Is venture capital truly a power law?

Hi, and welcome to the first post in our series about the quantitative methods we use at Element 14 Capital!

In our series, we will both introduce some key aspects of financial modeling and show you some practical examples of quant-assisted decision-making at our VC fund. We’re fully embodying the spirit of breaking down ideas so that they’re accessible to all and not just the few. So, we strive to provide you all with key investment takeaways and short, to-the-point explanations.

Modeling can be very nuanced, and often there is not a single solution to a problem, so feel free to share what modeling methods you would like us to consider and perhaps also write a post about. Especially if you’re managing a VC fund yourself, don’t hesitate to schedule a call with us to discuss what quantitative methods can be helpful to you, and we can also brainstorm together! Now, without further ado, let’s jump right into the first problem we’ll be covering.

The premise

Venture returns are often said to follow a power law. However, does that mean that we can use a power-law distribution to model the returns?

01: Power law gets the idea right

When you do a quick search on how to model venture capital returns, the answer you’ll get is a power-law distribution. This is intuitive because venture returns are highly concentrated, an idea often summarized with the 80/20 rule: roughly 20% of the inputs generate roughly 80% of the outputs. This is a heuristic, not a fixed ratio guaranteed by every power-law distribution. Very high returns on a single investment are possible, albeit rare, but they’re the ones that ultimately bring the money in. Cambridge Associates’ analysis illustrates that concentration: the top 100 investments accounted for at least 72% of total venture value creation in each investment year it studied, from 1995 through 2012.

A function that captures this heavy-tailed behavior is the Lomax distribution, a shifted form of the Pareto distribution whose support starts at zero. We chose one of the parameters governing the Lomax distribution to resemble the behavior of IPO returns.

Figure 1Model output

Median · 50 / 50Mean · average return

Tail index α — lower values put more weight in the extreme tail

2.50

Median (held fixed)

1.49×

Mean

2.98×

Below the mean

70.9%

Above 5×

16.1%

Showing the default view.

Reset

Show the underlying values

Statistic	Value
Median	1.49×
Mean	2.98×
Share below the mean	70.9%
Share above 5×	16.1%

Use the toggle in Figure 1 to mark the median at 1.49× or the mean at 2.98×. How do we interpret this, and what is the difference between these two? Essentially, the median tells us which point splits the probability in half while the mean tells us the average of the values drawn from the distribution. At the default settings, 70.9% of outcomes fall below the mean, and only 29.1% exceed it. The probability of exceeding 5× is 16.1%.

The mean being higher than the median is a direct consequence of the fact that most returns will be meager, but the occasional high returns will shift the mean upwards. Move the tail-index slider to see how the mean changes while the median stays fixed. This also shows how brittle the nature of venture investing can be because so much depends on an improbable outlier. A big fund can allow a few not-great investment batches because it has more opportunities for a rare winner to appear. But small funds such as ours don’t have this liberty.

02: Power law gets the risk wrong

The reality of partial loss returns

Some of you reading this might have already noticed that something is not quite right with the Lomax plot. Yes, it captures the idea of concentrated returns, but the way it handles losses doesn't match our working assumptions. Lomax spreads failing investments smoothly across small positive returns like 0.2× or 0.6×, whereas, if a company is struggling, a complete shutdown is often much more likely than a tiny positive exit, especially in the Silicon Valley environment. After all, the “go big or go home” mindset is very much real. That’s why, at Element 14 Capital, we opted to use a distribution that is a mix of a continuous function with a discrete probability of failed 0× investments. Instead of using one smooth Lomax curve for the entire range of possible returns, we split the distribution into two parts.

Figure 2Model output

Element 14 mixLomax baseline

Model

Element 14 mix

Mean deal MOIC

3.17×

Mass at exactly 0×

67%

10×+ of all deals

10.03%

Show the underlying values

Mix statistic	Value
Exactly 0×	67%
At least 1×	33%
Positive floor	1×
Mean	3.17×
10×+ share of all deals	10.03%
Tempering starts	50× (no hard cap)

Toggle Figure 2 to compare the Lomax baseline with the Element 14 mix. In the mix, the blue spike represents the 67% of investments modeled as a complete loss of the invested capital — 0×. The burgundy curve covers the remaining 33%, starting at 1×, or break-even.

