A simulation of angel investing

Posted on April 27, 2010 by Jeff Miller

In angel investing, it’s the extreme distribution of payoffs that keeps things interesting.

If anything, it resembles buying a deep out-of-the-money call option, but with nonlinearity. If you win big you might find yourself in on the ground floor of the next Google or Facebook. That’s incredibly unlikely, but still possible.

More likely, you’ll end up with a solid 2x-5x return from a startup that grows into a viable long-term business. But most likely of all–by a long shot–you’ll lose your entire investment in another failed startup.

The most successful angels invest in a long series of deals over many years. They know that any one startup in isolation is a gamble, and to eventually hit a big return, an investor needs to draw repeatedly from the payoff distribution.

How many deals?

A discussion with Gabriel Weinberg on this topic piqued my curiosity about the relationship between the number of deals an angel invests in, and the shape of the payoff he or she can expect from that specific number of deals.

It’s clear that a single investment would have a terrible expectation and huge variance, but how about five deals? 20? 100?

How many angel investments are needed to make the combined payoff look attractive from an investment standpoint?

Monte Carlo simulation of angel investing

I coded the following simulation in Python. [view source code]

1. Create a pool of 10,000 different investors, each investing in D deals, with a fixed time horizon and a fixed distribution of payoffs. Randomly simulate each investor’s total payoff, then compute the mean and standard deviation of the returns in the overall pool.

2. Assume all D deals are made at the same time and that the payoff occurs in 5 years. When computing returns, use the Internal Rate of Return (IRR) over those 5 years.

3. For each angel investment, assume the following distribution of payoffs:

Prob. Payoff  
50% 0x lose entire investment
20% 1x get investment back
15% 3x  
13% 10x  
2% 20x  

(source: Gabriel Weinberg’s angel investing scenario spreadsheet)

Simulation results

- After the 4th deal, the expectation turns from negative to positive, but the variance is still huge.

- An investor would have to do 10 deals minimum to just have the expectation of breaking even. Meaning: losing money would be a > 1 standard deviation event. That’s still fairly bleak.

- After 20 deals, an angel investor cuts their risk to almost half of the 10-deal scenario while achieving an expectation that is very near to the best they can get. This looks a candidate for the sweet spot.

- Beyond 20 deals, the payoff statistics improve at a very slow rate. To reduce the risk to half of the 20-deal scenario, an investor would have to do about 80 deals.

- At 100 deals, the mean return reaches its unconditional value of 18.3% with a standard deviation of only 4.21%.

My takeaway from this experiment:

New angel investors should have the capital, time, and deal flow to support making at least 20 investments. Anything less, and the odds are against them.

Continue reading: A simulation of angel investing, part 2

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  • eah71
    nice post.

    this is a really nice proof of the efficient frontier in portfolio theory. personally though i suspect its all a bit more human than the mathematicians will have us think. when a portfolio gets above 20+ investments it gets harder for an active investor to maintain a deep enough subjective human insight into each of his investments. consequence of this is that the marginal impact that this savvy active investor makes on his total portfolio diminishes as the number of investments rises (above 20).

    so the maths is useful but lets not forget that:

    1. Both Merton & Scholes were behind LTCM in the late 90s and they chased their model off the cliff! (http://en.wikipedia.org/wiki/Long-Term_Capital_Management)

    2. if things get hard at 20 investments, active investor can always work as a team and scale things up!

    cheers

    ed
  • Nice idea. We always need more angel investors in the industry
  • It's the huge possible payday that makes people continue to invest in long-shot schemes. I think Harvard business school recently did a survey where angel-investors actually made more money than any other type of investor on average.
  • There is more discussion of this post on Hacker News:

    http://news.ycombinator.com/item?id=1298124

    I'm planning a follow-up post to address some of the issues raised with using rate of return as the measured variable.
  • egp4
    Vary the time horizon of investments so they vary systematically each year and also vary the pay-off timeline systematically with start-ups failing faster and less walking dead after 3 years.
  • This is a very interesting exercise. However, do you really thing that there is a 50% probability of loosing it all... I think that is much greater... I would like to see more "pessimistic" results... It is always better to undershoot in these situations. Good idea though.
  • djfische
    If your goal is to maximize your return for the risk given a known distribution of payoffs and their probabilities you need only to make a slight derivation to the Kelly Criterion and invest a percentage of your investing capital. This means that if your first investment fails, your second investment will be smaller than the first. However, if your second investment pays off, your third investment could be considerably larger since how much you invest is always a percentage of your total capital.

    Given the distribution of outcomes you described, you would optimally invest about 23.3% of your capital per startup. However, 23.3% is a very high output from the Kelly Criterion and in this case, I'd probably check the accuracy of your outcome distribution.
  • vessenes
    Hey Davey, does the Kelly criterion take into account the time value of money? My memory is that it glosses over this when it proves optimality. One difference between say horse betting and angel investing is that your bet has an unknown amount of time until payoff; measured in years. Functionally most angels don't want to wait 3-10 years to see the result of their 'bet' before making another one, even those who don't discount rates of return in their head very well.

    Perhaps in this case a more appropriate way to use the Kelly criterion is to use it to size out how much of your investments go to your first round of angel investments (e.g. the pool)?

    Of course, this is all from memory, so beware!
  • djfische
    Kelly was originally derived for cases where the time value of money (TVM) was not an issue. However, it is not a particularly complex derivation to add in TVM [1]. You simply have to have an accurate assessment of how alternative investments would do in the mean time. Derivations of the Kelly Criterion can deal with just about any case: TVM, complex outcome distributions, (inversely) correlated investments, etc.

    [1] http://www.castrader.com/kelly_formula/
  • vessenes
    Interesting, thanks!
  • Bob Miller
    If you'd like to refine your simulation with real data, you should check out Rob Wiltbank's research. He's been measuring real angels' success rates for a while.

    http://www.willamette.edu/~wiltbank/
    http://www.willamette.edu/~wiltbank/AtTheIndividualLevel7.pdf
  • Thanks. I've seen that research paper and it's a great resource. I would like to do a future post that explores some different payoff distributions and how they affect the simulation numbers.
  • JS Cournoyer
    Angel investors should invest in seed funds to coinvest with them and get access to enough deal flow to find 20 good deals to do. This approach would also provide them with a portfolio management and company support structure while they learn the trade. Less risky than going at it alone. Just make sure you partner with small seed funds, $100M or less, that make small initial investments, $1M or less, so that the interests are aligned.
  • scottswitzer
    Interesting analysis! Here are some other factors that could be interesting to model out:

    An angel who has 10 investments may lower the bar to find 10 more investments (and thus raise their chances for success according to the graph above). I wonder what the graph would look like if the % success rate was sliding depending on the number of investments that you have. Also, active angels who have time to spend with their companies (e.g. have fewer investments) could help change the % success rate (especially at the lower levels).

    Also, a 20x return is not unreasonable when investing at the angel stage. If you assume that you are investing at a $1M pre (pretty high for angel) on all of your deals, and assume that there are dilution events of 20% option pool, and three rounds of investing at 40%, 25%, and 15%, then you will need an exit of $50M to get your 20x return. Perhaps a 30x return (equivalent of $100M exit using my assumptions above) may not be out of the question...
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