Expected shortfall could be defined as the average of expected losses which could be equal to the Value at risk or greater than the value at risk. Where Value at risk is could be defined for the level of loss which is exceeded in a certain level of the confidence during a pre-defined time period. Expected shortfall could be expressed as the conditional Value at risk, where the standard Value at risk represent as the worst possible loss under the simple situation over the specific period on a given confidence level.
For example: if for one month period, Value at risk is 2 million on 99% of confidence level, which means that out of under the normal situation the maximum loss for one month will not exceed 2 million dollars. The expected shortfall will cover the remaining 1% which covers the fat tails on the distribution. Expected shortfall and Value at risk helps are two measures that helps institutions to manage interest rate risk.
For financial institution informs an agent that the one day 99% VAR of the trader’s portfolio must be reserved less than $1 million. There is a risk that the agent will build a portfolio where there is a 99% possibility that the everyday failure is less than $1 million and a 1% probability that it is $50 million. The trader is pleasing the risk restrictions compulsory by the financial institution, but is clearly taking intolerable risks. Expected Shortfall calculate that produce better incentive for trader than VAR is expected shortfall.
This is also at times referred to as conditional VAR, or tail loss. Where VAR asks the question ‘how bad can things get?’, Expected shortfall asks “what is our expected loss, if the thing would worse than the worst-case scenario?”Uses of the Value at risk and Expected shortfall:Value at risk and Expected Shortfall can predict the maximum loss for a certain time period , so that companies can hedge their positions and protect them self from the worst-case scenario. Basel III has used Expected Shortfall to replace the Value at Risk. Expected Short has been used and introduced by BCBS (Basel Committee on Banking Supervision) after the crisis because most of the companies lost more than the expected loss calculated by VAR. While in the Basel I is used for the main assets and liabilities of the banks, at what could be the maximum loss in the specified with these assets of the bank on given confidence level, so that in Basel I Value at risk recommended to protect the risk.