What is Positive Expectancy?
This is a important concept that all Van Tharp students knows by heart and second nature. They no longer thinks about it consciously. Every trade is assessed against this Positive Expectancy framework during the Trade Planning process.
"Expectancy" refers to the Expectancy Per Trade, which is simply calculated as follows:
Expectancy = Win % x Win Size + Lose % x Lose Size, where:
1. Win % = expected win rate over a number of trades. For example, if you are able to find 10 similar trades and win 6 times, lose 4 times, then, your Win% = 60% and your Lose% = 40%.
2. Win Size = this is the win size expressed as R-multiples. For example, if the Reward per trade = 2R, then, Win Size = 2R.
3. Lose% = 1 - Win%.
4. Lose Size = expected lose size, which is usually 1R. 1R is basically how much $$$ you plan to lose in that 1 trade, if losses were to occur.
Note that these are simple statistical concepts. The critical underlying belief is that trading has uncertain outcomes. No one knows (not even Adam) how a trade taken today will turn out in the future. If you don't accept this belief, then, it is unlikely that you'll be able to trade Adam's (and pretty much every other trading coach) methods over the long term. All reasonable coaches will tell you that trading is always about PROBABILITY and never certainty.
Once you've accepted that trading is about probabilities, then, every trade that you plan should consider the Win % and Lose %. Initially, you may not have an idea on how to assess Win %, but over time, with more experience and practice, you will be able to have a reasonably good guess.
A simple yardstick is this.
1. Assuming a random Entry Price, where the Profit Target is equal distance away from the Stop Price, then, the Win % should be roughly equal to the Lose %, since both are equally far away and random. Here, the Win % can be roughly 50%, and Lose % roughly 50% also.
2. The Win % is a function of many things, one of which is the relative distance from the Entry Price to Profit Target vs Stop Price. Imagine if the Profit Target is $10 away, but the Stop Price is only $0.01 away. The odds of hitting the Stop Price, even if it is buying on the strongest Uptrend with strongest Support is near certainty.
This has important implications. If your Entry Price was truly random, and you have a Profit Target of 2R and risking 1R, then, your Win% can drop to below 50%. In a truly random situation, the Win % may only be 33%, and the Lose % twice that since the Reward distance is also double the Risk distance.
3. In real life trading, price movements may appear random, but is not truly random all the time. There are concepts like momentum. Momentum tends to drive prices in the same direction than against it. So, if you take the entry with the momentum, odds of achieving the Profit Target tend to be better than 50% even if the distances are the same. Not every trade has the same momentum strength - and differentiating one from another is a lifelong learning journey of studying tens of thousands of different charts.
4. Prices also tend to behave in a non-random fashion near Support & Resistance, but not always. If there is very Strong Support nearby with a confluence of strong supports, then, it is less likely for price to be able to successfully penetrate that strong Support Zone. Conversely, a stock making new high in the early stages of a bull market can run very, very far, as there are no prior resistance. So, the presence or absence of Support and Resistance can alter the Win %. Again, learning and differentiating various Support and Resistance and combining that with Momentum to assess win rates can be a very interesting lifelong learning journey.
5. One of the best ways to learn is to make as many practice trades as possible in your Demo accounts, using methods taught by your coach such as Adam, and sharing / discussing the specific trades in a group setting with others for different perspectives. If your entries follows the setups identified here, then, you can develop experience to assess win % for various RRR.
The Relationship between Win % and RRR
RRR = Reward to Risk Ratio = Reward / Risk.
Simplistically, if the Reward = 2R and the Risk = 1R, then, RRR = 2R / 1R = 2 times.
In a random trading system, there is a trade-off relationship between Win % and RRR. A system that generates large RRR basically has a larger distance to Profit Target, compared to the Stop Loss. As implied in point 2 above, the larger RRR tends to have a lower Win%, if the trading system was truly random.
Most new traders tend to favour large win %. Actually, the easiest way to achieve a high win% is to constantly take profits when it appears, even if it's just a few cents. You may achieve 99% win% with this strategy. Unfortunately, when you have losses, a single loss can undo the work of 10 profitable trades or even more. Many, many traders have tried this method on and off over the history of trading, and it is extremely difficult to grow one's equity over the long term using this method. The exceptions are extremely few, done by full time professional scalpers with special equipments, special training, incredible discipline, lots of practice, mentoring, etc. and special commission rates that provides them with edges over 99.9% of the market participants. HFT (High Frequency Trading) Traders are in this category, and one study I've seen is that they hardly ever lose at all. But to you and me, we simply do not have this edge that the HFT traders have.
A low win % like 33% isn't necessarily a bad trading system. If you study Van Tharp's books and materials and also study performance results of Trend Following traders, there are actually many Trend Followers with win rates around 35% but have equity growth that are very, very profitable over the long term. This is because when they lose, they lose 1R, but when they win, they are in that winning trade for a very long time and the strong trend that they've found enable them to have RRR that is very large. The average R-multiple is 3 times, and sometimes, they can have 5, 10 or even 20 R multiple outcomes. This enables them to have a very decent trading system. Financial markets are not truly random. There are many studies that shows that trends tend to persist longer than what statistical models predicts. Hence the typical saying that the "Trend can last longer than you can stay solvent". Many of the famous bankruptcies like LTCM occurs because they failed to understand that financial markets are not random all the time, even if they appear random most of the time. The 1% exception can deliver massive returns to the Trend Followers offsetting all the prior small losses. This is especially so in the Commodity Futures, and also appear in single theme stocks.
