Answer to Question #90090 in Financial Math for Thatayaone

Question

How do I calculate the value at risk given a discrete distribution?

Answer 1

A value-at-risk measure calculates an amount of money, measured in that currency, such that there is that probability of the portfolio not loosing more than that amount of money over that time horizon. In the terminology of mathematics, this is called a quantile, so one-day 90% USD VaR is just the 90% quantile of a portfolio’s one day loss in US dollars.

For example, if a portfolio of stocks has a one-day 5% VaR of $1 million, that means that there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one-day period if there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day out of 20 days (because of 5% probability).