Get 25 monkeys to throw darts at S&P 500 stock symbols on January 1st of each year. The chance that at least one monkey outperforms 5 years in a row is about 55%. (The target areas need to be proportional to market capitalization etc.)
That's if you have one trade per year. How would you model this if you have 25 monkeys throwing, say, 300 darts at the board per day, for every day that the market is open (252 days), for five years?
If you're going to quantify survivorship bias, you can't use entire years as data points, because that doesn't properly represent the amount of activity that occurs. We should reason about each event, because if consistency emerges on an event basis we might not even need more than one year for our sample. The decision-making that is being empirically examined here (i.e. acumen capable of beating the market beyond chance) ostensibly functions on trading events, which means years are not the correct data point to use (and will provide an incorrectly pessimistic sample).
> That's if you have one trade per year. How would you model this if you have 25 monkeys throwing, say, 300 darts at the board per day, for every day that the market is open (252 days), for five years?
If the data is reported on a yearly basis then it's pretty much the same thing.
No it isn't, because each firm doesn't have a 50% chance of beating the market each year. Unless you're postulating that that is the case, it's not at all the same.
I can quibble about the odds of each individual trade resulting in profit or less being binary, but for the sake of argument it'll do. But a 50% chance of beating the market each year isn't supported by anything.
The grouping of data reporting doesn't suggest anything about the underlying data if it doesn't also share the same probability distribution. The trades are the events which determine if a fund will outperform on an annual basis, and we can group those trades by day, week, month, year, etc.
