The Rational Approach to Take Profits and Position Sizing by Stephen Duneier
In Freedom of a Straightjacket, we explored the many benefits of a proactive decision making process and a number of ways that decision trees can help investment managers with executing it. Given the high volume of questions that followed from the piece, I thought it worth taking it one step further for the benefit of all subscribers.
In particular, I’d like to show how the same process can and should be used to determine the correct take-profit level, while also dispelling some of the myths regarding sizing that I discussed in What Makes Trading So Difficult. I will keep the example simple, so that we can focus on the logic behind the approach. Recall the following from Straightjacket: Imagine you are contemplating going long XYZ stock. The catalyst for your potential investment is a court ruling due to be settled 1 month from today. Having done your research, you believe the probability of a favorable ruling is 80%. If the ruling does turn out to be favorable, you believe the stock has an 80% chance of trading to $30 versus a 20% chance of dropping to $10. If it turns out to be unfavorable, the odds flip (see 1st Decision Tree, left). Based on the probabilities you have assigned as a result of your research, and the expected profit/loss in each scenario, when you fold back your decision tree, you come to the conclusion that you should expect a return of 18% if you purchase XYZ stock today at $20. (see 2nd Decision Tree right).
Let’s assume you decide to invest in XYZ. At what price should you take profit? You might think the answer is $30, and you’d probably be in good company, but would it be an appropriate investment strategy? Rather than just providing the answer, let’s explore the answer in the same way that we approached the decision to enter the trade. After all, if every moment you hold a position, you are truly asking the question, “Would I buy it here?”, then the decision making process should remain consistent, throughout. Let’s go with the intuitive answer that $30 should be our take-profit. That means when the stock is trading at $29, we must believe it is still a good hold. Since the ruling has not yet been made, all of the expectations, including the probabilities and price targets remain exactly the same. As a result, when the stock is trading at $29, the expected return on the investment is -18.6% (see table below). In other words, based on your own research and the resulting expectations, you expect to lose 18.6% on your invested capital. Given that expectation, if you didn’t have this position on at that moment, would you put it on now? I should hope not. Therefore, the take-profit prior to the court ruling should be somewhere below $29, thereby ruling out $30 as the appropriate answer.
If you think about it, a positive expected return tells you that the market is undervaluing the company relative to your expectations. A negative expected return tells you the market is overvaluing it. When the expected return is zero, you believe the market is appropriately pricing the stock, and in that case, there is no edge. Based on your research, that would put the fair value at $23.60 (see table above). Therefore, in order to be consistent in the logic applied when you entered the trade, you should be exiting the trade at $23.60. In other words, that should be your take profit.
This same analysis can be done at every level for the stock price. At $20, the expected return is 18%, comprised of a 68% chance of a +50% return and a 32% chance of a -50% return. You may deem it attractive, and certainly more appealing than when it is trading at $29, but not better than if you had the opportunity to enter at say $15. For at $15, the expected return is 57.3%, with a 68% chance of a 68% return and 32% chance of a 10.67% loss. So the expected return is far better, and so is the balance of risk vs reward. This leads me to the issue of position sizing.
In What Makes Trading So Difficult, I made a seemingly controversial claim that your maximum position size should be at the bottom of an upward sloping trend channel while gradually reducing the position until there is nothing left just below the top of it. Well, here is the explicit argument for just such an approach.
The most attractive part of the trade, according to your expectations, occurs when spot is closest to the stop/loss. That is where the risk/reward and expected return is at its maximum, which is why your position size should also be at its maximum. That is the meaty part of the trade.
Unfortunately, that is also the moment when it is most difficult to have a great deal of confidence in your expectations. After all, you are sitting at the bottom of the range, which likely means all of the news flow and chatter (read: noise) is running counter to your argument. That is why it is vital to set your expectations and define what is signal as opposed to noise, before you are faced with the decision as to whether or not you should be entering the trade at the bottom. That is how you avoid having cognitive bias adversely affect your decision in the moment. The alternative is the approach most investors take. Wait until it bounces back up to $20, thereby “confirming” your view, which gives you confidence to size up the position, but at a far less attractive level.
