Before we answer your question, let's first define tracking error and ex-post risk. Tracking error refers to the amount by which the returns of a stock portfolio or a fund differ from those of a certain benchmark. As you might expect, a fund that has a high tracking error is not expected to follow the benchmark closely, and it is generally seen as being risky.

The other component of the question is ex-post risk, which is a measure of the variance of an asset's returns relative to a mean value. In other words, ex-post risk is the statistical variance of an asset's historical returns. Many individuals would argue that tracking error is not the best measure to determine ex-post risk because it looks at the returns of a portfolio relative to a benchmark rather than looking at the variability in the portfolio's returns. Tracking error can be a useful tool when determining how closely a portfolio mimics a stable benchmark, or how efficient a portfolio's manager is at tracking a benchmark, but many would argue that this is not a good measure of how much an investor can expect to gain or lose on any given trading day. However, ex-post risk, unlike tracking error, can provide an estimate of the probability that the expected return of a portfolio will drop by a certain amount on any given day, which is why it is a common risk metric used by professionals when studying things such as value at risk.

Using tracking error as a measure of ex-post risk would only make sense when tracking error is equal to zero because when an investor's portfolio consists of many stable companies that have produced predictable, stable returns, the historical variance of the benchmark's returns would be equal to those of the portfolio.

To learn more see, Introduction To Value At Risk (VAR) - Part 1 and Part 2 and Determining Risk And The Risk Pyramid.

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