3 ms·

Reading Peter Thiel's lecture notes and I think it is the sixth one that goes into great detail about the returns of new companies following a power law. Hence

Reading Peter Thiel's lecture notes and I think it is the sixth one that goes into great detail about the returns of new companies following a power law. Hence, the average is mindbendingly irrelevant. I am certainly not buying into facebook, but not due to this analysis.

patrickk 14y ago
That's actually a great point. Even after reading those notes I still wouldn't have thought of applying the power law to my thinking about Facebook (I don't think Facebook will prove anything special long term but it's always useful to be critical in your thinking and consider multiple points of view). As an aside, those notes are an incredible way of thinking about the world differently. I've gotten a lot out of it.
dododo 14y ago
if it is a power law in the sense that a few companies return a lot, whilst most return a little, how does that make the mean irrelevant? the mean of a power law of this form is more skewed by the few companies returning a lot than it is by the majority. assuming that more than 50% of the companies return a little, the median would be irrelevant, but the mean is very sensitive to outliers.
- tedunangst 14y ago
  Consider four companies' returns: [1, 1, 1, 100]. The median, 1, is a reasonable predictor for the next company's return. The mean, 25, doesn't seem like a likely outcome.
  - dododo 14y ago
    there is not a normative way to discriminate between those two predictions. it comes down to what kind of loss you incur for making an incorrect prediction. for mean, it's a squared loss (which penalizes you for being wrong in the tails more heavily) but for a median it's the absolute loss. the argument being made was that fb is an outlier and (as I read it) the mean didn't reflect it, so the maths was "lazy" as it didn't take that into account. actually the mean does take these outliers into account (since it's corresponding loss function penalizes you harshly for being wrong in the tails) and so is probably not too unreasonable at predicting on outlier companies (certainly better than the median).
daguar 14y ago
"New companies" versus "companies that go IPO" are completely different categories. It's an obvious point when you think about it. This is survivorship bias: many new companies fail (with a return of ~zero) before becoming a part of the IPO sample.
- hessenwolf 14y ago
  Yes, but a Pareto distribution looks just the same if you left censor it at some point.

patrickk 14y ago

That's actually a great point. Even after reading those notes I still wouldn't have thought of applying the power law to my thinking about Facebook (I don't think Facebook will prove anything special long term but it's always useful to be critical in your thinking and consider multiple points of view). As an aside, those notes are an incredible way of thinking about the world differently. I've gotten a lot out of it.

dododo 14y ago

if it is a power law in the sense that a few companies return a lot, whilst most return a little, how does that make the mean irrelevant? the mean of a power law of this form is more skewed by the few companies returning a lot than it is by the majority. assuming that more than 50% of the companies return a little, the median would be irrelevant, but the mean is very sensitive to outliers.

tedunangst 14y ago
Consider four companies' returns: [1, 1, 1, 100]. The median, 1, is a reasonable predictor for the next company's return. The mean, 25, doesn't seem like a likely outcome.
- dododo 14y ago
  there is not a normative way to discriminate between those two predictions. it comes down to what kind of loss you incur for making an incorrect prediction. for mean, it's a squared loss (which penalizes you for being wrong in the tails more heavily) but for a median it's the absolute loss. the argument being made was that fb is an outlier and (as I read it) the mean didn't reflect it, so the maths was "lazy" as it didn't take that into account. actually the mean does take these outliers into account (since it's corresponding loss function penalizes you harshly for being wrong in the tails) and so is probably not too unreasonable at predicting on outlier companies (certainly better than the median).

daguar 14y ago

"New companies" versus "companies that go IPO" are completely different categories. It's an obvious point when you think about it. This is survivorship bias: many new companies fail (with a return of ~zero) before becoming a part of the IPO sample.

hessenwolf 14y ago
Yes, but a Pareto distribution looks just the same if you left censor it at some point.