z=(1-x)*(1+y*x)

No...I actually find this interesting. I am reading up on Kelly's formula in the Fortunes Formula...book that is. I didn't;t get to the part about the formula yet, so I can't really argue. But I believe that this is interesting. :cool: :cool: :cool:


Just curious. How did you derive this formula?
 
Math was never my strong point.. Did OK in stats and cal; but still never used a formula to figure out my loss or risk ratio; and there is a very good reason for this. There is no way to configure what large stock holders do, funds do, terrorists, dollar, market sentiment, etc. If the market was all X's and O's, everyone would be a zillionaire.

Just my opinion though. :cool:
 
Math and trading are seperate animals. Trading is the beast that needs to be tamed, the math part is simple.

The math is just looking at the bottom line and reflects how well you have tamed the beast........... :D
 
Quote from bighog:

Math and trading are seperate animals. Trading is the beast that needs to be tamed, the math part is simple.

The math is just looking at the bottom line and reflects how well you have tamed the beast........... :D
More...

easy huh? I was a physics major and I see some of the quantitative finance stuff and my jaw drops.
 
Quote from late apex:

qll, what exactly are you trying to do with your formula for z?

If you'd like to calculate the theoretically optimal fraction f of portfolio to risk in order to maximize expectancy, given reliability P (% wins, or probability of a win) and average win/loss ratio R, then your formula is incorrect.

The correct formula for (Kelly) optimal f is

f = ((R + 1) * P - 1) / R

In your examples, R = 1; P = 75% and 90%. Therefore, f = 50.00% and 80.00%, respectively, not ~34% and ~44%.

Yes, the optimal fraction f here is "too high". Its computation is intended strictly to maximize expectancy per trade and, thus, terminal wealth / portfolio value. It assumes a stationary distribution and a sufficiently large number of trades, among other things. It also ignores the whole notion of drawdowns on the yellow brick road to the aforementioned terminal wealth, unlike in the real world.
More...


I think Kellys formula is this....
K = W - (1-W)/R

Where:
K = Fraction of Capital for Next Trade
W = Historical Win Ratio (Wins/Total Trials)
R = Winning Payoff Rate

Ex: For example, say a coin pays 2:1 with 50-50 chance of heads or tails. Then ...
K = .5 - (1 - .5)/2 = .5 - .25 = .25.
Kelly indicates the optimal fixed-fraction bet is 25%.
 
Quote from bighog:

Math and trading are seperate animals. Trading is the beast that needs to be tamed, the math part is simple.

More...

Trading is easy, making money is the hard part.
 
Quote from rateesquad:

I think Kellys formula is this....
K = W - (1-W)/R

Where:
K = Fraction of Capital for Next Trade
W = Historical Win Ratio (Wins/Total Trials)
R = Winning Payoff Rate
More...

K = W - (1 - W) / R = (WR + W - 1) / R = ((R + 1) * W - 1) / R

I had:

f = ((R + 1) * P - 1) / R

Different notations, same formula.
 
Quote from late apex:

K = W - (1 - W) / R = (WR + W - 1) / R = ((R + 1) * W - 1) / R

I had:

f = ((R + 1) * P - 1) / R

Different notations, same formula.
More...



Just a question.....

How did you get WR in the equition?
K = W - (1 - W) / R = K=W-((R^-1)-(WR^-1))
Is isn't it how it supposed to be if you break it down?
Or is my calculations wrong?
 
No, nothing wrong with your calculation that I can see.

To simplify to a single fraction (which is what gets WR in the equation), multiply and divide W by R:

K = W - (1 - W) / R = WR / R - (1 - W) / R = (WR - (1 - W)) / R, then as above.
 
You must log in or register to reply here.
Back
Top