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.

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?

I coded the following simulation in Python. View the source code here.

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)

- 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.

Related post: A simulation of angel investing, part 2