How any investor/entrepreneur can (almost) guarantee a 5x return

[First published on Medium in 2013. Read it again recently, decided to vanity post on LinkedIn.]

How tech start-up entrepreneurs and angel investors survive in Extremistan: Applied AntiFragility

Nassim Taleb is a great thinker (Wikipedia describes him as an ‘epistemologist’, which if I get to be born again, I am going to make my new-life-goal), and an equally great bombast. I remember when I read The Black Swan back in 2007?—?I felt like he was repeatedly kicking me in the Gaussians until I understood – no, agreed with?—?his points. Of course, when one of his Black Swans trampled all over the financial centres in 2008, one couldn’t help a kind of masochistic pleasure in recalling those ‘epistemological’ bruisings, for here, at terrifying scale, was precisely his point.

I recently listened to Taleb on the Stanford Entrepreneurial Thought Leaders Lectures podcast, where he was talking about (his new book) AntiFragile. Primarily, Section IV: Optionality, Technology, and the intelligence of Anti-Fragility. And it got me thinking how of what he was saying in that lecture related to a bunch of work I had done at the back end of last year running Monte-Carlo simulations on a probability distribution derived from arguably the biggest data-set of Angel returns (on US start-ups): something which I think is worth sharing.

Extremistan

To give the Anti-Fragile idea a one-sentence elevator (and therefore to do it virtually no credit at all): It is the idea that we can be set up in such a way that we can benefit from randomness, opacity and volatility?—?specifically in those systems (for which there are many) that contain Black Swans. In Extremistan, these systems dominate. One Black Swan win can crush all losses?—?or one loss can crush all wins. But we have no (real) idea where that win (loss) comes from. Those with the temerity to make predictions are made to look like fools.

Both Tech entrepreneurs and investors live in Extremistan; Taleb specifically calls out Google and Microsoft as Black Swan companies.

Randomness

This is not the place to go into detail the dissonance that comes with (at least some) knowledge of the ubiquity of randomness but armchair pop-scis have been treated to some excellent recent expositions: Nobel Prize winning Daniel Kahneman’s best seller Thinking Fast & Slow, Leonard Mlodinow’s The Drunkards Walk and even Taleb’s own Fooled by Randomness – and, suffice to say, we should all be armed with at least a passing appreciation of its power to deceive. Not least – its power to hoodwink into seeing patterns where non-exist. Or, famously, to attribute skill to a VC or fund manager who is just lucky enough to be that VC or Fund that happens to be on the far right of the gains spectrum in a place wholly predicted by the Rules of Randomness: especially in an industry of extreme volatility.

Convex Function of Chaos

Lets go back to our one-sentence elevator of anti-fragile: that we can be set up to benefit from randomness, opacity and volatility within a Black Swan system. What does this mean? Taleb, in his own post on Edge, puts this in simple terms, with the use of a straightforward mathematical function. One that shows an asymmetry of gains/losses under a stochastic process – where gains/losses are dependent upon the determination of some ex anteunknown (set-of) variable(s) (x). What is important here, is that determination of that set is sufficiently, and unremittingly, complex; that even using all of the universe’s atoms as a computing machine we could still not determine x. And working out whether any start-up will be a success is likely to be this complex: Pinterest, Instagram, anyone?

Figure (i) (from Taleb himself) demonstrates one of these asymmetries. Specifically, where the function is convex to chaos (or randomness, or volatility or luck or whatever). It is asymmetrical because the gains from the variable x being at (say) x+10 are different from the losses at (say) x-10. And it is convex because the gains at x+10 are greater than the losses at x-10.

Optionality of Things

AntiFragile is no more or no less complicated that option trading. You have the right but not the obligation to follow a bet, therefore your downside risk is managed (ideally minimized) but you can follow the gains, so your upside is maximised.

Investors, of course, know this well. It is the essence of seed investing.

If fact, Taleb himself has called it the ‘Optionality of Things’: and his post on Edge.org relates it to the optimum method for making gains in Research.

Fragile Swans

Taleb himself holds entrepreneurs up as heroes. And I think there is little doubt that tech start-ups have the opportunity to show Black Swan type returns – but it is far more likely that those start-ups will fail, bringing untold woe to the entrepreneurs (and some-told woe to their investors). Here’s to the risk-takers.

The AntiFragilista embraces the individual failure – or at least he is philosophical about it?—?for, that failure delivers knowledge, and, they have set themselves up in such a way that the loss (their downside risk) has been minimised. They also know that despite all the losses they suffer, when they hit that Black Swan – that start-up that hits global scale and millions of dollars of value – all those small losses will be swamped.

