What AngelList Data Says About Power-Law Returns In Venture Capital

Supporters of the power-law hypothesis point to a handful of anecdotes on portfolio construction, but until now data that could rigorously evaluate the power-law hypothesis in venture capital has been absent. To evaluate the distribution of early-stage investment returns, we selected all of the AngelList platform investments prior to Series C that are at least one year old and have a valuation change, or that have already exited. That provides us with a universe of 1,808 investments to examine1.

Below is a figure of a power-law fit over the subset of those investments that have positive returns (realized or unrealized), before fees, on the platform2: (The right-hand bound of this figure is truncated at a 100x multiple for obfuscation; the fit line is made with untruncated data.)

The x axis of this plot is the log-scaled return multiplier of the investment (i.e., 1x = money returned without profit, 10x = 900% return). The y axis is the log-scaled fraction of positive investments that generate at least that return multiple. For instance, the red dot at (22, 0.01) indicates that 1% of positive investments have at least a 22x return. Since both of the axes in the figure are log-scaled, this is colloquially known as a “log-log plot” and is a standard way of showing power-law distributed data.

To confirm a power-law fit, we can compare the way it forecasts the distribution of startup valuations against a competing hypothesis. In a world where startups receive a sequence of well-behaved random percent changes in their valuations (e.g., the company's business improves or falls by 1% each day at random), then it is well-known that company valuations should follow a log-normal distribution.

While this distribution has many similar properties to a power law distribution on a log-log plot the log-normal distribution follows a parabolic curve rather than a straight line, with likelihood falling off at right tail of return multipliers. The orange line below shows the log-normal distribution that was fit to the observed spread of our real data:

The plot shows that the log-normal distribution closely fits the data for smaller multiples before beginning to diverge at around a 10x return multiple. The top-performing early-stage investment on AngelList has a return of over 100x; a return of this magnitude would be virtually impossible under a log-normal distribution (recall that this is a log-log plot, making the parabolic drop-off in likelihood of the orange line especially severe). Consequently, the AngelList data supports rejecting the log-normal fit in favor of the power-law fit.

Power laws are a continuum; the question is not only whether returns follow a power law, but also what kind of power law they follow, a question that we need AngelList’s data to answer. As background, power-law distributions are parameterized by their shape, α. As α goes towards 1 (its theoretical minimum) the power law distribution becomes more extreme. This shape parameter is crucial because any power-law distribution with α < 2 has an undefined expected value; if early-stage investments followed such a distribution it would carry the unsettling implication that any early-stage venture investment, at any price, is worth making because it could return an unbounded amount of money.

Using the open-source Python implementation of the fitting and validation routines originally developed in Clauset et al., we found that the shape parameter α of early-stage return multiples is about 2.3. This value means that early-stage venture investments have a heavy right tail of very high multipliers and that the early-stage investment universe is close to the α < 2 shape that implies unbounded returns to the asset class.

Peter Thiel refers to the putative power law of returns as “rooted in middle-school math”, and suggests that there is an easy, powerful simplification (“Only pick investments that can return your whole fund”3) that is complicated by culture and emotion. But I respectfully disagree with Thiel: these derivations are complex and have several important and non-trivial implications that we will continue to study in future posts. As it happens though, the most important implication runs directly contra Thiel’s portfolio construction advice to pick “seven or eight companies."

Power-law returns mean only top-quartile VCs beat the market

Thiel’s “seven or eight” investments seem fewer4 than what most early-stage venture funds put money into, so let’s round up to 10. Here are the distribution of returns for hypothetical investment managers that roughly followed Peter Thiel’s advice and made 10 investments out of the universe of 1,808 that we originally selected:

The black vertical line represents the market return, which is what you would get from writing an equal-sized check into all of the potential AngelList investments. All of the probability density to the left of that vertical line represent hypothetical portfolios that underperformed the market return. The most frequently observed outcome from a 10-investment portfolio, the peak of the curve, is slightly positive performance, well under the market return. This is a consequence of the power-law returns of venture capital: the typical manager fails to pick any outsize winners in their 10 chances, whereas the market portfolio is assured of selecting all of the return-driving winners. On the other hand, all of the probability density to the right of that line represents hypothetical portfolios that outperformed the market. It is important to note that the tail of return multipliers does not stop at the 5x shown on the plot but instead keeps going. Our experiments indicate that portfolios also showed a heavy right tail, just like their underlying investments. We found that the best simulated 10-investment portfolio from 50,000 random draws generally has around a 19x multiplier, far off the chart.

