## What Is 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, i.e. after the fact. 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.

Ex-post can be contrasted with ex-ante.

### Key Takeaways

- Ex-post risk looks at an investment's historical results after they have occurred and utilizes them to project its future risk.
- This technique weights historical data based on its variance around the mean and is used in risk models such as historical VaR.
- Because the past is not always a good predictor of future outcomes, the ex-post method should be used with caution.

## Understanding Ex-Post Risk

Ex-post risk refers to the risks experienced by a portfolio in the past (ex-post = after the fact). It involves 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 (VaR) analysisâ€”a tool used to give investors the 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.

## Example: 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.

## Example: Ex-Posit Risk and Historical VaR

The historical method for computing VaR simply re-organizes actual historical returns, putting them in rank order from worst to best. It then assumes that history will repeat itself into the future.

As a historical example, consider the Nasdaq 100 ETF (QQQ), which began trading in March of 1999. If we calculate each daily return, we produce a rich data set of more than 1,400 points that can be arranged in order from the best daily return to the worst. For instance, there were more than 250 days when the return was between 0% and 1%. At the same time, there was a single day (in January 2000) when the QQQs rose 13% in a single day. On the other side of the tally would be daily losses. The greatest 5% of daily losses range from 4% to 8%. Because these are the worst 5% of all daily returns, we can say with 95% confidence that the worst daily loss will not exceed 4%. Put another way, we expect with 95% confidence that our gain will exceed -4%, ex-post.