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# If the optimal f is less than zero or, shoud I throw away the system?

Discussion in 'Risk Management' started by elitetradesman, Apr 13, 2011.

I'm using this definition of the optimal f.

optimal f = (percentage of wins * (profit factor + 1) - 1) / profit factor

According to this, the optimal f will be zero or less if the percentage of wins is less or equal to 1 / (profit factor + 1).

If I use the optimal f for position sizing and the optimal f is less than zero, does that mean I should simply discard the system?

Also, even if the optimal f is not zero, but relatively small, like 5%, the amount to invest for a small account would be really small. For example, for a \$10K account, 5% is only \$500. Commissions alone would eat away all the profits if there are any. Does that mean I need to throw away the system too?

Thanks.

2. ### AK100

\$500 is risk, not the amount of stock to be traded.

5% risk per trade with a half decent system/strategy and a lot of money can be made, with reasonably manageable drawdowns.

I use Optimal f but only on small amount of money and risk no more than 10% of account equity per trade. If you hit a good running streak profits can really mount up.

Are you sure this is true?

This example says to multiply the trading capital by the optimal f to determine the optimal position size.

http://www.dummies.com/how-to/content/the-optimal-f-money-management-style.html

4. ### jordanf

First, hopefully you understand the pitfalls of applying Kelly to a trading system.

But anyway....

Lets say you have a stock system where you take profits when the stock moves 2% in your favor, and stops out when the stock moves 1% against you. These are the only two outcomes (haha). The win rate is 36.7%. You have a \$10,000 account.

Your pf is 2, using kelly you get a f of .05

To use that to size a position, first divide max loss by f (Vince calls this f\$)

So for a \$50 stock

f\$ = maxloss/f = (.01 * 50)/.05 = \$10

then divide equity by f\$

shares = accteqty/10 = 10000/10 = 1000 shares

good luck

5. ### Gabfly1

Adhere to optimal f and you can be assured of being optimally f'ed.

Thanks, your formula seems like what my book calls the secure f, a variation of the optimal f which I have in my original post.

The book says the secure f more accurately estimates the optimal position than the optimal f because it takes into account the drawdown, but does not elaborate much.

What'd be the shortcoming of the secure f? Have you used it in live trading?

Thanks again.

Is it because it often gives you a number larger than 2%?

Any suggestions other than optimal f/secure f?

8. ### dloyer

Optimal f is only optimal if future trades have the same distribution of results as past trades. Not likely.

It is good to know what optimal f is for your system, but dont go near it.

9. ### goodgoing

Where did you get that? Do you have a reference. It is certainly wrong.

Optimal and secure f are based on max loss and max drawdown resp. and are complicated to calculate. What you wrote looks similar to %Kelly but the formula is wrong.

Aha, I just figured out your error. You basically confuse the ratio of avg. win to avg. loss with the profit factor. I have noticed others here making the same error. If instead of the profit factor you use R, the ratio of avg. win to avg. loss in your formula you get (w is the win rate):

(w * (R -1 ) -1)/R = (wR - w -1)/R = w - (1-w)/R

which is %K

for details see this paper. It explains well how %Kelly is related to expected mean returns and also the pitfalls from using it:

http://www.priceactionlab.com/Literature/Kelly.pdf

Thanks, goodgoing!

I'm reading Technical Analysis: The Complete Resource for Financial Market Technicians.

Attached is an excerpt of the book.

Could it be that the book has a variation of the optimal f or is it downright wrong?

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#10     Apr 16, 2011
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