Breaking Good: VaR & OaR Breakage Rate Regimes

December 2, 2025

Regimes help model builders differentiate market behavior into more stationary (and hence predictable) groupings. Regimes are commonly defined in terms of levels or growth rates in macroeconomic variables and market indices. Research on regime based models dates back at least to 1989¹.

Here we discuss a regime framework built around the thesis that volatility surprises influence positioning. More specifically, this framework references trends in breakage rates of Vector Model one day forward Value at Risk (VaR) and Opportunity at Risk (OaR), at the 95th and 99th percentiles, respectively, across VecViz’s ~150 ticker coverage universe.

VaR & OaR breakage influence positioning…

Value at Risk, or VaR as it is discussed in this blog, is an estimate of the maximum amount an investor could lose by being long a ticker at the end of a specified forward time horizon, at a specified level of probability.

VaR Breakage refers to forward returns being below the VaR estimate for the corresponding horizon date. VaR breakage in excess of expectations puts upward pressure on capital charges and margin requirements for regulated and levered investors. Mandatory closing or hedging of positions typically follows . Many of the rest of us are risk averse, and declines beyond those anticipated by models are also often beyond what we have stomach for.

Opportunity at Risk, or OaR as it is discussed in this blog, is an estimate of the maximum amount an investor could gain by being long a ticker at the end of a specified forward time horizon, at a specified level of probability.

OaR Breakage represents greater upside price moves than anticipated. For levered investors holding short positions the aforementioned margin and capital dynamics are likewise triggered. For the rest of us, FOMO (Fear of Missing Out) and associated incremental long risk taking is a common response.

… if the VaR and OaR estimates reflect Fear and FOMO pressure points.

We utilize VecViz’s support and resistance based, machine learning powered “Vector Model” to generate VaR and OaR estimates. These estimates and their associated breakage rates are well suited to capture “fear” and “fomo” in the sense that:

• they have asymmetric, jumpy, long tailed, stochastic (i.e., random) behavior, similar to real-world volatility
• the support and resistance levels that are inputs to their calculation are used by technical oriented investors to estimate ticker upside and downside.
• their long term average breakage rates are consistent with expectations and therefore the estimates themselves are consistent with real-world volatility

Finally, we note that most investors are naturally ‘long’ risky assets and behavioral finance teaches us that the pain of loss is sharper than the regret of missing out. Therefore, we set the bar lower for downside breakage (95th percentile VaR) but higher for upside surprises (99th percentile OaR).

Historic Breakage Rates & Associated Regime Timeline

We present breakage rate charts for 95% VaR (“95D”) and 99% OaR (“99U”) below for the February 1, 2022 through November 30, 2025 period. Vector Model analytics are depicted in blue and bell curve based “Sigma” analytics are depicted in red, for comparison.

Ideal VaR and OaR breakage rates would reside consistently on the black lines that reflect the target rate of breakage (5% for 95% VaR, 1% for 99% OaR). On average over the period depicted, 95% VaR and 99% OaR breakage for the Vector Model were 4.90% and 1.07%, respectively, nearer to target than Sigma, which experienced 4.15% and 1.40% breakage rates, respectively.

From the breakage rates plotted above we derive nine regimes comprising all combinations of “hi/mid/lo” breakage trend for VaR and OaR. Trend is defined by the ratio of a short term moving average of breakage rates to a longer term moving average of breakage rates.

The regimes are plotted at 2 week intervals over the February 2022 to April 2024 regime training period, in the first row, and the May 2024 through November 2025 test period in the second row. The test period spacing is wider per 2 week period because it is a shorter period overall. Nevertheless, it is clearly skewed more toward ‘Mid/Mid” 95% VaR and 99% OaR breakage.

Cross Regime Return Ranking Exhibits Some Test vs. Training Consistency

Consistency in the rank ordering of the average return by regime in the Training and Test period would be good evidence for the presence of a “regime” worth building a model around. The regimes were identified in a training period spanning February 1, 2022 through April 30, 2024 and tested over the May 1, 2024 – September 30, 2025 period.

With the exception of “95D_Brk_Mid” regimes there is a fair bit of rank order consistency evident of returns by regime , as detailed below and the bullets that follow:

• The correlation of average Test return to average Training returns across all 9 regimes was 0.07.
• The rank within the “Lo” and “Hi” 95D_Brk regimes is consistent across the Training and Test period, but inconsistent within the “Mid” 95D_Brk regimes. We note that the influence of breakage upon positioning is conceptually at a minimum when breakage is “Mid”.
• When the “Mid” regimes for 95D_Brk are consolidated into one category and their average returns aggregated on an observation count weighted basis, as depicted in the table below, the correlation of average Test return to average Training return across the resulting 7 regimes becomes 0.66.

Feature Performance by Regime Also Exhibited Some Test Vs. Training Consistency

We identified eight features that exhibited some association with forward price returns during the February 2022 – April 2024 training period. They are comprised of VecViz’s V-Score and certain Vector Model inputs and outputs and are described in the Appendix of the Performance Report entitled “VecViz Regime Based Expected Return Composites”.

