Money Management

[gbos]

Hello I would like to add some comments to the above…

This famous formula seems simple enough [Edge/Odds].

The formula is not simple at all. Only if you assume a Bernoulli distribution for your trades it takes this simple form.

This is because you typically have no edge within an efficient market.

Then why are we trading?

And, the odds are truly uncertain. It is a random variable with an undefined distribution (it is not normal).

Uncertain but quantifiable within limits. Nothing is 100% certain but you can use your data to take an estimation for a range of your edge.

This formula, per the author, also suggests that there is an optimal level of risk beyond which you are going to get hurt and wipe out your capital.

Correct.

This is contrary to investment theory that suggests that additional risk should always be compensated with extra return otherwise no investors would be willing to take on this additional risk.

Wrong. Kelly optimizes for the median wealth. Taking additional risk will optimize your average wealth. The problem is that rare events are the main contributors for this average wealth so in the vast majority of scenarios what you are interested in is the median (most probable scenario). Additional risk doesn’t always compensate with extra return but on average and I explained from where this average originates.

However, the Kelly formula is only applicable to strategies where every winner is the same size and every loser is the same size - hardly the case in actual trading.

Wrong. It is applicable in every case. An example of a ‘system’ with 3 possible outcomes…

R-multiple Probability
-1 ----- 1%
-0.05 ----- 10%
+0.13 ----- 89%

1/10 Kelly = 9%

Monte Carlo of Wealth after 100 trades (median 248, starting capital 100)

Again for anyone interested how Kelly is implemented in the real world, read Ed Thorp’s paper. He has managed billions of dollars for decades using Kelly and is one of the best mathematicians around.

Regards

 

[OddTrader]

Quote from StreamlineTrade:

Odd - Interesting insights. Thank you.

Those input are other people's insights/ ideas, not mine. I'm still learning.

 

[ES335]

Quote from OddTrader:

Just 2 cents:

When people can freely and arbitrarily choose a fraction (say 1/2, 1/3, 1/4, etc.) of an optimised whole Kelly value in order to derive a supposingly suitable position size to fit an individual's subjective purposes/ needs, mathematically and logically people would Not need Kelly anymore.

However, I believe Kelly would be still good and useful for some MM vendors to promote and market their trading services, just like many TA vendors do.

For someone who is "still learning" you sure have a lot of opinions...

(sigh)

 

[OddTrader]

Quote from gbos:

R-multiple Probability
-1 ----- 1%
-0.05 ----- 10%
+0.13 ----- 89%

1/10 Kelly = 9%

Thanks for pointing us to the generalizations, variations and practical aspects of applying Kelly principle, rather than a static Kelly value.

 

[Murray Ruggiero]

I have a free tutorial on my site on optimal f.

Here is the link

http://tradersstudio.com/Default.aspx?tabid=36

 

[Murray Ruggiero]

I have a free tutorial on my site on optimal f.

Here is the link

http://tradersstudio.com/Default.aspx?tabid=36

 

[OddTrader]

Quote from ES335:

For someone who is "still learning" you sure have a lot of opinions...

(sigh)

Would you mind to point out anything wrong with the opinions, so that I could learn more from this borad (that's why I come here)? Thanks in advance!

 

[gbos]

Quote from OddTrader:

Thanks for pointing us to the generalizations, variations and practical aspects of applying Kelly principle, rather than a static Kelly value.

This was an answer to

However, the Kelly formula is only applicable to strategies where every winner is the same size and every loser is the same size - hardly the case in actual trading.

If you don't like the static framework there are papers on the net for a Bayesian dynamic updating of the Kelly optimal allocation.

Anyway no-one can force you to accept as useful the idea of optimizing the median of your payoffs. I am convinced that this is the best way and I use it to size my positions.

Regards

 

[OddTrader]

Quote from gbos:

I am convinced that this is the best way and I use it to size my positions.

Regards

When you mention "1/10 Kelly = 9%", are you implying Kelly = 90%? Why use 1/10? Are you using 1/10 of Kelly all the times? I'm just curious, and wondering. TIA.

 

[gbos]

Quote from OddTrader:

When you mention "1/10 Kelly = 9%", are you implying Kelly = 90%? Why use 1/10? Are you using 1/10 of Kelly all the times? I'm just curious, and wondering. TIA.

Yes I imply that in this example Kelly=90% so 1/10th Kelly is 9%. The fraction of Kelly you are going to use depends on many factors. First is how tolerant are you to drawdowns. For example there is 34% chance that you are halved before doubled if you are using 1 (full) Kelly.

Other considerations are how uncertain you are about your system statistics. Uncertainties in system’s expectancy, variance etc. must be taken into account before making a meaningful choice.

Also you need to make considerations for black swans by assuming a small but non zero probability to a very damaging event. This also must make you more conservative in choosing the appropriate Kelly fraction.