# Tradesim Expectancy



## AMSH (30 March 2009)

Hey,

I've got some Tradesim results that are confusing me. The results are as follows:

System 1
Win Rate: 47%
Avg Win:1,612
Avg Loss: 364
Win/Loss: 4.42
Expectancy ((Win/Loss*Win Rate)-Loss Rate): 1.54
Expectancy as per Tradesim Report: 1.49

System 2
Win Rate: 42.5%
Avg Win: 3,168
Avg Loss: 758
Win/Loss: 4.17
Expectancy ((Win/Loss*Win Rate)-Loss Rate): 1.19
Expectancy as per Tradesim Report: 1.76

So why does the second system show stronger expectancy if the stats are weaker? Is the expectancy calc used by TS different to that above (inclusion of standard error or something)? I've had a look in the TS manual and can't find anything relating to the calculation. Even if the calculation is different, I can't imagine what would make such a large difference to the result - system one seems a million miles better than the second (system one also has lower DD). Any ideas?

Any help greatly appreciated,

Cheers,

AMSH


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## pilbara (30 March 2009)

if both systems utilise the same amount of capital, then the second one makes more money, the wins/losses are nearly twice the size of the first

I can't make the figures work out exactly, but if the first system has closer to 48% win rate, then

system 1 expectancy = 0.48*1612 + 0.52*364 = $584.48
system 2 expectancy = 0.425*3168 + 0.575*758 = $910.55

so if both systems started with $100,000 and made 84 trades
system 1 = $100000 + 84*548.48 = $149096.32
system 2 = $100000 + 84*910.55 = $176486.20

system 1 multiple of original capital = 1.49
system 2 multiple of original capital = 1.76


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## AMSH (31 March 2009)

Hey Pilbarra,

Thanks for the reply. 

I'd actually considered what you put forward as the problem, but had thought that this couldn't be the answer. I thought that expectancy wouldn't be affected by the dollar value of the avg win and avg loss, but only their values in comparison to one another - in other words the win/loss ratio. In theory a system with avg win of $10 and avg loss of $1 should return the same expectancy as one with $100 and $10 respectively because the win/loss is the same in both cases.

If the actual dollar values associated with avg win and loss do have an effect, then doesn't this mean that when using expectancy as a performance measure, we should:
1. Never use profit pyramiding
2. Always use the same position value amount per trade

I've expanded the testing results below to reflect all the required info.

System 1
Capital: $20,000
Trades: 90
Win Rate: 46.67%
Avg Win: $1,612
Avg Loss: $364
Win/Loss: 4.42
Expectancy ((Win/Loss*Win Rate)-Loss Rate): 1.529
Expectancy as per Tradesim Report: 1.49

System 2
Capital: $20,000
Trades: 212
Win Rate: 42.45%
Avg Win: $3,168
Avg Loss: $758
Win/Loss: 4.178
Expectancy ((Win/Loss*Win Rate)-Loss Rate): 1.198
Expectancy as per Tradesim Report: 1.76

So using the updated stats, your calcs would look like this:
System 1 expectancy = 0.4667*1612 - 0.5332*364 = $558.24
558.24 / 364 = 1.533 Expectancy

System 2 expectancy = 0.4245*3168 - 0.5755*758 = $908.59
908.59 / 758 = 1.198 Expectancy

So if both systems started with $20,000 and made X trades
System 1 = $20000 + (90*558.24) = $70,241.60 (this is correct as per TS)
System 2 = $20000 + (212*908.59) = $212,621.08 (this is correct as per TS)

System 1 multiple of original capital = (70,241.60 / 20000) = 3.51
System 2 multiple of original capital =  (212,621.08 / 20000) = 10.63

This can't mean that I've got systems with 3.51e and 10.63e.

I thought I had a good grasp of what expectancy represented but I'm lost on this one.

Any ideas?


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## tech/a (31 March 2009)

I'll Direct David Samborsky the designer of Tradesim to this thread to help sort it out.