The PitchBook report says that roughly one-third of seed investments fail outright, another one-third return less than the invested capital, and the remaining one-third generate positive outcomes. For our model, we decided to couple the outright failed investments with the partial returns so that we could model a more extreme case that is more relevant to the “go big or go home” behavior that we frequently observe in the kind of environment in which we make our investments.

The positive component in our mix model has the same $\alpha$ parameter as the Lomax distribution we discussed earlier. Both begin with the same power-law tail index, though their scales and exponential decay rates differ. Maurice calibrated the positive scale toward the PitchBook seed-return buckets, including a roughly 10% share of deals returning 10× or more. With the supplied parameters and normalization, that share is 10.03%.

Treating failed investments as harsh 0× returns makes our loss assumption deliberately conservative by discarding partial recoveries. It is open about the high-risk nature of VC investments, but does not prove that the mix is the true distribution of venture returns. In this comparison, the smooth Lomax baseline gives a much more optimistic picture of capital-loss risk. For a 5-investment micro-fund, the baseline estimates a 8.0% chance of capital loss, while the mix estimates 31.1%. The relative difference is even higher for a 20-investment portfolio: 0.11% versus 6.4%.

Figure 3Model output

Element 14 mixLomax baseline

Select a position on the chart or use the slider. The ratio is mix loss probability divided by Lomax loss probability.

Number of investments in the portfolio

10 deals

Portfolio size

10 deals

Chance of loss, our model

17.2%

Chance of loss, Lomax baseline

1.8%

Estimated risk ratio

9.6×

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Reset

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Portfolio size	Element 14 mix	Lomax baseline	Estimated risk ratio
1 investments	67.0%	38.3%	1.7×
2 investments	51.6%	24.1%	2.1×
3 investments	42.2%	16.5%	2.5×
4 investments	36.0%	11.5%	3.1×
5 investments	31.1%	8.0%	3.9×
6 investments	27.3%	6.0%	4.6×
7 investments	23.8%	4.3%	5.5×
8 investments	21.5%	3.2%	6.7×
9 investments	19.2%	2.3%	8.4×
10 investments	17.2%	1.8%	9.6×
11 investments	15.4%	1.3%	12.0×
12 investments	13.8%	0.98%	14.0×
13 investments	12.5%	0.72%	17.5×
14 investments	11.2%	0.56%	20.2×
15 investments	10.2%	0.43%	23.9×
16 investments	9.6%	0.30%	31.7×
17 investments	8.5%	0.23%	36.7×
18 investments	7.7%	0.19%	40.3×
19 investments	6.9%	0.15%	46.3×
20 investments	6.4%	0.11%	57.2×
21 investments	5.8%	0.081%	71.6×
22 investments	5.4%	0.073%	73.6×
23 investments	4.8%	0.050%	96.6×
24 investments	4.6%	0.030%	152.9×
25 investments	4.2%	0.025%	166.4×
26 investments	3.7%	0.026%	142.6×
27 investments	3.4%	0.009%	374.4×
28 investments	3.1%	0.018%	173.8×
29 investments	2.9%	0.008%	365.9×
30 investments	2.7%	0.014%	190.6×

Select a portfolio size in Figure 3 using the chart or slider. The marker follows both downside-risk curves, and the readout compares their estimated chances of returning less than 1× and the ratio between those estimates. The calculation assumes independent investments of equal size, before fees, carry, dilution, and follow-on decisions. The table contains 100,000 simulated portfolios per size. Rare-event probabilities — and especially their ratios — are noisy, so these are estimates rather than exact risk multipliers.

Risk and return go hand in hand in investing, as many of you know, and both are central to our interests whenever we perform a quantitative analysis at Element 14 Capital. In the next post, we will investigate how much increasing the number of investments decreases risk, as well as how much better a small fund needs to perform than a big fund with more investments for the risk to be justified to LPs.