If assets are perfectly negatively correlated, what can be said about the portfolio's VaR?

When assets in a portfolio are perfectly negatively correlated, it implies that the movements of these assets are inversely related. In this context, when one asset increases in value, the other decreases by a corresponding amount, and vice versa.

In a scenario where the assets are perfectly negatively correlated, the risks associated with price movements cancel each other out to some extent. This relationship leads to an interesting outcome in terms of Value at Risk (VaR), which is a measure used to assess the risk of loss on a portfolio.

If we consider the VaR of individual assets, a perfectly negatively correlated situation allows for the possibility of a complete offset in the effects of losses. As a result, when calculating the VaR of the overall portfolio, the gains from one asset can completely offset the losses in another. Essentially, the maximum potential loss from the portfolio can be minimized to zero, as the negative correlation negates the volatility associated with both assets.

This unique nature of perfectly negatively correlated assets means that the overall portfolio VaR can indeed equal zero, leading to a very stable and potentially risk-free profile under this extreme correlation condition. Thus, this reasoning validates that if assets are perfectly negatively correlated, the portfolio VaR equals zero, reflecting the balanced risk that arises