In the context of portfolio management, Value at Risk (VaR) is a statistical measure that quantifies the level of financial risk within a firm or investment portfolio over a specific time frame. VaR is most commonly used by investment and commercial banks to determine the extent and occurrence rate of potential losses in their institutional portfolios. When the assets in a portfolio are perfectly correlated, the portfolio’s VaR would be equal to the undiversified VaR. This is because perfect correlation implies that all assets in the portfolio move in the same direction at the same time. Therefore, there is no benefit from diversification, and the portfolio's risk is equivalent to the sum of the individual asset risks, which is the definition of undiversified VaR.

Choice A is incorrect. Component VaR refers to the proportion of total portfolio risk that can be attributed to a particular asset or investment. In this scenario, we are dealing with a perfectly correlated portfolio, not individual assets.

Choice B is incorrect. Marginal VaR measures the change in portfolio risk resulting from an incremental investment in a new asset or security. This concept does not apply here as we are discussing the overall risk of a perfectly correlated portfolio, not changes due to additional investments.

Choice C is incorrect. Diversified VaR would refer to the risk measurement of a diversified portfolio where assets are not perfectly correlated and thus provide some level of diversification benefit by reducing overall portfolio risk. However, in this case, all assets in the portfolio are perfectly correlated which eliminates any potential diversification benefits.

Things to Remember

• Correlation measures the relationship between the movements of two assets or variables. A correlation of +1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.
• Portfolio diversification involves spreading investments across different asset classes to reduce risk. Diversification helps to lower the overall risk of a portfolio by investing in assets whose returns do not move in perfect unison.