How does MEDGE compute Conditional Value at Risk (CVaR)?

CVaR is computed historically as the arithmetic mean of returns below the α-quantile, where α defaults to 95% and 99%. The sample is the full backtest window. For multi-asset portfolios the joint return distribution is preserved — we do not assume Gaussian marginals or constant correlations. CVaR is then converted to euro terms by multiplying by the current portfolio value.

What return model does the Monte Carlo simulator use?

Geometric Brownian Motion calibrated on the backtest window with the empirical mean and covariance matrix of daily log-returns. We run 10,000 paths and report P5, P25, P50, P75, P95 over the user-selected horizon. The model assumes log-normal returns — it is honest about its assumptions and ignores fat tails, which the documentation states explicitly.

Which annualisation convention is used?

All annualised figures use 252 trading days. Mean returns are multiplied by 252; standard deviations and Sharpe denominators are multiplied by √252. Drawdowns are computed peak-to-trough on the total return series, not calendar-based. Backtest performance includes 5 basis points round-trip transaction costs by default.

How is portfolio optimization implemented?

For convex objectives (Min Vol, Min CVaR, Max Sharpe with covariance shrinkage) we use quadratic programming via the OSQP solver. For non-convex objectives (Max Sortino, Max Omega) we use sequential quadratic programming with multiple random starts. Constraints support box bounds, group caps and turnover penalties. All 12 objectives operate on the same input universe and constraint set so direct comparison is honest.

Where does the regulatory data come from?

SEC Form 4 + 13F + 13D/G from EDGAR full-text search. CFTC TFF and Disaggregated COT from the weekly CFTC reports. ECB balance sheets, SHS holdings and policy decisions from the ECB Data Portal SDMX REST API. Fed H.4.1 and SLOOS via FRED CSV. FCA UK short interest from the SPR weekly file. U.S. Treasury TIC + Daily Treasury Statement from the FiscalData API. IMF COFER from the SDMX 2.1 API. BIS Credit-to-GDP from the BIS Stats API.

Are backtests in-sample or out-of-sample?

Backtests are in-sample by default — the user-selected window is also the calibration window. The reports flag this explicitly. For walk-forward / out-of-sample analysis, the Compare module supports user-defined sample splits and reports both in-sample and out-of-sample performance for the same strategy. Walking-forward an optimization across years is on the roadmap.

Does MEDGE Capital ever provide investment advice?

No. MEDGE Capital is an analytics platform. The outputs are statistical descriptions of historical and simulated behaviour. Nothing on the site, in exported reports or in the AI-narrated PDF constitutes a personalised investment recommendation. Past performance does not predict future results. See the full Risk & Investment Disclaimer at /disclaimer.

Methodology Reference

How MEDGE Capital computes its numbers.

Every metric, optimization objective, simulation parameter and data feed is documented below with formulas, assumptions and academic citations. This page exists so researchers, analysts and advisors can verify the methodology before adopting the tool — no proprietary black box.

Risk methodology

Conditional VaR (95% / 99%), historical and Cornish-Fisher VaR, Maximum Drawdown peak-to-trough, Ulcer Index, Pain Index. All metrics computed on the user-selected backtest window. Outputs surfaced as a paired (VaR, CVaR) so the tail premium is visible.

Performance & optimization

Sharpe, Sortino, Calmar, Omega, Rachev reported on every backtest. 12 portfolio optimization objectives — Max Sharpe / Sortino / Calmar / Omega / Rachev, Min Vol / CVaR95 / CVaR99 / Drawdown / Ulcer, Risk Parity, Max Return. Convex objectives solved by OSQP, non-convex by SQP with multistart.

Simulation & scenarios

Monte Carlo simulation runs 10,000 paths under geometric Brownian motion calibrated on the backtest window. P5-P95 fan charts. Crisis Library presets — 2008 GFC, 2020 COVID, 2022 Bear, 2018 Q4 — backtest the live portfolio weights on dated historical windows with one click.

Regulatory & macro data

SEC EDGAR (Form 4, 13F, 13D/G) for insider and institutional flows. CFTC TFF + Disaggregated COT weekly reports. ECB Data Portal SDMX (balance sheets, SHS holdings). FRED for Fed H.4.1 and SLOOS. FCA SPR (UK short interest). U.S. Treasury Fiscal Data API (TIC, debt-to-penny, DTS). IMF COFER + BIS Credit-to-GDP.

Conventions

The numerical conventions are fixed and apply to every report. Documenting them once here keeps the per-metric pages clean.

