Here we take excerpts from the VaR Performance Report on our website to review breakage rates, and associated Return on VaR Based Capital (ROVBC) for Vector Model and Sigma 99% VaR 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 VaR track record and also show where aggregate VaR stands in that context.
Before we begin, please note that (1) VaR addresses the left tail of the return distribution, (2) what we refer to as “Sigma” is also commonly referred to as Exponentially Weighted Moving Average VaR, (3) aggregate measures of VaR and ROVBC reflect the simple average of ticker level VaR 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 VaR Breakage Rates
Consistent with the widely reported historic nature of April’s volatility, we saw new highs in VaR 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 63% on April 3, 2025 for our coverage universe of ~150 tickers (vs. a peak breakage of 34% for Vector Model 99% VaR, also on April 3rd).
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 “VarBreak_V”, and “Ticker_S” and “VarBreak_S”, respectively. Overlap in the ticker lists for the two models is approximately 40%-50%, reflecting their very different methodologies.
Aggregate ROVBC for 99% VaR
The Vector Model had higher Return on VaR Based Capital (ROVBC) for both the 1d and 10d time horizon over the last 30 days. Deviation from Sigma was a bit better than typical out of sample experience, for the 10d horizon more so than the 1d.
As a reminder, ROVBC for Sigma is set to the return of the ticker, and for the Vector Model ROVBC is that return multiplied by the ratio of Sigma VaR to Vector Model VaR, subject to a cap and floor of 3x and 0.333x, to reflect how much more or less risk you would take to the given ticker if you were VaR constrained investor using the Vector Model instead of Sigma. This is a very basic measure, with no adjustments for transaction costs or financing charges for levered (i.e. >1x multiplier) positions.
Ticker Level ROVBC
There is substantial deviation in ROVBC by ticker between the VM and Sigma, for both 95%tile and 99%tile VaR. Here we look at the 20 tickers for which 95% and 99% ROVBC 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% ROVBC for the Vector Model had the greatest shortfall vs. Sigma over the last 30 days, for both the 1d and 10d time horizons.
Placing 99% VaR 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% VaR by forward time horizon and lookback window. It shows that the last 30, 90 and 365 days has actually seen above average 99% VaR 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% VaR are listed below. Note that ROVBC metrics attempt to correct for systematic levered or underinvested positions relative to Sigma:
For those familiar with Kupiec Proportion of Failures test and the Christoferson 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% VaR is Trending
As we end April, average 95% VaR across ticker coverage for Vector Model (blue) and Sigma (red), have fully converged. This is unprecedented at the 1d horizon, but was common at the 10d horizon between mid-2022 and early 2024.
In contrast, 99% VaR across ticker coverage for Vector Model (blue) and Sigma (red), are still far apart, though they are trending in the direction of convergence. It is probably notable that 10d Vector Model VaR has never been more benign, though please note that the historic VaR levels reflect some tickers that are no longer with us (SIVB, SBNY, FRCB, etc.).
Please review the report further for yourself here, and check out related reports on OaR (Opportunity at Risk, aka the right tail), Expected Body, Option Fair Value, and V-Score as well.