A simulation of angel investing

http://jmillerinc.com/2010/04/27/angel-investing-simulation/

by epi0Bauqu • 16 years ago

47 14 16 years ago

gizmo2• 16 years ago

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

The author uses expectation in a different way than I usually do, I consider this the definition of the expectation:

    PAYOFFS = [ 0, 1, 3, 10, 20]
    PROBS = [0.50, 0.20, 0.15, 0.13, 0.02]
    PAYOFFS.zip(PROBS).inject(0.0){|s, i| i[0] * i[1] + s} => 2.35

So you're expected to double your money (and then some) for each investment.

Given that you have to be an accredited investor ($200k+ income or $1m+ net worth, iirc) to do an angel investment in the first place the investment shouldn't negatively affect your quality of life if it doesn't work out. So unless you can get a higher return than 2.35x somewhere else, the angel investment seems like a really good deal to me.

po2• 16 years ago

I saw your original comment and started to respond, but in the edited version it is much more clear what you mean.

> So you're expected to double your money (and then some) for each investment.

Over time that is true. The average over time is what to look for. With a single investment and you can expect to lose your money.

gizmo2• 16 years ago

But why does the average over time matter more than the expected result? Any single investment is (according to the numbers) going to make a significant expected contribution to the economy and to the investor. So why not go for it?

According to this logic it would be bad for 20 people (with a net worth of $1m+) to invest $100k each, but it would be good for one wealthy person to make 20 investments of $100k each. That doesn't compute.

kaddar• 16 years ago

I definitely agree, the article uses some messy statistics.

An additional concern is that if your argument is that 10 investments reduce variance, you want to keep in mind correlation effects. The probability of one investment failing is likely to be dependent on other investments from the same domain, due to the nature of booms and busts.

gjm11• 16 years ago

Everything of interest here is a consequence of the author's decision to use annual rate of return as his figure of merit.

Simplified example: you have a pool of investment opportunities where with probability 0.01 you gain $100 and with probability 0.99 you lose $1. So your expected gain from making a bunch of these investments is a gain of 1c per investment. If you make a million of them then with very high probability you gain something very close to $10k in total, on your $1M investment, a 1% gain. Now, suppose each of these investment opportunities takes 10 years to do whatever it does. Then (to first order) your return rate is 0.1% per year, more or less all the time; so your average return rate is about 0.1% per year. So far, so good.

Now suppose that you can only make one investment. Then your annual return rate is 99^(1/10)-1, 1% of the time, and -1 the rest of the time. Key point: 99^(1/10)-1 is about 0.6, which is a lot less than 99/10. So your average return rate is now absolutely wretched.

So, have we just discovered something interesting about the real costs and benefits of high-variance investments, or merely blinded ourselves with science? The latter, I think. I'll try to explain why.

Why use averages to summarize things, in the first place? Because they describe what usually happens in the aggregate. When they fail to, or when that isn't what you care about, averaging is unlikely to tell you what you want to know. So, does our averaged return rate tell us anything useful about what happens in the aggregate? Why, no. Suppose A and B both invest $1; A loses his money and B doubles his. And suppose each of these things happens over 10 years. Then their return rates are -1 and +0.072 respectively; their average return rate is extremely negative; but A and B collectively neither gained nor lost any money. Similarly, if you make a whole lot of investments then the average of your return rates is not the same as your overall return rate. (That's exactly why the author's calculation produces the results it does.)

Here's another way of looking at it, which I actually prefer. There's nothing magical about annual return rates. But the author's curve would look completely different if he plotted six-monthly return rates (it would be worse [EDITED TO ADD: than the author's annualized curve) for smaller numbers of investments) or five-yearly return rates (it would be flat and show a positive result for any number of investments). So what the curve illustrates is not a fundamental truth about investment, it's an artefact of preferring to look at return rates over a time period that differs from the length over which the investments make whatever return they do.

secretasiandan4• 16 years ago

I would phrase it that he's taking an aggregate after applying a mapping which is (effectively) de-weighting the higher/positive returns.

If he did the mapping (took the IRR) after doing the aggregate, it would be fine and would be what my intuition said which is that mean return doesn't depend on number of deals.

You want to do the mapping to figure out how it compares to other alternatives that work on different time scales. But to do the mapping first warps the results and makes it seem like angel investing is a losing proposition without volume. Its not, its just a high variance proposition.

meterplech2• 16 years ago

Also, the article doesn't consider the extremely unlikely long-tail results. I.e the Facebooks and Googles it is trying to explain. In addition to the 1% 20 times return, there is the opportunity for a .1% 100 or greater fold return. If the initial 500k investment in Google Peter Thiel made diluted to even .01% of current Google stock that would be worth about $170million in current market cap. A return of 340 times initial investment in around 10 years. Obviously these exits are extremely rare, but the long tail possibilities of a distribution can be very important in calculating expected value(like when they predict colossal mortgage failures).

secretasiandan4• 16 years ago

My philosophy is to not include the huge upside tail events that are of minuscule probability, but do include the huge downside events of minuscule probability.

If you include miniscule probability but huge payoff upside events, you can chase some ridiculous things. My favorite is when the powerball jackpots is over $300MM or something like that. Even after taxes (with lump sum payment) its positive expected value and pays off in days if you win. That would suggest you should take all your money and buy lottery tickets.

meterplech2• 16 years ago

While that philosophy is valid (especially as the higher expected value also obviously comes with higher variance), if you are an investor who invests in dozens of companies over years it seems like an argument worth considering. Obviously though, these events get more media coverage, blog attention etc... than the ones that fail.

secretasiandan4• 16 years ago

I don't think he is trying to explain googles/facebooks. He mentions them but none of they payouts/percentiles he has are 1000x/.001

From the article : "More likely, you’ll end up with a solid 2x-5x return from a startup that grows into a viable long-term business." Also, if you look at the expected value contributed by the unlikely 20x return, its .4 out of a total of 2.35.

He's trying to hit hard ground balls, not homeruns.

chrishaum• 16 years ago

I've taken the author's code, changed it slightly, and placed it in a publicly viewable notebook on sagenb.org. Please feel free to view and edit the notebook.

http://www.sagenb.org/home/pub/2014/

jmillerinc• 16 years ago

I'm the author of this article. I've posted a follow-up that incorporates some of the comments I read here on Hacker News. Thanks for everyone's feedback.

http://jmillerinc.com/2010/04/28/angel-investing-simulation-...

A simulation of angel investing

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