A coherent risk measure is a risk metric that satisfies a set of properties, such as subadditivity, positive homogeneity, and translation invariance. These measures typically involve increasingly sophisticated weighting functions, which means that the weights used in the calculation are determined by the underlying characteristics of the portfolio or asset under consideration. The 'average VaR' is a simple method for estimating the VaR of a portfolio or assets by averaging the VaR of each component, with equal weights assigned to each component. However, because different components may have varying levels of risk, correlation, or impact on the overall portfolio, this approach may not be appropriate for all types of risk measures. Therefore, the appropriate weights must be chosen based on the underlying component characteristics and the specific risk measure being evaluated to estimate any risk measure using a weighted approach. This is why option C, 'Weights appropriate to risk measure being estimated', is the correct choice.

Choice A is incorrect. Average weights are not an appropriate replacement for equal weights in the 'average VaR' to estimate any risk measure. This is because average weights do not take into account the specific risk characteristics of each individual asset in the portfolio, which can lead to inaccurate risk estimates.

Choice B is incorrect. Exponential weights may be used in some cases, but they are not universally applicable for all risk measures. The use of exponential weights assumes that recent data points are more relevant than older ones, which may not always be true depending on the nature of the risks being estimated.

Choice D is incorrect. Fixed weights regardless of risk measure being estimated would also be inappropriate as it does not allow for adjustments based on changes in market conditions or portfolio composition over time. This could result in a misrepresentation of potential losses and therefore an inaccurate estimation of Value at Risk (VaR).

Things to Remember

• Coherent risk measure: A risk metric that satisfies properties like subadditivity, positive homogeneity, and translation invariance.
• Subadditivity: The risk measure of a portfolio is less than or equal to the sum of the risk measures of its components.
• Positive homogeneity: Scaling the portfolio by a positive factor scales the risk measure by the same factor.