Expectancy & Expectancy Uncertainty - Psychology and Money Management | futures io social day trading
futures io futures trading


Expectancy & Expectancy Uncertainty
Updated: Views / Replies:1,217 / 4
Created: by serac Attachments:0

Welcome to futures io.

(If you already have an account, login at the top of the page)

futures io is the largest futures trading community on the planet, with over 90,000 members. At futures io, our goal has always been and always will be to create a friendly, positive, forward-thinking community where members can openly share and discuss everything the world of trading has to offer. The community is one of the friendliest you will find on any subject, with members going out of their way to help others. Some of the primary differences between futures io and other trading sites revolve around the standards of our community. Those standards include a code of conduct for our members, as well as extremely high standards that govern which partners we do business with, and which products or services we recommend to our members.

At futures io, our focus is on quality education. No hype, gimmicks, or secret sauce. The truth is: trading is hard. To succeed, you need to surround yourself with the right support system, educational content, and trading mentors – all of which you can find on futures io, utilizing our social trading environment.

With futures io, you can find honest trading reviews on brokers, trading rooms, indicator packages, trading strategies, and much more. Our trading review process is highly moderated to ensure that only genuine users are allowed, so you don’t need to worry about fake reviews.

We are fundamentally different than most other trading sites:
  • We are here to help. Just let us know what you need.
  • We work extremely hard to keep things positive in our community.
  • We do not tolerate rude behavior, trolling, or vendors advertising in posts.
  • We firmly believe in and encourage sharing. The holy grail is within you, we can help you find it.
  • We expect our members to participate and become a part of the community. Help yourself by helping others.

You'll need to register in order to view the content of the threads and start contributing to our community.  It's free and simple.

-- Big Mike, Site Administrator

Reply
 
Thread Tools Search this Thread
 

Expectancy & Expectancy Uncertainty

  #1 (permalink)
Elite Member
Arizona, USA
 
Futures Experience: Intermediate
Platform: NinjaTrader
Broker/Data: MB Trading
Favorite Futures: Cello
 
serac's Avatar
 
Posts: 116 since Jan 2011
Thanks: 321 given, 137 received

Expectancy & Expectancy Uncertainty

As I develop and refine several discretionary and automated strategies, I have encountered the nagging question of "How do I know I have enough data to support going live with this method?" I am sure most everyone here at Big Mike's would say to look at the expectancy. Recent conversations with RM99 made me think more.

Expectancy is a good metric. But, like all statistical measures, expectancy is easy to misuse. A profitable system must necessarily have a positive expectancy. But, how do you know your expectancy is positive? There is uncertainty in all the parameters you use to compute expectancy, and thus, there is necessarily uncertainty in the expectancy metric itself.

Below, I am going to derive a simple measure of expectancy uncertainty. I am sure others could do better, as statistics is not my strong point. This is the take-home idea: If your expectancy uncertainty is greater than your expectancy, you cannot say for certain that your expectancy is not negative.

The expectancy, E, of a set of trades with a gain/loss set of T = {x1, x2, x3, ..., xN}, is:

E = Pwin * Xwin - Plose * Xlose,

where P is the probability of a winning trade (number of positive T entries divided by N, the length of T), Xwin is the average win gain (average of all positve entries in T), Plose is the probability of losing (Plose = 1- Pwin), and Xlose is the average loss (average of all negative entries in T). Note that in this notation, Xlose is a positive number because I have used a negative number before Xlose in the equation above.

Now, Pwin, Xwin, and Xlose are actually estimates. We do not know their "true" values because we have a finite trade history. The less data we have (the shorter data set T), the more uncertainty we have of these estimates. The total uncertainty of expectancy is determined via the propagation of uncertainty of these point estimates.

We'll call the uncertainty of expectancy UE. You calculate UE using calculus (the sum of the absolute values of the product of point estimate untertainties and the derivative of E with respect to each variable) that I won't show here unless somebody really wants to see it (if you actually care then you can probably do it yourself). When I do the math, I get:

UE = (Xwin + Xlose + Pwin(Swin - Slose) + Slose)/ Sqrt(N)

where Swin and Slose are the standard deviations of the profit/losses of the winning and losing trades, respectively. I am using the uncertainty of Pwin to be 1/sqrt(N), and the uncertainty of the means to be the sample standard deviations over sqrt(N).

The idea is that your expectancy must be greater than the expectancy uncertainty. We can equate a breakeven point by assuming that the uncertainty always goes against you:

E == UE

From this equation, we can solve for N, the minimum number of trades to prove positive expectancy:

N = (Xwin + Xlose + Pwin*Swin + Plose*Slose) / (Pwin*Xwin + Plose*Xlose)

Note that the signs before Plose*Slose and Plose*Xlose are both positive (this means that the denominator isn't quite expectancy itself).

