Ex-Post Risk

What Is Ex-Post Risk?

The term ex-post risk refers to a risk measurement technique that uses historic returns to predict future risks associated with an investment. This type of risk manages risks associated with investment returns after the fact. Future risk is determined using the statistical variance from the relative mean of long-term returns in the past for a particular asset.

Using the ex-post risk method can help investors and financial professionals estimate the maximum potential for losses during any given trading period provided there are no surprising events or circumstances.

Key Takeaways

  • Ex-post risk looks at an investment's historical results after they occur and utilizes them to project its future risk.
  • This technique weighs historical data based on its variance around the mean.
  • Ex-post risk is commonly used in risk models such as historical VaR.
  • This method should be used with caution because the past isn't always a good indicator of future outcomes.
  • Ex-post risk is the opposite of ex-ante risk, which is a more uncertain way to look at risk because the outcome must be predicted before it actually occurs.

Understanding Ex-Post Risk

Ex-post is another word for actual returns and is Latin for after the fact. In that manner, ex-post risk refers to risks that take place after the fact by accounting for historical returns as a base or guideline. It involves the analysis of actual historic return streams to ascertain the variability of that return stream over time.

Using historic returns to measure future risk is a common method traditionally used by investors and financial professionals to determine how much risk is associated with a particular asset, such as a stock, mutual fund, or exchange traded fund (ETF). As noted above, using historical returns is the most well-known approach to forecast the probability of incurring a loss during a certain trading period—normally a specific trading day.

Keep in mind, though, that ex-post risk doesn't take into account any shocks or drastic changes, whether they pertain to surprising market upsets or gains. So if there's an economic event that occurs, it could sway the way the investment performs. Similarly, a change in market conditions (say, a big rally) could push stocks up, changing the returns for a mutual fund.

Ex-post risk is often used in value at risk (VaR) analysis, which is a tool used to give investors the best estimate of the potential loss they could expect to incur on any given trading day.

Ex-Post Risk vs. Ex-Ante Risk

A related but opposite term is an ex-ante risk, which refers to the future projected risks of a portfolio. Ex-ante is the Latin term for "before the event". This means that the outcome must be predicted before it actually takes place, making it uncertain. Ex-ante risk refers to any of the returns that an investment earns before that risk actually takes place.

This kind of analysis looks at the risk of current portfolio holdings and estimates future return streams and their projected variability based upon statistical assumptions. 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-ante risks are future risks that are not based on actual data while ex-post risks take actual returns into account.

Ex-Post Risk vs. Ex-Post Analysis

Remember that ex-post risk refers to a way to measure how much risk comes with a certain investment by accounting for its past returns. Ex-post analysis is a way to analyze any information related to an investment's earnings and price changes that take place after the fact to determine the potential for returns.

When you use an ex-post analysis, you compare the ex-ante or projected return with the ex-post or actual return. This helps figure out how accurate the way risk assessment is done by a professional or investor. In order to conduct the ex-post analysis, it's important to choose the type of asset class in question, then use regression analysis to figure out the potential for gains or losses.

Examples of Ex-Post Risk

Here are two examples to show how ex-post risk works. The first one examines how it works with gambling through a simple coin toss. The second involves ex-post risk by looking at historical VaR.


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 on an ex-ante or ex-post basis. If you judged the toss by the information available to you at the time, it was a good bet ex-ante, since on average you could expect to come out 50 cents ahead. But if you judged by the information available to you after the coin was flipped and you had lost, you should expect a possible loss of $1 on an ex-post basis.

Historical VaR

The historical method for computing VaR simply re-organizes actual historical returns by ranking the order from worst to best. It then assumes that history will repeat itself in the future. As a historical example, consider the Invesco QQQ ETF (QQQ), which began trading in March 1999. If we calculate each daily return, we produce a rich data set that can be arranged in order from the best daily return to the worst.

On one side, you'd have any gains experienced by the ETF while the other side would be populated by daily losses. Let's say 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.

What Is Ex-Post Variance?

Ex-post variance is a forward-looking measure of risk. It attempts to determine an investor's maximum amount of loss for an investment over a specific period of time within a certain degree of probability.

What Is Ex-Ante Demand and Ex-Post Demand?

Demand can be both ex-ante and ex-post. Ex-ante demand refers to any demand that doesn't result in the payment for or exchange of money for goods and services. Ex-post demand, on the other hand, means the actual demand for goods and services that are purchased during a single year within the economy.

What Is an Ex-Ante Cost?

Ex-ante costs are any investment expenses that are both implicit (those that take place without the exchange of cash) and explicit (those that affect an investment's overall profitability). These costs are normally based on the last 36 months of the investment's costs compared to its average total assets under management (AUM).

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  1. Invesco. "Invesco QQQ Trust, Series 1."

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