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Discussion in 'Risk Management' started by kut2k2, Mar 4, 2013.

1. ### kut2k2

There is Good Kelly and there is Bad Kelly.

K = p - (1-p)/(W/L) , where

K is the Kelly ratio,
p is the winrate,
W is the average winning trade,
L is the absolute value of the average losing trade.

It is the result of some dunce shoehorning trading into the simplest form of Kelly, that derived from the basic casino bet. It is based on the incredible assumption that your average losing trade is identically equal to your trade size.

That. Never. Happens.

Not in the real world of trading, it doesn't.

This "win/loss form of Kelly" is the one responsible for Kelly's undeserved reputation of blowing up trading accounts. Good Kelly never blows up trading accounts.

One form of Kelly that is much better is

K = p/S - (1-p)/R , where

K is the Kelly ratio,
p is the winrate,
R is the average winning trade return,
S is the absolute value of the average losing trade return.

* * *

Let's look at an example :

There is a 70% chance that you lose your bet.
There is a 10% chance that you lose five times your bet.
There is a 20% chance that you win ten times your bet.

As demonstrated in my previous Kelly thread (qv), the exact Kelly fraction is .0451

Using Bad Kelly, we calculate K = .2 - .8/(10/1.5) = .0800

Using LessBad Kelly, we calculate K = .2/1.5 - .8/10 = .0533

Clearly both results are overbetting (always a bad thing) due to simplifying a 3-outcome situation down to a 2-outcome situation, but Bad Kelly is the worst by a lot.

Always use Good Kelly (see my previous Kelly thread) and avoid Bad Kelly.

espresso likes this.
2. ### Yana

kut2k2,

Thank you for this post. Following up for everyone's benefit and hoping to raise an intelligent debate:

- Where did this "good kelly" formula come from, can you explain the rationale behind it?

- What would be the argument to use "good kelly" instead of say half-kelly which many people advise

- How does one determine overbet? A lot of places throw out do not risk more than 2%/5%/x% of capital per bet, if by that rule we wouldn't need to talk about good/average/bad kelly ratios.

Yana

3. ### kut2k2

It's all been explained in my previous Kelly thread (qv). If I post the link for you then you won't become familiar with the search page which would be bad. Just use kut2k2 as the username, use Kelly as the keyword, check the title box at the bottom and hit the search button.
Nothing wrong with using half-Kelly but you don't know what that is until you determine what the full Kelly fraction is. That's what the Good Kelly is for, to get you to the real Kelly fraction, then you can go to half-Kelly if you want.
Overbetting is when your trading fraction is larger than the Kelly fraction for your particular trading situation. Because the Kelly fraction represents the point of maximum geometric growth of your trading account, going past that point both decreases your growth rate and increases your maximum possible drawdown. That's a lose-lose situation, which is why overbetting is always bad.

If you stick to the 2% rule and your Kelly ratio is 10%, you're leaving an awful lot of money on the table. Your choice of course but some people don't want to take forever to make significant market gains.

The appeal of half-Kelly and other fractional Kelly strategies is to decrease the maximum account drawdowns but all of that is dependent on knowing what the actual Kelly fraction is.

Do a Google search on "fractional Kelly" to find all the alleged advantages.

4. ### traitor786

Putting aside that the Kelly was actually developed to clean up static on phone lines and not trading.

I vote for the original Kelly as it makes more sense in the long run in the real world of trading.

6. ### small_beer

So do I. This is a very simple formula and it is rather unlikely that you can squeeze much out of it by some small modifications.

8. ### traitor786

Have you decided to no longer use the formulae?

9. ### traitor786

Its long and complex and has those Z type symbols, he must know his stuff. To top it off, it is was presented in Canada. It is a bit hard for me test the idea from my igloo.

I just have one question, around page 10 or 20 we see that .5 becomes 0.51.

Being mathematically stupid, I wonder If I can simply copy and past the 0.51 over my current P value. Do I really need the rest of the formulae?

Also I wonder if you can show that this strategy is better then mine :

If P =(P+K) Where P is the "real" probability K is a copy and past of .01
and K is > then cost of trade (fees)
Then use U- D.D.-BS at T intervals to create Pr
After every T, add Pr to U-D.D and repeat.
(Here U= the unlimited amount of money used in the article
D.D= the maximum draw down in dollars, BS= black swan in dollars and T = time as a TICK and Pr = profit)

Simplified It is BS=U
Which further simplifies to U= Happy
So all that is needed is U to be happy, and the market is to occupy your time.
Now if you do not have U, you can simply deduce BS=Happy
It seems silly but shorting a black swan would be neat. I estimate the odds of that happening at the inverse of 95% or 5%.

You are seriously telling me that your trade plan revolves around math that has Such variables ? Seriously ? Unlimited money ?

Look, the article seems well written and alot of thought put in to it. Pages are given to the formulae, one paragraph is given to the math of getting a 1% edge by trading correlated instruments. If you have a 1% edge, you only keep her around for her company.

Maybe I missed the part about the black swan or 1 % or an example of a fixed number of dollars.

10. ### kut2k2

Thorpe overcomplicates things. Besides, his presentation is fantasy. He's talking about investors with no transaction costs in a world of continuous prices. I live in the real world where (a) I'm a trader, not an investor, (b) I pay real transaction costs, not zero transaction costs and (c) prices are not continuous, i.e., price gaps are real.

Come back when Thorpe writes a paper based in the real world, not his Disneyland version of the markets.

#10     Mar 9, 2013
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