Modeling Returns in Venture Capital: Power Law Hybrid

Before building models to sensitize the returns of different portfolio constructions we need a representation of an individual company's return. Empirically we know roughly 50% - 75% of seed stage companies die and that the hyper success case is, well, hyper-rare, maybe 1 in 200. Of course any mathematical representation of the returns likelihood of a seed stage company is steeped in uncertainty. The best we can do is use a distribution that doesn't seem too implausible. 

By many people's estimation the Power Law is the most 'usable' and 'accurate' distribution to model seed stage returns. The Power Law is also the basis of our approximation. But we create a mutant hybrid with the Log Normal because in generating and experimenting with various Power Law configurations it seems a little too harsh on the death rate (>75% die in many cases.) The Power Law also seems a little too willing to produce hyper-success cases (1 - 2 in 100.)

In sensitizing and understanding the returns of our portfolio constructions, these two 'errors' (the lower than realistic death rate and higher than realistic unicorn case) can be accepted. Indeed in any fund there must be some 'unfair advantages' that the fund manager has (superior network, proprietary deal flow, superior selection rate etc.) for he fund to exist in the first place. For Hone Capital machine learning models support our lower seed stage death rate and the AngelList network supports the higher than normal unicorn rate. 

With return (measured in multiple of original post-money valuation) the Log Normal is run with the mean at 0.3x and the standard deviation at 1.0x. The Power Law is modeled using a Power Law coefficient of 1.159. Both shown below (vertical axis cut for clarity.)

With these coefficients we can see that the 'effective' death rate is approximately 40%, another 40% return 1.0x - 3.0x heavily weighted towards the former and around 1.5% go to exit at 'unicorn' status. It is pretty clear these are just approximations which help us get a sense of the sensitivity of a portfolio construction. They are at best over-engineered and at worst wrong.