In first of the three tables below we detail which was most closely associated with 10d forward returns during each regime during the training period. For convenience let’s refer to those features as the “best” feature for each regime.

The second table reflects a daily rolling update of that evaluation during the test period. At each refresh, we used all available data through two weeks prior—avoiding look-ahead bias.. The results are presented in terms of the % of the test period regime experience for which the feature column was considered “best”.

Consistency in the features identified as “best” across the training and test period would be another hallmark of a strong regime framework. The third table reveals the % migration of the “best” designation across features by regime during the Test period from the Training Period. Some observations:

• Total migration of the “best” feature designation within each regime during the test period from the feature identified as best in training across the seven other feature alternatives available averaged 43%. This is arguably too high relative to the 59% proportion of the average ticker cumulative price return generated during the Test period vs the combined Training and Test period², which would point to ~30% expected migration.
• The regimes for “Mid” levels of 95D_Brk experienced the highest migration rate by far, at 64% (vs. 40% for “Lo” and 27% for “Hi”). This is consistent with our theory that swings in breakage trends trigger changes in positioning… when the trend is “Mid” the influence on positioning is generally at a minimum.
• That said, we note that the migration within the 95D_Brk_Mid regime was entirely concentrated in the “Lo” and “Mid” 99U_Brk sub-regimes, with 0% migration occurring in the 99U_Brk_Hi regime. This is consistent with our theory that breakage trends trigger changes in positioning. FOMO is strong when 99U_Brk is “Hi”, even when 95D_Brk is “Mid”.
• Excluding the 95D_Brk_Mid regimes reduces the average migration rate to ~33%, solidly below half the 73% proportion of ticker return residing in the Test period for the remaining regimes.
• Migration was concentrated in conceptually adjacent regimes. For example, most migration from feature “F1” flows into “F2”, which differs from F1 only in the sense that it penalizes tickers with greater 95D.

Portfolios built with this framework trailed “T252d” but beat SPY and 1/n

We did a study of VecViz analytics, including the regime based expected return feature discussed above, as inputs to portfolio mean-variance optimization (MVO)³. In this study we compared the VecViz inputs to each other and to simple trailing 252d return based alternatives. You can find the full study, entitled “VecViz Analytics Performance as MVO Portfolio Optimization Inputs” here.

The study ranks portfolios based on a metric we call “SummaryZ”, which contemplates standardized scores for Annual Average Return, Max Drawdown, Sharpe Ratio, Calmar Ratio, Alpha, and Kupiec P-Value⁴.

The table below, excerpted from the report, indicates the results across a grid search of constraints and rebalance frequencies. The regime based process described here is denoted as “Ret_VV” and the trailing 252d based alternative is denoted as “Ret_T252d”.

Key to Input Variable Abbreviations:

• 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

While Ret_VV underperformed the trailing 252-day baseline, which was bolstered by the prolonged AI-mega trend during the test period, we note that the “SummaryZ” score for SPY and 1/n were below that of the average portfolio constructed using Ret_VV (-1.62 and -1.41 for SPY and 1/n, respectively, vs -1.24 for Ret_VV reliant portfolios). See the ““SummaryZ” Performance Score Table” of the report and the associated Appendices for more detail.

Conclusion

The results presented here are strong enough to suggest an interesting regime structure is to be defined using Vector Model VaR and OaR breakage. Given that VaR is perhaps the most maligned metric in the history of quant finance, we admit taking some satisfaction in finding something positive to say about its potential contribution to the investment process.

However, the results presented here are also modest enough to demand humility with regard to how well we have defined that regime structure and the features best corresponding to it. To the extent we have fallen short we are encouraged that the shortcomings reside primarily in the “Mid” regimes of 95D Breakage, where influence of the regime structure on positioning is conceptually expected to be minimal.

My thanks to Yushuang (Sylvia) Wu and Roy Zhou for their help in developing these regimes and associated features.

Notes:

1. J. D. Hamilton, “A new approach to the economic analysis of nonstationary time series and the business cycle,” Econometrica, vol. 57, no. 2, pp. 357–384, 1989. ↩︎
2. If every ticker had zero price return throughout the Test period the “Best” feature designations would all be unchanged. Using the proportion of ticker price return in the test period as the direct benchmark for assessing the rate of migration requires either assuming that the entire Test period return happened immediately and instantaneously. More reasonable though far from exact to assume that it happened steadily over time… hence the 30% (approximately half the 59%). ↩︎
3. 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). ↩︎
4. “Kupiec P-Value” = Kupiec Test Statistic P-Value, which here 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. Note that we utilize 95% VaR, not 99% VaR when determining regimes, but we include the Kupiec P-Value for 99% VaR in the SummaryZ statistic to assess how predictable tail risk is for the portfolios generated in the study. ↩︎