
A simulation of angel investing - epi0Bauqu
http://jmillerinc.com/2010/04/27/angel-investing-simulation/
======
gjm11
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
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.

------
gizmo
> 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
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
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
>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.

------
meterplech
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
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
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
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.

------
jmillerinc
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-...](http://jmillerinc.com/2010/04/28/angel-investing-simulation-
part-2/)

------
chrishaum
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/>

