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# Secret Formula: Sqr(3) * Kelly Ratio?

Discussion in 'Strategy Development' started by shortie, Aug 8, 2010.

1. ### 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==

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).

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...

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

5. ### teun

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

6. ### 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

7. ### 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.

8. ### jp_njc

I have come across the Kelly Formula in terms of Sharpe Ratio and I dont see that it matches your formula:

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.

9. ### MGJ

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).

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