The Trader's First Job is to Design Trades with Positive Expectancy
In general, if you can find trades with an Expectancy of 0.2R, 0.25R or higher, you should do very well if you utilized the right Position Sizing strategies.
For example, the various systems below with various win rates have very decent Positive Expectancies:
For example, with 50% win rate, and RRR of 1.5 times (called Win Lose Size Ratio or WLSR), the Expectancy of the Trade = 50% x 1.5R + 50% x (-1R) = 0.25R or 25%.
Similarly, if your win rate is lower at 40%, but your RRR = 2 times, then, you still have a fairly good trading system with an average Expectancy of 0.2R.
Conversely, if your RRR = 1, but your win rate is higher at 60%, then, your Trade Expectancy = 0.2R as well.
In short, your job as a Trader is to find Trades with Positive Expectancy, at least 0.2R to 0.25R or even higher.
For example, using Entry Method #1 (called Buy the Dips), this type of trade tend to have good RRR if you bought the bounce off Support, since the Risk is just below Support and the Reward tends to be higher than the new High. In addition, as you are trading with the broader trend, your win rate can be 50%. In this case, you can afford to be safe and wait for a higher bounce off Support before jumping in, and still have RRR = 1.5 times. With 50% win rate, your trade can have at least 0.25R. So, Entry Method #1 is a system with Positive Expectancy.
Similarly for all the Entry Methods taught by Adam. If you just follow these trades, you will have found trades with Positive Expectancy.
The Table Above are Minimums, your Trade Plan should aim higher
For example, in a 50% win rate situation, it is usually better to aim for RRR of 2 times or more. Then, if you must take profits at 1.5R, then, you will still have a decent Trade Expectancy. Trade Plans should have decent Margin of Safety.
The Difference between a Positive Expectancy Trade and a Zero Expectancy Trade is a fine one
Now, imagine you are using Entry Method #1, which is Buy the Dips. Imagine that you only planned the Trade with RRR = 1.5 times instead of 2 times. You entered the trade. Half way through the trade, the stock paused, showing a "Harami" candlestick pattern. Your gain is only 1R so far. You are tempted to sell and lock in a sure 1R gain. Should you always do this?
Granted, occasionally, you should if there are extremely good reasons. However, in this case, the Harami candlestick pattern is not a very strong reversal signal. This pattern requires confirmation first. Also, you are still trading in the broader uptrend. What happens if you always take profits earlier, instead of following the Trade Plan?
The following illustrates the situation if your RRR (or WLSR) is 2/3rd of the above.
In short, you the Trader, have just turned a great trading system, into a lousy system!
If you trade the first table systems, you can grow your equity extremely well. However, if you have a tendency to take profits too soon, you turn a good system into a mediocre / a losing system. You may not be aware, but if you trade like this over the long term, you will not be able to consistently grow your equity.
The Trader's Second Job is to Trade the Plan
Once you have found a good trade, a trade with Positive Expectancy (like Buying the Dips), and you have planned the trade in terms of Entry Price, Support, Stop Price, Resistance, Target Price, and have assessed the win rate to be 50% with RRR = 2 times, you have a good Trade Plan in hand.
Your next job then is to Trade that Plan. Try as best as you can to execute it faithfully. If your stop is hit, accept the loss as pre-defined, and move on. If it feels like it takes a long time to get to 1R, be patient, and let the trade unfold itself. However, once the trade has earned a significant profit (like 1R), it is time to be diligent and not allow this profit to become a loss. A trailing Stop to Entry Price, and subsequently revising it upwards to Pivot Lows may be one good way of allowing the Trade to reach its full potential / 2R and not be tempted to take profits prematurely. Hence, the popular saying "Plan the Trade and Trade the Plan".
Other Thoughts
Trading is not so simple unfortunately. Daily, in our existing trade positions, we are confronted with the temptation to take profits when it is there, before they disappear.
One common solution is to take partial profits. Imagine if the position is up 1R, and you decide to take 50% off. What do you have to do to make that trade produce an overall 1.5R winner?
The answer is that you now need to hang on to that trade even longer, until it reaches 2R. This is so that 50% x 1R + 50% x 2R = 100% x 1.5R or a 1.5R winner, as you planned.
In general, it is not always a good thing to take 50% profits off. If you are unable to hold on to the winning position up to 1R, odds are even poorer that you will be able to hold the same position until it reaches 2R. In other words, premature profit taking tend to begets even more premature selling, that effectively, you, the Trader have turned a great system into a losing system. Hence the popular saying that "The biggest weakness in any Trading System is the Trader himself".
