What does a correlation of -1 signify in terms of total VaR?

A correlation of -1 indicates a perfect inverse linear relationship between two assets. This implies that when one asset's value increases, the other decreases in a perfectly inverse manner. When assessing the total Value at Risk (VaR) of a portfolio, this correlation has significant implications for risk assessment.

In the context of a portfolio containing two assets with a correlation of -1, the assets can completely offset each other’s risks. This means that the combined risk of the portfolio is mitigated to the point where the total VaR could reach zero.

In mathematical terms, since the assets move in exactly opposite directions, any potential loss in one asset due to adverse market movements would be completely countered by a gain in the other asset. Consequently, the overall risk exposure of the portfolio shrinks significantly, leading to a situation where the total VaR is zero.

This highlights how diversification can lead to reduced overall risk, and in scenarios where assets have perfectly negative correlations, the total risk (or VaR) can be minimized effectively.