7 ms·

A simulation of angel investing

47 points by epi0Bauqu 17y ago

gizmo 17y 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.
- po 17y 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.
  - gizmo 17y 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.
    - po 17y ago
      >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? Who's numbers? Yours or his? His simulation is saying that (as an individual angel) you have a 50% chance of losing all of your investment on your first deal. He's running 10,000 angels simultaneously doing deals and looking at the average performance across those angels. Think of it like a piano with 10,000 keys. When you're in the money the key is up and when you're not its down. (I know the keys can go above 0 but I can't think of a better analogy.) After everyone does their first deal, a full 50% are completely down at 0. A few are way up. It takes four "turns" for 50% of the keys to be up above the starting point "Average over time" is perhaps the wrong phrase for it. I should have said number of deals. >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. I don't see how that follows from the article.
- kaddar 17y 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 17y 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.
- secretasiandan 17y ago
meterplech 17y 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).
- secretasiandan 17y 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.
  - meterplech 17y 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.
    - secretasiandan 17y ago
      I would disagree strongly. Perhaps we have different meanings of the term miniscule. Do you still include it if its on the order of 1E-6? Lets say you have interest 100 companies over 30 years, which is pretty hard to do anyways. What percentile event is it that you get a piece of a 1E-6 event in one of your companies? Pretty low. My thought is that you don't increase your wealth meaningfully and especially don't feed your family with lottery tickets. And that is the exact example I brought up.
chrishaum 17y 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/ http://www.sagenb.org/home/pub/2014/
jmillerinc 17y 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-part-2/ http://jmillerinc.com/2010/04/28/angel-investing-simulation-...

47 points by epi0Bauqu 17y ago

gizmo 17y 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.

po 17y 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.
- gizmo 17y 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.
  - po 17y ago
    >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? Who's numbers? Yours or his? His simulation is saying that (as an individual angel) you have a 50% chance of losing all of your investment on your first deal. He's running 10,000 angels simultaneously doing deals and looking at the average performance across those angels. Think of it like a piano with 10,000 keys. When you're in the money the key is up and when you're not its down. (I know the keys can go above 0 but I can't think of a better analogy.) After everyone does their first deal, a full 50% are completely down at 0. A few are way up. It takes four "turns" for 50% of the keys to be up above the starting point "Average over time" is perhaps the wrong phrase for it. I should have said number of deals. >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. I don't see how that follows from the article.
kaddar 17y 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 17y 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.

secretasiandan 17y ago

meterplech 17y 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).

secretasiandan 17y 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.
- meterplech 17y 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.
  - secretasiandan 17y ago
    I would disagree strongly. Perhaps we have different meanings of the term miniscule. Do you still include it if its on the order of 1E-6? Lets say you have interest 100 companies over 30 years, which is pretty hard to do anyways. What percentile event is it that you get a piece of a 1E-6 event in one of your companies? Pretty low. My thought is that you don't increase your wealth meaningfully and especially don't feed your family with lottery tickets. And that is the exact example I brought up.

chrishaum 17y 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/ http://www.sagenb.org/home/pub/2014/

jmillerinc 17y 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-part-2/ http://jmillerinc.com/2010/04/28/angel-investing-simulation-...