Value At Risk

Important terms that have significance in understanding the meaning of Value at Risk (VAR):

Financial Risk:

Financial risk is referred as the unexpected changes in the financial conditions, such as prices exchange rates, credit rating, and interest rate etc. and broadly this risk can be divided into Counter party risk, Political Risk(though this is not a financial risk in direct sense), Interest rate risk and currency risk.

Risk Management:

Risk management is the management of risk in the financial world, through analysis and acceptance or mitigation of uncertainty in investment decisions. For example we calculate standard deviation in risk return analysis , this is just to find out the level of risk in respect of return in the portfolio of investment and hence thereby we can select appropriate combination of securities to mitigate risk and its risk management.

Variance:

Variance (σ2) in statistics is just a measure to find out how widely numbers in a data set are spread. That is, it measures how far each number in the set is from the mean and therefore from every other number in the set. Example: How far a particular return in a portfolio is from the mean return of portfolio. In other words we can say that in a investment portfolio comprising of stocks ,through variance we can analyse a  stocks performance(suppose in terms of returns) against each other and with the mean.

Co-variance:

this just provides a direction between two or more numbers. Whether they are moving in the same direction or in the opposite direction. For example if value of co-variance between two asset is positive this means they are moving in the same direction and if it is negative they are moving in the opposite direction. For measuring strength of relationship one has to use coefficient of correlation , which can be measured by dividing co-variance between two assets divided by stand deviation first asset and standard deviation of 2nd asset.

Standard Deviation:

In finance like variance this is also used to determine the risk(change) . This is calculated as a square root of Variance.

Z-score:
As per Investopedia
"A Z-score is a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score. A Z-score of 1.0 would indicate a value that is one standard deviation from the mean. Z-scores may be positive or negative, with a positive value indicating the score is above the mean and a negative score indicating it is below the mean.
Z-scores are measures of an observation's variability and can be put to use by traders in determining market volatility. The Z-score is more commonly known as the Altman Z-score".

The Z-score,is the number of standard deviations a given data point lies from the mean. To calculate Z-score, simply subtract the mean from each data point and divide the result by the standard deviation.
For data points that are below the mean, the Z-score is negative. In most large data sets, 99% of values have a Z-score between -3 and 3, meaning they lie within three standard deviations above and below the mean.

What is VAR:

VAR using the degree of Confidence measures the maximum possible loss in a given Portfolio for a particular(specified) time period. Say one day, one week etc. If say a portfolio with investment $1 million has at 95% confidence level (a day time period taken) has VAR $12000 this simply means that the risk manager is 95% sure that the maximum possible loss in a day could not exceed  $12000 and there is only 5% chance that loss will exceed $12000.($12000 is taken just for illustration, for exact VAR calculation one needs Z-score at 95% confidence level and Standard Deviation). Z-score when multiplied by Standard Deviation will give VAR.