In the real world, of course, neither this level of performance nor the performance of the market is achievable to investors, because managers as well as AngelList fund advisers charge fees for their services. We assume for purposes of this analysis that managers charge a cumulative management fee of 10% of the fund’s capital, as well as 20% of carry for the portfolio as a whole5. Investing on AngelList, by contrast, typically means paying carry of 20% of the positive returns on any single investment6.

Here is the same plot, after including fees from managers for the distribution of portfolio returns and fees from AngelList in the market return:

While the effect of fees is to reduce the performance of both the market and portfolio returns, the typical hypothetical manager in our experiments still underperforms the market by a large margin. Our simulations demonstrated that the management fees charged by funds tend to outweigh the mitigating effects of netting returns within a portfolio, which results in an increase in the fraction of managers that are outperformed by the market portfolio after taking into account fees.

Prior blog posts on power laws have advocated the use of simulated data for robustness, since the random realization of outliers can so substantially skew summary statistics. Accordingly, we also ran this same 10-investment portfolio experiment over several simulated sets of early-stage investment returns from 1,808 investments. We made these simulations by drawing investment returns as follows: first, we test a potential investment for whether it will lose money or not, by doing a uniform random draw against the fraction of our real 1,808 investments that have lost money. If the investment loses money, it gets a return sampled from the real set of money-losing AngelList investments. On the other hand, if the investment makes money, its return is drawn from a power-law distribution with shape parameter α ~ 2.3, the best fit value that we found above. We then simulated the returns of 10-investment portfolios as well as the market return on the same 1,808-investment universe, so that the two competing approaches were fairly compared on identical universes of potential early-stage investments.

Real DataMedian of Five SimulationsMarket Return vs. Hypothetical Manager ReturnsMarket > 66% of ManagersMarket > 73% of ManagersMarket Return vs. Hypothetical Manager Returns Net of FeesMarket > 82% of ManagersMarket > 84% of ManagersMarket Return Net of Fees vs. Hypothetical Manager Returns Net of FeesMarket > 74% of ManagersMarket > 78% of Managers

The experiments on simulated returns have the market portfolio outperforming even more hypothetical managers than our experiments on real returns (78th percentile for the median simulation vs. 74th percentile for the real data). The implication is that the market’s outperformance of the typical portfolio can be explained by the power-law returns of investments rather than another systematic or idiosyncratic artifact of AngelList’s specific investment universe. Put another way, if we expect venture returns to continue to follow a power law in the future, then the market will continue to substantially outperform the typical venture portfolio.

The 74th-percentile figure that we found from our real data seems to be quite meaningful in the larger context of venture capital. There are many VC herd-following practices, and one of them is the signaling value of being a “top-quartile fund.” The desire to signal that you have been, currently are, or have the potential to be in the top-quartile could be a folk-wisdom approximation to the result we produced here through a lot of math and data: it takes a top-quartile VC fund to outperform the early-stage venture market.

An index for venture capital?

After decades of index-investing success, big investors like pension funds have begun to replace fund managers with indexing strategies. For instance, CalPERS exited the hedge fund space in 2014, and has no plans to re-allocate towards it in the future. Perhaps those same investors should give up on picking early-stage VCs as well?

Footnotes

1 We stress-tested these results for several different, a priori reasonable ways to select the early-stage investment universe. The results all seemed to be qualitatively and quantitatively similar.

2 Money-losing investments do not appear to follow a power law; this is consistent with Clauset et al., the original paper on empirical power laws, which suggests that it only makes sense to discuss power laws in relation to values greater than some lower bound.

3 VCs generally put their own spin on Thiel’s advice; I have heard VCs tell me “I expect every check I write to turn into a billion dollars” or that a “Billion (dollar exit) is about 10x too small for me.”

4 We tested different several different portfolio sizes for our hypothetical fund managers; smaller portfolios led to a wider spread of returns and larger portfolios led to a narrower spread of returns but the performance of the market portfolio was consistently around the 75th percentile of manager returns, both net of fees. The exception was for very large portfolios (100+ investments) where management fees pushed manager returns consistently below the market return.

5 This is a simplification of the fees that fund managers actually charge. It does not take into account management fees (generally 2% or more a year of called or committed capital) or waterfall structures around carry based on returns. But since we assume a fairly conservative value for total management fees over the life of a fund we believe it is more likely that we are under-estimating, rather than over-estimating, the real fees that LPs pay to their managers.

6 Observe that it is not immediately evident which approach results in higher fees, because AngelList’s platform takes 20% of every positive investment, while managers’ losing investments are netted out from their positive investments before taking carry.