Now I know, many of you will argue that you should move the stop-loss up along the way, thereby reducing the potential maximum downside. And yes, it does reduce the maximum potential downside, allowing you to size up the position, but when you do that, you must also shift the probability of triggering that stop-loss, significantly higher (see chart below, left). Since in this trade we have binary expectations, meaning these probabilities are a function of hitting the take-profit level prior to the stop-loss level and vice-versa, if we raise the probability of triggering the stop-loss, we must also reduce the probability of triggering the take-profit by a commensurate amount. The combination of which will have a negative impact on your expected return. So, while moving the stop-loss up will reduce the maximum drawdown, it doesn’t make it a more attractive investment. Certainly nowhere near as attractive as it is near the bottom of the range. There is a way to make it a more attractive investment opportunity, though. Given that technical support (ie the bottom of the range) represents a discrete moment, where the odds of spot trading below that point drop disproportionately, simply moving the stop-loss to a level just below the support line will have a disproportionate impact on the attractiveness of the trade (see chart below, right).
Now let’s assume the court ruling came out as you expected. Does it change anything? Do we need to make any adjustments? Absolutely. The expected returns change, even if the maximum potential drawdown doesn’t. The table below reflects the updated expectations. As you can see, your take-profit should be raised to $26.
As I stated at the beginning, I have purposely kept this example simple. However, the approach can be expanded to accommodate all of your expectations, no matter how detailed. In order for any of this to work to your benefit though, you must properly define all of your expectations ahead of time. Once again, we see the benefits of shifting from the standard reactive approach to decision making, to a proactive one. Yes, it requires a significant amount of work and cognitive strain to be invested up front, but it dramatically reduces the number of decisions that need to be made throughout the life of the trade. Most importantly, it reduces the number of decisions that will need to be made under emotional distress and time constraints, thereby improving the odds of more rational choices being made throughout. In the end, that is the key to better returns.
About the Author For nearly thirty years, Stephen Duneier has applied cognitive science to investment and business management. The result has been the turnaround of numerous institutional trading businesses, career best returns for experienced portfolio managers who have adopted his methods, the development of a $1.25 billion dollar hedge fund and 20.3% average annualized returns as a global macro portfolio manager.
Mr. Duneier teaches graduate courses on Decision Analysis and Behavioral Investing in the College of Engineering at the University of California. His book, AlphaBrain, is due to be published in early 2017 (Wiley & Sons).
Through Bija Advisors' coaching, workshops and publications, he helps the world's most successful and experienced investment managers improve performance by applying proven, proprietary decision-making methods to their own processes.
Stephen Duneier was formerly Global Head of Currency Option Trading at Bank of America, Managing Director in charge of Emerging Markets at AIG International and founding partner of award winning hedge funds, Grant Capital Partners and Bija Capital Management. As a speaker, Stephen has delivered informative and inspirational talks to audiences around the world for more than 20 years on topics including global macro economic themes, how cognitive science can improve performance and the keys to living a more deliberate life. Each is delivered via highly entertaining stories that inevitably lead to further conversation, and ultimately, better results.
His artwork has been featured in international publications and on television programs around the world, is represented by the renowned gallery, Sullivan Goss and earned him more than 50,000 followers across social media. As Commissioner of the League of Professional Educators, Duneier is using cognitive science to alter the landscape of American K-12 education. He received his master's degree in finance and economics from New York University's Stern School of Business.
Bija Advisors LLC In publishing research, Bija Advisors LLC is not soliciting any action based upon it. Bija Advisors LLC’s publications contain material based upon publicly available information, obtained from sources that we consider reliable. However, Bija Advisors LLC does not represent that it is accurate and it should not be relied on as such. Opinions expressed are current opinions as of the date appearing on Bija Advisors LLC’s publications only. All forecasts and statements about the future, even if presented as fact, should be treated as judgments, and neither Bija Advisors LLC nor its partners can be held responsible for any failure of those judgments to prove accurate. It should be assumed that, from time to time, Bija Advisors LLC and its partners will hold investments in securities and other positions, in equity, bond, currency and commodities markets, from which they will benefit if the forecasts and judgments about the future presented in this document do prove to be accurate. Bija Advisors LLC is not liable for any loss or damage resulting from the use of its product.