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This is part of a thread at Chuck LeBeau's Trader's Club forum... the rest
can be found on the "Overall Trading Questions" page, beginning at the
bottom of the page.
Here's the index: http://www.traderclub.com/discus/board.html search for
"Profit Factor"
- - - - -
(Summary of this is about seven paragraphs down)
It is a common fallacy to believe that either
•1 If % wins is much much greater than % losses, the system will have
positive expectation
•2 If the average losing trade is much much less than the average winning
trade, the system will have positive expectation
Both of these are false. This may be demonstrated by means of trivial
examples.
•1 You and I place bets on a game using a deck of 52 ordinary playing cards.
At each play we shuffle the deck and you draw one card. If you draw any card
other than the Ace of Spades, I pay you $1. But if you draw the Ace of
Spades, you pay me $500.
If you and I play this game for many many draws, you will have a winning
percentage slightly greater than 98% (51/52). Despite this huge winning
percentage, your average profit per draw will be -$8.63. Approximately every
52 draws you will make $51 of profit and -$500 of losses. The "system" has
negative expectation for you --- and positive expectation for me. But it has
a huge winning percentage for you.
•2 You and I place bets on a game using five ordinary dice. At each play you
roll all five dice. If you roll five "1"s, I pay you $5000. But if you roll
any combination of dice other than five "1"s, you pay me $1.
Each roll of the dice only has two possible outcomes: either you win $5000,
or else you lose $1. The average winning trade is +$5000 and the average
losing trade is -$1. This game might appear to be quite favorable: its
average losing trade is much much much less than its average winning trade.
But the game is not favorable. There are 6^5 = 7776 different throws of 5
dice. You make +$5000 profit on one of them, the throw where all 5 dice come
up "1". You make -$1 loss on all the other throws. Your average profit per
throw will be -$0.36. The "system" has negative expectation for you --- and
positive expectation for me, even though the average winning trade is
enormously bigger than the average losing trade.
These little examples show that %wins doesn't predict whether a system has
positive expectation, and also that average winning trade vs. average losing
trade doesn't predict whether a system has positive expectation. Okay then
it is fair to ask, what does predict whether a system has positive
expectation? Luckily, the major software packages like Metastock and
Tradestation produce several output statistics that measure this.
One is "Average $ outcome per trade". This is simply (Net Profits) divided
by (total number of trades). If you have included realistic commissions and
slippage in your testing, then if "Average $ outcome per trade" is positive,
the system has positive expectation. If "Average $ outcome per trade" is
negative, the system has negative expectation.
Another is "Profit Factor". This is simply (Gross Profits) divided by (Gross
Losses). If you have included realistic commissions and slippage in your
testing, then if "Profit Factor" is greater than 1.0, the system has
positive expectation. If "Profit Factor" is less than 1.0, the system has
negative expectation.
Now let's think about a third game, played with two coins. At each play you
flip both coins. If they both come up heads, I pay you $5. But if either
coin comes up tails, you pay me $1. In this game your winning percentage is
25%, your average winning trade is $5, and your average losing trade is -$1.
Does the game have positive expectation for you?
Yes it does. If we play this game many many times, you will make $5 on 25%
of the plays and you will lose -$1 on 75% of the plays. Your average profit
per play will be +$0.50. Your "Profit Factor" (which is equal to Gross
Profits divided by Gross Losses) will be 1.667. Your average profit per
trade is a positive number, so the "system" has positive expectation.
Similarly your Profit Factor is greater than 1.0, so the "system" has
positive expectation.
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