DEFINITION of Ex-Post Risk
Ex-post risk is a risk measurement technique that uses historic returns to predict the risk associated with an investment in the future. This type of risk measurement determines future risk by weighing the statistical variance from the relative mean of past long-term returns from a particular asset.
BREAKING DOWN Ex-Post Risk
Ex-post risk refers to the past risks of a portfolio (ex-post = after the fact). It is the analysis of actual historic return streams to ascertain the variability of that return stream over time. A related but opposite term is ex-ante risk, which refers to the future projected risks of a portfolio (ex-ante = before the event). It is the analysis of current portfolio holdings to estimate future return streams and their projected variability based upon statistical assumptions.
Using historic returns as a measure of future risk has been a traditional method used by investors to determine the riskiness of a given asset. Ex-post risk is often used in value at risk analysis—a tool used to give investors a best estimate of the potential loss that they could expect to incur on any given trading day.
Ex-Ante vs. Ex-Post
Ex-ante, derived from the Latin for "before the event," is a term that refers to future events. An example of ex-ante analysis is when an investment company values a stock ex-ante and then compares the predicted results with the actual movement of the stock's price.
Ex-post is another word for actual returns and is Latin for "after the fact." The use of historical returns is the most well-known approach to forecast the probability of incurring a loss on an investment on any given day.
Ex-Post Risk and a Coin Flip
Imagine a bet on a coin flip: Heads you win $2, tails you pay $1. You agree. The coin is flipped, and it comes up tails.
Whether you should have made the bet depends on whether you judge it ex-ante or ex-post. Ex-ante, judged by the information available to you at the time, it was a good bet, since on average you could expect to come out 50 cents ahead. Ex-post, judged by the information available to you after the coin was flipped and you had lost, you should expect a possible loss of $1.
Ex-ante, almost all bets placed in Las Vegas are losing ones; the casino, like an insurance company, sets its rates so that the money that comes in when it wins covers not only the money it pays out, but also its operating expenses. Nonetheless, some bets placed are winning ones, ex-post.