London has a new early-stage venture fund, called Hoxton Capital. This is great news for us in London, but also for the European startup scene in general. Read the TechCrunch article for more details.

One thing that caught my attention is their laser sharp focus on only the big exits, ignoring anything smaller than $\$ $1b: “We're entirely outlier driven, meaning we want to find companies that will become$ \1b+ companies” Given that $1b+ companies aren't created so often, this sounds to me like a very harsh utility function, and it got me thinking what the implications of this statement is on the investment strategy Hoxton Ventures should follow. Assume for a second that Europe will produce only a single$ \1b+ exit during the lifetime of Hoxton's first $\$ $40m fund, from the pool of companies they may invest in. (Hoxton Ventures partner Hussein Kanji estimates there's 3-5, see comments section) If so, we can reformulate Hoxton's investment strategy as follows: 'Find out which company will become the billion dollar hit, and maximise our ownership in that company'. Let us denote the percentage of ownership Hoxton will have in company$i$as$a_i$. After observing which company becomes a billion dollar hit (call this company$j$), Hoxton's perceived utility of its investment portfolio$U(a,j)$is simply the percentage of this company owned, that is$ U(a,j) = a_j. $Note that this utility function indeed ignores the ownership levels in all other portfolio companies, only cares about$j$, the big winner. How should Hoxton set the target ownership values$a$given this utility function? By maximising their expected utility, which in this case is:$ \hat{U}(a) = \sum_i p_i a_i $This expected utility should be maximised subject to the constraint that Hoxton have exactly$40m to spend, and therefore:

$\$40m = \sum_i v_i a_i $, where$v_i$denotes the valuation of each startup$i$at the time when they invest (corrected for expected dilution for simplicity) The solution to this very simple linearly constrained linear optimisation problem has a trivial solution: invest all your money into a single startup, one for which the ratio$\frac{p_i}{v_i}$is maximal. In other words: if you have a startup idea with nonzero subjective probability that turn out positive, simply start your own company :) It is easy to extend the analysis to accommodate multiple$1b+ exits. In this simple model, as long as your goal is to maximise your total combined share in all these companies, the trivial strategy is still optimal. I'm not suggesting of course that Hoxton Ventures should follow this naive strategy, but I think it's good exercise to evaluate what their words mean in terms of strategies, expected behaviour and risk.

Good luck Hoxton Ventures, it will be interesting to watch which companies you invest in (and how much).