VC fund allocation and Conditional Probability

Image via Wikipedia

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.

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.

New report on Potential for Renewable Energy use in the US

http://www.nap.edu/napbookwrapper.swf

1. Renewable could account for 10% of US energy needs by 2020
2. To increase the usage of renewable energy greater than 10%, significant investment, technological progress, policy changes and incentives need to exist
3. technological developments and consistent policy will need to be coordinated with manufacturing capacity and access to capital in order to accelerate deployment of renewable electricity

Icelandic Krona vs US Dollar – A Power Law Distribution

Image via Wikipedia

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.

Related articles by Zemanta

McKinsey agrees…

English: Benoît Mandelbrot at the EPFL, on the 14h of March 2007 (Photo credit: Wikipedia)

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!http://mitworld.mit.edu/flash/player/Main.swf?host=cp58255.edgefcs.net&flv=mitw-00235-mandelbrot-27nov01&preview=http://mitworld.mit.edu//uploads/mitwstill00235mandelbrot27nov01.jpg

Are bank executives immune to Randomness?

Well, it was a dumb question but I don’t know then why every journalist and research papers keep asking the question:

How did the bank executives takes so much risk and were disconnected with the risk reward relationship?
I have a simple answer, they are HUMAN and we are wired to miscalculate risk, read the work of Daniel Kahenman & Amos Tverskey and Dan Gilbert… they have proved that everyone, I mean everyone of us has what they termed as Heuristics and Biases. Heuristics are something like a short cut and bias is of course Bias. We tend to make decisions based on our Heuristics and our biases, there is no complicated risk reward equation involved in dealing with the decisions the executives of the banks were making. Well, how did they get this right before… simple, they got lucky! period!