If you find yourself constantly in this situation, one way to overcome that is in the Trade Plan itself. Look only for the strongest trade. Know yourself. Plan for the fact that even though you are targeting 1.5R, look only for trades with 2R, 3R or even 4R multiples, so that should you need to take profits early, your RRR is still quite decent with good expectancies. Of course, it is better to also work on your tendency to profit take often, but self work is hard when it is built into our nature, and so, we try to find other easier ways to overcome it like the Trade Plan. Hence, the importance of the Trade Plan, and Know Yourself. Unfortunately, you cannot know yourself until you have taken hundreds of trades and journal them. It's Catch 22.
Conclusion
The Trader's First Job is to design and find trades with Positive Expectancy. If the expectancy is negative, zero or extremely small, do not take the trade. Throw it away, and look for a new idea.
If in doubt, assume a lower win rate in the Trade Plan. This invariably leads to finding trades with high RRR. The safe way is to look for trades with RRR of at least 3 times, or more, when the win rate is in doubt.
The Trade Plan is the most important arsenal in the professional Trader's tool kit. It is what gives him the Edge over 99% of amateurs. The Trade Plan forces the Trader to plan in advance, all possible outcomes. It prepares the Trader mentally on how to act when losses occur, and what targets to aim for, when the trade moves his way. It is a map that the Trader has drawn up in advance to guide him on his daily journey of monitoring his trades. Yet, most amateurs still do not utilize the Trade Plan - they often do not know Risk vs Rewards before entering the trade. Is it a wonder that their results are mediocre?
Hence Van Tharp's saying, that the Primary Job of the Trader is to design trades with high R-multiples. When designing the Plan, know yourself. The more you know yourself in terms of how you manage the trades on a real life day to day basis, the better it is for you to design plans that fits you. As with all plans, you should build sufficient Safety Margins, so that if the expected and unexpected happens, you still have high odds of success. The easiest way is to look for trades with very high R multiples, even if you cannot assess the win rate.
Designing Trade Plans does not have to be elaborate. With repeated practice, Trade Plans can be constructed within 10 minutes, some even much faster. Hence, do not engage in Intra-day Trading when you first start off trading. Intra-day Trading tend to encourage the Trader to skip Trade Plans and do the wrong things. Once the habit is ingrained, it is extremely hard to shake it off - it is always easier to learn trading the right way, than to unlearn old established habits.
And once you've designed your Trade Plan, the next job is to execute it unfailingly. Imagine there is another side of you called the Executor. This Executor's job is to simply execute the Trade Plan. It doesn't question the Trade Plan. It just does, and it doesn't care about the outcome of the Trade, except to follow the Trade Plan. The trader who can automatically, effortlessly and happily execute the Trade Plan with discipline, and have designed a superior Trade Plan with Positive Expectancy is one (large) step ahead than the majority of the market participants. He has an Edge in Trading.
In short, design trades with positive expectancy / plan the trade. Then, Trade the Plan.
Good luck in planning your trades.
Typical Questions
Question: I am surprised why you think 50% win rate is a good thing. In the recent dip, I put in 10 trades without a Trade Plan, and the next day, 9 out of that 10 trades turned positive - don't I have a 90% win rate here that easily beats the professionals?
Answer: The win rate above is not necessarily the number of trades that turned green the next day. Green can be meaningless, if the gain the next day is only 1 or a few cents. Odds are you can't sell the trade and be positive after deduction commissions & fees.
Rather it is the probability of the trade entered yesterday reaching the profit target, which may be $4 away, if your Risk is $2 away on the other side, assuming RRR of 2 times. The further the distance to profit target, the more challenging it is to get a 50% win rate over many trades entered.
Imagine this extreme case where the trader is complacent. Let say he got onto a good trade. The trade is correct right from the start. Over days, the unrealized gain is now $3.90, just 10 cent shy of $4 profit target. He decides to hang on for that extra 10 cents. But the extra 10 cent never happened. Instead the trade turned south ... over days, it keeps going down. The trader stares at the screen in disbelief. He refused to sell at +1.5R. He refused to sell at +1R, +0.5R. 0R, .... Eventually, it hit his stop loss and he lost 1R. Did this trader has a win or a loss? The obvious answer is that he has a loss. If this is the only trade he made, the win rate is zero and the lose rate 100%. Therefore win rates doesn't care about the trajectory of the price. All it cares about is whether the trade reaches the Profit Target (or closed at a profit) or the Stop Loss (and closed at a loss). The Win Rate is a different concept than Win Size. If the Trader closed the trade when the price falls to +1.5R, then, his win size is no longer +2R but +1.5R. However, at +1.5R, he does have a Win and if this is the only trade he makes, then, his Win Rate = 1/1 = 100%.
Of course, in the example where the Trader didn't close the trade at a profit, the Trader has made numerous trading mistakes, but that is a different issue altogether. The key point is that the win rate is not necessarily green trades the next day, but relative to profit targets and stop loss, which for the typical trader trading Adam's systems. Typically, stop losses tend to get hit first, due to the nearer distance, and it could take days/weeks to reach the Profit Target.
Best wishes,
SH
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