The "Holy Grail" Formula for Trading

Let’s develop the “holy grail” formula for trading.

Collect all the trades you did last year, separate them into two groups: winners and losers. Now calculate the following:

AverageWin=(Sum of all winners in dollar amount)/(total number of winners)
AverageLoss=(Sum of all losers in dollar amount)/(total number of losers)

Total numbers of trades= (Total number of winners) + (Total number of losers)

Win% = (Total number of winners)/ (Total numbers of trades)
Loss% = (Total number of losers)/( Total numbers of trades)


Total Profit = (Sum of all winners in dollar amount) – (Sum of all losers in dollar amount)

Divided by (Total number of trades) on both sides of the above equation,

(Total Profit)/(Total number of trades) = (Sum of all winners in dollar amount)/ (Total number of trades) – (Sum of all losers in dollar amount)/ (Total number of trades)

Now let’s study the first term of right side of the equation: (Sum of all winners in dollar amount)/ (Total number of trades)

(Sum of all winners in dollar amount)/ (Total number of trades) = AverageWin * Win%

Similarly,

(Sum of all losers in dollar amount)/ (Total number of trades) = AverageLoss * Loss%

Now let’s define:

Average Profit per trade =(Total Profit)/(Total number of trades),

Now we have:

Average Profit per trade= AverageWin * Win% - AverageLoss * Loss%

Since Loss%=1-Win%, so the above equation becomes,

Average Profit per trade= AverageWin * Win% - AverageLoss * (1-Win%)

Average Profit per trade= (AverageWin + AverageLoss )* Win% - AverageLoss

Now if divided both sides by AverageLoss,

(Average Profit per trade)/(AverageLoss)=(1 + AverageWin/AverageLoss) *Win%– 1

Before we continue to make conclusions from the equation, let’s use some actual numbers. Let’s say your collect all your trades last year, the numbers are as follows:

Total Trades=100;
Total number of winners=60
Total number of losers=40
Sum of all winners = $12,000
Sum of all losers = $4,000
Total Profit=$12000 - $4000 = $8000
Average Profit per trade=$8000/100=$80

AverageWin = $12000/60 = $200
AverageLoss = $4000/40 = $100
Win%=60/100

Now let’s calculate the right side of our final equation:

(1 + AverageWin/AverageLoss) *Win%– 1 = (1+ 200/100) * 60% -1 = 1.8 -1 = 0.8

So,
(Average Profit per trade)/(AverageLoss)=0.8 =80%
Or,

(Average Profit per trade)=80% * (AverageLoss) =0.8*100=$80.


Now let’s again look at more details about this equation

(Average Profit per trade)/(AverageLoss)=(1 + AverageWin/AverageLoss) *Win%– 1
We can make the following conclusions:

If the right side (1 + AverageWin/AverageLoss) *Win%– 1 is equal to 0, then Average profit per trade is zero

If the right side (1 + AverageWin/AverageLoss) *Win%– 1 is less than 0, then Average profit per trade is less than zero, i.e., we will lose

If the right side (1 + AverageWin/AverageLoss) *Win%– 1 is greater than 0, then Average profit per trade is always positive, i.e., we will win.

In summary, if we want to win, all we have to do is to make
"(1 + AverageWin/AverageLoss) *Win%– 1" great than zero.

We can call the term as “expected gain” or I’d like call it “Edge”

"Expected Gain" or Edge = (1 + AverageWin/AverageLoss) *Win%– 1
To be winners in the market, all we have to do it is to make “Edge” positive.

There are two factors determine the Edge:

1.The ratio of AverageWin/AverageLoss
2.The win%

Engineers are usually smart people, they always try to be perfect. That’s why they always try to get a higher Win%.

“…engineers and accountants are usually bad traders” -claimed by many trading experts, especially people with psychology backgrounds in books or internet articles.

Let’s say your Win% is 80%, but AverageWin=100, AverageLoss=1000,

Your Edge or expected gain is

(1+ 100/1000)*0.8 -1 = -0.12, Which is NEGATIVE, that means you will lose money.

So, Win% is 80% means nothing if your AverageWin/AverageLoss is small.

Now, if your Win% is only 50%, but your Win/Loss ration is 2, then your edge is

(1+2)*0.5 – 1 =0.5

That means you will win.

“My percentage of winners is only about 50/50, because I cut my losers very quickly. The maximum loss I allow is 7 percent, and usually I am out of a losing stock a lot quicker. I make my money on the few stocks a year that double and triple in price. The profits in those trades easily makes up for all the small losers. “ - David Ryan
Next time, if you see some advertisements such as this one, "Join us, Trade Stocks, Futures, And Forex With Up To 80% Accuracy …",you know what to ask them.



“Human nature does not operate to maximize gain but rather to maximize the chance of a gain. The desire to maximize the number of winning trades (or minimize the number of losing trades) works against the trader. The success rate of trades is the least important performance statistic and may even be inversely related to performance.
Two of the cardinal sins of trading - giving losses too much rope and taking profits prematurely - are both attempts to make current positions more likely to succeed, to the severe detriment of long-term performance.”- William Eckhardt