Answer to reader quiz: likelihood of takeover

August 18th, 2009

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In our previous article, we gave our readers a short quiz to assess the likelihood of a takeover. The purpose of this quiz was not to be a lesson on takeover analysis- the takeover discussion was a red herring to distract you from the core of the issue. As Pete, one of our readers said,

Whilst looking at these takeover targets from a “what has happened in the past” perspective seems intelligent, takeovers rely on much more than is mentioned in those points.

Instead, the purpose of this quiz is to show you a very common mental pitfall that will deceive the minds of many unsuspecting investors.

Now, let’s take a look at this paragraph in the quoted Eureka Report article:

Of the six [takeover likelihood criteria], I find that the presence of strategic shareholdings is the strongest predictor of corporate activity; in fact, since 2000 about 60% of listed Australian companies receiving takeover bids had such strategic shareholders already on their register, even though only about 20% of total companies in the ASX 300 index fulfil this condition.

Upon reading that paragraph, it is easy to conclude that if a company fulfils all the six criteria, then its likelihood of takeover (based on statistical probability and assuming that all takeover bids are successful) is at least 60%.

Unfortunately, even if you believe that statistical probability is an accurate gauge of takeover probability (those who believe in that must read Failure to understand Black Swan leads to fallacious thinking), that number is wrong. The reason why 60% is the wrong number is because it is skewed by survivorship bias.

As we quoted an article in Mental pitfall: Survivorship Bias, the

… tendency for failed companies to be excluded from performance studies because they no longer exist. It often causes the results of studies to skew higher because only companies which were successful enough to survive until the end of the period are included.

That 60% is based on companies who were taken over. It does not include companies who fulfil those criteria and were not taken over. If we take the entire sample of all companies that fulfil those criteria, the proportion of those who was taken over could well be far below 60%.

Today’s lesson on survivorship bias is very instructive on how statistics can be misused to lie and deceive.

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