Here we take excerpts from the OaR Performance Report on our website to review breakage rates, and associated Return on Long OaR Based Capital (ROLOBC) for Vector Model and Sigma 99% OaR (Opportunity at Risk) analytics, in aggregate, across VecViz’s ~150 ticker coverage universe and at the ticker level. We focus on the last 30 days given its historic volatility. We finish by placing this performance in the context of VecViz’s overall out of sample OaR track record and also show where aggregate OaR currently stands in that context.
Before we begin, please note that (1) OaR addresses the right tail of the return distribution, (2) what we refer to as “Sigma” is also commonly referred to as Exponentially Weighted Moving Average VaR when applied to the left tail, (3) aggregate measures of OaR and ROLOBC reflect the simple average of ticker level OaR analytics and associated actual forward returns, (4) results for forward horizons > 1d reflect overlapping periods, for both the Vector Model and Sigma, unless noted otherwise.
Aggregate OaR Breakage Rates
Consistent with the widely reported historic nature of April’s volatility, we saw new highs in OaR breakage rates for both the Vector and Sigma for the out of sample period. Sigma’s breakage rates far exceeded the Vector Model’s, reaching as high as 76% for our coverage universe of ~150 tickers on April 8, 2025 (vs a 33% breakage rate peak for Vector Model 99% OaR, also on April 8th).
Presented again below on a 20-day moving average basis, for greater clarity of the differential between Sigma and the Vector Model:
Here are the same two graphs presented for the 10d forward time horizon. See the full report for the same for the 21d (~1 month), 63d (~3 months), 126d (~6 months) and 252d (~1 year) forward time horizons.
Ticker Level Breakage Rates
The top 30 tickers that drove breakage for the Vector Model and Sigma for the 1d and 10d time horizon over the last 30 days are presented below, under the headings “Ticker_V” and “OaRBreak_V”, and “Ticker_S” and “OaRBreak_S”, respectively. Overlap in the ticker lists for the two models is approximately 30%-40%, reflecting their very different methodologies.
Aggregate ROLOBC for 99% OaR
The Vector Model lagged Sigma in terms of Return on Long OaR Based Capital (ROLOBC) for both the 1d and 10d time horizon during the downturn of April, but has eclipsed Sigma for the 1d horizon as the month closes, and is catching up to Sigma at the 10d horizon.
As a reminder, ROLOBC for Sigma is set to the return of the ticker, and for the Vector Model ROLOBC is that return multiplied by the ratio of Vector Model OaR to Sigma OaR, subject to a cap and floor of 3x and 0.333x. This is a very basic measure, intended to represent the disposition of a highly risk tolerant / aggressive return seeking investor, with no adjustments for transaction costs or financing charges for levered (i.e. >1x multiplier) positions.
Ticker Level ROLOBC
There is substantial deviation in ROLOBC by ticker between the VM and Sigma, for both 95%tile and 99%tile OaR. Here we look at the 20 tickers for which 95% and 99% ROLOBC for the Vector Model most exceeded Sigma over the last 30 days, for both the 1d and 10d time horizons.
Here are the 25 tickers for which for which 95% and 99% ROLOBC for the Vector Model had the greatest shortfall vs. Sigma over the last 30 days, for both the 1d and 10d time horizons.
Placing the performance of 99% OaR over the last 30 days in the context of the entire VecViz out of sample period
The table below presents the % of performance criteria met for 95% and 99% OaR by forward time horizon and lookback window. It shows that the last 30 days has actually seen above average 99% OaR performance relative to the overall VecViz out of sample track record period.
The performance criteria considered in the table above and the associated performance by lookback window, with scores for 95% VaR and 99% OaR are listed below. Note that ROLOBC metrics attempt to correct for systematic levered or underinvested positions relative to Sigma:
Apologies for the page break in the middle of the table above!
For those familiar with Kupiec Proportion of Failures test and the Christoferson OaR (more typically, VaR) Violation Independence test they can be found in the report linked to below, for both the Vector Model and Sigma. Note that for such tests we utilize non-overlapping periods for each forward time horizon.
How Aggregate 95% and 99% OaR is Trending
As we end April, average 95% OaR across ticker coverage for Vector Model (blue) and Sigma (red), remain far apart at the 1d horizon but have almost fully converged at the 10d horizon. The closeness of the proximity between the 10d horizon 95%tile OaR between the two models is unprecedented in the out of sample results period.
In contrast, 99% OaR across ticker coverage for Vector Model (blue) and Sigma (red), are still far apart, though they are trending in the direction of convergence at the 10d horizon.
Please review the report further for yourself here, and check out related reports on VaR, Expected Body, Option Fair Value, and V-Score as well.