Dynamically Weighted
Multivariate Factor Scored Model
- Quantitative Stock Selection Technique
Prepared and Presented by:
Steve Bartlett
Adrian Campelo
Steve Foertsch
Joe Kippels
Carter Vance
Overview:
We modified a pre-existing multivariate factor model that had been developed by Joseph Kippels in conjunction with an independent study moderated by Cam Harvey ( We ran additional stock screens and looked at how susceptible the factors were to macroeconomic changes, such as the slope of the yield curve based on the yields of the 1 year and 10 year treasury securities. The equal weighted modified model delivered an arithmetic average long-short long tier 1-short tier 10 “zero investment” monthly positive return of 1.32% with a monthly standard deviation of 5.7% (annually 19% with 20% standard deviation) ignoring all transaction costs and assuming all cash from shorts could be reinvested. The portfolio consisting of going long tiers 1 and 2 and short tiers 9 and 10 produced a monthly return of 1.1% with a standard deviation of 4.3% (annually 16% with 13% standard deviation). More interestingly, the long-short portfolio had a negative correlation with the S&P500 promising a further expansion of the efficient frontier in an overall portfolio strategy. Year by year returns by decile were as follows:
Overlayed on a simple S&P 500 tracking portfolio the dynamic long tier 1 short tier 10 portfolio would have delivered the following annual returns:
From this base we delved further into the model and historical tiers to determine what sort of returns could be expected following the trading strategy outlined in the model based on various assumptions regarding trading costs and short sales. Assuming trading costs of $0.05 per share for long positions and $0.10 for shorts, the equal weighted modified model still delivered an arithmetic average long tier 1 – short tier 10 annual positive return of 13% with an annual standard deviation of 21%. Year by year returns by decile were as follows:
Additionally, the fractile size and rebalancing period were examined to determine their effect on the strategy. The results of this analysis are as follows:
Of particular noteworthiness is the interaction of rebalancing frequency and transaction costs. Without transactions costs, the models perform best when they are rebalanced monthly. However, when portfolios are examined after transaction costs the performance lost with less-frequent rebalancing is largely offset by reduced transaction fees. The significant increase in performance when portfolio size is reduced, moving from a 5- to 10-fractile model, is also notable.
Note also that transaction cost is the single overlay in this analysis. Adjustments for market impact and bid-ask spread have not been made in presenting these results. Based upon the favorable conclusions drawn from the model accounting for the single overlay, it is deemed a worthwhile and necessary exercise to model in the additional variables in order to speak to the true value of this model.
Outline and Process:
We started our model based on Joe Kippels’ independent study from fourth term last year. The foundation of our model is the multi-factor model he initially came up with. The separate factors he was using were Earnings Yield, Return on Equity, 1 Year minus 1 Month Price Momentum and Cash Flow Yield. All are described in more detail below. We re-ran his screens as well as some additional ones since we now have access to both expected earnings and historically expected earnings through the IBES database via Factset. In the end we decided to add the IBES expected 2 year earnings yield. We did all of these through 2002, holding out 2003 and 2004 for our “out of sample” This was found by taking the mean EPS estimates and dividing them by the current share price.
We also looked at potentially changing the price momentum factor originally used but didn’t find any substitutes better then the one that Kippels originally used. We liked the intuition of rewarding companies that had done well over the 12 months preceding the previous month and punishing those that had done well over the last month based on previous studies of price momentum and subsequent returns.
We then looked at how susceptible the factors were to changes in the slope of the yield curve measured by the difference in the 10yr and 1yr treasury spreads. We found that the difference between tier 1 and tier 10 for the historical earnings yield and cash flow yield were statistically significantly greater at the 95% confidence interval when the slope of the term structure of the yield curve was negative. We then constructed a dynamic weighting scheme in our model to overweight these two factors in time periods with a negative term structure. For the periods we examined there were 15 months with a negative term structure.
The Scored Multivariate Factor Model:
The final screen was performed using 5 factors to determine the tiers. The factors used were: Earnings Yield, Return on Equity, 1 Year minus 1 Month Price Momentum, Cash Flow Yield, and 2 Years Out Expected Earnings Yield. Scoring varied based on whether the slope of the yield curve was positive or negative based on the yields of the 1 year and 10 year treasury securities. In these two environments scoring was as follows:
The factors were determined by the following definitions:
Earnings Yield - Monthly
Stocks were tiered based on the earnings yield as of month-end for the dates requested. This is calculated as Latest Twelve Months EPS divided by Price, multiplied by 100. The data was lagged by 90 days to account for the amount of time it takes individual companies to disclose earnings to the market.
Return on Average Total Equity
This returns the annual return on average total equity as of the fiscal year-end for the dates requested. This is calculated as Net Income Before Extraordinary Items divided by the one-year average of Total Stockholders Equity, multiplied by 100. The data was lagged by 90 days to account for the amount of time it takes individual companies to disclose earnings to the market.
Price Momentum – One Year Minus One Month Price Momentum
This ranks stocks based on their one year percentage gain, minus their one month percentage gains. Stocks in the first tier of this category are those whose positive difference between their previous year’s percentage gain and their previous month’s percentage gain is the greatest.
Price to Cash Flow
This is based on the latest twelve months of the quarterly price to cash flow ratio for the fiscal quarter for the dates requested. This is calculated as Price divided by latest twelve months of Net Cash Flow from Operations per Share. The lower the price to cash flow ratio, the closer to the first tier the stock will be.
2 Years out Expected Earnings Yield
This takes the mean 2 year out forecasted earnings per share as collected via IBES and divides is by the current share price. The higher the expected earnings yield, the closer to the first tier the security will be.