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Power laws with pooling: a better model of venture returns

TLl;DR:

In the last post I built some models of venture portfolios of different sizes based on the idea that venture outcomes are powerlaw distributed. The conclusion there was, for venture portfolios, more investments is better with around 150 being table stakes. Those models assumed each investment was new minted from an infinite world of possible investments, which is unrealistic. This model I think is more realistic and overall dampens expected returns, without changing the overall trends.



In the last post we simulated over 45M independent outcomes (sum(x=5->300) x*1000).

But in practice portfolios are not completely independent; VCs often invest in the same companies as other VCs. Our first model is more like a simulation of venture builders, where the fund creates its own independent businesses.

How about instead we create a pool of businesses that receive investment, and our portfolios sample from this pool? In other words, in the investing life of a fund, a finite number of funded businesses will be created. Every fund will be choosing from that pool of businesses.

How big should that pool be ? Well according to crunchbase, in 2016/2017 around 3,500 angel and seed funding rounds happened globally per quarter:


Let's say there's some under-counting, and that the number is growing, and round up to 5,000 rounds per quarter.

So in the 3-5 year investing life of a typical fund, there's a unverse of 60,000-100,000 companies that they theoretically could invest in (of course they probably couldn't see that many deals, but that's another story).

Let's split the difference, and take a pool size of 80,000 companies. What I'm going to do next then is generate this pool, and have each 'fund' draw its investments at random from the pool. Here's a histogram of 10,000 companies drawn at random from this pool, compared to the correlation ventures data, and the full powerlaw distribution:

Reasonably similar.

How about the performance of the funds drawn from the pool ? 


Compared to the full powerlaw model:


So very similar - hard to tell the difference.







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