Valuation, Lean Startup and Uncertainty

Image via WikipediaAlbert Wenger has an interesting post about Valuation of startup companies and the main challenge in valuation of company on the exponential growth path. I could not agree more, this is the same problem that I have highlighted several times with my posts on Power Law and the failure of extrapolations and the Normal Probability Distribution. Albert points out a practical challenge from both sides of the venture table, as an entrepreneur you are not sure how long you need the funding to hit that inflection point and as an investor you are struggling to make sure you are not paying too much for a business that might not pan out. The solution is actually "common sense" but of course "Common Sense" is never "Common Practice", I digress, the solution is to get to a sustainable model where your revenues/cash flows funds the company... you grow your customers base, revenue and cash position... Problem solved! Really, is it that simple, YES it is. 

Image via Wikipedia

Of course all those companies that are building their business model on the Hope that they will draw enough crowd onto their site where in they can monetize the traffic with ads are working on a loosing premise. I know Huffington Post just got paid etc but there are so many content aggregators why only Huff Post got bought out? why not the others? once again the theory of the power law works here. So my take on this is very simple, entrepreneurs should focus on creating value by solving some problem for which someone is willing to pay a price for. If the universe of those willing to pay are price is HUGE then you are onto something.

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My first academic paper - Can Power Law help us avoid high impact tail events?

As I wrote about previously, I have been accepted into the PhD program in Economics in University of Iceland. The first paper that I wrote is complete and has been accepted to be published as part of the University of Iceland's annual journal. In addition to that I will be giving a talk about the paper on October 30, here is the program details. Here is the link to paper:

Can Power Law help us avoid high impact tail events?

Abstract:

Some observable data related to social sciences can be described using the power law distribution. Can we understand the impact of tail events better if we used the power law distribution instead of the typical Gaussian 'Normal' distribution? The purpose of this paper is to investigate this premise in the context of the Icelandic economy and present the findings.

"The traditional Gaussian way of looking at the world begins by focusing on the ordinary, and then deals with exceptions or so-called outliers as ancillaries. But there is also a second way, which takes the exceptional as a starting point and deals with the ordinary in a subordinate manner - simply because that 'ordinary' is less consequential"
                   - Nassim Nicholas Taleb and Benoit Mandelbrot

Although power law distributions do not have the predictive power of a Gaussian Normal distribution, can Power Law help us avoid the high impact Tail Events?

Policy implications if we use Power Law distribution

I have been working on my first paper with the title "Can Power Law help us avoid highly improbable tail events?" the premise of the argument is that if some economic variables fall in the Power Law distribution then policies associated with those economic variables need to be handled differently. For example, I am taking the problem of the Icelandic Krona, I have written about the Icelandic Krona before and I am convinced that it follows a Power Law distribution.

If we know that ISK follows a power law distribution and future fluctuations in ISK are going to follow the Power Law distribution should the Icelandic state still use the currency in its current form? or should it switch over to a more stable currency say the Euro? this debate is on-going in Iceland and I am afraid people are viewing this decision with their political lense and not the economic lense.

Just a simple switch in the probability distribution of the ISK has some serious policy implications. Lets do a simple thought experiment: The Financial Supervisory Authority of Iceland used a 20% devaluation of the ISK as a basis to stress test the banks in Iceland, why did they choose 20% because they thought ISK followed a Gaussian Normal Distribution and a 20% devaluation is a 2 or 3 sigma event or a very low probability of occurance, however if we change the distribution to Power Law a 20% devaluation of the ISK has a much higher probability therefore they would have chosen a much higher deviation for the stress test say 50% this would have shown the true color of the Icelandic banks capital adequacy and vulnerability to wholesale funding. The question is if the stress test had been done in 2006 when Iceland had a mini crisis, the FSA could have put a stop to the aggressive borrowing by the Icelandic banks which in turn would have reduced the leverage of the companies in Iceland and the citizens.

So choosing the right probability distribution matters! atleast that is the basis for my PhD thesis lets hope the thesis could influence some policy choices.

