The Proof is in the Portfolios: Evaluating VecViz Analytic Features via Constrained Optimization and Ablation

December 2, 2025

Each month we publish a 100+ page report for each individual VecViz volatility and expected return related features so that we can readily answer any of the following common concerns about summary performance stats:

Quant Feature	Quant Feature Eval Criteria	Common Concerns:
Expected forward return	1) correlation to forward returns 2) interquartile range average forward return differential	reliance of the results upon: 1) outliers 2) illiquid tickers 2) industry concentration 3) long vs. short signals
Expected ticker vol	1) Kupiec Ratio 2) Christoferson Ratio	1) severity of the tail vs. expectations 2) influence on capital availability through the cycle

Going forward we will also provide a new report on quant feature performance that pre-empts these concerns via constrained portfolio optimization.

In so doing, we modify and expand upon the methodology presented in the 2024 paper, ‘Markowitz Portfolio Construction at Seventy’ (Boyd, Johansson, Kahn, Schiele, Schmelzer). That study varied constraints across a series of Mean Variance Optimization (MVO)¹ experiments to maximize MVO performance. Our study likewise relies on ablation² to evaluate performance, but holds the constraints consistent, and instead focuses on evaluating which MVO feature inputs consistently add value. To expedite the assessment of “added value” we also introduce a metric we call “SummaryZ”.

Grading the “ingredients” on the basis of the “cake” produced!

Like flour, eggs and butter are best evaluated by the cake they produce, investment analytic features are best evaluated by the portfolios resulting from them.

Just as one needs to know their cake won’t cause them an allergic reaction, investors need to know their portfolios were designed with their profile in mind. Fortunately, constraints akin to “no tree nuts” can be imposed upon the portfolio “recipes”, which take the form of optimization algorithm.

By evaluating each feature based on the performance of the portfolios generated by the constrained optimizations to which it was an input, we preempt many of the aforementioned concerns.

We conducted a balanced and broad portfolio optimization “bake-off”.

By testing a feature across a broad grid search of optimization constraints, we are no longer asking, “Is this a good ingredient?” We are asking, “Does this ingredient consistently improve the flavor and quality of the cake?”

Specifically, we ran optimizations for all 12 possible combinations of VecViz and trailing 252d based (“Trailing”) input parameters to MVO across a grid of

Three max ticker weight constraints (3%, 6%, 10%)
Three max expected portfolio vol constraints (10%, 15%, 20%)
Three portfolio rebalance frequencies (10d, 21d, 63d).

This amounts to 12x3x3x3 = 324 optimized portfolios in all. Our study design is detailed below, followed by the many associated strategy cumulative return paths during the test period, and a scatterplot of the associated annualized return and volatility:

Optimization input sources are conveyed in each strategy’s name, with the initials following the underscore denoting input sources for return, volatility, and correlation, in that order. Specifically, 1) T = Trailing 252d; 2) V = VecViz; 3) VecViz correlation is either “e” (VecEvent-based) or “f” (VecViz analytic fingerprint). For example, S8_TVVe is a strategy that uses Trailing for the expected return input, VecViz for the ticker vol, and VecViz’s VecEvent similarity measure for correlation between tickers. The table reflects balance and consistency with regard to use of VecViz vs. Trailing for each input. For example, there are six that use Trailing for expected return (S1, S5, S7, S8, S11, S12), and six that use VecViz (S4, S6, S9, S10, S13, S14). Note that there is no S2 or S3.

S1, portrayed in red, is comprised entirely of Trailing Return based features. S10 and S14, in blue, are comprised entirely of VecViz based inputs. The purple lines represent all the possible “hybrid” mixtures of Trailing and VecViz based inputs. Note that results presented do not reflect any trading cost.

The behavior of the 5/1/2024 thru 11/30/2025 price paths presented earlier are summarized in the charts above, with the performance of the SPDR S&P 500 Trust ETF (SPY) and an equally weighted portfolio (“1/n”) presented as yellow triangles. Note that the results presented do not reflect any trading cost adjustment.

“SummaryZ” is our well balanced, nuanced portfolio “taste-test” metric.

