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#1394 
The goal of most traders should be to maximize the expected value of each trade. There may be some exceptions, like you had some kind of “hard” P&L goal (like “don’t lose money,” or “you need to make $X to keep your job”, etc) and/or if there was some kind of time constraint (like “quarterend”, “yearend” etc). But for the most part, what you want to do is maximize the P&L over all outcomes.
If you take the probability of each possible event occurring and multiply that by the gain (or loss) of your trade, and add them all up, you will get the expected value of your trade. I need to keep the analysis as simple as possible (because you can do an analysis over multiple time periods, adjusting position sizes, etc.). At the very basic level, if we just look at a trade at the end of one time period, there are there are three possible outcomes:
1) trade makes money
2) trade breaks even
3) trade loses money.Call me Captain Obvious. The reason I am breaking it out like that is because for now, I just want to discuss #1.
[to be continued]

[I will move this later as the top Introductory Post] The genesis of this post is that a lot of people develop this feeling that they left a lot of money on the table if they don’t buy near the lows and/or sell near the highs. This just makes for terrible trading psychology, because “90+% of the time,” you are not going to capture the bulk of the move. And when you think about it logically, trying to capture the bulk of the move should not be your goal. Your goal should be to: MAXIMIZE THE EXPECTED VALUE OF THE TRADE.
Let me give you a very simplified example. Say you sold S&Ps at 2000 because we expect a large dip and afterwards we will spike back higher.
* 31.5% of the time we are wrong.
* 30% of the time we get to 1950, our EV is 15
* 20% of the time we get to 1900, our EV is 20
* 10% of the time we get to 1850, our EV is 15
* 5% of the time we get to 1800, our EV is 10
* 2.5% of the time we get to 1750, our EV is 6.25
* 1% of the time we get to 1700, our EV is 3I realize this is not a realistic example. But my main point is that you should be ecstatic when the S&P gets to 1900, since that is where you maximize your expected value. However, if we only get to 1950 you’re miserable (since we didn’t get to your target), if we get to 1850 and lower you’re still miserable (since you took profit at 1900, and missed 33+% of the move), and if we get to 1700, you may even be depressed (since you took profit at 1900, and missed 67% of the move). So basically, you thought up of this great trade, but 80% of the time, you are going to be unhappy. But why? You made the most positive EV decision, based on all of the information given to you.
[to be continued]

Of course the above is a gross simplification of how the markets work. In particular, we only made one decision, whereas in actual markets, you can have an infinite number of decisions. Before we get to 1900, we first must get to 1950. Below are some of the things you need to assess once you get to 1950:
* Did the probabilities change, now that we are at 1950? Are the circumstances such that we are still operating within the confines of the original probability distribution? OR is the fact that were are at 1950 (or the way we got to 1950) a sign that something has changed? In particular, did the size of the downside tail now increase?
* You then have to assess what the (new?) conditional probability distribution is now, given that we reached 1950. You can use the initial probability distribution, or you may have to adjust accordingly, based on the risk.
* At (any point between 2000 and) 1950, we can consider adjusting our position – add to the position, or take some (or all) of the position off. Does it make sense to make a change to the positioning?Answering the above will help determine if we need to take partial profit, add to the position, set a stop, or change our takeprofit levels… all with the goal of maximizing our EV.
[next: simple example]

Let’s say you think there is only a 10% chance (2.5bps) that the Fed hikes 25bps at its September meeting.
If you buy (say FFV5) when it is pricing in 40% (10bps), you expect to make 7.5bps 90% of the time, and lose 15bps 10% of the time. The expected value is +5.25bps. That’s a pretty good trade. But the real world is not a two timeperiod game. The real world has many more decision points. An interesting thing happens on the way from 40% to 10%…
Say the markets now price in 20% (5bps). The markets have moved 67% of the way to our target and we have made 5bps. We still think the Fed hikes with 10% probability. So now, we make an additional 2.5bps with 90% probability and lose 20bps with 10% probability. Our EV from this point is only +0.25bps. That’s barely a trade worth doing – especially in light of the fact that we can lose 20bps. If we take it a step further and say the markets price in 16% (4bps), we make 1.5bps 90% of the time and lose 21bps 10% of the time, for an EV of 0.75bps. So clearly the optimal exit point was somewhere much earlier than our original target of 10%. To try and hold to 10% (even if it is your strong view) or even 15% is a mathematical error.
In terms of just maximizing EV on this one trade, that occurs when the markets are pricing in 19% (5.25bps, which was our original EV), assuming your view hadn’t changed on the way from 40% to 19%. This is an example of how even if you had a belief on a particular level (in this case 10%), many times it will not be optimal to hold on until you get there.
And… there are factors other than just EV that you need to take into account when putting on a trade…

FACTOR #1) NOT ALL EV IS THE SAME
Consider the following three payouts – rank in order of preference:
a) make 5bps 75% of the time, lose 5bps 25% of the time.
b) make 10bps 50% of the time, lose 5bps 50% of the time.
c) make 10bps 90% of the time, lose 65bps 10% of the time.The EV in all 3 cases is 2.5bps. Are they really “equivalent”? Unless you and the shop you work at are completely riskneutral (highly unlikely), you should prefer in the following order: a, b, c. The reason is because of the standard deviation (volatility). There is a reason why using Sharpe Ratios (and other riskadjusted return measures) make a lot of sense. While the “bottom line” may be the most important performance performance criteria, you also need to factor in the performance with respect to the amount of risk taken.

FACTOR #2) JUST BECAUSE A TRADE IS +EV DOESN’T MEAN YOU SHOULD HAVE IT ON
Just because a trade is +EV doesn’t mean that there aren’t other trades that are even MORE +EV or trades that fit your risk profile or portfolio better. As you look through the various trades available to you (even the various way to express the same view), you will assess different levels of expected value for each trade. The goal is not to do every +EV trade. You need to find the optimal mix of trades to fit your view and to fit your portfolio. Factors to consider include:
* optimal mix (and quantity) of trades to express a view
* maximum downside on each individual trade, and the portfolio as a whole
* effect on capital allocation and risk management systems[I will add to the above list]

Most people who are used to trading based on technicals think about entry, stop and takeprofit levels on a “static” basis. After all, the chart’s previous data is not going to change, so you can predetermine most levels. For example, if you like buying something at a support level, you set your stop if we “decisively” break the support. Profit levels can be determined in a number of ways, but most people would use some function of a retrace of the previous move.
While a static approach can be useful and has the advantage of simplicity, there may be times when you may do a trade based on other lesstangible factors as well. For example, if you liked a trade that had no relevant history (because you were in a new regime). You may need to adjust your entry, stop and takeprofit levels on a “dynamic” basis. When you do such a trade, you need to constantly assess what the appropriate profit and stop levels are at regular intervals. For example if you liked being short (rates) for the March FOMC meeting, historicals aren’t going to be particularly useful, when we hadn’t had liftoff before. How do you know a priori what your takeprofit level is going to be? You have no relevant chart history because we’ve never had liftoff in the recent past. You probably don’t want to hold until the meeting is 25bps priced. And the data is constantly changing, which should affect your view on the trade.
[to be continued]

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