I'm reading Thinking, Fast and Slow by Daniel Kahneman and I came across the following text

Some years ago I had an unusual opportunity to examine the illusion of financial skill up close. I had been invited to speak to a group of investment advisers in a firm that provided financial advise and other services to very wealthy clients. I asked for some data to prepare my presentation and was granted a small treasure: a spreadsheet summarising the investment outcomes of some twenty-five anonymous wealth advisers, for each of eight consecutive years. Each adviser's score for each year was his (most of them were men) main determinant of his year-end bonus. It was a simple matter to rank the advisers by their performance in each year and to determine whether there were persistent differences in skill among them and whether the same advisers consistently achieved better results for their clients year after year.

To answer the question, I computed correlation coefficients between the rankings in each pair of years: year $1$ with year $2$, year $1$ with year $3$, and so on up through year $7$ with year $8$. That yielded $28$ correlation coefficients, one for each pair of years. I knew the theory and was prepared to find weak evidence for the persistence of skill. Still, I was surprised to find that the average of the $28$ correlations was $0.01$. In other words, zero. The consistent correlation that would indicate differences in skill were not to be found. The results resembled what you would expect from a dice-rolling contest, not a game of skill. No one in the firm seemed to be aware of the nature of the game that its stock pickers were playing. The advisers themselves felt they were competent professionals doing a serious job, and their superiors agreed.

Kahneman continues and claims that the financial industry is largely based on the illusion of skill.

Question: Why would this example show that the financial industry is based on the illusion of skill/that the stock picking requires no skill? I understand that the correlation between the rankings in different years says something about the relative skill of the stock pickers. That is; how the skill of stock picker $A$ compares to the skill of stock picker $B$. But I don't understand why it would say anything about the skills of the stock pickers as a group.

Suppose that you have a group of golfers that are all exactly as skilled as Tiger Woods. If you would calculate the correlation coefficients of their succes over eight years, you should get zero correlation as well, but that doesn't imply that they are weak players/have no skill.

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    $\begingroup$ Kahneman's book is full of bold claims like that :) He got the economics Nobel though. He's crazy popular in fintech these days, among robo adviser crowd $\endgroup$ – Aksakal Feb 10 '18 at 15:18

Daniel Kahneman is writing about consistency. If you went to a casino and came back with a large amount of money, then you would be lucky. If you went to a casino on another day and lost a large amount of money, you would be unlucky. However if you went to a casino for a number of days in the row and won some pretty large amount of the money each time, then either something unlikely would have happened, or you could be a skilled player. Is something is about skills, then it should be consistent over time (you are either good, or bad, if it changes, it changes rather gradually then dramatically, so it is auto-correlated). If something does not depend on skills, but luck, then it can change dramatically and wouldn't be auto-correlated.

As about your argument about golfers, you'd need to prove it with data for it to be valid, otherwise it is a bold claim. Nonetheless, many things in sports depends on luck rather then skills. On another hand, I see your point that there is no comparison group of people who knew nothing about finance, who would be monitored over the time in terms of their investment successes.

  • $\begingroup$ Thanks for your reply! I don't think what I said about the golfers is a bold claim. Suppose they all have the exact same physical abilities, they all perform under pressure equally well, they all have optimised their practise routines, they all have access to the best equipment, etc. Then their performance is entirely based on luck and their rank, say per month, should look like a random sequence, right? I don't think you can compare the example you gave about the casino to the case of the stock pickers. Kahneman didn't look at the correlation between win/loss for every pair of years. He... $\endgroup$ – titusAdam Feb 10 '18 at 12:47
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    $\begingroup$ looked at the correlation between the rank of the players for every pair of years. Which means (as you agree) that they could be outperforming the market by a large margin, yet Kahneman seems to imply that they're not the competent professionals they think they are. $\endgroup$ – titusAdam Feb 10 '18 at 12:49
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    $\begingroup$ You have a point that the test just proves that no adviser in this group is better than any other. As @Tim says, a comparison with a control group of unskilled group of people would be more reliable, and in such kind of comparison investors are usually compared with investing at random. However, in the view of the quoted author, it's unlikely that all advisers are equal and good and it's more likely that skills don't matter on performance. For example, I wouldn't expect any group of 28 golfers to be in the same level. $\endgroup$ – Pere Feb 10 '18 at 13:02
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    $\begingroup$ @Pere I don't necessarily agree with the part it's more likely that skills don't matter on performance, and the golfers were probably a bad example. Isn't it possible that after a certain level of skill the marginal effect of extra skill on profit becomes zero? $\endgroup$ – titusAdam Feb 10 '18 at 14:00
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    $\begingroup$ Your interpretation could be compatible with the results, although it seem the same interpretation of Kahneman but restricted to top performers. However, I'm not an expert on the field while Kahneman is, and he might be interpreting those results in light of other observations and his expertise. $\endgroup$ – Pere Feb 10 '18 at 14:17

This is not the best way to do it. Fund managers will do better in different market conditions, etc. For each fund manager, you would just perform a t-test on the 8 years of returns (adjusted for risk, so you're only getting the portion of returns caused by stock-selection ability) and test whether the mean statistically different from 0. If it's not, you have no evidence of skill.

The power of his 'correlation method' will be very small since only 8 years of returns are provided.

  • $\begingroup$ Thanks for your reply. This is answer barely relates to my question though! I suggest that you edit your answer or make it a comment instead. :) $\endgroup$ – titusAdam Feb 12 '18 at 9:55

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