VaR: Validation & Alternativesintermediate

PaR, EaR and CFaR

The VaR idea, a worst outcome at a confidence level over a horizon, can be applied to quantities other than trading P&L. Earnings at Risk (EaR) is the maximum shortfall in accounting earnings; Cash-Flow at Risk (CFaR) is the maximum shortfall in operating cash flow; and Profit at Risk (PaR) applies the same logic to project or business-unit profit. These corporate measures suit non-financial firms whose chief worry is not a trading book marked daily but the chance that earnings or cash flow fall below the level needed to service debt, fund investment, or pay dividends over a quarter or a year.

Why it matters

A bank cares about the value of a portfolio today; a manufacturer cares whether next year’s cash flow covers its loan payments. Same statistical question, different variable. EaR and CFaR move the lens from a one-day market loss to a one-year earnings or cash shortfall, which is what a treasurer actually loses sleep over. They translate market-risk thinking into the language of the income statement and the cash-flow statement, distinguishing accounting earnings from the cash that pays the bills.

Formulas

Cash-Flow at Risk

\Pr\!\left(\,CF < \overline{CF} - \mathrm{CFaR}_{\alpha}\,\right) = 1 - \alpha

Over the horizon, cash flow falls more than

\mathrm{CFaR}_{\alpha}

below its expected level

\overline{CF}

with probability

(1-\alpha)

. Replace

CF

with earnings for EaR or unit profit for PaR.

Worked examples

Scenario

An airline forecasts expected annual operating cash flow of $500m. Its 95% one-year CFaR is $180m. What does this tell the treasurer, and why use CFaR rather than trading VaR?

Solution

With 95% confidence, cash flow will not fall more than $180m below the $500m forecast, so the downside case is roughly $320m. The treasurer sizes liquidity lines and fuel hedges against that shortfall. CFaR fits because the airline has no daily-marked trading book; its risk is that fuel prices and demand push annual cash flow below what covers debt service and capex.

Common mistakes

✗EaR, CFaR and VaR measure the same thing. They share the quantile logic but target different variables: VaR a portfolio value loss, EaR an earnings shortfall, CFaR a cash-flow shortfall.
✗These measures are only for banks. EaR and CFaR were designed for non-financial corporates, whose key risk is earnings or cash flow falling short over a quarter or year, not a daily trading loss.
✗Earnings at Risk and Cash-Flow at Risk are interchangeable. Accounting earnings include non-cash items, so EaR and CFaR can diverge; the cash-based measure is what determines the ability to pay obligations.
✗A longer horizon makes these measures less useful. The corporate horizon is deliberately long (a quarter or year) because that matches the firm’s budgeting and debt-service cycle.

Revision bullets

•Apply the VaR quantile idea to variables other than trading P&L
•EaR: worst earnings shortfall; CFaR: worst cash-flow shortfall; PaR: worst profit shortfall
•Built for non-financial firms over quarterly or annual horizons
•Focus on covering debt service, investment, and dividends
•Distinguish accounting earnings (EaR) from cash flow (CFaR)

Quick check

Cash-Flow at Risk (CFaR) is most useful for

How does Earnings at Risk differ from Cash-Flow at Risk?

Connected topics

VaR Definition VaR Limits Expected Shortfall

Sources

Jorion (2007), Ch. 17
Jorion, P. Value at Risk: The New Benchmark for Managing Financial Risk. 3rd ed. McGraw-Hill, 2007.
Extends the VaR framework to corporate risk measures including cash-flow and earnings at risk.
RiskMetrics (1999), CorporateMetrics
RiskMetrics Group. CorporateMetrics Technical Document. RiskMetrics Group, 1999.
Introduces Earnings at Risk and Cash-Flow at Risk for non-financial corporations.

How to cite this page

Dr. Phil's Quant Lab. (2026). PaR, EaR and CFaR. Derivatives Atlas. https://phucnguyenvan.com/concept/frm-par-ear-cfar

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