Which is all very well, but raises an obvious question. Can we use data to work out how likely it is that we can catch the tail. Because, if we had at least a probablistic idea about the regularity of the Black Swan in any particular system, then we can be even more anti-fragile.

In the Edge article, Taleb specifically states:

‘A “1/N’ strategy is almost always best with convex strategies… reducing the cost per attempt, compensate by multiplying the number of trials and allocating 1/N of the potential investment across N investments, and make N as large as possible. This allows us to minimize the probability of missing rather than maximise profits should one have a win… ‘

In other words, he is acknowledging that in the real world there is the real possibility that with finite resources one could run out of resource before a Black Swan swims along.

Which brings us to the relevant question. How many bets – and at what level – should we be making?

Chasing the tail

Following the trail of a Techcrunch article, I first came across the work of Robert Wiltbank – who had, with his graduate students, put together the largest data-set of angel returns, authoring a number papers?—?and then, via the same Techcrunch article, I managed to reach a very interesting man indeed. His name is Irving Ebert, he is out of Ottawa, is an ex engineer by trade, is a prolific angel investor, is Co-founder of PurpleAngel and founder of ArchAngel Capital. Irving, who, while working at Nortel, worked with Professor Eric von Hippel at MIT (who is best known for his work developing the concept of user innovation – that end-users, rather than manufacturers, are responsible for a large amount of innovation) to see how – even when the web was in its relative infancy?—?they could tap internet users as a source of product innovation. His is a technical but commercial mind.

Irving, as leader of an angel group, was specifically interested in analysing the potential performance of pooled angel funds such that they are invested on a portfolio basis across a number of investee companies. Given access to Robert’s published and unpublished data, Irving derived a probability distribution function upon which he performed Monte-Carlo simulations of many thousands of cycles to make predictions of returns for fund portfolios of n-companies following his own recommended investment strategy. That investment strategy is proprietary to him, and can’t be revealed here, but Robert – in his Techcrunch article – described Irving’s work as ‘outstanding’ – and so it is.

What was crucial from the data was that it showed that there is tail of ~7%of angel funded (assuming we make a ￡300k investment) start-ups hit a 20x return. And, what was equally as interesting, is of that 7% it was equally likelythat the return would be 100x+ as it would be 20x.

Irving’s general conclusions are under wraps, however, Irving was kind enough to share his methodology with me: and has had me working hard creating my own probability distribution function so I could perform my own Monte-Carlo simulations. He has kindly allowed me to publish some of my results.

Lets do stats – the AntiFragile angel investor

Figure 1 below shows cumulative distribution functions representing results of Monte-Carlo simulations based on the PDF derived from the Wiltbank data for 1, 10 and 40 companies. The vertical (y) axis is multiple return for the fund, and the horizontal (x) axis charts the likelihood of that return. The mean is a constant: the mean return on my PDF (which is rather more coarse grained than Irving’s) is about 5.25x – Irving’s is different, but not by much. So, looking at the n=1 line, it demonstrates that there is a 55% probability of a zero return – which matches what we know about start-up failures.

The really interesting stuff lies further down – and further up – the curves. On the n=40 line, at what probability should we expect a zero return? The answer is – somewhere between 0 and 5%. In fact, there is only a 5% probability that we would get a 1.4x return or less. Or, to put it another way, there is in the order of a 95% probability that we will get at least 140% of our money back.

But, at n = 40 it also predicts a 40% probability of achieving an almost 6x return, in fact there is a 10% chance of getting an almost 9x return. A nine times return over 5 years is an IRR of ~73. All of this with a 95% probability of getting at least 140% of our money back.

This sounds like an antifragile angel investment strategy to me.

The AntiFragile Entrepreneur

But what about those lowly entreprenurs. Unlikely to afford the time, energy or expense to make tens of low-level investments in the hope of catching the Black Swan, are they, in the majority, left only with Taleb’s gratitude and honor in sacrificing themselves at the Great Altar of Extremistan?

I’m not so sure. After all, the Optionality of Things is not just about money (and even if it was, by starting 10 companies you still have a 50% change of getting a 3.36x return). It is also about time, interest, capacity, knowledge, skill: all of which should be allocated on a minimised downside risk basis while we await the Black Swan. Why should the Optionality of Things simply be vertical? Why not horizontal? Remember, the essence of optionality is theoption not the obligation to follow any particular stream: to tinker, to bricolage; and to not continue unwavering along any path based on grand narrative and ex ante ‘knowledge’ (by the way, the similarity to the Lean Startup principles has not escaped me). For, as Taleb himself says, Understanding is a Poor Substitute for Convexity.