VC investments and Elaine's Sponges

The structure of Venture Capital funds means that VCs always have to execute on "online algorithms", in a setting of imperfect information

There is this hilarious paper by game theorist Avinash Dixit (of Princeton) that I never tire of quoting - it’s to do with Elaine’s contraceptive sponges. Now, I don’t watch TV shows, and wouldn’t have even known who Elaine is if not for this paper, but I’d consider this one of the most insightful papers I’ve ever read.

If you are like me, and don’t like watching TV shows, this snippet should be enough to give you context.

Basically, there is a contraceptive sponge that has gotten taken off the market. Elaine has bought everything that was in her drugstore. Now, she needs to carefully use them with all the men she meets.

When Elaine uses up a sponge, she is giving up the option to have it available when an even better man comes along. Therefore using the sponge amounts to exercising a real option to wait, and spongeworthiness is an option value. It can be calculated using standard option-pricing techniques. However, unlike the standard theory of financial or many real options, there are no complete markets and no replicating portfolios. Stochastic dynamic programming methods must be used.

In other words, she has to evaluate every date against every potential future date to determine whether they are worthy of the sponge.

Now this is eerily similar to how a VC fund is structured. The way it works (from what I understand so far) is that the VC raises a “fund” from a set of “limited partners”, and then has a time duration during which they need to deploy the funds.

So let us say that our VC has a $60M fund, and they have decided that they’ll invest $1M in every company they decide to invest in. This means they have the capacity to invest in 60 companies. Putting it another way, they have “60 sponges” (the same number Elaine buys in the above clip).

Every time they come across a prospective investment, their decision-making is similar to Elaine’s in this Seinfeld Episode - is this company “spongeworthy”? Because every company they invest in now is one fewer company they can potentially invest in the future.

Dixit uses Bellman equations (from dynamic programming; I last used them when I was a Quant at Goldman) to get a neat solution, but his basic principle is that Elaine should use her sponge iff the “value” of a man she meets is more than a threshold. And what this threshold is, is a function of the number of sponges left AND Elaine’s “discount rate”.

I’d first read this when it came out, when Bellman equations were a regular part of my job. Now, as an entrepreneur who is in the process of raising funds, how should I interpret this paper, especially given that I’ve just discovered that VC funds work like Elaine’s sponges? Apart from the fact that I need to prove ourselves “spongeworthy” to investors, of course.

• We have a better chance with VCs who are early in their funds. According to Dixit, Q* (the quality threshold for spongeworthiness) decreases with the “number of sponges left” (number of investments that a VC can make from this fund), irrespective of what the VC’s discount rate is. Leaving this picture from the paper here, without context:

  

• The “discount rate” (utility of investing today versus tomorrow) plays an important role in determining the Q*. If a VC can be infinitely patient (no compulsion at all to deploy funds), then Q* can be really high even with a large number of sponges left.

• The discount rate, however, is not constant across companies. If the VC is aware that there is sufficient demand for this company (lots of “live” processes), they will want to move quicker than their competitors. In the above table, this translates to a lower Beta. And lower Beta means lower Q*, keeping number of “sponges” constant. And so, when VCs want to move quick with respect to a particular company, they have lower thresholds

• This has nothing to do with the paper, but to do with Online Algorithms (which was the subject of my B.Tech. project at IIT Madras in 2004). What makes online algorithms hard is that you need to make decisions with incomplete information (you don’t know who is available later). One trivial way to ease the problem is to convert this into an offline algorithm.
  
  So instead of immediately deciding to invest, the VCs can decide to wait. And then after having seen a bunch of companies, “pick the best of the lot”. This allows them to make a better decision, subject to all the companies being available of course. The downside to this approach is discounting - with a low beta, there is a chance that an opportunity they saw earlier is not available any more

In any case, all of the above is tactical, and what ultimately matters is that we manage to convince investors that we are “spongeworthy”. Nothing else matters.

Oh, and we started talking to VCs earlier this week. And I happened to mention this blog (and sent links) to a few of the VCs we met. Which means some of them will be reading this! Like the paper, this should change nothing.

PS: Now I’m worried about my sideburns