This approach to evaluating both risk and return features through the performance of associated portfolios requires consideration of both the risk and return of those portfolios. We therefore evaluate each such portfolio by the well balanced mix of risk and return metrics that together comprise SummaryZ, listed below:

1) PR = Average annualized portfolio price return
2) MDD = Max draw down of cumulative portfolio price return
3) SR = Sharpe Ratio (PR / Standard Deviation of Price Returns)
4) CR = Calmar Ratio (PR / MDD)
5) A = Alpha of portfolio price return to SPY, MTUM, VLUE (the S&P 500 ETF, the Momentum Factor ETF,
the Value Factor ETF)
6) KPV = Kupiec Test Statistic P-Value, which reflects the probability that the portfolio’s 99% VaR, as implied by its volatility constraint, (assuming normality, and independent, identically distributed daily returns) was well specified.

Reviewing the list reveals that Summary Z has:

2 return oriented metrics (PR and A),
2 risk oriented metrics (MDD and KPV) and
2 return / risk metrics (SR and CR).

We also believe the breadth with which it addresses risk and return to also be noteworthy:

with regard to risk it considers tail (MDD), non-tail (sigma is the denominator of SR), and predictability (KPV)
with regard to return it considers not just outright return (PR) but also factor alpha (A).

To calculate “SummaryZ” we first calculate the z score of each portfolio by metric relative to all other portfolios generated. The SummaryZ score (“Z_Sum”) then aggregates those metric z scores as follows:

Z_Sum = Z_PR + Z_MDD + Z_SR + Z_CR + Z_A + Z_KPV

SummaryZ scores across the optimization “recipe”/ constraint/ rebalance frequency grid

Average SummaryZ scores for our study by constraint level, and by portfolio optimization input combination are provided in the table below, with results for SPY and 1/n included for context:

### STRATEGY rows are defined by input sources for return, volatility, and correlation (in that order): T = Trailing 252d; V = VecViz. VecViz correlation is either “e” (VecEvent-based) or “f” (VecViz analytic fingerprint). For example, S9_VTVe uses VecViz for Expected Return, Trailing 252d for volatility, and VecEvent based correlation. ### CONSTRAINT LABELS: those preceded by a “w” are max weight constraints, those followed by a “d” are rebalance frequencies, and those preceded by a “v” are max annualized expected portfolio volatility constraints. Cells in a given constraint column represent the average outcome for that constraint, across the 9 combinations of the other two constraints and rebalance frequencies. Cells in the “Total” column represent the average value across all 27 constraint outcomes for each strategy. Note that results do not reflect any trading cost.

Feature level SummaryZ averages across feature utilizing portfolios

The features in the table below are rank ordered in terms of the average SummaryZ of the portfolios generated using them as components of the MVO process. Note that these average SummaryZ values can also be compared to the 1/n and SPY SummaryZ values in the prior table. All metrics except Vol_T252d performed well on that basis.

Average values for the SummaryZ metric components of those portfolios are also provided, detailing the strengths and weaknesses of each metric in terms of its contribution to portfolio quality. A key defining the input variable abbreviation follows the table.

*Here we depict the average SummaryZ for each portfolio each feature contributed to, along with the average non-standardized value of the features contributing to SummaryZ (once standardized).* *Note that the results presented do not reflect any adjustment for transaction cost.*

Key: Vol_VV = VecViz’s 99D_Ret (i.e. VecViz 99% VaR)
Correl(VE)_VV = VecEvent based correlation
Ret_T252d= average price return over the prior 252 days
Correl(FP)_VV = VecViz analytic metric “fingerprint” based correlation
Ret_VV = VecViz’s VaR and OaR breakage regime based expected return metric
CorrelT252d= correlation of price returns over the prior 252 days
Vol_T252d = standard deviation of price returns over the prior 252 days

Conclusion

With the breadth and balance offered by constraint grid search and SummaryZ we believe that this “bake off” / ablation approach to feature evaluation can satisfy a broad range of quant palette sensitivities.

The full study can be found here. We are happy to report that, as you would expect from the intro, it is < 100 pages, far smaller than any of our single metric focused performance reports, and yet delivers deep insights on the performance of seven analytic features.

My thanks to Mohamed Azahriou for his help in developing an algorithm for much of the process described in this blog.

Notes:

Mean-Variance Optimization (MVO) is a quantitative tool used to construct portfolios. It weighs three factors: the expected return of an asset (the Mean), the risk of that asset (the Variance) and how the asset relates to other assets under consideration (correlation). MVO identifies the portfolio with the maximum expected return for a given level of risk and other user defined constraints (ex: max ticker weighting). ↩︎
An ablation study is a controlled experiment where components of a system are systematically removed or disabled to observe the resulting change in performance. ↩︎