3 ms·

Nassim Taleb, Loaded Questions and Statistics for Hackers

11 points by bko 9y ago

fwdpropaganda 9y ago
> A stock (or a fund) has an average return of 0%. It moves on average 1% a day in absolute value; the average up move is 1% and the average down move is 1%. It does not mean that all up moves are 1% — some are .6%, others 1.45%, etc. Assume that we live in the Gaussian world in which the returns (or daily percentage moves) can be safely modeled using a Normal Distribution. Assume that a year has 256 business days. The following questions concern the standard deviation of returns (i.e., of the percentage moves), the “sigma” that is used for volatility in financial applications. What is the daily sigma? What is the yearly sigma? Doesn't excuse the wrong answers, but the question has been engineered to make it look like the answer is in the question. As for me, I have the suspicion that at least part of the wrong answers are more laziness than ignorance. I think that at least some of the people who answered wrong on some random questionnaire because they couldn't be bothered do some calculations, would do the calculations if their money depended on it. I'm not sure I learned anything from this, other than "Nassim Taleb invented a question that bets on you having the intuition that standard deviation is the mean value of the absolute distance to the mean" and being lazy. EDIT: The proof that this question is betting on people's laziness and he knows it is the fact that in the question he presents not one but TWO things which are completely irrelevant to his point. One is the number of days in the year, the second is that he asks for yearly sigma. But notice that neither of those are relevant for his point, which is that people have the intuition of "standard deviation" as "mean absolute deviation." They are only there because if they weren't and people would just asked for "daily sigma" they would think "the answer is in the title, there must be a trick, oh wait a minute I got it". So not only he's betting on your laziness but additionally he's making all he can to tip the scales in his favor.
nicholast 9y ago
The paper claims "there exists some function that converts mean absolute deviation to standard deviation" which is surprising and goes against my intuition barring cases where you make assumptions about the underlying distribution (such as approximating as Gaussian). The process of calculating mean absolute deviation includes taking the absolute value of distance from mean for individual points in the series, in which process information is lost. More on the diifference between the two here: https://stats.stackexchange.com/questions/160436/converting-mean-deviation-to-standard-deviation https://stats.stackexchange.com/questions/160436/converting-...
- nicholast 9y ago
  Come to think of it I also addressed more about the differences between the two in this medium post discussion of the Kelly Criterion. https://medium.com/@_NicT_/an-optimal-trade-a374064fda91 https://medium.com/@_NicT_/an-optimal-trade-a374064fda91
OscarCunningham 9y ago
Since s.d. is larger than m.a.v. you would think that muddling the two would make things seem more risky than they are, and hence promote risk aversion. So it's strange that Taleb is highlighting this since he usually worries about the underestimation of risk.
- bko 9y ago
  What I find ironic is that mean absolute deviation is just a lot more intuitive and useful for describing a distribution for laymen. Doesn’t excuse the professional mistaking the concepts. But it’s not like the models the professionals rely on are using m.a.v. in their calculations rather than standard deviation. So the whole controversy is a bit overblown ion my opinion
  - fwdpropaganda 9y ago
    > But it’s not like the models the professionals rely on are using m.a.v. in their calculations rather than standard deviation. Exactly! This is another point I wanted to make on my response in this thread, but I had already written too much. Fortunately you made the same point in one line. > So the whole controversy is a bit overblown ion my opinion Just take it for what it is, which is a marketing piece for Nassim Taleb's personal brand.

11 points by bko 9y ago

> A stock (or a fund) has an average return of 0%. It moves on average 1% a day in absolute value; the average up move is 1% and the average down move is 1%. It does not mean that all up moves are 1% — some are .6%, others 1.45%, etc. Assume that we live in the Gaussian world in which the returns (or daily percentage moves) can be safely modeled using a Normal Distribution. Assume that a year has 256 business days. The following questions concern the standard deviation of returns (i.e., of the percentage moves), the “sigma” that is used for volatility in financial applications. What is the daily sigma? What is the yearly sigma? Doesn't excuse the wrong answers, but the question has been engineered to make it look like the answer is in the question. As for me, I have the suspicion that at least part of the wrong answers are more laziness than ignorance. I think that at least some of the people who answered wrong on some random questionnaire because they couldn't be bothered do some calculations, would do the calculations if their money depended on it. I'm not sure I learned anything from this, other than "Nassim Taleb invented a question that bets on you having the intuition that standard deviation is the mean value of the absolute distance to the mean" and being lazy. EDIT: The proof that this question is betting on people's laziness and he knows it is the fact that in the question he presents not one but TWO things which are completely irrelevant to his point. One is the number of days in the year, the second is that he asks for yearly sigma. But notice that neither of those are relevant for his point, which is that people have the intuition of "standard deviation" as "mean absolute deviation." They are only there because if they weren't and people would just asked for "daily sigma" they would think "the answer is in the title, there must be a trick, oh wait a minute I got it". So not only he's betting on your laziness but additionally he's making all he can to tip the scales in his favor.

nicholast 9y ago

The paper claims "there exists some function that converts mean absolute deviation to standard deviation" which is surprising and goes against my intuition barring cases where you make assumptions about the underlying distribution (such as approximating as Gaussian). The process of calculating mean absolute deviation includes taking the absolute value of distance from mean for individual points in the series, in which process information is lost. More on the diifference between the two here: https://stats.stackexchange.com/questions/160436/converting-mean-deviation-to-standard-deviation https://stats.stackexchange.com/questions/160436/converting-...

nicholast 9y ago
Come to think of it I also addressed more about the differences between the two in this medium post discussion of the Kelly Criterion. https://medium.com/@_NicT_/an-optimal-trade-a374064fda91 https://medium.com/@_NicT_/an-optimal-trade-a374064fda91

OscarCunningham 9y ago

Since s.d. is larger than m.a.v. you would think that muddling the two would make things seem more risky than they are, and hence promote risk aversion. So it's strange that Taleb is highlighting this since he usually worries about the underestimation of risk.

bko 9y ago
What I find ironic is that mean absolute deviation is just a lot more intuitive and useful for describing a distribution for laymen. Doesn’t excuse the professional mistaking the concepts. But it’s not like the models the professionals rely on are using m.a.v. in their calculations rather than standard deviation. So the whole controversy is a bit overblown ion my opinion
- fwdpropaganda 9y ago
  > But it’s not like the models the professionals rely on are using m.a.v. in their calculations rather than standard deviation. Exactly! This is another point I wanted to make on my response in this thread, but I had already written too much. Fortunately you made the same point in one line. > So the whole controversy is a bit overblown ion my opinion Just take it for what it is, which is a marketing piece for Nassim Taleb's personal brand.