Expectancy is always zero
In fact, without some advantage, expectancy is negative because of commissions and spreads. Here's the reason why.
Most traders will be knowledgeable about the standard expectancy equation:
W = win rate
G = average Profit (or predefined TP when there's one)
L = average reduction (or predefined SL point if there's one)
Expectancy = WG - (1-W)L
This is similar to trading math 101 but it is extremely persuasive to new traders who believe that it is the trick to sure consistent achievement. After all if I cut my losses to ten pips, and let my transactions run to 30 pips, then if I win 30% of the time then I would still be ahead!
That is of course since (0.30 x 30) - (0.70 x 10) = 9 - 7 = 2 pips/trade.
Wow! Any dolt can be appropriate only 30% of the time, so all I must do is make a million transactions and I'll be up two million pips! Right? Right????
Ummm, no. :
Let's get beyond trading math 101 to another step. What's wrong with the train of thought over is that the win rate is actually a function of your risk/reward ratio.
Suppose you set your stop at 1 pip along with your TP at 800 pips on every transaction. How many do you think you would win? Your triumph rate would be virtually zero. Now if you reversed the position and set your TP at 1 pip along with your stop at 800 pips then your win rate would be quite close to 100% If your SL and TP are at precisely the same distance from your entrance, then your win rate should be about 50%. In reality, your win rate (all else being equal) should be equal to the distance to the stop divided by the whole distance from the stop to the goal.
For example if your SL is 20 pips from entrance along with your TP is 80 pips from entrance, then your win rate on transactions such as that should be around 20%. If you specify a stop at 20 pips and a TP at 5 pips then your win rate should be about
20 / (20 5) = 20/25 = 80 percent
So I am saying that in regard to the factors in the typical expectancy equation, the win rate is actually equal to: L / (L G)
So let us plug that into the expectancy equation and see what we get will we? We started with:
E WG - (1-W)L
but today we know that W = L (L G) so...
E = LG / (L G) - L L^2 / (L G) note: L^ is L shaped squared.
Multiplying the center term on the right by (L G)/(L G) that is 1:
E = LG / (L G) - L(L G) / (L G) L^2 / (L G)
mixing into one fraction with a common denominator:
E (LG - L(L G) L^2) / (L G)
E = (LG - L^2 - LG L^2) / (L G)
E= 0 / (L G)
E = 0
And that in a nutshell is why trading can be difficult. Just on tap bromides that are old like cut your losses and let your profits run, or you can't go broke taking profits, although they sound good will not get you everywhere.
Sure, if you cut your losses short, you know what you get? A lot of small losses that just about equal your big wins that are infrequent. If you abide by the opposite suggestions that you can't go broke taking profits, and opt to use stops and goals guess what? You get a lot of small profits that just about make up for that reduction you take every so often.
All of those cute slogans do nothing more than represent different points across the risk/reward spectrum, but traders should bear in mind that every one of these points has an expectancy of roughly zero. And that's not such prices. So forget the slogans. The trick to trading is to find an advantage that moves that E value to the positive side of your prices.
