Secret Formula: Sqr(3) * Kelly Ratio?

[shortie]

just something i stumbled upon on WL forum...

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paul3nt
8/5/2010 11:44 AM


I've discovered a curious rule-of-thumb: When trading any number of strategies with a fixed percent of equity, the percent of equity that maximizes the WL score or Sharpe Ratio or the "Recovery Ratio" ( better known as the Sortino ratio) always seems to be very close to Sqr(3) * Kelly Ratio. [ Kelly Ratio is = SharpeRatio^2 * 252/Average Profit ] .

Does anyone have any idea why this seems to work ? Is it related to some kind of adjustment to the Kelly Ratio derivation when the distribution of trades differs from a normal distribution having long tails ?

http://www.wealth-lab.com/Community...hbFq4+9YYyFGkHvD6WjrEw2DFqgzSoEPOW16e8QoJ9Q==

 

[tradingjournals]

There is something I did understand. SQRT(3) is greater than 1, and we know that one should use less than kelly (not more than Kelly).

 

[intradaybill]

But with sqrt(3) ~1.73 he is using more Kelly, actually 1.73 times more.

For example, if his win rate is 65% and his avg. win to avg. loss is 3 Kelly is:

K = .65 - (1-.65)/3 = 0.533 or %K = 53.3% of capital, that is the amount to risk per trade.

1.73 x %K = 92.2% or risking it almost all on one trade.

Good luck...

 

[tradingjournals]

Using more than Kelly reduces the return, and increases the variance. Using less than kelly reduces the return, BUT decreases the variance.

 

[teun]

Doesn't he mean 3^2 instead of 3^0.5?

 

[shortie]

don't know what he meant, sorry.

it is strange to write Sqr(3) instead of 1.73. the formula he posted could be incorrect

 

[dloyer]

Everytime I tried to optimize the fixed fractional based on a risk adjusted fitness function, I got a result much less than kelly as expected since kelly is optimizing for profit.

 

[jp_njc]

I have come across the Kelly Formula in terms of Sharpe Ratio and I dont see that it matches your formula:
Kelly=(MeanAnnualReturn-RiskFreeRate)/StandardDeviation^2, as seen at: http://nickgogerty.typepad.com/files/kellysharpechan.xls.

Chan's book explains it further: http://nickgogerty.typepad.com/desi...es-a-little-something-to-upset-everyone.html. I havent gone back to look at the explanation, but I may ahve to now. I dont think that the fat tails is working itself into the sqrt(3), which is 1<sqrt(3)<4. Usually the optimal is between 1 and 1.3 in my experience, and that is why long/short funds are commonly long 130.

 

[MGJ]

Quote from dloyer:

Everytime I tried to optimize the fixed fractional based on a risk adjusted fitness function, I got a result much less than kelly as expected since kelly is optimizing for profit.

In (this plot), the optimum fixed fractional risk-per-trade which maximizes (profit/drawdown) is different from the optimum fixed fractional risk-per-trade which maximizes profit.

Maximum (profit/drawdown) is the green dot

Maximum profit is the blue dot.

Notice that they appear at two different values of the fixed fractional risk-per-trade (along the horizontal axis).