Discounted maximum loss, also known as worst-case risk measure, is the present value of the worst-case scenario for a financial portfolio.

In investment, in order to protect the value of an investment, one must consider all possible alternatives to the initial investment. How one does this comes down to personal preference; however, the worst possible alternative is generally considered to be the benchmark against which all other options are measured. The present value of this worst possible outcome is the discounted maximum loss.

Definition

is the order statistic is the discount factor.

Given a general probability space denotes the essential infimum.

Properties

• The discounted maximum loss is the expected shortfall. It is therefore a coherent risk measure.

• is the most conservative (normalized) risk measure.

Example

As an example, assume that a portfolio is currently worth 100, and the discount factor is 0.8 (corresponding to an interest rate of 25%):

References