Value at Risk, Conditional Value at Risk, expected shortfall

Mar 9, 2018

monsmatglad

I am working on Value at Risk and expected shortfall/conditional Value at Risk.The formula I have is this:

What I do not understand is numerator of the second part. If for example I want to look at an expected shortfall when p=0.01 (ignoring the average and the standard deviation). what value will the numerator have?

Mar 9, 2018

magoo

I don't see a formula

Mar 11, 2018

monsmatglad

magoo said:

I don't see a formula

What is Value at Risk (VaR)?

Value at Risk (VaR) is a statistical measure used to estimate the potential loss of an investment or portfolio over a specific time horizon and at a given confidence level. It is typically expressed as a dollar amount and represents the maximum amount of money that could be lost with a certain probability, usually 95% or 99%.

What is Conditional Value at Risk (CVaR)?

Conditional Value at Risk (CVaR), also known as Expected Shortfall, is a risk measure that estimates the expected loss in the worst-case scenario. It is an extension of VaR and takes into account the magnitude of potential losses beyond the VaR threshold. CVaR is typically expressed as a percentage of the expected portfolio value and represents the average of all losses that exceed the VaR.

What is expected shortfall?

Expected Shortfall, also known as Conditional Value at Risk (CVaR), is a risk measure that estimates the expected loss in the worst-case scenario. It is an extension of Value at Risk (VaR) and takes into account the magnitude of potential losses beyond the VaR threshold. Expected Shortfall is typically expressed as a percentage of the expected portfolio value and represents the average of all losses that exceed the VaR.

How is Value at Risk (VaR) calculated?

There are several methods for calculating VaR, including historical simulation, Monte Carlo simulation, and analytical VaR. In general, VaR is determined by taking the expected return of the portfolio and subtracting the product of the portfolio volatility and a certain number of standard deviations, which is based on the desired confidence level. The result is the maximum potential loss of the portfolio over a given time period with a certain probability.

What are the limitations of Value at Risk (VaR)?

VaR has several limitations, including the fact that it only considers the potential losses in the worst-case scenario and does not take into account the potential gains. It also assumes a normal distribution of returns, which may not always be the case in financial markets. Additionally, VaR does not account for events that have not occurred in the past, making it difficult to predict extreme events or black swan events. Therefore, it is important to use VaR in conjunction with other risk measures and to regularly review and update the assumptions used in its calculation.