and the last fractile, diversification seems reduced the maximum consecutive loss.
- Dividend Yield
a. Long Plot:
b. Short Plot
c. Long-short plot:
d. Maximum of one-month loss
e. Maximum of one-month gain
f. Number of losing periods, percentage of losing money, percentage of time making money, number of periods of making money
Number of losing periods Percentage of losing money
Percentage of time making money Number of periods making money
g. Consecutive losing periods
h. Maximum consecutive loss
- Cash Price
- Long Plot:
- Short Plot:
- Long-Short Plot
- Maximum of one-month loss
- Maximum of one-month gain
- Number of losing, periods, percentage of time losing money, percentage of time making money, number of periods of making money
Number of losing periods Percentage of losing Money
Number of Periods making Money Percentage of time making Money
- Consecutive losing periods
- Maximum Consecutive loses
- Average Volume
- Long Plot
If we long the first fractile, the data doesn’t indicate that there is an optimal number of companies per fractile. It seems that the sharp ratio continues to increase with diversification.
- Short Plot
If we go short the last fractile then the optimum fractile size is 20 stocks. Further diversification decreases the sharp ratio.
- Long-short plot
If we long the first fractile and short the last fractile there is a smooth line across different fractile sizes. The optimal fractile size is about 50 companies per fractile.
- Maximum of one month loss
- Maximum of one month gain
- Number of losing periods, percentage of losing money, percentage of time making money, number of periods making money
Number of losing periods Percentage of losing money
Percentage of time making money Number of periods of making money
- Consecutive losing periods
- Maximum consecutive loss
Trading Costs
One important consideration in implementing any type of trading strategy is the trading costs. While difficult to come to a direct conclusion on the actual in numerical terms it is possible to measure the relative trading costs of the strategies. As expected the fewer the number of firms, or greater the number of fractiles, the trading cost of the portfolio go up. This additional cost must be compared to any benefits derived from greater number of fractiles.
Conclusion
It appears there are some benefits to focusing on fewer companies by having more fractiles in terms of higher sharp ratios. However there is a definite costs associated with this in terms of higher trading costs which needs to be evaluated further.
Areas for further Study
One area for further investigation is the relationship between the R^2 and the slope of the trend line of the fractiles. In essence these two variables take into consideration how well the factor predicts returns, similar to a heat map. The greater the slope, for a given number of fractiles, the greater the expected return between the F1-FN portfolio. The standard error should be a measure of how much variability there is around the line. In combination or in a ratio these values would seem to give an indication on the quality of the fractile. This can be seen in the figure above. Even more interesting is the slope from previous periods in addition to the deviation from the average slope from previous periods seems to have predictive power for the future slope. This obviously would be a good indicator of when to overweight or underweight the portfolio based on the expected slope. After running a few regressions it became very clear the t-stats were always significant (~2) with a small but viable R^2(1-5%). There also seems to be an optimum moving average to use to calculate the deviation of the slope variable. It would be very interesting to see if this holds true for other factors. The basic logic here is there is some type of regression to the mean over time and momentum for the slope of the fractile trend line. All of this analysis was done while looking at the IBES Sue parameter.
Another idea for further investigation is to use, in a similar manner as above, the optimum weights from the optimization of the dynamic weighting from previous periods to try and predict the ideal weights for the coming periods. Again this would be based on momentum and regression to mean.
[1] http://mba.tuck.dartmouth.edu/pages/faculty/kent.womack/teaching/UnderstandingFF3Factor.pdf