Expected value (EV) or expectancy is a very important trading concept that few traders understand and actively discuss as an element of their trading. So what is EV and why is it so important? EV is simply the average result over a number of trades. Mathematically, it is the sum of the probability of winning/losing in a trade multiplied by the magnitude of that winning/losing trade.
Frequency x Magnitude = Expected Value (EV)
Most people do not think in these terms. For example, let’s play a game. Suppose you play a casino game where you pay $2 to win $2 and your odds of winning are 99 out of 100 (99%). However, you have a 1 in 100 chance of losing $300. Do you play? The answer is no, because the expectancy of the game is -$1.02. This means over the long run, you’re going to lose an average of $1.02.
|Odds (Frequency)||Result (Magnitude)||Expected Value|
Let’s view a trading example. In this example below, a systematic trader executes a buy order based on a certain technical set-up in the eMini S&P 500 (e.g., when the 5-day moving average (MA) crosses over and higher than the 20-day MA and the price is trading above the 50-day MA). For the ten trades he’s taken using this entry system, 40% of the time he profits an average of 4.0 points or $200. But, 60% of the time he loses an average of 5.5 points or $275.
|40% Probability of Winning x Winning Trade is $200 =||+ $80|
|60% Probability of Losing x Losing Trade is $275 =||– $165|
|Expected Value||– $85|
Thus, over time, he’s currently employing an entry system that isn’t profitable based on how he is using it. On average, he can expect to lose $85 every time he trades it. In order to make it profitable, he will have to tinker with it. Perhaps he will have to alter the risk/reward parameters- cutting down the initial risk amount? Maybe he needs to increase his profit through a different position sizing strategy, e.g. adding to the position as it goes in his favor? The point is, the trader can now alter the system and make adjustments.
So why is it so important to understand EV? Remember, EV is composed of two parts- frequency and magnitude. I believe average traders focus on frequency. Successful traders do the opposite and focus on magnitude. This divergence leads to a significantly different outlook on how risk is ultimately managed.
Average traders are more concerned about having as many winning trades as possible. While every trader wants to win 100% of the trades they enter, it is simply unrealistic to attain. However, this doesn’t stop the average trader from trying. This mentality typically leads to poor risk management techniques. Traders will stay in losing positions hoping for them to come back to even or even worse, averaging down with the hope of cutting losses or being profitable.
If you are in a losing position, the market is telling you that your trading idea is wrong. Yet, traders hold on or even double down regardless of what the market is telling them. Think of it this way: let’s say you are asked a true or false question like “The United States declared independence in 1776.” You answer “False.” The examiner says that your answer is incorrect and asks you the same question. You then answer “False!”
Successful traders tend to be much more concerned with the magnitude of their wins and losses rather than how many. For example, successful traders have no problem taking small, manageable losses because they understand that all it takes it one good trade to make up for all the small losses and turn a potential profit. Good traders understand that the market may never move again to their breakeven point, so the best they can do is take a small loss, before it turns into a large loss. As such, successful traders tend to cut off losing trades quickly since they do not like having large losses and let winning trades run.
Let’s look at Trader 1 (below), an eMini S&P trader who doesn’t fully appreciate the role of EV in his trading. Thus, when a position goes against him, instead of looking to get out of a trade, he looks for ways to get back to “break-even” or create a profitable trade. In this case, he decides to add to the position or “average-down”. Many times, this strategy works and brings a losing trade back to even or profitable. Trades 1-5 look okay. There are five winning trades and one losing trade making the EV +$45 ($225 / 5). However, Trade 6 is a material loser as the trader follows their normal strategy of “hoping” the position comes back. Worse, the trader adds to losing trades since he frequently watches trades come back to even. A $700 loss is ultimately taken. The EV of their trading instantly drops from +$45 to -$ 79 as Trade 6 wipes out all profits and then some. The trader continues with no major problems and ends ten trades with an EV of -$45. One trade adversely affected his whole trading for this period because the trader did not understand that the market does not care where you “got in” or where your “breakeven point” is.
