Even if an investor has obtained superior results over an extended period, is this sufficient proof that these investment results were actually due to skill rather than just a lucky streak?
No, these investment results could still be due to chance. For example, take a large population, such as all individual investors in the U.S., and have each person perform a random chance operation like flipping a coin repeatedly. After many repetitions, a small portion of the population could appear to have remarkable results.
After 10 consecutive coin flips, some investors probably would have flipped 10 heads in a row (HHHHHHHHHH). If each head were to indicate a consecutive win in the stock market, that person might seem like an investment genius. However, ten heads in a row is no more or less likely than any other particular sequence of heads and tails. The person who flipped THTTHTTHHH has a sequence that is just as unique as 10 heads in a row. The person who flipped THTTHHTHHH, which is different only on the sixth coin toss, also has an equally unique sequence. However, to many people, these sequences of heads and tails would not appear to be nearly as exceptional as 10 heads in a row, even though the really are.
Repeated investment success may still be the result of luck rather than skill.
While it may appear that the person who got 10 heads in a row did something remarkable, it just appears to be more unusual, because the results were all the same. In a similar vein, if a large population of investors were each to choose investment securities at random and were to do this repeatedly, the results will be purely accidental. However, those who happened to pick securities with better results might seem like geniuses.
Given human propensities, you could almost guarantee that the longer the sequence of their accidental winners, the more the chests of these lucky winners would inflate with pride. They would probably also become increasingly vocal. The fact that they are no more or less likely to be a winner in the next round than any other participant, might be lost on them and anyone who hears their story, until the results of the next round are known. In addition, even if they lose the next round, they may conveniently not report their loss. Too many lucky throws of the investment dice [...]