Perfect correlation between the assets in a portfolio results in an undiversified VaR. This is because when assets are perfectly correlated, they move in the same direction to the same degree. Therefore, there is no diversification benefit as all assets would gain or lose value simultaneously. In such a scenario, the portfolio VaR is the sum of the individual VaRs of the assets in the portfolio. This is also known as undiversified VaR because the risk is not spread out or diversified across different assets, but is concentrated in assets that behave similarly.

Choice A is incorrect. Positive correlation between assets in a portfolio does not necessarily result in an undiversified VaR. While it is true that positive correlation can increase the risk of a portfolio, it does not mean that the portfolio is undiversified. Diversification can still be achieved with positively correlated assets if they are not perfectly correlated.

Choice C is incorrect. Negative correlation between assets in a portfolio actually contributes to diversification and reduces VaR, rather than leading to an undiversified VaR. This is because when one asset's returns fall, the other asset's returns rise, offsetting the loss and reducing overall risk.

Choice D is incorrect. No correlation between assets also contributes to diversification and reduces VaR as the performance of one asset has no impact on another's performance.

Things to Remember

• Correlation measures the degree to which the returns of two assets move in relation to each other. It can be positive, negative, or zero.
• Diversification is the strategy of spreading investments across different assets to reduce risk.
• Value at Risk (VaR) is a measure of the potential loss in value of a portfolio over a specific time period under normal market conditions.
• Undiversified VaR occurs when the assets in a portfolio are perfectly correlated, leading to increased risk.
• Perfect correlation implies that the assets move in the same direction to the same degree, resulting in no diversification benefit.