4 ms·

But what are the fees he charges? I bet that 2 million figure doesn't incorporate fees.

jjoonathan 12y ago
Also, how are they accounting for survivor bias in the "best of" lists? I often hear the outliers make claims like "the models predict that we shouldn't exist -- if the analysts are right, there shouldn't be any outliers as good as we are." The implicit argument is that the people claiming "on average, stock pickers don't beat the index" don't know what tehy're talking about. But it's widely acknowledged that the tails are exactly where modeling of this kind tend to fail, so I'm not convinced. A model that gets the tails wrong might still be much better at figuring out expected value, which is what investors should actually care about. How do I make sure that they're not just trying to sell a product with sub-par expected return by chopping off yesterday's heavy tail and waving it around?
- fsk 12y ago
  Survivor bias doesn't really matter here, because we're looking at only the best. In order to properly correct for survivor bias, you'd have to count the # of funds that were created in the past 40 years, and then figure out (assuming a normal distribution of performance), what you expect the best fund performance to be. He has to beat that number to be considered genuinely better (rather than being the luckiest). For example suppose that the volatility of the S&P 500 is 10% per year. In a 40 year period, the volatility is thus 0.10 times sqrt(40), the central limit theorem, or 63%. So, a 1 standard deviation move in the S&P 500 over 40 years is 63%. To outperform by 2% per year, is 1.02^40 = 2.28 = 128% gain. 63% * 2 = 126% So, this guy performed two standard deviations above the mean over 40 years. That certainly is within the realm of random chance, considering he was the best/luckiest. Therefore, I conclude he did not outperform the market by a statistically significant margin. Actually, I'd expect the best fund to be 3 or 4 standard deviations above the mean (given the # of funds), so this result is an argument AGAINST active managers. Actually, the volatility of the S&P 500 is more than 10%, so I overestimated his performance. It's closer to 15% long-term, but it's varied a lot over 40 years.
  - jjoonathan 12y ago
    > assuming a normal distribution of performance If someone assumes that performance is normally distributed (e.g. by dividing by standard deviation and using the gaussian CDF to reject null hypotheses), couldn't you arbitrage against them by creating a bunch of "heavy tail" funds, waiting for a few of them to beat the market in a more extreme fashion than the normal distribution would predict is possible, and then using the normal distribution to "prove" that it couldn't have happened by chance?
    - fsk 12y ago
      No, because 1. You can't normally short sell mutual funds. As a retail investor, short selling is hard. Plus, short selling has fees, even for institutional investors. 2. Even if a fund gets lucky (or unlucky), its future returns are also normally distributed. I.e, if a fund beats the market 20% one year, its next year is just as likely to be lucky again as unlucky. Funds that underperform the market severely are closed or merged into other funds. Funds that get lucky and trounce the market tend to stay open. If your 5 year track record is +20%/year, and you have a "bad" year, your 6 year track record is still +15%/year.
pwg 12y ago
Based upon the Prospectus Summary (http://www.nicholasfunds.com/NF/Summary.html http://www.nicholasfunds.com/NF/Summary.html) the total annual fund operating expenses are 0.73%. Contrast that with Vanguards S&P 500 fund (http://www.vanguard.com/pub/Pdf/p040.pdf http://www.vanguard.com/pub/Pdf/p040.pdf) at 0.17% for Investor Shares and 0.05% for Admiral Shares

Also, how are they accounting for survivor bias in the "best of" lists? I often hear the outliers make claims like "the models predict that we shouldn't exist -- if the analysts are right, there shouldn't be any outliers as good as we are." The implicit argument is that the people claiming "on average, stock pickers don't beat the index" don't know what tehy're talking about. But it's widely acknowledged that the tails are exactly where modeling of this kind tend to fail, so I'm not convinced. A model that gets the tails wrong might still be much better at figuring out expected value, which is what investors should actually care about. How do I make sure that they're not just trying to sell a product with sub-par expected return by chopping off yesterday's heavy tail and waving it around?

fsk 12y ago
Survivor bias doesn't really matter here, because we're looking at only the best. In order to properly correct for survivor bias, you'd have to count the # of funds that were created in the past 40 years, and then figure out (assuming a normal distribution of performance), what you expect the best fund performance to be. He has to beat that number to be considered genuinely better (rather than being the luckiest). For example suppose that the volatility of the S&P 500 is 10% per year. In a 40 year period, the volatility is thus 0.10 times sqrt(40), the central limit theorem, or 63%. So, a 1 standard deviation move in the S&P 500 over 40 years is 63%. To outperform by 2% per year, is 1.02^40 = 2.28 = 128% gain. 63% * 2 = 126% So, this guy performed two standard deviations above the mean over 40 years. That certainly is within the realm of random chance, considering he was the best/luckiest. Therefore, I conclude he did not outperform the market by a statistically significant margin. Actually, I'd expect the best fund to be 3 or 4 standard deviations above the mean (given the # of funds), so this result is an argument AGAINST active managers. Actually, the volatility of the S&P 500 is more than 10%, so I overestimated his performance. It's closer to 15% long-term, but it's varied a lot over 40 years.
- jjoonathan 12y ago
  > assuming a normal distribution of performance If someone assumes that performance is normally distributed (e.g. by dividing by standard deviation and using the gaussian CDF to reject null hypotheses), couldn't you arbitrage against them by creating a bunch of "heavy tail" funds, waiting for a few of them to beat the market in a more extreme fashion than the normal distribution would predict is possible, and then using the normal distribution to "prove" that it couldn't have happened by chance?
  - fsk 12y ago
    No, because 1. You can't normally short sell mutual funds. As a retail investor, short selling is hard. Plus, short selling has fees, even for institutional investors. 2. Even if a fund gets lucky (or unlucky), its future returns are also normally distributed. I.e, if a fund beats the market 20% one year, its next year is just as likely to be lucky again as unlucky. Funds that underperform the market severely are closed or merged into other funds. Funds that get lucky and trounce the market tend to stay open. If your 5 year track record is +20%/year, and you have a "bad" year, your 6 year track record is still +15%/year.

pwg 12y ago

Based upon the Prospectus Summary (http://www.nicholasfunds.com/NF/Summary.html http://www.nicholasfunds.com/NF/Summary.html) the total annual fund operating expenses are 0.73%. Contrast that with Vanguards S&P 500 fund (http://www.vanguard.com/pub/Pdf/p040.pdf http://www.vanguard.com/pub/Pdf/p040.pdf) at 0.17% for Investor Shares and 0.05% for Admiral Shares