From the web and my previous reading: “for data which follows a log-normal distribution, the geometric mean should be same as the median.”
One of the things we are doing at P123 is buying multiple stocks and capturing the mean return (arithmetic mean) over a short period and compounding that return: by rebalancing and reinvesting. Note: the arithmetic mean return is always higher than the median return in a log-normal distribution.
Compared to buying and holding one stock: we are converting our compounded returns from the median to the mean of the “average” stock price. This is a factor in why we make money and how the author makes buying stocks look like a worse idea than it is: at least the way we do it. We are also getting some time diversification. So, no matter what you think of the paper, some of it may not apply to us.
This is discussed in detail in William Poundstone’s book “Fortune’s Formula.” Shannon’s demon, from the book, is an extreme example of this. “Shannon’s demon” is able to make money using this principle even though the price of a highly volatile stock, in this example, fluctuates around one value.
But here is how “Shannon’s Demon” would work at P123. If this demon had control of P123 he would simply change the statistics>trading to logarithmic returns. Then when you looked at that trade statistics with “Realized winners” = 50% you would be making money even if the “Avg Return” for the winners and losers were equal.
It is like that little demon can turn volatility-drag in his favor. Admittedly, this is a small factor for us with the volatility we are dealing with. This is the same as saying for small percentage returns the percentage return and the log return are nearly equal. But you might consider looking at the volatility of individual stocks (not the portfolio as a whole) in your ports and seeing how that correlates with your annualized returns.
With absolute certainty this is why a port with just your highest rank stock usually does not do that well but the trade statistics can look good. You are not getting the benefit of rebalancing and putting the stocks in your portfolio near equal weight. Obviously, different ports will behave quite differently when you try this (law of small numbers). But I have never seen a single stock work all that well with any ranking system and this part of the reason.
Like Marc, who uses a Mac too, I cannot pull up the link on Safari. I will try it at the office. But is sounds like the author already knows this and is playing with us a bit. But, in a way, he is pointing out what Poundstone wrote about–and proves it.
And BTW, one of the reasons you should use log returns—for the port as a whole--if you ever bootstrap.
All things considered, I think Marc said it best. I try to stay away from the punctuations keys (“#&%*”), however. Marc should have a little more leeway on this.
Also, I keep following Yuval around on the posts because he has such great posts: detailed, mathematical and with evidence that can be discussed. He is spot on with regards to diversification, IMHO.
-Jim