# Angels with fat tails

By Shaun Hendy 01/03/2010

A couple of years ago, I had a chance conversation after a Dragons’ Den exercise organised by Industrial Research Ltd.  (I didn’t go so well in the Dragons’ Den — I won’t go in to the gory details, but suffice to say that someone later said that they could tell I was a university lecturer!)  Afterward, a Dragon talked me through his day job as an Angel Investor.

His first point:  when evaluating an investment, he wanted to know the maximum pay-off, rather than the most likely pay-off.  He already knew that the most likely outcome of any of his individual investments would be failure — sure things are backed by banks, not Angels.

His second point:  he expected to pull the plug on nine out of every ten investments within two years.  He then relied on the sale of the tenth to repay his fund with net profit.

On the face of it, this may not surprise you.  An Angel’s business is that of making risky investments, and a pay-off from one in ten is much better odds than playing Lotto.

But one in ten is an interesting number.  If the value of each investment was distributed on a bell curve, it seems unlikely that the Angel would make a profit by winding up nine and keeping one.  Instead, it appears that the Angel relies on the Pareto principle — that is, almost all of the pay-off from his portfolio will be generated by just one of the investments in it.

In other words, the distribution of pay-offs has what is sometimes called a ‘fat tail’.  A bell curve (more technically, a normal or Gaussian distribution) does not have a fat tail:  the likelihood of large pay-offs falls off exponentially.  For distributions with fat tails, pay-offs are not necessarily clustered around the mean, and the likelihood of large pay-offs drops off more slowly.

As I’ve come to learn, fat tails often crop up in economics, but my conversation with the Angel was the first time I had come across a fat tail outside of physics.  If you’re a regular reader of this blog, you will have seen a fat tail or two when when we looked at the distribution of patents among applicants.

Does this tell us anything about innovation?  Angels invest in ideas, which are then tested in the marketplace.  Some of these ideas fail or have little impact, but the way that Angels invest does suggest that there is a fat tail of ideas that succeed spectacularly.

This may be something that is characteristic of innovation.  Thomas Kuhn, author of The Structure of Scientific Revolutions, argued that science did not progress by incremental accumulation of knowledge, rather it developed via occasional revolutions called paradigm shifts.  Kuhn called the humdrum stuff that most of us scientists do in between paradigm shifts ‘normal science’.

It is quite tempting to draw the analogy between Kuhn’s scientific revolutions and the Angel’s one in ten investment that pays out.  What if the impact of scientists’ work and ideas was distributed according to a Pareto principle?  In this picture, Kuhn’s paradigm shifts would be those bits of science that live way out in the tail.  However, the analogy is not complete; a scientific Pareto principle would require that the impact of science is distributed across a continuum, rather than in a dichotomy, where some ideas shift paradigms, while others have no outcome.

I will explore this idea further in another post.

### 0 Responses to “Angels with fat tails”

• […] the arrival of far-reaching innovations like the internet, wars or terrorist attacks. As I have discussed previously, such rare events seem to be important for progress in science; the â€˜Black Swanâ€™ of science […]