Three Methods for Calculating Equity Portfolio Value at Risk

Summary

The document presents three approaches to estimating value at risk (VaR) for an equity portfolio using asset weights and return data. The historical method calculates portfolio returns over a calibration period and takes the chosen lower-tail percentile; it makes no distributional assumption and can accommodate nonlinear assets. The covariance method assumes normally distributed returns, estimates asset means and covariances, and derives the portfolio return distribution. The Monte Carlo method specifies asset dynamics, simulates sample paths, and estimates VaR from the resulting outcomes.

Each approach has trade-offs. Historical VaR is direct but relies on the calibration period as a guide to risk. Covariance VaR can incorporate alternative estimates to create a forward-looking view, though its quality depends on covariance estimation and the distributional assumption. Monte Carlo allows flexible dynamics and nonlinear exposures, at the cost of computation and model specification. The answer outlines the methods but does not discuss validation, tail risk beyond VaR, or selecting a confidence level and horizon for a particular portfolio.

Key ideas

• Historical VaR is estimated from the lower percentile of observed portfolio returns.
• The covariance method assumes normal returns and uses portfolio weights with asset means and covariances.
• Monte Carlo VaR is obtained by simulating returns under a specified stochastic process.
• Historical VaR avoids a distributional assumption but depends on the calibration sample.
• Monte Carlo is flexible but computationally demanding and sensitive to model choices.

Tags

# How to compute VaR of a simple equity portfolio?


# How to compute VaR of a simple equity portfolio?












How do I compute VaR of a simple equity portfolio? I know current weights and can easily access the history of the stocks' daily returns.

## Answer by msitt (score 5, accepted)

https://quant.stackexchange.com/a/33329

There are a few different ways to calculate VaR.

### Historical Method

For this method, you calculate the return of your portfolio each day, and get a list of daily returns over your calibration period. Once you have this, then you find the 5th percentile to give the 95% VaR.

The advantage of this method is that it is the most straightforward to compute, and you don't need to make any assumptions on the distribution of returns to make this calculation, and it can handle nonlinear assets.

### Covariance Method

For this method, you assume returns are normally distributed. First compute the mean and covariance matrix of your assets, then using the weights of your portfolio you can compute the distribution of portfolio returns. Calculate the 5% point of the CDF to get the 95% VaR.

The advantage of this method is that you can calculate a "forward looking" VaR by incorporating a different return/covariance matrix. Care must be taken to estimate the covariance matrix for this method.

### Monte Carlo Simulation

For this method, you specify the stochastic process for your assets and run a bunch of simulations. The VaR is calculated based on all the sample paths.

This can be computationally expensive, but the good thing about this method is that you have complete freedom to define the underlying dynamics and it can handle nonlinear assets.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.