Monte Carlo Methods for Risk Management: VaR Estimation in Python

Source: https://www.researchgate.net/figure/Illustration-of-the-Expected-Shortfall-metric_fig2_322701819

1. Value at Risk

Risk Metrics

A technique for quantifying the risk in a portfolio is known as a risk metric. This gives us a way of numerically describing the amount of uncertainty in that portfolio.

• Examples: Volatility/Variance and Correlation which give an idea of the extent to which a portfolio’s value could decrease and how susceptible it is to massive swings in value.

However, to fully characterise these risks, we would need the distribution of returns to be multivariate normal — which is very unlikely.

Therefore, we use a general metric as the Value at Risk (VaR)

Value at Risk (VaR)

Value at Risk (or VaR) gives an indication of how much you stand to lose on a portfolio with a given probability, over a specific time period.

This can be measured in absolute terms (we could lose $100 in portfolio value) or in relative terms (the value of our portfolio will decrease by 5%).

Let our current portfolio value be 𝑋(𝑡), then we can define the return on the portfolio until some fixed time T as:

Interpretation:

• We can interpret VaR as being a quantile…