What does a correlation of 1 indicate in relation to Value at Risk (VaR)?

A correlation of 1 indicates that two assets move perfectly in tandem. When determining the Total Value at Risk (VaR) of a portfolio that consists of multiple assets, this relationship affects how individual risks combine.

If the correlations between the assets are perfect (correlation of 1), total portfolio VaR will be equal to the sum of the individual VaRs of those assets. This is because, in such cases, the risks do not offset each other; instead, they contribute to the overall risk in a linear fashion. Therefore, the total risk of the portfolio rises proportionately with the individual risks.

Conversely, if the correlation were lower, individual assets might offset each other's risks, leading to a total VaR that is lower than the sum of individual VaRs. In scenarios involving a correlation of 1, the individual risks simply aggregate without mitigation from diversification, reinforcing the idea that the portfolio will behave as if it contains one risk factor rather than multiple independent ones.