Discounted maximum loss
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Discounted maximum loss is the present value of the worst case scenario for a financial portfolio.
An investor must consider all possible alternatives for the value of his investment. How he weights the different alternatives is a matter of preference. One might require a pension fund never to go bankrupt. If this is the case, the manager of its portfolio must consider the worst alternative as the benchmark. Finally, as the investment takes place today he must evaluate the alternatives in their present value, hence the discounting.
[edit] Definition
Given a finite state space S, let X be a portfolio with payoff Xs for 
. If X1:S,...,XS:S is the order statistic the maximum loss is simply δX1:S, where δ is the discount factor.
[edit] Properties
The Discounted maximum loss is the 1-expected shortfall. It is therefore a coherent risk measure.
[edit] Example
As an example, assume that the discount factor is 0.8 (corresponding to an interest rate of 25%) and consider the following portfolio:
| probability | value |
|---|---|
| of event | of the portfolio |
| 40% | 100 |
| 30% | 80 |
| 20% | 150 |
| 10% | 20 |
In this case the discounted maximum loss is simply 
.
