Damn you, Mr. Sharpe

[Banjo]

"I do realise that trading since the financial crisis has been difficult and the risk-on/risk-off environment has made it very tough to apply any meaningful portfolio strategies but that doesn’t mean hedge funds should not be accountable anymore"

http://barnejek.wordpress.com/

 

[kut2k2]

The Sharpe ratio sucks ass. Always has, always will

 

[bwolinsky]

Quote from kut2k2:

The Sharpe ratio sucks ass. Always has, always will

Right, we'll need to rely on the Kelly Criterion moreso.

 

[nonlinear5]

Quote from bwolinsky:

Right, we'll need to rely on the Kelly Criterion moreso.

My dictionary defines "moreso" as a "Japanese term for "I'm about to leak!"":
http://www.urbandictionary.com/define.php?term=Moreso

 

[kut2k2]

Quote from bwolinsky:

Right, we'll need to rely on the Kelly Criterion moreso.

Standard deviation is the lazy man's measure of risk.

 

[nonlinear5]

Quote from kut2k2:

Standard deviation is the lazy man's measure of risk.

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.

 

[kut2k2]

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.

"Continuous Kelly" sounds like an oxymoron. Trades are discrete events and the Kelly fraction can only be calculated from solution of a discrete polynomial equation of trade returns. The Kelly formulae I use look nothing like what you posted. If people are using this "continuous Kelly", small wonder they're failing and consequently hating Kelly sizing.

 

[SplawnDarts]

Quote from kut2k2:

Trades are discrete events and the Kelly fraction can only be calculated from solution of a discrete polynomial equation of trade returns.

This isn't true. Any reasonable (read: subject to integration, does not result in a negative ending bankroll in any case) distribution of trade returns allows the computation of a Kelly fraction. You solve:

MAX(across f, INTEGRAL(across PMF range, (PMF*ln(EBR)))

Where EBR is your ending bankroll: starting bankroll - (f*trade result)
with trade results reported in units of bankrolls.


Then trade about 1/5th the Kelly fraction.

 

[actionzip54]

I'm pretty sure Kelly uses E=M(C)2

 

[kut2k2]

Quote from SplawnDarts:

This isn't true. Any reasonable (read: subject to integration, does not result in a negative ending bankroll in any case) distribution of trade returns allows the computation of a Kelly fraction. You solve:

MAX(across f, INTEGRAL(across PMF range, (PMF*ln(EBR)))

Where EBR is your ending bankroll: starting bankroll - (f*trade result)
with trade results reported in units of bankrolls.


Then trade about 1/5th the Kelly fraction.

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.