Value at Risk (VAR)

What is Value at Risk (VaR)?

Value at Risk (VaR) is a statistical measure used to assess the level of financial risk within a firm or investment portfolio over a specific time frame. This metric estimates the potential loss in value of a portfolio with a given probability, due to adverse market movements. It can be used to manage the risk within a portfolio and contribute to controlling the overall level of risk exposure.

Methods of Calculating VaR

VaR can be calculated using different methods, each with its own approach to estimating potential losses. To calculate VaR, analysts will need to set out a specific time-period, a percentage of confidence, and a potential loss amount. The output VaR should disclose the maximum amount (or worst loss) that an investor can expect over a period given a percentage of confidence (i.e. 99% that the outcome is likely to happen).

The three primary methods are the Historical Method, the Variance-Covariance Method, and the Monte Carlo Simulation.

Historical Method

The Historical Method involves analyzing historical market data to estimate potential future losses. This method assumes that past market behavior is indicative of future performance.

Variance-Covariance Method

The Variance-Covariance Method, also known as the Parametric Method, uses statistical measures such as the mean and standard deviation to estimate potential losses. It uses parameters to represent the underlying structure of the data. In the context of bonds, parametric models can be used to calculate the Value at Risk (VaR) for bonds. This involves using historical changes in yield to maturity (YTM) and applying them to the bond’s modified duration and market value to estimate potential losses.

This method assumes that returns are normally distributed and is a useful method if the distributions are fairly reliable.

Monte Carlo Simulation

The Monte Carlo Simulation method involves running a large number of simulations to model potential future market scenarios. It is also known as multiple probability simulation. This method uses random sampling and statistical modeling to estimate potential losses.

It differs from the other methods as it uses multiple values in the probability calculations and then takes a mean average to produce the estimate.

Calculating Historical VaR

Calculating historical Value at Risk (VaR) uses past returns to understand how much risk is being taken. This method assumes that historical returns will continue in the future.

To calculate historical returns:

• Collect historical data: gather historical price data for the asset or portfolio being analyzed
• Calculate periodic returns: compute the returns for each period (e.g. daily, monthly) using the formula:
• Organize returns: list the returns in a table or spreadsheet to analyze the distribution of returns starting with the worst returns
• Analyze distribution: use the organized returns to understand the distribution and calculate the Value at Risk (VaR) based on historical data – results can be put into a histogram to show the distribution and highlight where the worst outcomes are
• Calculating VaR: The formula for historical VaR is shown below:

m = Number of days of historical information

Vi = Number of variables on day i

Using 252 as the annual trading days in the year, the formula will calculate percentage change of each risk factor provided.

Download the Financial Edge template and perform VaR calculations following our step-by-step guide. The bespoke excel template provides the steps and excel formulas to calculate items such as: frequency, standard deviation, percentiles and aligns the data to derive VaR. Working with real data from listed companies is the ideal way to improve your understanding of how to calculate Value at Risk.

Advantages and Disadvantages of VaR

As with all financial analysis there are pros and cons of methodologies. Let’s look at VaR from this perspective:

Advantages

• It provides a clear and quantifiable measure of potential losses, usually a percentage which is easy to use and compare
• VaR helps with risk management and regulatory compliance to quantify risk into a universal measure
• It can be applied to various types of financial instruments, asset classes and portfolios

Disadvantages

• Each method has its own downside, for example the Historical method assumes that past data is indicative of future performance, which may not always be true
• It may not accurately capture extreme market events or tail risks as it does not report the maximum loss potential
• Different methods can yield different results, leading to potential inconsistencies in the data

Applications of VaR

VaR is widely used in finance for risk management, regulatory reporting, and performance measurement. It helps financial institutions and investors understand the potential risks associated with their portfolios and make informed decisions. By using the metric companies can set internal parameters to provision for potential losses or reshape a portfolio (or investment) to avoid high levels of risk.

Value at Risk (VaR) Example

To calculate Value at Risk (VaR), follow these steps:

1. Determine the Confidence Level: choose a confidence level (e.g. 95% or 99%) for the VaR calculation and populate the left-hand column
2. Calculate Historical Returns: compute the historical returns for the asset or portfolio
3. Organize Returns: list the returns in a table or spreadsheet to analyze the distribution of returns
4. Identify the Percentile: identify the return at the chosen confidence level percentile
5. Calculate VaR: multiply the identified return by the initial investment to get the VaR in dollar terms

For example: if you have a 1-day VaR of -4.44% at a 99% confidence level for a $100,000 investment, the VaR would be $4,439. This means that there is a 1% chance that the investment may lose $4,439 over the time period.

How Do You Calculate Value at Risk (VaR) in Excel?

In this example, we are asked to calculate the daily Value at Risk (VaR) for various confidence levels for an investment in Apple stock.

1. Determine the time frame for the VaR calculation, which in this case is daily
2. Collect historical price data for Apple stock for the desired period
3. Calculate the daily returns from the historical price data
4. Compute the mean and standard deviation of the daily returns to understand the volatility
5. Choose your confidence level(s), such as 95% or 99%
6. Apply the VaR formula, which is typically the mean (or zero for simplicity) minus the product of the standard deviation and the Z-score corresponding to your chosen confidence level
7. Scale the result to your investment size, which is $300,000 in this case

Download the example Historical VaR Workout and see more calculation details in our Financial Edge template.

Excel VAR vs VARP

In Excel, the VAR and VARP functions are used to calculate the variance of a dataset, but they differ in terms of the population they consider:

• VAR: This function calculates the variance based on a sample of the population. It is used when you have a subset of the entire population and want to estimate the variance of the whole population.
• VARP: This function calculates the variance based on the entire population. It is used when you have data for the entire population and want to calculate the exact variance.

Here is a summary of the differences:

Variance is the measure of how much data differs from the mean value. These functions are useful in statistical analysis to understand the dispersion of data points in a dataset.

Conclusion

Understanding and applying Value at Risk (VaR) is crucial for effective risk management and informed decision-making in finance. By leveraging different methods to calculate VaR, financial institutions can better assess potential losses and navigate market uncertainties.

As with all financial models, the outcomes rely on the accuracy of inputs, so analysts should use appropriate sensitivities for confidence levels and capturing a wide enough range of data.