Are you a good judge of probability? Do you take into account probability when making decisions that involve an element of risk? <\/p>\n\n\n\n
According to former options trader Nassim Taleb<\/a>, most people have a poor grasp of real-world probability, and as a result, they misunderstand the likelihood of rare events<\/a> and consequently don\u2019t plan for risk appropriately. In his book Fooled by Randomness<\/a><\/em>, he cites three reasons for our difficulty in understanding how probability plays out in the real world: 1) we don’t properly interpret the past, 2) we can’t predict the future<\/a>, and 3) we don’t insure against risk properly. <\/p>\n\n\n\n We’ll explore the three reasons that reflect this difficulty below.<\/p>\n\n\n\n\n\n\n\n People find it hard to properly assess the likelihood\u2014or probability\u2014of randomness for several reasons: <\/p>\n\n\n\n One reason we’re bad at assessing and preparing for risk and random events is that we are not good at learning from the past. We mistakenly believe that because something has never happened before, it can\u2019t happen now. <\/strong>We then defend our lack of planning accordingly: \u201cThat had never happened before!\u201d <\/p>\n\n\n\n A longer-term examination of history shows that rare events of all kinds do, indeed, happen. The very definition of a rare event is its unpredictability. History is littered with examples of events that never happened before. If history\u2019s past brought surprises, why shouldn\u2019t our own past do the same? <\/p>\n\n\n\n Even when we do remember a past rare event, we tend to falsely believe that we now understand the events that led up to it, and we therefore think we can \u201cpredict\u201d it; that is, if it were to happen again, we wouldn\u2019t be taken by surprise. We\u2019d be more prepared for, and therefore less exposed to, any negative fallout from a similar rare event. <\/p>\n\n\n\n We also tend to falsely believe that mistakes of the past that led to these events have been resolved, making it even more unlikely that they would happen again. For example, people know that 1929 proved that stock markets can crash, but they often chalk that up to specific causes of that time. They believe, in other words, that the event is contained and non-repeatable.<\/p>\n\n\n\n We thus like to imagine that if we were to live through certain historical events, such as the stock market crash of 1929, we would recognize the signs and wouldn\u2019t be taken by surprise in the way that people at the time were. This is the \u201chindsight bias,\u201d otherwise known as the \u201cI knew it all along\u201d claim. However, seeing something clearly after<\/em> the fact is much easier than seeing it clearly in real time. <\/p>\n\n\n\n In the same way, a manager taking over a trading department might do an analysis and find that only a small percentage of the trades made that past year were profitable. She might then point out that the solution is to simply make more of the profitable trades, and less of the losers. Unfortunately, such a statement of the obvious doesn\u2019t provide any usable guidance for future trading decisions. <\/p>\n\n\n\n One reason it\u2019s hard for us to understand real-world probability and anticipate the risk of rare events is that when we examine the past, we are looking at a specific set of events that actually did happen, while ignoring the possible events that might have happened. This points to a fundamental problem with inductive reasoning<\/em>: While deductive<\/em> reasoning tries to make sense of the world by coming up with a theory and then finding data to support it, inductive<\/em> reasoning works in the opposite direction: You observe data, detect patterns, and formulate a theory based on those observations.<\/p>\n\n\n\n The problem with induction is that when your theories of the world are based on only what you can personally observe, you\u2019ll miss rare events. For example, you may look at thousands of swans, see that each one is white, and conclude that all swans are white. However, some swans are black. They are rare, and if you don\u2019t live in Australia you might never see one, but they do exist and they disprove your conclusion. <\/p>\n\n\n\n You can use observations to disprove a theory, but you can\u2019t use them alone to prove one. <\/strong>Just one counterexample is enough to disprove a theory based on millions of observations. The same thing holds for observations of history. You can point to historical events to refute a conclusion, but you can\u2019t make a sound conclusion based on a lack<\/em> of historical events. For example, before September 11, 2001, you might have said that airplanes are never purposefully flown into skyscrapers. Your theory, based on a lack of comparable events, would have been disproven by the events of that one date. <\/p>\n\n\n\n Therefore, if you base your understanding of the market on what you have observed, you do not allow for the rare event, and you leave yourself vulnerable to it. You might say, \u201cThe market never drops by thirty percent in any four-month period,\u201d and point to the fact that it\u2019s never happened to prove your theory. But \u201cIt has never gone down\u201d is different from \u201cIt never goes down.\u201d<\/p>\n\n\n\n One reason we misconstrue inductive reasoning is that we confuse <\/strong>absence of evidence<\/em><\/strong> with <\/strong>evidence of absence<\/em><\/strong>. <\/strong>This faulty reasoning shows up across all industries. For example, imagine a drug trial shows improved outcomes of 2 percent, but the researcher decides that her sample size was too small and the improvements she found were too slight to be decisive<\/a>. She might report that she has found no evidence as of yet of improved outcomes. Other doctors might then read that and decide she means, \u201cThis medicine does not help.\u201d <\/p>\n\n\n\n In the same way, looking at history and saying \u201cthis hasn\u2019t happened\u201d is often interpreted as \u201cthis cannot happen,\u201d an attitude that blinds people to potential risks.