P(now) plus a random variable with zero mean
Except that the mean is not zero but
significantly positive. And thats why i'm just hodling (besides some automated risk rebalancing to convert the randomness into profit).
Well, it depends on when you start to compute the mean...
Start at 2013-01-01 and the mean of log increments is positive; start at 2013-11-18, and it is zero; start at 2013-11-29, and it is negative.
If the past is relevant, the recent past (say, the last two months) should have more weight than the remote past, no? So why is the mean since 2011 more likely to be correct than the mean since 2013-11-29?
But if the mean increment is indeterminate to that degree, it becomes part of the zero-mean random term, just increasing its variance.
That observation is the key to rising from Level One to Level Two.
BTW, even if one starts at 2011, the mean increment per time step is not "strongly" positive: it is still small compared to the standard deviation of the random term.