November 8, 2012

Combining Quant Models for Enhanced Portfolio Performance

by Jason Ribando

Since the 2008-09 financial crisis, the value of using quant factors for stock selection has been questioned. However, recent studies by the StarMine quant research team show that quant factors are again working very well, exhibiting both long-term outperformance and remarkable gains during the past 12 months.:

Chief among the many difficulties a portfolio manager faces is how to reconcile conflicting views on expected returns when selecting securities. The problem may flare up when members of the investment committee have differing views on a particular stock, but choices also arise for the lone manager who runs a strictly quantitative strategy based on multiple models. Like the investment committee members, each quant model will have a different ranking of expected returns that needs to be resolved. This research note illustrates a simple strategy for combining quant models and offers some alternative techniques for enhancing portfolio returns.

For the purposes of this note, we assume a single portfolio manager uses multiple quant models to do equity portfolio selection, and each quant model outputs a ranked score. StarMine equity and credit risk models output 1-100 scores, with 100 being a top-ranked company. Hence, they provide enough resolution to distinguish many shades of predicted performance while placing all models scores on the same normalized scale—a convenience when combining models.

Figure 1: Using top quintile Val-Mo stocks, rebalanced monthly, and optimizing filter thresholds for Earnings Quality and Short Interest performs very well on a universe of US small cap stocks with sufficient daily liquidity.

Suppose a portfolio manager wants to combine several such models to make a single stock ranking model. The most straightforward thing to do is take the sum or mean of model scores. Inevitably, though, the PM believes some factors are better than others, in which case a linear combination or weighted average is needed. Recognizing that some models work better during certain market conditions, the PM then may try to dynamically weight the stock-picking models—perhaps inserting macroeconomic models¬ into the mix—but quickly gets frustrated tweaking the parameter knobs for so many variables. In the end, just what is the PM to do?

Case Example: Additive Performance from a Simple Combination of Three StarMine Models
Let’s build a simple combination model from scratch. It is simple because we combine three factors using only screening on model scores.

Benchmark and universe: For the investable universe we use US small cap stocks (less than $1B) with at least $200K average daily trading volume, roughly comparable to the Russell 2000 (R2K). We rebalance monthly, reinvesting any dividends at the beginning of the month. For performance we compare our strategy to both R2K and an equal-weighted version of the investable universe, which outperformed R2K going back to 2004 since small caps outperformed large caps during this period.

Initial screen: Let’s begin with the stalwart of the StarMine lineup: Value-Momentum. StarMine Val-Mo combines StarMine’s two valuation models, StarMine Intrinsic Valuation and StarMine Relative Valuation, along with StarMine’s two momentum models, the StarMine Analyst Revisions Model and the StarMine Price Momentum, into one powerful stock ranking model [2]. As Val-Mo is already a combination model, it has proved to be a robust and steady performer in all regions. Filtering on the top quintile of stocks by Val-Mo score achieves an impressive 25.9% per year, even including the large drawdown from September 2008 to March 2009.

Additional screens: Having backtested all StarMine quant models on a stand-alone basis, we know that StarMine Short Interest is an effective signal in the US (SI model scores begin in Jan. 2004, constraining the start date in our study), and StarMine Earnings Quality has low correlation to both Val-Mo and SI. StarMine Short Interest is a US stock ranking model that ranks stocks based on the hypothesis that stocks with high (low) number of shares shorted will under (out) perform [5]. StarMine EQ identifies companies that are likely to experience especially high or low earnings sustainability over the subsequent twelve months based on decompositions of past earnings into sustainable and non-sustainable components [4]. Adding a second filter to the Val-Mo strategy—that further requires an EQ score above 70—increases annual returns by 4.5%. Adding a third filter for stocks with SI score above 30 nets another 3.1%, for total annual returns of 33.3% (28.3% above the equal-weighted R2K benchmark). At this point the strategy holds 30 to 45 stocks per month, a reasonable number for a well-diversified strategy.

Figure 2: The optimal strategy achieves 32.9% active returns by equal-weighting stock holdings and using StarMine Val-Mo, Earnings Quality, and Short Interest models.

Optimized strategy: We can even do better if we optimize on the various filter thresholds. In fact, the Val-Mo > 80, EQ >65, SI >70 strategy returns 37.9% per year—a full 32.9% active return over R2K. Not bad for a long-only strategy on US stocks! Of course, the historical backtest provides no guarantee that similar returns can be achieved or that the same combination will be optimal going forward. Figure 1 shows the additive total returns you can obtain with successive StarMine filters and then optimizing on the filter thresholds. Figure 2 shows a breakdown of active returns for the three filter strategy and its optimized version.

Combination Strategies: Variants on a Theme
Beyond the simple screening used in the Val-Mo/Earnings Quality/Short Interest strategy above, there are various techniques for combining stock ranking models to enhance returns. As a guiding principle, choose quant models with low correlations to each other to create synergies for total returns, reduce volatility of returns, and make for a more robust combination model in changing market conditions.

Positive vs. negative screens: We tend to separate simple screens into two categories: positive screens and negative screens. Roughly speaking, positive screens select top ranked companies while negative screens eliminate bottom ranked companies. Use your primary, i.e., strongest, ranking model as a positive screen and secondary models as negative screens. You can screen for more companies than the desired portfolio size then apply a human overlay as the final “screen” to further limit the universe and achieve the desired number of securities.