Let's say you have a swing system with the following performance:

Pwin = 75%
profit factor = 0.5 (Xwin/Xlose),

and for simplicity, let us say Swin = Slose = 0 (we're lazy).

This profit factor and Pwin yields an expectancy of 12.5%. But, to prove that this estimate of expectancy is actually greater than zero, you need (using the formula above) N = 144 trades. If Swin and Slose are nonzero (and we know they are), your N balloons into a larger number.

To say it a different way,
For N < 144, UE > 12.5%,
for N >=144, UE <= 12.5%

Letting Swin = 2 and Slose = 1, we get N = 676 (it pays to keep track of your sigmas!).

So, to show that you have positive expectancy, you a) need to show positive expectancy, and b) show that you have a sufficient number of trades.

Hopefully this helped somebody?

Reply With Quote
The following 2 users say Thank You to serac for this post:
 
  #2 (permalink)
Quick Summary
Quick Summary Post

Quick Summary is created and edited by users like you... Add FAQ's, Links and other Relevant Information by clicking the edit button in the lower right hand corner of this message.

 
  #3 (permalink)
Elite Member
Bellingham, WA
 
Futures Experience: Intermediate
Platform: Ninja
Broker/Data: Zen-Fire
Favorite Futures: 6E, CL
 
Dragon's Avatar
 
Posts: 494 since Aug 2009
Thanks: 747 given, 253 received


I am not seeing the math, how did you get 12.5% in your example? It seems you need to know the value of either Xwin or Xlose in your profit factor of .5 to solve for expectancy.

Reply With Quote
 
  #4 (permalink)
Elite Member
Arizona, USA
 
Futures Experience: Intermediate
Platform: NinjaTrader
Broker/Data: MB Trading
Favorite Futures: Cello
 
serac's Avatar
 
Posts: 116 since Jan 2011
Thanks: 321 given, 137 received


Dragon View Post
I am not seeing the math, how did you get 12.5% in your example? It seems you need to know the value of either Xwin or Xlose in your profit factor of .5 to solve for expectancy.

I should have explained that better - I was trying to make it simpler. Let Xwin = f, and Xlose = 1 so that your average wins are normalized to your average loss. In these terms, a breakeven expectancy equals one. So, a positive expectancy of 12.5% is 1.125.

I was writing this all from memory, and I didn't want to make up unrealistic numbers. Looks like I may have muddied things.

Reply With Quote
 
  #5 (permalink)
Elite Member
Bellingham, WA
 
Futures Experience: Intermediate
Platform: Ninja
Broker/Data: Zen-Fire
Favorite Futures: 6E, CL
 
Dragon's Avatar
 
Posts: 494 since Aug 2009
Thanks: 747 given, 253 received

So what is f?

Reply With Quote

Reply



futures io > > > Expectancy & Expectancy Uncertainty

Thread Tools Search this Thread
Search this Thread:

Advanced Search



Upcoming Webinars and Events (4:30PM ET unless noted)

Jigsaw Trading: TBA

Elite only

FuturesTrader71: TBA

Elite only

NinjaTrader: TBA

Jan 18

RandBots: TBA

Jan 23

GFF Brokers & CME Group: Futures & Bitcoin

Elite only

Adam Grimes: TBA

Elite only

Ran Aroussi: TBA

Elite only
     

Similar Threads
Thread Thread Starter Forum Replies Last Post
Expectancy and SQN RM99 Psychology and Money Management 6 August 18th, 2011 12:54 AM
Expectancy custom fitness sam028 EasyLanguage Programming 13 September 29th, 2010 10:23 PM
Expectancy Big Mike Terms (Glossary) 0 July 11th, 2010 10:12 PM
Minimum tradable expectancy? solom113 Traders Hideout 2 January 29th, 2010 02:37 AM
Expectancy/Probability for zwentz steve2222 Psychology and Money Management 0 November 8th, 2009 01:59 AM


All times are GMT -4. The time now is 07:00 PM.

Copyright © 2017 by futures io, s.a., Av Ricardo J. Alfaro, Century Tower, Panama, +507 833-9432, info@futures.io
All information is for educational use only and is not investment advice.
There is a substantial risk of loss in trading commodity futures, stocks, options and foreign exchange products. Past performance is not indicative of future results.
no new posts
Page generated 2017-12-14 in 0.10 seconds with 19 queries on phoenix via your IP 54.226.227.175