System's Expectancy
Author: akardar1
Creation Date: 9/25/2009 6:21 AM

#### akardar1

#1
Hi,

Where does WL5 stand with regards to Expectancy?
How does one go about getting a system's expectancy?
I can see some WL4 forums where this was discussed and 'perfscript' was mentioned.

#### Eugene

#2
Hi,

Wealth-Lab 5 doesn't have "Expectancy" currently.

Sounds like you have a formula for "Expectancy"? Have you already tried to code it?

#### akardar1

#3
Hi Eugene

Positive expectancy is defined as how much money, on average,
we can expect to make for every dollar we risk .

E(R) = (PW x AW) - (PL x AL)

where;

E(R): Expectancy/ or Expected Return
PW: Probability of winning
AW: Average win
PL: Probability of losing
AL: Average loss

I havent tried to code it, i thought I'd check if you could point me in the right direction,
as I can see that it was raised a few times in WL4 forums.

#### Cone

#4

Then, PL = 1 - PW

#### Eugene

#5

How do you plan to utilize the formula, in Strategy code or somewhere else?

#### akardar1

#6
Ideally, this would be something used as a performance measure.
I am assuming it would be best utilized in either the "Performance Extras" or "Strategy Ranking"
I am trying to see how I would go about taking this concept forward....
it is outlined by Tharp is his latest book "The definitive guide to Position Sizing"
I think Pardo's book may have also outlined a similar concept.. but dont quote me.

Expectancy (corrected)= (((AW*PW) - (AL*PL)) / avg risk amount)

"Expectancy" will give us the mean (average) R-muliple (risk reward) for a system.
"Variability" would be the standard deviation of expectancy.
"Expectunity" How many R we expect to be up after 1 month (or how many times our intial risk)

*************************************************************************************************
Example:

7 -1R
1 -5R
2 +10R
20% win rate

So...
(7*-1) + (1*-5) + (2*10) = Total 8R
Expectancy = 8R / 10 trades = 0.8
Expectunity = 0.8 * 25 trades per month = 20R

***************************************************************************************************
Then...

System Quality Number (SQN)
We can now evaluate the system based on its SQN, where:

SQN = ((Expectancy / Std Dev "R") * Square root of number of trades)

As apposed to just expectancy, this method considers the variability of the system.
So system will have:
- Expectancy / Std Dev = 0.16
- Square root of number of trades = 5
- SQN = 0.8

Would be useful to generate this number (SQN) on square root of a number of trades generated in one year,
OR the square root on a fixed number of trades, like 100. Using the latter, Tharp states:

Quality score
< 1 Probably hard to trade
1.01-2.00 Average system (needs 1.7 to be statiscally signigicant)
2.01-3.00 Good system
3.01-5.00 Excellent Sytem
5.01-7.00 Superb System (few exist)
> 7 Holy Grail sytem .......... i doubt many fall here.

NOTE: one issue with this is that when you have too many trades, it can strong overestimate the SQN.
if you have over 100 trades, just multiply the ratio (of expectancy divided by std dev) by 10, so we assume we have 100 trades.

For stats fans, Tharp mentions that this method is basically a t-score, 'comparing one sample agaisnt an assumed mean of zero, if you have a positive expectancy, the t-score shows whether or not your results are significantly different from a zero or negative return. The higher the SQN,the more likely is it that we can reject the hypothesis that it has a negative or zero return on the average'.

There is probably alot of "noise" here.. but wanted to run this concept past you.
Is any1 familiar with this ? How would one implement this ?
R is just Risk, so the concept also hold for risk/reward...

#### Eugene

#7
QUOTE:
I am assuming it would be best utilized in either the "Performance Extras" or "Strategy Ranking"

Agreed. I think we have all set up in their code to add Expectancy in both places.
QUOTE:
Expectancy (corrected)= (((AW*PW) - (AL*PL)) / avg risk amount)

Hmm, I'm somewhat reluctant to include multiple versions of the same thing so as not to confuse the other users; in addition, a) what's that "avg risk amount" is, percentage or dollar? b) where can I read about what for was it included in the formula?
QUOTE:
"Expectancy" will give us the mean (average) R-muliple (risk reward) for a system.

By the way, we already have the "average risk/reward" number for a system in Perf.Extras and Ranking/Optimization.
QUOTE:
"Variability" would be the standard deviation of expectancy.
"Expectunity" How many R we expect to be up after 1 month (or how many times our intial risk)

From the context, I can't see why these metrics are mentioned?
QUOTE:
SQN = ((Expectancy / Std Dev "R") * Square root of number of trades)

This one will be pretty trivial to include in the next release of Community.Visualizers since we already have it all (working internally).

#### akardar1

#8
1 - Great, this should facilitate the implementation.

2 - I agree that multiple versions would be confusing, however, the second version is correct as per Tharp. The 1st version I posted apparantly adds less value, version 2 is more useful because it
expectancy will reflect the average profit per dollar risked, whereas version 1 only gives the average profit, in his latest book, he admits to having adjusted the formula.

A)I assuming as most useful would be % of risk/reward (R) number, as the \$ amount becomes irrelevant as the account equity grows and the "avg amount" would not be a constant.

B)Some of these expectancy concepts are outlined in "Trade your way to financial freedom"(2nd edition)
Also, the new book "Definitive Guide to position sizing" covers this entire topic,
but i think one can only purchase the book from his site! Maybe I could photocophy/upload some pages?
I have some links pasted below.

3 - Great, this should facilitate the implementation.

4 - "Variability" this is useful alone, but it fits into the SQN formula.
"Expectunity" also useful alone, puts the expectancy into a context which considers number of trades provided by a system.

5 - Great news.

http://www.iitm.com/sm-Expectancy.htm

#### Eugene

#9
Update on SQN:

We're not going to implement it because in latest Tharp's book, SQN is a registered trademark.

#### Eugene

#10
Dr. Van K. Tharp coins the term "Position sizingSM":

Dr. Tharp’s Definitive Guide to Position SizingSM

QUOTE:
I totally eliminated the term money management and coined a new one, position sizingSM.

Psychobabble + copyright mania = explosive!

#### akardar1

#11

The bitter irony... how in the world does one come to own the term 'position sizing'..
I want to apply his metrics to develop a feel for my systems..
I am assuming I can pull the trades from WL into excel (via copy to clipboard)
and get an SQN there if I manually re-create the formula. Would you agree?

#### Eugene

#12
QUOTE:
how in the world does one come to own the term 'position sizing'..

Agreed, that's nonsense.

P.S. A couple of enlightening links from Ed Seykota:

An exchange between Doc Tharp and Seykota
Seykota.com, March 2006

#### Eugene

#13
Once having had an epic fail trying to glue a trademark to a simple math formula and the phrase "position sizing", Van Tharp now has hired a lawyer:

Trader's Roundtable > Trademarks on "Position Sizing" and SQN ("System Quality Number")

Theater of the absurd continues.

#14