# Historical VaR

### Reviewed by Subject Matter Experts

Updated on July 12, 2023

## What Is Historical VaR?

Value at Risk (VaR) is a widely used risk management metric that quantifies the potential loss in the value of a portfolio or investment over a specified time period and at a given confidence level.

VaR is used to estimate the maximum potential loss that an investment or portfolio could incur under normal market conditions. There are several methods for calculating VaR, one of which is the Historical VaR method.

Historical VaR, also known as empirical VaR or non-parametric VaR, is a method of calculating Value at Risk that relies on historical data to estimate the potential loss of an investment or portfolio.

It involves analyzing the historical returns of the investment or portfolio over a specified time period to determine the likelihood of experiencing a certain level of loss in the future.

The Historical VaR method is based on the assumption that past market behavior is a good indicator of future market behavior. It does not make any assumptions about the distribution of returns, which distinguishes it from other VaR calculation methods, such as Parametric VaR and Monte Carlo VaR.

## Calculation Methodology of Historical VaR

### Data Collection

The first step in calculating Historical VaR is collecting historical data. The chosen time period, frequency, and data source will have an impact on the results.

It is essential to use reliable data sources and consider factors such as market conditions, structural changes, and economic events when selecting the time period.

### Data Processing

Once the data is collected, the next step is to calculate returns, sort them, and identify the VaR threshold. The returns are calculated as the percentage change in value over the specified time period.

The sorted returns are then used to determine the VaR threshold, which represents the loss amount at the specified confidence level.

### Determination of Historical VaR

Historical VaR is determined by selecting a confidence level, holding period, and identifying the corresponding loss amount. The confidence level represents the probability of not exceeding the potential loss, while the holding period is the length of time for which the risk is being estimated.

Historical VaR has several advantages, including simplicity and ease of calculation. It does not require any distribution assumptions and incorporates actual historical events, making it a more realistic representation of potential losses.

## Limitations of Historical VaR

However, Historical VaR also has limitations. It assumes history will repeat itself, making it sensitive to the chosen time period.

It may not accurately capture recent trends or structural changes in the market and has limited usefulness in stress testing, as it may not adequately account for extreme events.

## Historical VaR vs Other VaR Methods

### Parametric VaR

#### Definition and Overview

Parametric VaR, also known as Variance-Covariance VaR, assumes that asset returns follow a known distribution, typically the normal distribution. This method relies on the calculation of the mean and standard deviation of returns to estimate potential losses.

#### Calculation Methodology

Parametric VaR is calculated using the mean, standard deviation, and confidence level. It assumes that the returns are normally distributed and uses the standard normal distribution to determine the VaR threshold.

Parametric VaR is computationally efficient and easy to calculate. However, its reliance on distribution assumptions can lead to inaccurate estimates, especially for assets with non-normal return distributions.

### Monte Carlo VaR

#### Definition and Overview

Monte Carlo VaR is a simulation-based method that generates multiple scenarios of future asset returns to estimate potential losses. It is a more advanced approach that accounts for the correlations and non-linearities in asset returns.

#### Calculation Methodology

Monte Carlo VaR involves simulating a large number of scenarios based on historical data, calculating returns for each scenario, and determining the VaR threshold by sorting the simulated returns.

Monte Carlo VaR can provide more accurate estimates, as it accounts for non-normal return distributions and correlations. However, it is computationally intensive and requires sophisticated modeling techniques.

### Comparison Summary

Historical VaR, Parametric VaR, and Monte Carlo VaR have their unique advantages and limitations. Historical VaR is suitable for portfolios with limited historical data and is easy to compute, but may not capture recent trends or extreme events.

Parametric VaR is computationally efficient but relies on distribution assumptions that may not hold for all assets. Monte Carlo VaR is more accurate and accounts for non-normal return distributions and correlations, but requires advanced modeling techniques and is computationally intensive.

## Real-World Applications of Historical VaR

### Financial Institutions

VaR is widely used by financial institutions such as banks, investment funds, and insurance companies for risk management, portfolio optimization, and regulatory compliance.

### Regulatory Environment

In the regulatory environment, the Basel accords and other regulatory frameworks require financial institutions to maintain adequate capital levels based on their risk exposure, with VaR being one of the key metrics used to assess this risk.

### Investment Strategies

Investment managers use VaR to optimize their portfolios, identifying the optimal trade-offs between risk and return. It is also used as a performance evaluation tool, allowing investors to assess risk-adjusted returns and make informed investment decisions.

## Criticisms and Controversies of Historical VaR

### Reliability of VaR

Despite its widespread use, the reliability of VaR has been questioned, particularly during extreme market events. The 2008 financial crisis highlighted the limitations of VaR in predicting and managing risk during periods of market turbulence.

### Alternative Risk Measures

As a result, alternative risk measures have gained prominence, such as Expected Shortfall (ES), Conditional Value at Risk (CVaR), and tail risk measures. These metrics aim to provide a more comprehensive view of risk, focusing on the potential losses in the extreme tail of the distribution.

## Conclusion

Historical VaR is a widely used method for estimating portfolio risk, offering simplicity and ease of calculation.

However, its limitations, including its sensitivity to the chosen time period and its assumption that history repeats itself, should be considered when using it as a risk management tool.

Despite its limitations, VaR remains an essential risk management tool in modern finance, helping financial institutions manage risk, comply with regulatory requirements, and make informed investment decisions.

As data and computation capabilities improve, more sophisticated VaR models can be developed to better account for market dynamics, correlations, and extreme events.

Integration with other risk measures and evolving regulatory requirements will ensure that VaR continues to play a critical role in managing risk in the financial sector.