What it means
"Ex post" is Latin for "after the event". When analysts calculate ex post risk, they take a series of historical returns, such as monthly or yearly results, and measure how much they varied.
A fund whose returns bounced between large gains and large losses had high ex post risk, while one with steady returns had low risk. The most common measure is standard deviation (a statistic showing how far results typically sit from their average).
Other measures include the worst loss from peak to trough, known as maximum drawdown, and the range between the best and worst periods. All of them describe what happened, not what will happen.
Ex post risk is useful because it is based on facts. It can be used to compare funds, check whether a manager took more risk than promised, and calculate risk-adjusted returns such as the Sharpe ratio.
Investors also use it to test whether a risk model was accurate by comparing the prediction with the outcome. Its main weakness is that the past may not repeat.
A calm period can hide risks that appear only in a crisis, and a stormy period can overstate the risk of a business that has since changed. The result also depends on the length of the sample and on how often returns are measured.
For a finance team, the lesson is to use ex post figures as evidence, not as a forecast. Combine them with forward-looking views, scenario analysis and judgement about current conditions.
A manager who points to low historical risk should be asked what has changed in the portfolio since then. Be careful to compare like with like.
Standard deviation based on monthly returns is not directly comparable with one based on annual returns unless it is converted to the same time basis. Always check the period, the frequency and the currency.
In practice
Real-world examples.
Example
A pension trustee reviews the past five years of a fund's returns. The standard deviation was 12%, which is higher than the 8% the manager had described when selling the fund. She asks the manager to explain the difference at the next review meeting.
Example
A risk analyst at a bank compares predicted losses with actual losses over the last year. She finds that the actual swings were larger than the model suggested, so the model is reviewed. The bank's risk committee asks for a report on whether the model assumed calmer markets than occurred.
Example
A private investor compares two funds with the same average return of 7%. The first had a standard deviation of 4% and the second 15%, so she picks the first as it delivered the same return with far less volatility. She notes that this tells her about the past and that the future may differ.
Formula
Calculation
Ex post risk (sample standard deviation) = square root of [ sum of (each return - average return)^2 / (number of returns - 1) ]
Worked example: a fund had annual returns of 5%, 15%, 5%, 15% and 10% over five years.
Step 1: Average return = (5 + 15 + 5 + 15 + 10) / 5 = 50 / 5 = 10%.
Step 2: Deviations from the average are -5, 5, -5, 5 and 0, and their squares are 25, 25, 25, 25 and 0, which add up to 100.
Step 3: Variance = 100 / (5 - 1) = 25, so standard deviation = square root of 25 = 5%.
The fund's ex post risk was 5% a year. A typical year ended about 5 percentage points above or below the 10% average.Case study
Seen in the real world.
Crestline Asset Management is a fictional firm that marketed a fund as low risk. Over three years, the fund's monthly returns had a standard deviation that was twice what the sales material had suggested.
The firm's risk committee reviewed the history and found that the manager had increased exposure to a few large positions. The ex post figures exposed a gap between the stated approach and the actual behaviour.
In this illustrative case, the firm updated its risk limits and revised its marketing documents. The episode showed that tracking ex post risk regularly can catch problems before clients do. The committee now reviews a one-page risk summary every quarter, with the figures for the last three years shown side by side.
Watch out
Common mistakes.
- Treating past risk as a guaranteed guide to future risk, when markets, portfolios and managers can all change.
- Comparing standard deviations calculated over different time periods or frequencies.
- Using a short or unusually calm period, which can understate the true risk.
Questions
People also ask.
What is the difference between ex post and ex ante risk?
Ex post risk looks backward at what happened, while ex ante risk is a forecast of what might happen.
Is a lower ex post risk always better?
Not necessarily, because the return matters too, so analysts look at risk-adjusted measures. A very low-risk fund may simply earn very little.
How many data points are enough?
There is no fixed rule, but more observations over a range of market conditions give a more reliable picture.
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