How tiny edge compounds.

Your tiny edge : 0.05%

Win.....P(win).....Loss.....P(loss).....E(x)
2,00%...0,35......1,00%.....0,65......0,05%

Knowing your optimal betting size is : 2.50%
Win.....P(win).....Loss.....P(loss).....E(x)
5,00%....""..........2,50%.....""..........0,12%

Trades per day: 1 (Multiply E(x))
E(x): 0,12%

Days per year: 253 (Compound E(x))
E(x): 37,17%

Year...Capital
0.......100 000
1.......137 170
2.......188 157
3.......258 095
4.......354 029
5.......485 623
6.......666 130
7.......913 732
8.......1 253 369
9.......1 719 249
10.....2 358 298

Moral of the story,
1. Find a tiny edge
2. Bet optimally
3. Compound
4. Be patient

EDIT:
5. All models are wrong, but some are useful

 

You are assuming that your edge never goes away. You are also assuming a consistent win/loss ratio as a percentage of an account over years and years. No model is useful if it does not account for the effect of having a loss compounded. By year 7 you get dinged, and lose half of what you earned. Yer back to year 5 again. 2 years of profits up in smoke.

Compounding is great. It is like scaling into winners over and over, until the winner turns into a big loser.

 

I agree. Lots of assumptions. This is too stylistic.
For this kind of simulation, the Monte Carlo method would do a better job at representing the plurality of paths around this idealization.
I believe the Win, Loss ratio can be AND should be consistent over the years if it's part of one's plan. Just take the fibs and do the math to risk your percentage.
As for the edge ... it's a trader's nightmare you're talking about. Even death looks prettier. But adaptation is part of the grand scheme.

Thanks

 

Yeah, tell me about it. I'm having a tough time adapting.

Win 9 out of 10 times and gain 1% of the account, great! Lose one time out of those 10 and lose 1% of the account, your W/L ratio is 90%, but your P/L is zero.

 

Finally done a Monte Carlo :


Guess there is a problem in what you've said.

 

My logic is infallible. If you trade nine times to gain 1% of your account, and then on trade number ten you lose 1% of your account including those profits, you are net zero.

So ten steps up to go 10 steps back. You go nowhere. Put that into your Monte Crisco and smoke it.

And if you do not believe me, GTFO of your simulations, and just trade your darn thing. Prove me wrong about the W/L ratio! Stop running atomic-bomb simulations, and trade your account.

 

Oki. My mistake.
Thought you were sayin +9-1=0
Got nothing to do but to sleep so I toy a little bit.

 

These 4 strategies all have an expectancy of 0.5%
But their P(win), P(Loss), %(Win) and %(Loss) are different.
We can see that strategy that win more often are less volatile / risky.
Even though their R/R is less than 1. Means are the same, profitability is equal.
A mean being lower than its median indicate greater downside risk so don't be fooled by its max.

For comparison I've set the risk equal among strategies (0.99 aka 1%)



This is for 253rd bet according to 50K paths starting from 100.

 

Err do you need to go through all this exercise ? Just read Virtu financial reports and you can see how a tiny edge(HFT) compounds to the moon.

 

Ok but it's less fun to read.

Thanks