Re: Bill Reid, Kelly Criterion

Hi,

My last post included all the previous ones, hmm.

I have yet to think about what you said about the actual numbers....
Anyway, I do enjoy the cleverness and will attempt to compensate for
my own lack of it, re the humour, in future posts.

I just want to see if you agree with this:


The standard deviation over T years is the 1/alpha power of T times
the standard deviation (of log changes) over one year. For the normal
case alpha=2 but Mandelbrot says alpha=1.7. So for example if you want
to control the risk of the terrible eventuality (finally some humour
from me) that the year-on-year percentage gain is any worse than 1%
less than the expected, you let r be the risk of being worse than 1%
less than expected in one year, and the risk of being worse than 1%
less than expected effective interest rate over T years is

-1/alpha
rT





So just for an example, if there is a 47% chance of having worse than
1% less than the expected Kelly rate after 1 year then to be sure
there is no worse than a 10% chance of being 1% less than having an
effective interest rate worse than 1% less than expected over T years,
you choose T so that
-1/1.7
.47 T

is 0.10
-1.7
So T= (.1/.47)

1.7
=(4.7)

=13.8 years.

------------------------------------------------

The thing about this is, it is what Mandelbrot's assumption about self-
similarity implies, but as you seemed to say, a mathematical model is
reliable because it is mathematical.

I think, real life is analogous to someone barging up to the
blackboard with an erasor and erasing the formula and saying 'So
there! The industry you have invested in no longer even exists.'

In other words, self-similarity is saying, what happened in the past
will continue into the future.

It is where self-similarity itself breaks down, of course, that people
lose their money.





.

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