Expected Body Performance Report Summary: 1/31/2025

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VecViz’s analytic performance reports document the behavior and performance of our analytics. This post focuses on the “VecViz Expected Up Body & Expected Down Body (EUB & EDB) Performance Report” as of January 31, 2025, Here we will summarizes the key findings, and explain how to use the report to investigate the performance of specific tickers. You can find this report on the “Reports” section of the VecViz website, along with updated reports over time.

Expected Up Body (EUB) and Expected Down Body (EDB) are the probability-weighted average prices between the model date price and the 95th probability percentile price upward and downward, respectively. We offer these metrics because “expected value”, inclusive of tail outcomes in a world of often fat tails, can easily clash with our common sense understanding of the term “expected”. EUB and EDB are likely of interest to investors seeking “base case” return scenarios to the upside and downside, respectively, such as those running portfolio optimization analytics. We believe that access to “Expected Body” analytics can help mitigate that tendency. Finally, expected body metrics could also be of interest to investors involved in call or put spreads, though we would also point such investors to our Option Fair Value Estimate performance report.

Performance Metrics Utilized in the Expected Body Report

The Expected Body Performance Report compares the behavior and performance of EUB and EDB calculated by VecViz’s Vector Model to the same as calculated by VecViz’s implementation of the Sigma Model¹. The primary performance metric discussed, Mean Absolute Error (“MAE”, expressed on a % of model date price basis), addresses accuracy. It is the average absolute deviation between expected body return estimates and actual forward price returns that reside inside of the respective model’s 95th percentile estimate. The secondary metrics the report utilizes are the Return on Expected Up Body (ROEUB) and Return on Expected Down Body (ROEDB)². These metrics address the potential value of EUB and EDB as investment signals.

MAE

Mean absolute error (MAE) for Vector Model EUB identifies all tickers with price returns for a given time horizon that are positive but less than the Vector Model 95U estimate for that time horizon. In other words, it identifies the tickers whose price returns for the given horizon were in the “Up Body”. Then it calculates the absolute value of the difference between each such actual price return and the corresponding Vector Model EUB estimate, and averages them. Vector Model EDB is calculated similarly, for price returns that negative but not as deeply negative as Vector Model 95D, calculating the average absolute difference with corresponding Vector Model EDB.

Sigma MAE for Sigma EUB and EDB is calculated likewise, but utilizes Sigma 95U and 95D as the defining bounds of the “Up Body” and “Down Body”, and comparing the actual returns for the tickers identified to Sigma EUB and EDB.

For a given model date if Vector Model 95U is > than Sigma 95U, it is likely that Vector Model EUB MAE will be calculated across a broader range of forward ticker returns than Sigma EUB MAE, and vice versa. Likewise with regard to EDB MAE and 95D differentials between the Vector Model and Sigma. In the table presented below, we partially adjust for this range disparity by multiplying Sigma EUB (EDB) MAE by the ratio of Vector Model 95U (95D) returns to Sigma 95U (95D) returns. The comparison is still vulnerable to differences in idiosyncratic variability resulting from differences in the ticker pools considered.

ROEUB and ROEDB

For a given level of normalized MAE, an EUB estimate that is less aggressive for tickers with below-average returns and more aggressive for tickers with above-average returns is preferable. Such an estimate would yield attractive ROEUB (see our FAQ or the report introduction for a definition). Maximizing ROEUB is an important, though secondary, criterion for evaluating EUB performance. Likewise for ROEDB and EDB.

The Expected Body report considers the “alpha” and “beta” of Vector Model EUB relative to Sigma’s EUB and Vector Model EDB relative to Sigma EDB² a couple different ways, detailed in the tables below, to help determine whether differentials in ROEUB and ROEDB performance are due to EUB and EDB differentials across tickers or relative changes in EUB and EDB over time.

EUB and EDB Summary Performance Tables

EUB, ALL TMD (1/31/2022 – 1/31/2025)	1d	10d	21d	63d	126d	252d	1d V / S	252d V /S	page(s)
Average EUB Estimated Gain Aggressiveness	V	V	V	V	V	V	1.7 / 1.6	41.6 / 25.4	11
Average MAE	S	S	S	S	S	S	1.3 / 0.9	28.8 / 14.5	26
Average MAE adjusted for 95U differentials3	V	V	S	T	V	S	1.3 / 1.5	28.8 / 24.3	26, 122
MAE Consistency Over Time4	S	S	S	S	S	S	na	na	25-30
MAE Consistency Across Tickers	S	S	S	S	S	S	na	na	31-42
Average ROEUB	T	T	V	V	V	V	0.0 / 0.0	25.6 / 15.3	44
VM ROEUB Alpha Across All TMD’S	-0.00	0.02	0.13	0.43	1.03	4.26	na	na	44
Average VM ROEUB Alpha By Ticker, Across All Model Dates	-0.00	0.01	0.05	-0.07	-0.81	2.47	na	na	44