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## pilbara (31 March 2009)

AMSH said:


> So if both systems started with $20,000 and made X trades
> System 1 = $20000 + (90*558.24) = $70,241.60 (this is correct as per TS)
> System 2 = $20000 + (212*908.59) = $212,621.08 (this is correct as per TS)



Did the systems make these trades over the same time period, for example 3 months, so system 1 only made 90 trades in 3 months compared to system 2 making 212 trades in 3 months?  I don't have TradeSim so I'm not sure what is included in the expectancy.  Given positive expectancy a system that worked your capital harder (traded more frequently) would be better.


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## AMSH (31 March 2009)

Thanks for that Tech.

Pilbara,
Yes, both systems are based on the same period.


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## pilbara (31 March 2009)

AMSH said:


> If the actual dollar values associated with avg win and loss do have an effect ...



I think what's important is the percentage of capital at risk, and maybe it's the worst loss (stop loss level?) rather than average loss that is being used.

Using the average loss of system 2, that's 3.79% of capital, compared to system 1 at 1.82%.  So to compare systems with equal risk, we'd need to use a smaller position size of 0.48 in system 2, compared to position size of 1.00 in system 1.

System 1 = $20000 + (90*558.24) = $70,241.60
System 2 = $20000 + (0.48*212*908.59) = $112,458.12


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## TradeSim (31 March 2009)

TradeSim calculates the trade expectancy as a normalized expectancy. This is because expectancy assumes constant dollar risk per trade, but if you use anything other than the fixed dollar risk positions size models then the risk per trade is not constant and varies from one trade to the next. For example the fixed % risk model assumes risk based on the total trading capital at any one time. If pyramid profits is enabled and trade equity increases so to will the risk and vice versa when equity decreases.

TradeSim calculates normalized expectancy as the average of all the trade R-multiples (reward to risk ratio). This has the effect of ignoring the heavier weighting given to trades where more dollar risk has been applied.


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## AMSH (31 March 2009)

Ok, cool. I'm pretty sure I follow that. 

My main concern with this was that I'd been using the expectancy values across systems using vastly different criteria and if, as it seemed, the expectancy was affected by these criteria then the only way to compare using expectancy is to turn off pyramiding and have minimal money management (like a constant dollar value). 

The normalisation of the results is what gives rise to the discrepancies described above, and also makes it possible to compare systems with different money management setups. 

So logically, the standard expectancy calculation (win rate * avg win) - (loss rate * avg loss) would only provide rational figures when the same dollar value is used for each trade in the sample (hence no pyramiding and minimal money management). Correct me if I'm wrong.

Cool. Thanks for the input gents.


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## pilbara (31 March 2009)

that makes sense now. TradeSim gives you the expectancy of the single path using the actual distribution of Rmultiples, instead of a ratio of averages afterwards.  There's always danger in using an average (a single number) to represent a distribution.  Maybe TradeSim can show a graph of the Rmultiple distribution and you can use those pictures to visually compare the two systems.  Also TradeSim is famous for the monte-carlo analysis where you could do many runs and then see a variety of expectancy values for the one system.


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## TradeSim (31 March 2009)

AMSH said:


> Ok, cool. I'm pretty sure I follow that.
> 
> My main concern with this was that I'd been using the expectancy values across systems using vastly different criteria and if, as it seemed, the expectancy was affected by these criteria then the only way to compare using expectancy is to turn off pyramiding and have minimal money management (like a constant dollar value).
> 
> ...




Correct. It assumes that the dollar risk per trade is always constant.


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## TradeSim (31 March 2009)

pilbara said:


> that makes sense now. TradeSim gives you the expectancy of the single path using the actual distribution of Rmultiples, instead of a ratio of averages afterwards.  There's always danger in using an average (a single number) to represent a distribution.  Maybe TradeSim can show a graph of the Rmultiple distribution and you can use those pictures to visually compare the two systems.  Also TradeSim is famous for the monte-carlo analysis where you could do many runs and then see a variety of expectancy values for the one system.




There is always a danger in using any single metric to characterize a trading system. Those who have tested a portfolio trading system using the Monte Carlo analysis in TradeSim will realize that trying to characterize a trading system using one single metric can be a red herring because of the statistical variations in results from one simulation to another.

Even if you did use a fixed risk position size model and calculated the correct expectancy then this figure would not necessarily apply to other simulations where you had random selection of multiple entry triggers. In this case each time you ran a simulation you would end up with a different expectancy.


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