<\/p>\n\n\n\n Not only do we incorrectly interpret the past, but we also have trouble using lessons of the past to predict future rare events\u2014no matter how hard we try\u2014for three primary reasons:<\/p>\n\n\n\n These three reasons are explored further below. <\/p>\n\n\n\n When people think they could have correctly predicted past rare events, they think that they can also correctly predict contemporary or future rare events. However, we can typically only have clarity on an event through the lens of time passed; in real time, there\u2019s usually too much \u201cnoise\u201d to be able to judge what\u2019s consequential and what\u2019s not. <\/p>\n\n\n\n \u201cNoise\u201d is the overwhelming deluge of facts that bombards us from newspapers, television, online outlets, and so on. It includes up-to-the-minute stock fluctuations, daily explanations of market moves, and endless analyses of companies\u2014most of which will be out of business within a decade. <\/p>\n\n\n\n Small changes in the market are most likely random, and paying close attention to them can lead you astray, convincing you that unimportant things have larger consequences than they actually do. This means that noise is not just useless, but can be actively harmful, if it leads you to make bad decisions<\/a>, such as selling a stock abruptly because of minor movements, when it would have been wiser to hang onto it. Only the passage of time reveals what is important and what is noise:<\/strong> Time filters out the inconsequential changes and allows you to see what matters, since it reveals which changes ultimately prove unimportant and which change the direction of history. <\/p>\n\n\n\n This is especially true for stock prices. Looking at the minutiae of constant price changes means you are focusing on the variance but not the returns. It\u2019s unhelpful, and the negative moments may even convince you to act prematurely. Imagine an investor is sitting on a portfolio that has a 90 percent chance of increasing over the course of a year. If she checks the stock prices every minute, she might experience 250 happy minutes each day as prices rise and 240 unhappy minutes as prices fall. <\/p>\n\n\n\n Because a person reacts more strongly to negative news than positive, she\u2019ll end each day exhausted. She\u2019ll also have 240 instances during which she\u2019ll question her strategy and consider changing course. However, if she only checks her balance yearly, she\u2019ll experience 9 happy moments for every one unhappy one, if that 90 percent chance of increase means she\u2019ll have good news 9 out of 10 years. Time will have filtered out the unhelpful noise. <\/p>\n\n\n\n This idea also holds for world events. The daily news covers all events, consequential or not, while historians can see, with the benefit of hindsight, which events turned out to be transformative. <\/p>\n\n\n\n Often when studying history to apply it to today, we look at one or two narrowly-framed past events and believe their lessons apply to the future as a whole\u2014at least as it relates to that general type of event\u2014without taking into account all the ways in which the world constantly changes on a fundamental level. <\/p>\n\n\n\n So many details change in the way things work that it calls into question the usefulness of studying history at all\u2014except, of course, to acknowledge its ability to serve up surprises. Lessons from previous eras may not apply to today. For example, the Asian markets of the 1990s bear little resemblance to the ones of today now that the structure of the world economy has changed so dramatically, so market strategies that worked back then might not work now.<\/p>\n\n\n\n Likewise, because the structure of the past can be so different from the structure of the future, we can only see similarities between the two from a distance, after the events have passed. In the moment, we\u2019re too close to judge. This is true for connections between specific past and future events as well as between broader past and future landscapes. <\/p>\n\n\n\n The future eludes us in another way, too: It is affected not just by outside influences but also by our own understanding of those influences. Our predictions of the future can themselves change it.<\/strong><\/p>\n\n\n\n For example, if traders as a whole notice that the market always rises in March, they would all buy stocks in February in anticipation of the rise. Consequently, the market would no longer rise in March; it would rise in February. <\/p>\n\n\n\n Because of this, even if we could fully and properly understand the past, if everyone<\/em> did so, our predictions would no longer hold true because the preparations people would make for a future event would prevent the event from happening as expected. The tendency of the future to repeat the past depends upon our being driven by the same invisible forces that drove past events. Thus, rare events like stock sell-offs exist because<\/em> they are unexpected; if they were expected, people would prepare for them and consequently, they wouldn\u2019t happen. <\/p>\n\n\n\n When people misunderstand past rare events, they misunderstand the likelihood of future rare events and consequently, they don\u2019t plan for risk appropriately. This mistake is apparent in how people feel about buying insurance<\/a>. <\/p>\n\n\n\n Often, people resist getting insurance for things that are highly unlikely. If they do get the insurance, and the unlikely event never happens, they often feel upset that they shelled out \u201cuseless\u201d money. When people do this, they conflate \u201cforecast\u201d with \u201cprophecy,\u201d and chastise a person for not prophesying correctly, instead of for accurately forecasting risk. <\/p>\n\n\n\nWhy We’re Bad at Assessing Probability and Randomness<\/h2>\n\n\n\n
1. We Don\u2019t Properly Interpret the Past<\/strong><\/h3>\n\n\n\n
We Can\u2019t Understand the World Through Observations Alone<\/strong><\/h4>\n\n\n\n
We Misunderstand Absence of Evidence<\/h4>\n\n\n\n
2. We Can\u2019t Predict the Future<\/strong><\/h3>\n\n\n\n
Reason #1: Noise Prevents Clarity<\/strong><\/h4>\n\n\n\n
Reason #2: Structures Change<\/strong><\/h4>\n\n\n\n
Reason #3: The Future Is Changeable<\/strong><\/h4>\n\n\n\n
3. We Don\u2019t Insure Against Rare Events Properly<\/strong><\/h3>\n\n\n\n