What is implied when correlation equals 0 regarding total VaR?

When correlation equals 0 in the context of total Value at Risk (VaR), it implies that the assets in question are uncorrelated with each other. This lack of correlation means that the risks associated with the individual assets do not influence each other, allowing for a specific method to calculate the total VaR.

The correct relationship arising from this condition is that the total VaR can be represented as the square root of the sum of the squared individual VaRs. This is derived from the statistical property of uncorrelated variables where the variances can be summed, leading to the total risk being calculated as the combination of those variances. This method provides a more nuanced understanding of the risk across a portfolio of assets, effectively capturing the diversification benefits that arise from holding uncorrelated investments.

Therefore, when correlation equals 0, the total VaR reflects a more comprehensive picture of the risk involved, acknowledging that the individual asset risks can work independently without affecting each other, which is encapsulated in the square root of the sum of their squared VaRs.