Finance
Portfolio Loss Expected Value Calculator
Compare baseline and hedged expected portfolio loss across routine, drawdown, and crisis scenarios with explicit probabilities and hedge cost.
SCENARIO-WEIGHTED DECISION
Price protection against a documented set of loss states
This page asks whether a hedge reduces probability-weighted loss enough to justify its known cost. The three states must be mutually exclusive and collectively exhaustive; otherwise the arithmetic can be exact while the decision frame is incomplete.
CURRENT DECISION RECORD
Scenario contribution ledger
Every row is generated from the current inputs and reused by Copy, TXT, and the page-specific PDF.
| Scenario | Probability (%) | Loss (%) | Loss ($) | EV contribution ($) | Loss after mitigation ($) | Hedged contribution ($) |
|---|
CURRENT CALCULATION PROCESS
Formula, substitution, intermediate values, and reconciliation
EV(loss) = sum(p_i x L_i); EV(hedged loss) = sum(p_i x L_i x (1-m)) + hedge cost; net benefit = EV(loss) - EV(hedged loss)
Waiting for valid inputs.
USE STEPS
Five steps for an expected-loss comparison
- Fix one portfolio value and one decision horizon for all scenarios.
- Define routine, drawdown, and crisis states so no outcome belongs to two states.
- Assign probabilities that sum to exactly 100% and document their basis.
- Estimate unhedged loss, mitigation, and certain hedge cost on the same value base.
- Review row contributions, break-even cost, and non-financial constraints before deciding.
FOUNDATIONS
Five concepts behind the weighted result
Collectively exhaustive states
The three scenarios must cover the entire modeled outcome space for their probabilities to total one.
Conditional loss
Each loss estimate is conditional on its scenario occurring, not an unconditional forecast.
Expected contribution
Probability times loss shows how much each state contributes to total expected loss.
Certain cost
Hedge premium is added in every state, so it can outweigh protection in low-loss scenarios.
Expectation versus tolerance
A lower expected loss can still leave an unacceptable crisis loss or liquidity obligation.
DEEP ANALYSIS
Three challenges before paying for protection
Probability sensitivity
Move probability between drawdown and crisis while preserving the 100% total. This isolates how much the hedge case depends on rare-event judgment rather than loss severity.
Mitigation realism
A constant mitigation percentage is deliberately simple. Real protection can have strikes, caps, basis risk, counterparty exposure, and timing mismatch; test a conservative mitigation value after those frictions.
Decision beyond EV
Expected value averages states. Organizations facing insolvency, covenant breach, or mission interruption may rationally pay more than break-even expected cost to reduce a specific tail state.
DECISION CASES
Two distinct hedge decisions
Endowment distribution reserve
An endowment has a fixed annual grant obligation. Its committee models routine, drawdown, and crisis losses, then compares a protective overlay with the cost of holding more cash. It uses expected net benefit as one criterion and the crisis residual as a separate solvency check.
Concentrated founder portfolio
A founder evaluates a collar before a lockup expires. The crisis state has low probability but a large loss. Even when the hedge has slightly negative expected benefit, preserving tax payments and operating liquidity can make the protection decision rational.
TERMS
Expected-loss glossary
- Scenario probability
- The assessed likelihood of one mutually exclusive state within the modeled horizon.
- Conditional loss
- The portfolio loss assumed if a particular scenario occurs.
- Expected loss
- The sum of each scenario loss multiplied by its probability.
- Mitigation rate
- The modeled fraction of scenario loss removed by the hedge before cost.
- Break-even cost
- The hedge cost at which baseline and hedged expected losses are equal.
- Basis risk
- The possibility that the hedge payoff does not track the portfolio loss it is meant to offset.
EVIDENCE
Preserve the scenario rationale
Store the valuation date, horizon, scenario definitions, probability owner, evidence used for each probability and loss, hedge term sheet, mitigation basis, cost quote, and approval decision. Preserve alternate probability sets when judgment is contested.
LIMITS
Model boundaries
- Only three loss states are represented and scenario losses are point estimates.
- Mitigation is constant across scenarios and ignores strikes, caps, timing, and basis risk.
- Expected value does not measure dispersion, path dependence, liquidity, or ruin probability.
- Probabilities are subjective unless tied to a documented statistical or market-implied process.
Disclaimer: Expected loss is one decision lens and should not replace legal, tax, investment, or counterparty review.
SOURCES
Risk and decision references
FAQ
Questions about scenario expected value
Why must probabilities sum to 100%?
The formula represents an average over the entire modeled outcome space. A missing or overlapping state breaks that interpretation.
Can the routine state be a gain?
This page accepts loss values from 0% to 100% so it focuses on loss budgeting. Use a richer payoff model if gains must offset expected loss.
Does positive net benefit prove I should hedge?
No. It supports the hedge under entered assumptions; counterparty, liquidity, tax, governance, and implementation risks still matter.
Why is hedge cost not probability weighted?
The simplified premium is paid regardless of which scenario occurs, so its probability is one.
What if mitigation differs by scenario?
Use separate instrument modeling. A single rate is suitable only when a common conservative approximation is defensible.
How often should probabilities be refreshed?
Refresh when the horizon rolls, portfolio composition changes, market regime evidence changes, or the hedge terms change.