Let’s contract this with Trader 2 (below), another eMini S&P trader who is very concerned about the magnitude of their trades and EV. Trades 1-8 are fairly nominal. No big losses or gains are taken and the EV is -$25 (-$200 / 8). Anytime a trade goes against him, he are out of the trade as they have a plan before the trade is placed and hoping a trade comes back is never a part of the plan. When a trade moves in his favor, risk-averse management is employed and stops are moved aggressively. On Trade 9, a homerun is hit. The trade continually moves in his favor and never comes back to the stop level. The trader actually “added” to their position as they were using the markets money. The EV jumps significantly to +$200 (+$1,800 / 9). Trade 10 is a nominal loser and the overall EV for these ten trades is +$170.
Trader 1 consistently puts himself in poor risk/reward situations. While most of the time he escapes, it only takes one large loss to wipe out many profitable trades. This compares to Trader 2 who is extremely concerned about risk/reward and understands it is critical to not take large losses and place himself in situations where large profits are possible. Think of it this way, small losses ensure large losses do not happen.
Why such a large divergence? Let’s look at typical characteristics between the two traders:
- No defined initial risk – No clear plan of when he will get out of losing trades go against him which can lead to getting out of losing trades too late.
- No defined initial target – No plan when things go in his favor which can lead to getting out of winning trades too early.
- Poor position-sizing – When trades go against him, he tends to “sit” in them or “add size”. Thus, he ends up taking more risk than he should. A position simply runs too far against him and he gets out when he can’t take it anymore. Worse, size is added and his risk significantly increases. If the trade comes back toward break-even or profitable, his strategy is validated. However, he does not calculate the odds of the position going further against him- sooner or later, large losses will be taken.
- Poor risk management strategy – No movement of stops to protect to downside or lock-in upside. These traders turn many profitable trades into losing trades.
- The mentality that you must win on every trade. Obviously, every trader wants to win 100% of their trades, however, there comes a time when a “profit-seeking” mentality must shift to a “capital-preservation” mentality. Those who cannot adapt between the two will have problems being a successful trader.
- Trading arbitrarily and with no defined catalyst. The trade is made with no technical or fundamental catalyst (event, trigger, expectation, etc.) Once the catalyst occurs, the trade is executed and the plan commences. Since no plan exists once the trade is placed, trading is usually based on emotion (e.g., hoping events happen).
- Defined initial risk – A clear plan, before the trade is entered, how of much initial risk will be taken.
- Defined initial target – A clear plan, before the trade is entered, when potential profits will be taken.
- A thorough understanding of how position sizing affects their profit/loss – Typically never adds to a losing trade and is actively seeking to cut off risk when things are not going to plan. When a trade is profitable, the trader is thinking about how to not let it turn into a losing position and has specific position sizing strategies to maximize gains. For example, a trader may add size when a new hourly/daily high is taken out looking for momentum follow through. With this said, the trader understands the risks associated with a larger position.
- A sound risk management strategy – When are stops to be moved (only when the trade is going in our favor) and why?
- A thorough understanding of when to be “profit-seeking” vs. when to be more concerned with “capital preservation”.
- Trading with a defined catalyst. The trade is made using a technical or fundamental catalyst (event, trigger, expectation, etc.) Once the catalyst occurs, the trade is executed and the plan commences. Exiting the trade has already been determined off some set of risk management rules or strategy.
Trader 2 can only gain this insight by having an understanding of the EV of each trade and how this affects their overall performance. As such, their risk management and position sizing reflect their understanding that the magnitude of one bad trade can wipe out an entire day’s, week, or year’s profit. Likewise, he seeks to place himself in situations where he can benefit from a trade that can make his day, week, or year. Successful traders understand the role of expected value in their trading and tend to me more concerned about the magnitude of each trade rather than the frequency of a winning or losing trade.