 Value at Risk (VaR) - Everything you need to know about VaR

Value at risk (VaR) is a popular method for risk measurement. VaR calculates the probability of an investment generating a loss, during a given time period and against a given level of confidence. It gives investors an indication of the level of risk they take with a certain investment. This can help them decide whether the possible gain is worth the potential maximum loss. VaR can be calculated for either one asset, a portfolio of multiple assets of an entire firm.

## Calculating Value at Risk

By calculating VaR the following question can be answered:

What can I, with a certain level of confidence, expect to lose in monetary or percentage terms, during a given period of time?

A VaR calculation consequently consists of three elements, that is to say confidence level, a time period and the expected maximum loss. This could result in a answer resembling the following:

With 85 percent confidence, I expect my worst daily loss not to exceed 3 percent

The first element is the level of confidence. This element represent the chance a certain risk may occur. Using the answer mentioned above, there is a 85 percent chance the worst daily loss will not exceed 3 percent. This element represents whether it is likely the maximum loss can be made and thus whether it is worth taking the risk.

The second element is the time period. This represents the time period over which the loss can be realized. This can be expressed in daily, monthly or even yearly periods. This element is a factor for determining whether an investment represents a short or long term risk.
The third element is the expected maximum loss. This element is crucial because it indicates what the worst case scenario would be, should the risk become reality. This element must be considered before making an investment, to determine what this maximum loss may do to a trading account. Furthermore it can aid in making the decision whether the loss is acceptable considering the potential profit made on the investment.
There are three different methods for calculating VaR where each method has different strengths and weaknesses.

## Historical

The historical method makes use of historical data to calculate the VaR. Historical data is used to identify the returns on a specific commodity or index. These daily or monthly returns are collected into a graph. This graph gives an insight in the historical return and frequency of the different returns. The higher frequency of a return the more likely it is a return will re-occur in the future. For example:

If a negative return of 5 percent respresents only 3 percent of the total of reruns, there is a change of 97 percent a daily loss will not exceed 5 percent

This is a relatively easy method for calculating VaR. Which gives it an edge over other methods especially for fairly stable markets, where history tends to repeat itself.

The weakness of using historical data is that it does not takes changing market conditions into its calculations. This may cause the VaR calculation to be out of sync with actual market developments.

## Variance-Covariance

The variance-covariance method is based on a normal distribution of returns. This requires estimating the expected (or average) returns and standard deviation. These two factors can be combined to create a normal distribution curve. Similar to the historical method, the variance-covariance method calculates the probability of a return occurring and creates a normal distribution graph based on this data.
The advantage of using a normal distribution curve is that it gives a clear overview of the most likely return on an asset. Furthermore it is the easiest method for calculating VaR. Whereas the other methods require far more historical data and calculations, the variance-covariance method requires only the expected average return and its standard deviation. This will also limit the work hours invested in calculating the VaR using this method. With the normal distribution curve formed it is fairly easy to say the probability of a certain return occurring.
The danger of using the variance-covariance method and consequently the normal distribution curve, is that the normal distribution may not be realistic. Off-market factors can increase price volatility, which results in the normal distribution curve being out of sync with actual market movement.

## Monte Carlo Simulation

The Monte Carlo Method creates simulations to calculate the VaR. A risk manager will perform a number of simulations, each simulation with different input variables. These variables may range from level of volatility, initial price, correlation estimates. These numerous simulations will generate different outcomes which appear in a similar fashion to that of the other methods. It will result in a graph which shows the number each return is realized in the simulation.
The advantage of using the Monte Carlo Method is that it will likely be more realistic compared to the other two methods. It also gives a risk manager the possibility to adjust his simulation to current market developments. This way his simulations can be more in sync with current market movements. It also gives the risk manager the opportunity to let his personal judgment be a factor for determining the probability at which a return may occur.
The Monte Carlo method however requires a lot of time and work to successfully be used in risk assessment. Furthermore with the number of factors influencing the returns, the number and complexity of the simulations must increase. This in order to simulate as many possible outcomes to get a reasonable estimate of the returns.