What is 'Conditional Value At Risk  CVaR'
Conditional value at risk (CVaR) is a risk assessment technique often used to reduce the probability that a portfolio will incur large losses. This is performed by assessing the likelihood (at a specific confidence level) that a specific loss will exceed the value at risk. Mathematically speaking, CVaR is derived by taking a weighted average between the value at risk and losses exceeding the value at risk.
BREAKING DOWN 'Conditional Value At Risk  CVaR'
CVaR is also known as mean excess loss, mean shortfall, tail Var, average value at risk or expected shortfall. CVaR was created to serve as an extension of value at risk (VaR). The VaR model allows managers to limit the likelihood of incurring losses caused by certain types of risk, but not all risks. The problem with relying solely on the VaR model is that the scope of risk assessed is limited, since the tail end of the distribution of loss is not typically assessed. Therefore, if losses are incurred, the amount of the losses will be substantial in value.CVaR was created to calculate the average of the losses that occur beyond the VaR cutoff point in the distribution. The smaller the value of the CVaR, the better.
Conditional Value at Risk Calculation and Example
Though the formula for CVaR uses calculus, it is still straightforward. The CVaR is calculated as:
CVaR = (1 / (1  c)) x the integral of xp(x)dx from 1 to VaR
Where
p(x)dx = is the probability density of getting a return x
c = the cutoff point on the distribution where the analyst sets the VaR breakpoint
VaR = the agreedupon VaR level
As a simplified example, assume a $500,000 portfolio with the possible gains and losses (along with the probability of them happening) below:
10% of the time, a loss of $500,000
30% of the time, a loss of $100,000
40% of the time, a gain of $0
20% of the time, a gain of $250,000
Given a probability of occurrence, q, the expected shortfall for this portfolio is:
5% = $500,000
10% = $500,000
20% = $300,000
30% = $233,300
40% = $200,000
50% = $160,000
60% = $133,300
70% = $114,300
80% = $100,000
90% = $61,100
100% = $30,000
This is calculated by probabilityweighting the loss for given chance of the loss occurring. For example, knowing that 10% of the time, the portfolio will lose all of its value, the expected shortfall for q=5% and q=10% are both $500,000. For higher values of q, an analyst would continue down the expected outcomes and weight them according. For example, consider q=40%. An analyst would use the following formula:
Expected shortfall (40%) = ((10% x $500,000) + (30% x $100,000)) / 40% = $200,000
Similarly, using interpolation, for q=90%, the expected shortfall is:
Expected shortfall(90%) = (((10% x $500,000) + (30% x $100,000) + (40% x $0) + (10% x $250,000)) / 90% = $61,100

Marginal VaR
Marginal VaR includes the change in portfolio VaR resulting from ... 
Value At Risk  VaR
A statistical technique used to measure and quantify the level ... 
Market Risk
Market risk is the possibility of an investor experiencing losses ... 
Probability Distribution
A statistical function that describes all the possible values ... 
Risk Management
Risk management occurs anytime an investor or fund manager analyzes ... 
Risk Assessment
The process of determining the likelihood that a specified negative ...

Personal Finance
Risk Management Framework (RMF): An Overview
A company must identify the type of risks it is taking, as well as measure, report on, and set systems in place to manage and limit, those risks. 
Financial Advisor
The Importance of a Client's Risk Assessment
Financial advisors and money managers must do a detailed risk assessment regarding each client before they can recommend a course of action. 
Investing
LowRisk vs. HighRisk Investments for Beginners
Understanding risk is key to better investing. Determining where risk lies and knowing the difference between low risk and high risk are crucial. 
Trading
Introduction To Counterparty Risk
Unlike a funded loan, the exposure from a credit derivative is complicated. Find out everything you need to know about counterparty risk. 
Financial Advisor
Example of Applying Modern Portfolio Theory (MPS)
Modern Portfolio Theory: brush up on key mathematical framework used in investment portfolio construction. 
Managing Wealth
Why Companies Need Risk Management
Implementing risk management strategies can save an entire organization from failure. Is yours up to snuff? 
Investing
Understanding Liquidity Risk
Make sure that your trades are safe by learning how to measure the liquidity risk. 
Investing
How To Manage Portfolio Risk
Follow these tips to successfully manage portfolio risk. 
Investing
Limiting Losses
It is impossible to avoid losses completely, but there is a systematic method you can use to control them.

What does Value at Risk (VaR) say about the "tail" of the loss distribution?
Learn about value at risk and conditional value at risk and how both models interpret the tail ends of an investment portfolio's ... Read Answer >> 
How to calculate Value at Risk (VaR) in Excel
Learn what value at risk is, what it indicates about a portfolio and how to calculate the value at risk of a portfolio using ... Read Answer >> 
What's the difference between a confidence level and a confidence interval in Value ...
Learn about the value at risk, how confidence intervals and confidence levels are used to interpret the value at risk and ... Read Answer >> 
What is the minimum number of simulations that should be run in Monte Carlo Value ...
Find out how many simulations should be run at minimum for an accurate value at risk when using the Monte Carlo method of ... Read Answer >> 
What's the difference between EaR, Value at Risk (VaR), and EVE?
Learn about earnings at risk, value at risk and economic value added, how these risk measures are used, and the difference ... Read Answer >>