The Freedom of a Straighjacket by Stephen Duneier
I often hear investors talk about wanting to remain agile, not wanting to be “straightjacketed”. They believe it’s important to be able react to new information as it becomes available, to reassess the situation as it unfolds and adapt. Very often, what they’re really saying is, they don’t want to have to contemplate all of the likely future events, variables and outcomes that can affect their investments, today. They’d rather deal with them as they occur. However, decades of studies in the cognitive sciences suggest that is a bad idea. By delaying the hard decisions, you are avoiding cognitive strain in favor of maintaining cognitive ease. Factors such as losses, gains and a whole host of emotional triggers, are likely to skew your objectivity in that future moment. Leaving you with the task of making difficult decisions at a time when extraneous factors, the kind that tend to create bias and result in mistakes, come to the fore. In the typical “agile” process, decisions are made with the benefit of new information, but also under heightened emotions, increased time constraints and bias inducing influences, like p&l. This reduces the weighting that the new information itself can have on the decision (see graph to right). If instead, we can identify the important information ahead of time, its possible effects and the resulting adjustment you should make to your forward expectations, then there is no decision to be made in that future moment. It can be made ahead of time, in a moment of greater objectivity and lucidity, thereby increasing the odds of a better decision.
Let’s use a decision tree to see how this works. Imagine you are contemplating going long XYZ stock. The catalyst for your potential investment is an impending court ruling. 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 and a 20% chance of dropping to $10. If it turns out to be unfavorable, the odds flip (see 1st Decision Tree below). 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 purchase XYZ stock. (see 2nd Decision Tree below).
It’s likely that the analysis to this point isn’t very different from what goes on in your own head. You’ve done it so many times over your career, you probably don’t see the need to take the time to lay out your thoughts on a decision tree or write down your expectations as they exist today. You believe that your expectations (i.e. probabilities assigned) today will remain constant, requiring adjustment only when new information is produced. When the ruling comes out, you’ll reassess the situation.
If you read that last sentence without skipping a beat, you’ve already made a mistake. You see, in your initial analysis, the one that led you to purchase XYZ ahead of the ruling, you set your expectations for the valuation of XYZ given that the ruling was favorable. Therefore, any adjustment to your “post-ruling expectations” after the ruling is announced will be the result of bias, not the ruling itself. Prior to the announcement, you believed there was a 68% chance that the stock would trade at $30 (80% chance in the case of a favorable ruling + 20% chance if it were unfavorable.) Once the ruling is announced, the only thing in your decision tree that should change, is the odds of a favorable vs unfavorable ruling (see Decision Tree to right). Strictly as a result of that adjustment, your expectation of achieving a loss on the investment has dropped from 32% down to just 20%. No flexibility or adjustment in the moment is necessary. The decision you made initially is the only one you need to make. If you raise your price expectation based solely on the fact that the ruling was favorable, you’re making a mistake, likely the result of a cognitive bias.
Of course, given that a great amount of uncertainty has been removed, the expected return on the investment has changed (even though the price target hasn’t). Therefore, it makes sense to reassess the investment from this point forward. Perhaps, it is wise to double down. I know what some of you are thinking. So you do have to make a decision in the moment! Actually, no. This decision can and should be made prior to the initial investment as well. Leaving only the execution for today. To the right, you will find the tree for the post-ruling decision to sell, hold or double down. Based on your expectations and the current stock price of $23, the expected return is positive, and doubly so if you were to double down from here. (Note: The original price paid is no longer relevant.)
There is a difference though, between simply making the decision to be long and the decision as to how long you should be. Let’s say, you want your expected upside to be twice your expected downside. Initially, that required an entry price below $20.30, which is why you had purchased it when it dropped to $20. Now, the decision is whether to hold, double down or sell it all. Again, you decide that you will double down after the ruling, if the expected upside is at least 2x the expected downside. If the ratio is below that, you’ll stick with what you have, and if it’s at $30, you’ll sell it all. Therefore, given your post-ruling probabilities, you should double-down if the stock is below $23.33.
Note that those parameters can, and should, all be set prior to entering the initial trade. Since those parameters are the decisions as they relate to this investment, no actual decision needs to be made as new information becomes available, only execution of those made in a moment of maximum objectivity. The Natural Beauty of (Decision) Trees Below is a decision matrix, created to assess the expected returns for a hedge fund manager that an allocator is considering for an investment. In the second column are the returns projected by an analyst for the seven mutually exclusive potential outcomes as he has defined them. The next column contains the probability that each of those scenarios will occur. We know these outcomes are both exhaustive and mutually exclusive, because the sum of the probability that each of them will occur totals 100%. As you know, the total expected return is a function of the expected returns for each scenario and their respective probabilities. If the first four columns were all we knew, it’d be difficult to find a flaw in the analysis. However, the content of column five calls everything that came before it into question. Let’s explore why that is, and what can be done to avoid this mistake going forward.