VC fund allocation and Conditional Probability

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I had a very interesting discussion with a friend of mine yesterday. I was suggesting to him that Venture Capital funds should allocate funds such that 15% of the capital goes into VC companies, 5% goes into growth companies (i.e companies that have stabilized the products or services, are generating cash and have broken even) and 80% should be cash or cash equivalent.

He made an argument that an investor wanting to invest in a VC funds would not choose the above allocation. I asked him to ellaborate and he said that the investor will not get the total bang for his buck... he said that if the above fund´s VC allocation returned say 100% of the allocated capital the investor would only get 15% of that 100%. Sounds logical but this is precisely the problem with our view of the world and our ability to calculate probabilities. We think about only the success scenario, we don´t think about failure and the proabilities of failure.

Lets do a thought experiment of comparing two funds:

1. A fund that invests all the capital into VC companies

2. A fund that does capital allocation similar to the one described in the first paragraph

We need to think of alternative universe of outcomes to calculate the expected return from the above two funds, lets conjure one for simplicity:

VC companies return 100% of capital invested with a probability of 50% and return -100% (i.e you loose all the capital) with a probability of 50%. Growth companies return the capital invested and Cash returns the same at the end of the investment time for simplicity sake.

Given the above outcome what is the Expected return for the above two funds, say for an investment of $100m?

Expected Return = P(success) x Return + P(failure) x Return

Fund 1: 50% x $200 + 50% x (-$100) = $50m

Fund 2: 50% x $30+ 50% x (-$15) + $5 + $80 = $92.5m

Even the above simple payoff matrix gives the second fund a return higher than the all VC fund. However the real world is much more complex and the payoffs and probabilities are much harder to calculate. In addition to the above when we do capital allocation there are time frames, return expectations and conditional probabilities involved, this further skew the results.

The above payoff matrix gives us different results when we add conditions to the problem:

What is the probability of Fund 1 giving a lower return than Fund 2 given VC companies all return 100%? or we can flip the question

What is the probability of Fund 2 giving a higher return than Fund 1 given VC companies all return 100%?

The above question needs us to calculate the probability of a VC company being a success or a failure and the distribution for VC success follows a Power Law. I think most VC fund managers understand that but I don't have data to prove it. My fear is that maybe fund managers do not compute probabilities using the Power Law but the Normal Gaussian Bell Curve, when we do that all the above analysis and results are incorrect.

My previous post about ISK

I started writing a blog entry about the ISK on Friday and completed it only today, but while I was doing that I found an interesting link through Zemanta, a tool I use with blogger. It was a question posted by Fred Wilson, in his blog:

Does Venture Capital funds fall within a power law?

I have been thinking about that myself and maybe his question and analysis needs to be revised again. He is analyzing the exits by VC funds and trying to figure out what is the exit percentage and size... it is an interesting problem as VC funds are often made to justify their existance with their return rate and sucess rate.

Icelandic Krona vs US Dollar - A Power Law Distribution

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The Icelandic Krona currency exchange index follows the Power Law, it can be seen in the most rudimentary of analysis...

Here is the analysis of ISK-USD exchange rate data for however long I could get, a simple histogram shows visually that the exchange rate is distributed by a power law. In addition, I was able to do a Log plot of the observations and it clearly follows a path that should give us

enough indication that the ISK exchange does not follow a Normal "Bell" curve distribution.

However, last week I was talking to a currency trader and he told me that before the crash of the Icelandic Krona last year, they calculated the proabability of ISK crashing and they found it to be a 8 sigma (read highly unlikely! or A Black Swan) event... the fact that it happened proves atleast to me that the methods and theory used to analyze the ISK is not correct. I am writing a paper with Dr.Helgi Tomasson with University of Iceland with the title "Can Power Law help us avoid the highly improbable tail events?" hopefully we will be able to answer the above question.

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McKinsey agrees...

Here is the latest article from McKinsey Quarterly, the summary is Power Law works in the Economic field and the implications for policy choices are very serious to ignore. Just what Dr.Taleb, Mandelbrot and others have been saying for decades. Listen to the video below where Mandelbrot explains his theory... fascinating stuff!

Thinking on the Margin: Do You Know What You Don't Know?

Thinking on the Margin: Do You Know What You Don't Know?