Money Management
- Thread starter cnms2
- Start date
The two formulas are exactly the same.
Page 2 of Kelly’s paper (the gambler with a private wire)…
q Probability of correct transmission (win)
p probability of wrong transmission
Same payoffs for win and loss
Growth Rate: G = q lof(1+f) + p log(1-f)
Kelly criterion maximizes the growth rate so calculating we have
dG/df = 0
q/(1+f) – p/(1-f) = 0
p(1+f)=q(1-f)
f(p+q) = q-p
answer : f =q-p
Simplified Kelly formula
f = ((1+1)q – 1)/1 = 2q -1 = 2q –q –p= q-p
You get the exact same answer for the same problem.
What do you mean ‘theoretical’ and ‘historical’ probabilities? The generator of the distribution is not observable in real life so you have to make estimations from the observed data. There is no shortcut to that.
As for the subjective element I explained that it is originates from the risk preferences of the portfolio owner.
The two formulas are Not the same. Mathematically they are Two different formulas. Which one did you use before? Did you use both to get the same figures in your previous posts?
Anyone (probably except you) applies actual figures with these two formulas would know clearly the simplified version is Only an approximation.
What's the base of the log above you use? 2, 10 or e?
Obviously you didn't observe all the conditions of the formula on page 919, in order to attain your goals.
In school, teachers use theorectical data/ probabilities. In backtesting, analysts use historical data/probabilities. In trading, traders get realtime data/ results that immediately become part of historical data/ probilities.
I really cannot understand what you are trying to say.
I just show you above that from the formula in the Kelly paper
g(f) = q log(1+f) + plog(1-f)
you got the formula
f* = q- p.
If you had uneven payoffs a,b the Kelly paper’s formula becomes
g(f) = qlog(1+af) + plog(1-bf)
Taking again the first derivative you get the practitioner’s used formula
f* = (aq – bp)/ab
where is the difference?
Kelly paper uses a base 2 logarithm because it calculates the growth as 2^g
Thorp’s paper uses the natural logarithm because it calculates the growth as e^g
No matter what base you use the results for the Kelly fraction are the same.
And yes you will need aproximations in more complex problems.
A short thread from Van Tharp's discussion board. It touches on position sizing and on evaluating somebody's trade system.
- Quote from the thread:I typically risk 1% of my account value and never have more than 5% of my account value exposed at one time. Also, at this time, I only trade equities listed on Nasdaq, Dow, or Amex.
I run a simple example of trading results and did a comparative calculation of the optimal f and of the Kelly ratio. They came out very close:
), i.e. the section:
Finding a profitable risk level.
- optimal f: 57.4%
- Kelly ratio: 56%
), i.e. the section:Finding a profitable risk level.
- Optimal-f - What it does
- About using optimal-f to chose risk - Looking for Low risk in all the wrong places.
- Finding True Optimal Risk
Hey C,
Do you actually trade? You seem to be a whiz, why not scratch out a formula for building a warp drive, or how about curing diseases. Speaking for myself, and most are probably the same, I do all my charting, and analizing on the back of a cocktail napkin.
Rennick out.
Do you actually trade? You seem to be a whiz, why not scratch out a formula for building a warp drive, or how about curing diseases. Speaking for myself, and most are probably the same, I do all my charting, and analizing on the back of a cocktail napkin.
Rennick out.