One factor mentioned in several of the scenario “reasons” comments on the performance of the “markets”, thereby implying that there is a beta component to this fund manager’s returns. In other words, there is a correlation between market returns and this fund’s returns. Based on the description in Scenario 1, that correlation is thought to be positive. According to this analyst, there are three other key variables that contribute to the fund’s returns - alpha, market volatility and the US economy.
In order for the probabilities of all 7 possible scenarios to add up to 100%, they must be mutually exclusive. Scenario 1 is very specific, calling for -35% returns for the Russell 2000 (very negative) over the next twelve months. Scenario 2 calls for a 7.5% decline (slightly negative) in R2K without any alpha generation. Scenario 3 calls for zero return in R2K, but positive alpha. Scenario 4 calls for R2K to rally 8% (slightly positive), plus 300 bps of alpha. The remaining scenarios make no mention of market returns, which means they could occur under any or all market outcomes, including those previously defined. Scenario 5 mentions only the fund’s future returns in isolation, so we know nothing about any of the variables upon which the fund’s returns are dependent. Scenario 6 anticipates volatile markets and positive alpha leading to a 24.1% return. Scenario 7 expects a strong economy and market returns, resulting in a 33.7% return for the fund. Even reading through the reasons one at a time, it’s difficult to see that there is a problem with the analysis, but there is a flaw, and it’s significant. Here is a summary of the information provided so far.
Even seeing it in this table format doesn’t really help us see the problem. To make it leap off the page, rather than using a matrix, let’s review the information one scenario at a time using decision trees (see next page).
If done correctly, every branch should be represented by one, and only one, mutually exclusive scenario. When added together, they will total 100%. As you can see in the image to the left, quite a few branches are part of more than one scenario, and we haven’t even included Scenario 5, because it isn’t defined according to the variables chosen by the analyst. The point I’m attempting to make here, is that the way these scenarios have been defined, they are neither mutually exclusive, nor are they likely exhaustive. That’s important, because it means the +12.5% expected return spit out at the end of his analysis is incomplete, incorrect, and essentially useless. The correct way to carry out such a complex expected return analysis begins by laying out the relevant variables (below, left). The analyst must then set his expectations for each and every branch segment (below, right). You’ll notice that each choice node (represented by circles) has a set of branches which add up to 100%.
The only things left to do then are set return expectations for each scenario and multiply each of them by the relevant probability. It requires time, effort and cognitive strain to produce this analysis, which is why so few do it, and so many struggle with trade management decisions during an investment’s lifecycle. The decision tree is not only an excellent tool for unearthing mistakes in an analysis, it may be the most valuable tool available for those looking to shift from a reactive decision making process to a proactive one.
Valuing Liquidity Let’s explore one final situation in which investors could benefit from the use of decision trees. This one helps us to truly appreciate one of the great advantages of liquidity.
Assume you are choosing between a private equity deal in which you are locked in for three years versus an allocation to a global macro hedge fund that allows for monthly liquidity. You’ve done a significant amount of analysis on the history of returns on your allocation decisions and it turns out that the two funds you are considering for an allocation share the same three year expected return profile as the average investment in your “Moderately Aggressive” risk bucket. Therefore, the decision tree for both investments should look identical, right? (see P/E Decision Tree). Of course, you recognize that there is a tangible benefit to the hedge fund’s liquidity terms, but how can you quantify that benefit so that it is appropriately and consistently assessed?
Well, the truth is, just because the expected return profiles for both investments are identical, doesn’t mean that the decision trees will be the same. They will differ for this investor for two reasons. First, she has recognized a trend in the investments she makes. Year 1 returns provide predictive value regarding year 2 returns and the combo of year 1 plus year 2 returns, offers valuable information about the likelihood of profitability in year 3. While this is true for both the private equity fund and the hedge fund, liquidity terms only allow the investor to capitalize on it in the hedge fund allocation. The ability to potentially act on that new information is the second reason the decisions trees will differ.
Let’s look at the decision facing the investor in the hedge fund at the end of a bad 1st year (see tree above right). The choice she faces is, whether to redeem from the current hedge fund and invest the proceeds in something else, or stick with the current hedge fund manager. Based on the investor’s data, the rational choice is to redeem and invest elsewhere. (After a good year 1, the rational choice is to stay with the current manager.) The same analysis should be done after a bad year 2 (see tree on right). Based on her data, she decides ahead of time that she will redeem and invest elsewhere whenever a hedge fund manager has a bad year. Given that information, we can create the full decision tree, and expected return, for an investment in the hedge fund (see bottom tree).
Turns out the expected return for the hedge fund is +2.6% vs +1.52% for the private equity investment with the only difference being the ability to make an adjustment to the investment as more information becomes available. (Notice, again, the decision is made ahead of time. Only the execution occurs in the moment the new information becomes available.)
"No matter what your current approach or internal processes, Stephen will have observations and suggestions that can improve it."
Portfolio Manager New York, NY $800 Million AuM
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.
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