Coherent Risk Measure

A coherent risk measure is a mathematical tool used in finance to assess and quantify the risk associated with an investment or portfolio. To be considered coherent, a risk measure must satisfy four key properties: monotonicity (higher losses mean higher risk), subadditivity (diversification reduces risk), positive homogeneity (doubling the portfolio doubles the risk), and translation invariance (adding a risk-free asset reduces the portfolio's risk by the same amount). Coherent risk measures are commonly used in risk management to ensure that risk is evaluated in a logical and consistent manner.

Example

Value-at-Risk (VaR), when modified to meet the four criteria, becomes a coherent risk measure, providing a more reliable estimate of potential losses in a portfolio.