Probability
Portfolio Loss Probability Calculator
Use a normal horizon-return approximation to calculate threshold breach probability, loss amount, expected ending value, and one-sided parametric VaR.
Loss-threshold z-score-
Probability return is at or below threshold-
Portfolio loss at threshold-
One-sided confidence z-score-
Normal-model return at confidence quantile-
Normal-model value at risk-
Expected end value-
Decision view
Portfolio return curve with threshold tail and VaR marker
Portfolio return curve with threshold tail and VaR markerThe live loss threshold shades the left tail while the selected confidence level places a separate parametric VaR boundary.
Exact scenario comparisonLoss threshold return (%) changes while all other entered assumptions remain constant.
| Loss threshold return (%) | Loss-threshold z-score | Probability return is at or below threshold | Portfolio loss at threshold | One-sided confidence z-score | Normal-model return at confidence quantile | Normal-model value at risk | Expected end value |
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How to use Portfolio Loss Probability Calculator
- Use expected return and volatility for the same horizon.
- Enter a negative return threshold.
- Choose a confidence level while remembering model risk.
Calculator guide
Understanding Portfolio Loss Probability Calculator
Portfolio loss probability asks how much of a modeled return distribution lies beyond a loss boundary. This screen keeps the selected threshold separate from a confidence-based VaR marker.
Detailed calculation process
Detailed portfolio loss-tail calculation
The default $100,000 portfolio has 7% expected horizon return, 18% volatility, and a -10% loss threshold.
General formula: z_L=(r_L-μ)/σP(R≤r_L)=Φ(z_L)L_T=V|r_L|z_c=Φ^(-1)(c)r_V=μ-z_cσVaR=V|r_V| The threshold uses a lower-tail z-score. VaR uses the positive one-sided confidence quantile subtracted from expected return.
What each symbol means
Worked substitution with the default inputs
The default model assigns about 17.25% probability to losing at least 10% and a 95% one-sided VaR near $22,607.
Worked situations
Practical examples
- A -10% threshold is 0.944 standard deviations below a 7% mean with 18% volatility.
- The normal approximation assigns roughly 17.25% probability to returns at or below that threshold.
Better inputs
Useful tips
- Stress skew, fat tails, and correlation changes.
- Use arithmetic-return parameters consistently.
- Compare parametric results with historical and scenario methods.
Before relying on the result
Limitations and common mistakes
- Returns are assumed normal with constant mean and volatility.
- Liquidity, path dependence, changing exposures, serial correlation, fees, and taxes are omitted.
- VaR does not describe the average severity beyond its threshold.
Reference
Key terms
- Loss threshold
- Return boundary whose lower-tail probability is measured.
- VaR
- A quantile loss estimate at a stated confidence and horizon.
- Model risk
- Risk that the assumed distribution understates real behavior.
Important note
This is educational screening, not investment advice or a complete risk system. Validate horizons, distribution fit, holdings, correlations, liquidity, and stress losses.
Frequently asked questions
Is 95% VaR the maximum possible loss?
No. Losses can exceed the VaR threshold.
Why can expected return reduce VaR?
The model centers the horizon distribution at the entered expected return.
Should volatility be annualized?
Use volatility matching the same horizon as expected return and threshold.