# Economic Capital vs. CVaR

#### RKenn4844

##### New Member
Subscriber
In the credit risk review for FRM L2, David talks about Economic Capital & Credit VaR. I know EC is a multiple of UL given that UL is one sigma around EL. However, there are two formulas used, CVaR is the quantile - EL whereas Economic Capital is mean + UL * sigma. And I recall that in some of the credit risk questions, unlike market risk, credit risk is in the right tail and this is why we add the mean instead of subtract. So I'm trying to figure out which is the calculation for Economic Capital and which is CVaR or can they be used interchangeably? Thank you.

#### gsarm1987

##### Active Member
Staff member
Credit RIsk
In the credit risk review for FRM L2, David talks about Economic Capital & Credit VaR. I know EC is a multiple of UL given that UL is one sigma around EL. However, there are two formulas used, CVaR is the quantile - EL whereas Economic Capital is mean + UL * sigma. And I recall that in some of the credit risk questions, unlike market risk, credit risk is in the right tail and this is why we add the mean instead of subtract. So I'm trying to figure out which is the calculation for Economic Capital and which is CVaR or can they be used interchangeably? Thank you.
Lets summarise,
Risk Capital: Risk Capital is similar to Economic Capital but incorporates Strategic Capital. Formula: RC = WL - EL (with a 1-year time horizon).

Economic Capital: Economic Capital is an internal estimate of the capital needed to ensure solvency with a specified level of certainty, similar to VAR calculation. Formulas:

Economic Capital = WCL - EL
Also, Economic Capital = Risk Capital + Strategic Capital.
(Also see David's response on 18 May 2010: https://forum.bionicturtle.com/threads/expected-unexpected-loss-and-economic-capital.3343/)

Risk Capital: Functions as a cushion for extreme events.

Strategic Capital: Represents potential losses or write-offs from investments with initially anticipated high probabilities of success. Proxied by burned-out capital and goodwill. Captures the idea that capital may be spent without providing future returns or with very low returns.

Credit VAR (Value at Risk): Quantile of loss minus the expected loss, also known as relative VAR. If correlation (corr) is close to 1, the portfolio behaves like one giant bond. If correlation is close to 0, the number of defaults follows a binomial distribution. Correlation influences volatility but not expected loss (EL).

Loss Quantile: UL (Unexpected Loss) is calculated as UL = d * V, where d is the number of defaults.