Morningstar Education
Investment Trusts Solutions
Understanding Z-stats on Investment Companies
Slide 2: Understanding Z-Stats on Investment Companies

The Z-statistic is a statistical measure designed to help assess whether a fund is cheap or expensive at its current discount level. It shows whether the current discount is close to the mean (average) for a given period. A positive Z-stat indicates the current value is higher than the mean; conversely, a negative value indicates that it is lower.

Slide 3: Understanding Z-Stats on Investment Companies

The magnitude of the Z-stat shows whether the difference between the current discount and the mean (average) is statistically significant. In simple terms, is this difference due to more than just random chance?

Slide 4: Understanding Z-Stats on Investment Companies

The calculation for the Z-statistic is:


Z = (current discount-mean)/standard deviation


Standard deviation measures the extent to which a value has varied around its average level during a past period. In this calculation, standard deviation is measuring the extent to which the discount has varied.

Slide 5: Understanding Z-Stats on Investment Companies

Let's illustrate this with an example. If a company has had a mean discount over the last 12 months of -10%, with a standard deviation of 2% and the current discount is -5%, then the 12-month Z-stat will be (-5+10)/2 = +2.5. So, in this case, the fund is "expensive" at its current discount, which is 2.5 standard deviations away from its mean.


Statistically, 66% of observations in a normal distribution should have a Z score between -1 and +1, and 95% should have a score between -2 and +2.

Slide 6: Understanding Z-Stats on Investment Companies

Some people like to consider the Z-statistic alongside mean reversion theory. Under this belief, prices and returns eventually move back towards the mean (average); so companies with large negative Z-stats will revert to the mean. In other words, their wide discounts should narrow over time. However, this relies on the market's perception of what discount the fund should trade at not changing. What we do know is that the Z-statistic proves the current discount is higher or lower than the average over the period for which it has been calculated.

Slide 7: Understanding Z-Stats on Investment Companies
If you choose to look at the Z-statistic when analysing investment companies, we suggest you consider both a short-term and a long-term score and not focus exclusively on just one. The short-term score will give a sense of recent market sentiment and behaviour of the fund, while the long-term one is a better reflection of its behaviour overall. We are firm advocates of long-term investing but the shorter-term score may help when it comes to the timing of a purchase or sale.
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