Damn you, Mr. Sharpe

Quote from kut2k2:

All I know is that my formulae are working for me, and part of that comes from not assuming some mythical stationary distribution of trade returns for which there is no evidence. I calculate my Kelly fraction based on trades that actually happened, not trades that "might" happen.
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What's mythical is that discrete does not assume 50% distributions. Trading is indeed continuous as in trend following but not for small intervals.
 
Discrete Kelly formula: used when the payout ratio is always the same.
Continuous Kelly formula: used when the payout ratio is variable (i.e., the winning amounts are not the same, such as in a trading system).
 
Quote from nonlinear5:

Discrete Kelly formula: used when the payout ratio is always the same.
Continuous Kelly formula: used when the payout ratio is variable (i.e., the winning amounts are not the same, such as in a trading system).
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Thus my point.

Kut2k2 is obsessed with binomial 50-50 win assumptions regardless of the fact only small intervals are actually that way.
 
Quote from nonlinear5:

Discrete Kelly formula: used when the payout ratio is always the same.
Continuous Kelly formula: used when the payout ratio is variable (i.e., the winning amounts are not the same, such as in a trading system).
More...
Quote from nonlinear5:

Both the Sharpe's ratio and the continuous Kelly use the standard deviation:

Sharpe = (mean excess return) / (standard deviation of returns)
Continuous Kelly = (mean excess return) / (standard deviation of returns)^2

So, in fact, one can be derived from the other one.
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Evidently I've misunderstood your use of "continuous.". That said, I have the following observations.

There's no explanation for why standard deviation appears in the denominator of your CK formula. Based on what I know about the Kelly fraction formulas, it doesn't belong.

What is excess returns doing in the numerator? The Kelly fraction is based on total trade returns, not excess trade returns.

Whoever dreamed up your CK formula has totally screwed the pooch. He got both the numerator and the denominator wrong.

Finally let me note that the Sharpe ratio is a performance metric while the Kelly ratio is a position sizing mechanism. I'm hard pressed to see any meaningful connection between the two.
 
Quote from kut2k2:

Whoever dreamed up your CK formula has totally screwed the pooch. He got both the numerator and the denominator wrong.
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The formula that you are questioning can be derived in a very straightforward manner. The author of that formula is Edward Thorp, who is a professor of mathematics and finance, a hedge fund manager, and a successful trader/investor with a long term record of 20% annual returns over the last 28 years.

Now, what are your credentials?
 
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