EDB, ALL TMD (1/31/2022 – 1/31/2025)	1d	10d	21d	63d	126d	252d	1d V / S	252d V /S	page(s)
Average EDB Estimated Loss Severity	S	S	S	S	S	S	1.7 / 1.6	41.6 / 25.4	67
Average MAE	S	S	S	V	V	V	1.2 / 0.9	11.2 / 12.9	77
Average MAE adjusted for 95D differences	T	V	T	V	V	S	1.2 / 1.2	11.2 / 10.9	77, 126
MAE Consistency Over Time	S	V	S	V	V	V	na	na	80-85
MAE Consistency Across Tickers	S	S	S	V	S	V	na	na	86-97
Average ROEDB	T	T	V	V	V	V	0.0 / 0.0	22.0 / 15.3	100
VM ROEDB Alpha Across All TMD’S	-0.01	-0.14	-0.31	-0.97	-1.82	-2.97	na	na	100
Average VM ROEDB Alpha By Ticker, Across All Model Dates	0.01	0.09	0.19	0.62	1.50	2.51	na	na	100

P-values for evaluating the reliability of the ROVBC alpha estimates can be found on the page indicated.

EUB Summary Conclusions:

Over the period studied, which includes both the bear market of 2022 and the bull market that followed up through most of January 2025, Vector Model EUB levels:

• were typically more aggressive than Sigma EUB
• had similar average accuracy (MAE) as Sigma EUB, on balance across horizons after adjusting for distance to “95U”. Note that if you review our OaR performance report (or blog summary thereof) you will find that the Vector Model 95U has a breakage rate closer to 5.00% than Sigma’s 95U for all time horizons, which arguably further justifies adjusting for the 95U distance differential when evaluating MAE accuracy.
• were less consistently accurate across time and tickers than Sigma EUB on an “95U” before adjusting for the Sigma Model’s typically smaller distance to 95U.
• had equivalent or higher ROEUB than Sigma for every horizon;
• had positive ROEUB alpha across tickers and model dates for every horizon beyond 1d. This was driven primarily by alpha across tickers, as ROEUB alpha by ticker across model dates was negative for three of the six horizons.

EDB Summary Conclusions:

Over the period studied, which includes both the bear market of 2022 and the bull market that followed up through most of January 2025, Vector Model EDB levels:

• were typically less severely negative than Sigma EDB
• had equivalent or better accuracy (MAE) as Sigma EDB, after adjusting for distance to “95D” for all horizons except 252D. Note that if you review our VaR performance report (or blog summary thereof) you will find that the Vector Model 95D has a breakage rate closer to 5.00% than Sigma’s 95D for all time horizons, which arguably further justifies adjusting for the 95D distance differential when evaluating MAE accuracy.
• were as consistently accurate as Sigma EDB across time and tickers, on balance, across horizons, before adjusting for the Vector Model’s typically smaller distance to 95D.
• had equivalent or higher ROEDB than Sigma for every horizon;
• had negative ROEDB alpha across tickers and model dates for every horizon. This was driven primarily by poor EDB alpha across tickers, as ROEDB alpha by ticker across model dates was positive, on average, for every horizon.

These strong results for the Vector Model relative to Sigma are fairly consistent across the trailing 365d, 90d, or 30d windows. See the report for further detail.

For further ticker level inquiry visit the Dashboards page. There you can:

• see EUB and EDB estimates as of yesterday’s close overlaid upon VecViz’s Vector Strength Histogram and detailed in a table (for the Vector Model EUB and EDB. Also of interest may be the 95% OaR and VaR estimates are presented alongside these EUB and EDB estimates.
• Explore role EUB and EDB play as part of VecViz’s V-Score criteria.

Note that the dashboards are best viewed on a desktop or laptop, that there are 8 of them, they load progressively as you scroll down, with a few of them taking 15-30 seconds to initially load. After the initial load they load much quicker as you toggle between tickers, horizons, etc.

Appendix: Ticker Level EUB, EDB, ROEUB & ROEDB Performance Report Inquiry

When we press “Ctrl-F” on the VaR report pdf file and enter “NVDA”, for example, we learn that it appears 171 times in the document. Clicking through the search results we learn that NVDA was (for most horizons and lookback windows and both models unless otherwise noted)

• “Top 30” ticker with regard to: EUB MAE, ROEUB, EDB MAE, ROEDB
• “Bottom 30” ticker with regard to: nothing

1. The EUB/EDB for Sigma occurs at +/-0.657 standard deviations from model date price. See the report for detail. ↩︎
2. See our FAQ page for detailed definitions of the Vector Model, Sigma, ROEUB, ROEDB, etc.. ↩︎
3. we partially adjust for the disparity in 95U (95D) values for Sigma and the Vector Model by multiplying Sigma EUB (EDB) MAE by the ratio of Vector Model 95U (95D) returns to Sigma 95U (95D) returns. ↩︎
4. We do not adjust EUB (EDB) MAE consistency for 95U (95D) differentials, though arguably we should. ↩︎