How tiny edge compounds.

Sekiyo said:
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%
More...
This is completely wrong.

Your expectation is not 0.0012, it is closer to 0.0008,

Formula for Kelly growth:

growthRate = 0.35 * 2 * ln(1 + 0.025) + 0.65 * 1 * ln(1 - 0.025)

growth Rate = 0.0008282536

exp(growthRate * 252) - 1 = 0.2320999

23% per annum, not 37%
 
Went to an online calculator and it says :

View attachment 218291
You tell me 0.08% and I get 0.12%... Strange.

We all agree about betting 2.5%.

I was indeed using an arithmetic mean rather than a geometric one.
Thanks for pointing this out. I was biased upward !

EDIT

The formula looks like this:
y = p * ln(1 + b * x) + (1 - p) * ln(1 - x)
y= 0.35 * ln(1+2*0.025) + 0.65 * ln(1-0.025)

Found 0.06% too.

However as per Monte Carlo, the average growth for the strategy is 37%
upload_2020-2-2_9-17-52.png


So I am not sure what to believe.
I do prefer Monte Carlo though.
 
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traider said:
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.
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Though it also shows that tiny edges may not exist when you take risk. They don’t want to be a prop firm, they make money by not taking risk, and hedge immediately when there would be risk. They would probably close the business if they were forced to “trade” vs being a service provider. And their compounding may work due to millions of trades (and strategies) vs an example number of 4 strategies discussed here.
They also don’t seem to grow every year. Their stock is often going down, so that compounding is suspiciously weak.
 
stock price doesnt indicate if firm makes money or not. Stock price is what is paid to shareholders, management can pay themselves a bundle before any leftover for shareholders.
Quant traders are paid at least 300K for mid level.
 
traider said:
stock price doesnt indicate if firm makes money or not. Stock price is what is paid to shareholders, management can pay themselves a bundle before any leftover for shareholders.
Quant traders are paid at least 300K for mid level.
More...


Of course. Though their revenues seem to be down in 2019 from 2018. At least they don’t seem to be compounding much.
But I do agree that they’re not a bad example to look at, just also consider the limitations of both the edge, the capacity, compounding, expenses, etc.
 
It all makes sense in theory...

If (true condition), then (true condition)...

If only we could trade like machines and not allow emotions or pride to cause losses!
 
Sekiyo said:
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
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The tiny edge is negative after factoring commission, fees, spread and a very slight change of market environment against you.
 
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