Investing Basics: Using the Z-score to value investment trusts

How a simple stat can help you make your investment decisions…by David Kimberley

 
Fans of statistics are probably familiar with the Z-score. Used for a variety of purposes, it’s a number that tells you how much a data point deviates from the mean.

For investment trusts it’s used as a quick way of identifying how an investment trust’s discount or premium compares to its historical average.

A trust trading on a discount which is much wider than its historical average may be seen as a good buy opportunity – unless there’s a clear reason for that broader discount. The opposite is also true, with a trust trading above its historical average potentially seen as being ‘expensive’.

Usually the Z-score is in relation to an average discount or premium. A discount is where a trust’s shares are worth less than its net asset value (NAV) per share. The reverse is a premium, where a trust’s shares trade at a price which is higher than the NAV per share.

Calculating an investment trust’s Z-score

To work out an investment trust’s Z-score you need to take its current discount or premium. You then subtract its average premium or discount over a set period of time from that value. You then divide that answer by the standard deviation of the premium or discount.

If the Z-score is below 0 that means the trust’s shares are trading at a lower price to their historical average. If it’s above 0 then they’re trading at a higher price relative to their historical average.
 
The formula looks like this:

Z-score =
 
N.B. that ‘discount’ in the formula could be replaced with ‘premium’.
 
To put this in more concrete terms, imagine an investment trust that has:
 

• A current discount of 10%
• An average discount of 5% over the past five years
• A standard deviation of 2 over the past five years

 
This trust’s Z-score will be equal to:

 
Z-score =

Z-score =

Z-score =

Z-score = – 2.5
 

Are Z-scores useful?

 
Like many financial statistics, a Z-score is only really of use in relation to other bits of information. Seeing that a trust’s shares are trading above or below their average over a set period of time doesn’t tell you much at all.

For instance, a trust might look ‘cheap’ compared to its historical average but then it may have made a terrible investment that’s led to its share price plunging. Similarly, a higher premium might mean a trust is expensive but then it may justify that price by providing strong returns.

Other things, like the trust’s actual portfolio, its long-term goals, or why it may have seen some fluctuations in its share price are all factors that should be considered alongside the Z-score.

The other point to consider is what average is being used to calculate the Z-score. A one-year average, for example, is not a long period of time in the grand scheme of things, so it’s debatable as to how much utility that can actually provide you with.

Another point to consider is that there is no reason why a trust’s share price should continue to cling to its past average price or that it has even done so in the past. A trust could have an average 10% discount, for example, but never have spent any meaningful amount of time trading at that level; which is merely the number representing the average of all the levels it has traded at. If that was the case, then drawing the conclusion that a number below that level would be a good time to buy would be misguided.

In short, the Z-score has the potential to be useful to get a rough idea of where a trust’s shares are trading and potentially, when looked at in conjunction with other factors, whether it’s worth buying. But looking at alone or thinking it’s a panacea to all your investment trust problems is not likely to end well.