Trading days per year252
Volatility annualisationσ_d × √252
Return annualisationμ_d × 252 (arithmetic) or (1 + μ_d)^252 − 1 (geometric)
Risk-free rateSet per portfolio — defaults to 0 unless an explicit cash leg is included
CVaR confidence levels95% and 99%, reported as a pair
Monte Carlo paths10,000
Transaction costs5 bps round-trip on rebalances (default, user-adjustable)
Drawdown conventionPeak-to-trough on total return series, not calendar-based
RebalancingMonthly by default — user can select daily / weekly / quarterly / annual / never

Frequently asked

How does MEDGE compute Conditional Value at Risk (CVaR)?: CVaR is computed historically as the arithmetic mean of returns below the α-quantile, where α defaults to 95% and 99%. The sample is the full backtest window. For multi-asset portfolios the joint return distribution is preserved — we do not assume Gaussian marginals or constant correlations. CVaR is then converted to euro terms by multiplying by the current portfolio value.
What return model does the Monte Carlo simulator use?: Geometric Brownian Motion calibrated on the backtest window with the empirical mean and covariance matrix of daily log-returns. We run 10,000 paths and report P5, P25, P50, P75, P95 over the user-selected horizon. The model assumes log-normal returns — it is honest about its assumptions and ignores fat tails, which the documentation states explicitly.
Which annualisation convention is used?: All annualised figures use 252 trading days. Mean returns are multiplied by 252; standard deviations and Sharpe denominators are multiplied by √252. Drawdowns are computed peak-to-trough on the total return series, not calendar-based. Backtest performance includes 5 basis points round-trip transaction costs by default.
How is portfolio optimization implemented?: For convex objectives (Min Vol, Min CVaR, Max Sharpe with covariance shrinkage) we use quadratic programming via the OSQP solver. For non-convex objectives (Max Sortino, Max Omega) we use sequential quadratic programming with multiple random starts. Constraints support box bounds, group caps and turnover penalties. All 12 objectives operate on the same input universe and constraint set so direct comparison is honest.
Where does the regulatory data come from?: SEC Form 4 + 13F + 13D/G from EDGAR full-text search. CFTC TFF and Disaggregated COT from the weekly CFTC reports. ECB balance sheets, SHS holdings and policy decisions from the ECB Data Portal SDMX REST API. Fed H.4.1 and SLOOS via FRED CSV. FCA UK short interest from the SPR weekly file. U.S. Treasury TIC + Daily Treasury Statement from the FiscalData API. IMF COFER from the SDMX 2.1 API. BIS Credit-to-GDP from the BIS Stats API.
Are backtests in-sample or out-of-sample?: Backtests are in-sample by default — the user-selected window is also the calibration window. The reports flag this explicitly. For walk-forward / out-of-sample analysis, the Compare module supports user-defined sample splits and reports both in-sample and out-of-sample performance for the same strategy. Walking-forward an optimization across years is on the roadmap.
Does MEDGE Capital ever provide investment advice?: No. MEDGE Capital is an analytics platform. The outputs are statistical descriptions of historical and simulated behaviour. Nothing on the site, in exported reports or in the AI-narrated PDF constitutes a personalised investment recommendation. Past performance does not predict future results. See the full Risk & Investment Disclaimer at /disclaimer.

References

The methodology builds on the standard quantitative finance literature. Each metric page in the glossary cross-references the relevant primary source.

[1]Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1). — Mean-variance optimization
[2]Sharpe, W.F. (1966). Mutual Fund Performance. The Journal of Business, 39(1). — Sharpe Ratio
[3]Sortino, F. & Price, L.N. (1994). Performance Measurement in a Downside Risk Framework. Journal of Investing, 3(3). — Sortino Ratio
[4]Artzner, P. et al. (1999). Coherent Measures of Risk. Mathematical Finance, 9(3). — Coherent risk measures, sub-additivity
[5]Rockafellar, R.T. & Uryasev, S. (2000). Optimization of Conditional Value-at-Risk. Journal of Risk, 2(3). — Linear programming for CVaR optimization
[6]Fama, E.F. & French, K.R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1). — Fama-French 3-factor model
[7]Carhart, M.M. (1997). On Persistence in Mutual Fund Performance. The Journal of Finance, 52(1). — Carhart 4-factor extension
[8]Keating, C. & Shadwick, W.F. (2002). A Universal Performance Measure. The Finance Development Centre. — Omega Ratio
[9]Rachev, S.T. et al. (2004). Different Approaches to Risk Estimation in Portfolio Theory. Journal of Portfolio Management, 31(1). — Rachev Ratio
[10]Grinold, R.C. (1989). The Fundamental Law of Active Management. Journal of Portfolio Management, 15(3). — Information Ratio decomposition

See the methodology in action.

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