Also, we find that quant models which screen for at risk companies work well as negative screeners. An example is the StarMine Structural Credit Risk (SCR) Model, which uses a Merton structural prediction framework that models a company’s equity as a call option on its assets [3]. Filtering out the lowest decile of companies by SCR score usually decreases portfolio volatility even if the increase in returns is marginal.

Decile spreads: For long-short portfolios, one should not assume symmetry between the long and short sides. For example, suppose your primary signal is Val-Mo and you run a basic decile spread strategy, i.e., long stocks with Val-Mo score 91-100 and short stocks with Val-Mo score 1-10. Suppose you find that StarMine’s Structural Credit Risk (SCR) Model best enhances the long Val-Mo portfolio by negatively screening for companies at risk of default or bankruptcy. That doesn’t imply that combining top-ranked SCR stocks work best with Val-Mo on the short side. Treat the long and short Val-Mo sides as separate portfolios when looking for models to combine with Val-Mo.

Weights: When devising strategies, we are often asked to optimize the weights of securities in the portfolio. Our advice is to avoid using your primary signal to determine weights. We find that once you select, say, top decile stocks by Val-Mo, there is little additional discriminatory power between a Val-Mo 91 stock and a Val-Mo 100 stock. When building combination quant models, seldom do we find a weight scheme that works better than equal weights for backtests of eight years or more. If you insist on differential weights, log(market cap in millions) is a good compromise between market cap weight and equal weight; it only gives two and a half times the weight to a $100B company as it gives a $100M company. Increasing the weights on small caps, where market information is less efficient, often increases the performance of a quant model.

Signal speeds: When using a single quant model, a good rule of thumb is to match signal speed with rebalance frequency. Signal speed can mean several things, but here we refer to the arrival rate of input data. For example, the StarMine Price Momentum (Price Mo) model, which provides a unique and comprehensive measure of momentum in security returns by intelligently combining information from multiple dimensions of price momentum [1], behaves very differently from StarMine EQ and StarMine SCR, both of which use financial statement data as inputs. You wouldn’t use EQ or SCR as a stand-alone factor for an intraday trading strategy just as you wouldn’t use Price Mo by itself for a long-term buy-and-hold strategy. However, combining two quant models with different signal speeds, say, daily and quarterly, can make your strategy more robust since the signals complement each other. See [7] for more on how signal speed influences turnover in StarMine models.

Addressing turnover: There are many techniques for reducing turnover to manage transaction costs. One approach is to limit the size of the investable universe with respect to the portfolio size. If your target portfolio size is 100 stocks, a top quintile strategy on the S&P 500 universe will have lower turnover than picking the top 5% of stocks in the Russell 2000. Why? Consider the extreme case of picking the top ranked stock from a universe of two versus from a universe of 100. It’s much less likely that a particular stock remains the top pick in the larger universe.

A different approach for reducing turnover is to use asymmetric entry/exit. Suppose your strategy is top decile by Val-Mo. Initiate the portfolio using stocks with Val-Mo score 91-100. On the next rebalance date, sell stocks that have fallen below a lower threshold, say, 70 and below. Replenish the portfolio with the highest ranked stocks until you achieve the desired portfolio size. This asymmetric entry/exit strategy holds the average stock longer than a top decile strategy by mitigating stocks whose score bounces back and forth across the filter threshold. For a detailed analysis of optimizing portfolios using StarMine equity models and asymmetric entry/exit, see [6].

Table 1 contains a summary of these combination strategy techniques.

Concluding Remarks
In this research note, we illustrated a case example where combining StarMine quant models achieved 37.9% annual returns during an eight year backtest for a long only portfolio on US small cap stocks. We also provided some general techniques for combining multiple quant models to enhance portfolio risk and returns. We focused on total return as the primary measure of success, but maximizing returns in backtests does not guarantee an optimal portfolio going forward. Consideration must be given to model correlations, volatility, rebalance frequency, turnover and transaction costs, and which models are likely to perform well in a given region over the investment time horizon. Combination quant models work best when the stand-alone models are robust and have low pair-wise correlations and when there is some insight and intuition as to why the models will create synergies in combination. We design and build StarMine models to have these properties. Using a robust set of quant signals in combination with the techniques described in this paper can help portfolio managers maximize their likelihood for success.

[1] Bonne, G., I. Erickson, and L. Jacobek, 2009a, StarMine Price Momentum Model (Price Mo): Overview and global performance, StarMine white paper.
[2] Bonne, G., I. Erickson, Y. Li, J. Stauth, and L. Jacobek, 2009b, StarMine Value-Momentum Model (Val-Mo): Overview and global performance, StarMine white paper.
[3] Erickson, I., and Lawson, D., 2012, StarMine Structural Credit Risk Model, StarMine white paper.
[4] Gaumer, T., S. Malinak, G. Bonne, P. Bae, and D. Sargent, 2009, The StarMine EQ Model: Introduction and Global Results, StarMine white paper.
[5] Renick, D., J. Stauth, and H. Genin, 2011, StarMine Short Interest Model, StarMine white paper.
[6] Ribando, J., 2011, QA Studio for StarMine Equity Trading Strategies, StarMine research note.
[7] Ribando, J., and Turowski, H., 2009, StarMine Research Note: A Comparative Study of Turnover and Signal Strength in StarMine Ranking Models, StarMine white paper.

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