In the shadow of probabilities: How randomness shapes the world of finance

Happenstance, luck, and unforeseeable events often affect our lives much more pervasively than we care to acknowledge. A lot seems logical and congruous in retrospect, but our hindsight is deceptive. We block out the large number of those who have failed and look for patterns among the successful in places where frequently only luck existed. While creditable success is often the result of prowess, spectacular success not infrequently stems from unique, irreproducible circumstances.

Why financial pros aren’t dentists

In the field of dentistry, success depends almost exclusively on the skills of the attending dentist. A dental surgeon who extracts a decayed tooth works with precise instruments under controlled conditions using well-established procedures. There is a clear relation between cause and effect here. The medical intervention, if performed correctly, produces a predictable, measurable outcome. What’s more, that outcome is repeatedly reproduceable under the same conditions. It’s a different story in the financial sector. Expertise, methods, models, and tools exist there, too, but the outcomes of financial decisions are rarely linear or directly controllable. Even well-grounded strategies can fail while reckless maneuvers may result in gains. The difference from dentistry lies in the fact that the market does not adhere to precise rules, but instead follows the whims of probability. In short, financial pros operate in an environment that is profoundly shaped by random chance. Mathematician, fund manager, and author Nassim Nicholas Taleb provocatively puts this in a nutshell: many instances of success on markets are not the result of superior skill, but are merely a product of luck. The difference is hard to recognize and often gets interpreted incorrectly in hindsight. This perspective shakes the self-image of many financial pros and challenges the myth of the “market beater.” What if many of those icons were merely in the right place at the right time?

When luck looks like skill…

Short-term successes in the financial sector frequently get rated as being proof of genius. But that can deceive because lucky guesses usually also look like sage decisions in retrospect. Success thus becomes anecdotal and not an objective measure. One striking example of this is the dotcom bubble around the turn of the millennium. Numerous fund managers who bet on technology stocks were deemed visionaries. Their funds earned spectacular returns, turning the managers into celebrated stars in the media. But when the bubble burst, it became evident that many of them had not acted strategically, but had simply followed the trend. Their success was less the result of superior skill and much more a product of favorable circumstances. The SPIVA Scorecard from S&P Dow Jones Indices also routinely shows that most actively managed funds do not outperform the market in the long run. Nevertheless, short-term outliers quickly get hailed as proof of exceptional investment skill. A simple thought experiment helps here: What if we could replay our lives a thousand times? In stable professions like dentistry, the outcomes would mostly resemble each other, with comparable incomes and similar lifestyles. In professions that involve high risk, such as that of entrepreneurs or traders, the outcomes would vary to extremes in contrast, with some lives ending in opulent wealth and others in ruin. It’s precisely this spectrum that illustrates how profoundly an outcome is shaped by chance. Whoever operates in an environment with a wide distribution of possible outcomes should be aware that spectacular successes are often a product of luck.

Worse than the benchmark | Fund managers seem unable to beat the market

Percentage of active US large-cap equity funds that did not outperform the S&P 500

Sources: S&P Dow Jones Indices SPIVA Scorecard, Kaiser Partner Privatbank

…and skill looks like luck

Yet we tend to attribute successes mainly to our own acumen while we like to chalk up failures to misfortune. This selective way of thinking is human nature, but it leads to dangerous false conclusions because whoever observes only the outcome ignores the actual core of a decision: the process that led to it. A decision can only really be judged with respect to the information, probabilities, and risks that were known when it was made. Even a smart decision can lead to a bad outcome, and conversely, a dubious decision can be rewarded by random chance. Moreover, what decisively matters is not just the outcome itself, but also the period over which it is observed. Let’s take, for an example, an excellent investor who sets up a well-thought-out portfolio with an expected annual return of +15% and an expected volatility of 10%. If one could observe that portfolio over 100 differently progressing years, around 95 of those years would end with a return between –5% and +35%. The probability of the portfolio performing positively in any given year actually even stands at around 93% – a decidedly bullish scenario. But the scene changes dramatically if the observation period is shortened. Picture that same portfolio on a modern trading desk with six monitor screens flashing prices in real time. In a time frame of a single second, the probability of the portfolio exhibiting a positive outcome suddenly hardly differs from a coin flip, or more precisely, the chance of an uptick right at that moment stands at exactly 50.02%.

Time is the best investor | Success requires patience

Probability of success over different periods (investment strategy with 15% return and 10% volatility)

Sources: Nassim Nicholas Taleb, Kaiser Partner Privatbank

This means that the shorter the observation period, the more dominant random chance becomes. And the more dominant that random chance is, the less information value there is in what we see in the observation period. Whoever passes judgement prematurely or stares too fixedly at short-term fluctuations runs the risk of making wrong decisions even if the underlying long-term strategy is sound. This is exactly where a frequently underrated benefit of private-market assets lies. Private-market assets are not valued second by second, their prices do not appear on flashing screens, and they do not urge constant reactions to market noise. The absence of momentary prices can be a blessing for many investors, especially those who tend to act impulsively and harm themselves through overhasty reactions.

Asymmetry: Why 50% down weighs more heavily than 50% up

One frequently underappreciated factor in dealing with risk is the asymmetry between losses and gains. The fact is that whoever loses 50% of his or her capital must gain 100% afterwards just to get back to the initial value. The way down is short and steep, but the reascent is long and arduous. This asymmetry matters not just mathematically, but is also emotionally and strategically crucial. Losses are harder to bear, not just financially, but also emotionally. They often lead to irrational decisions like completely exiting the market at the wrong time, for example. Whoever wants to build wealth must be mindful not only of opportunities, but also of the price of failure. Arguably there is hardly an investor who understands this principle better than the “Oracle of Omaha,” Warren Buffett, does. One of his most famous quotes puts it in a nutshell: “Rule number one: Never lose money. Rule number two: Never forget rule number one.”

Never lose money | Losses weigh more heavily than gains

Asymmetric return profile

Source: Kaiser Partner Privatbank

When it comes to the subject of risk, the probability of a given event occurring often gets underestimated, as does the force of its potential effects. Many decisions appear harmless at first glance because they lead to a small gain with a very high occurrence probability. But if an extremely improbable outcome is associated with a dramatically negative result, that can flip the expectation value. It then is only in hindsight that the decision reveals itself as obviously fatal. A simple example illustrates this. Picture a scenario in which a person earns a small one-dollar profit with a probability of 999 out of 1,000 times (event A). That sounds reasonable at first, but there’s a catch: in the one remaining case, a loss of ten thousand dollars looms (event B). Although that risk seems vanishingly small, it results in an average expectation value of negative nine dollars and in a decision that destroys wealth in the long run. This kind of asymmetry is particularly treacherous precisely in the world of finance, where complex risks often are communicated only in the form of probabilities. It leads to an underestimation of risks – even ones with existential implications – if they rarely actually occur. In the language of statistics, it’s not just how often something occurs, but above all what happens when it does that matters.

Tail risk | Improbable but fatal events

Asymmetric outcomes

Sources: Nassim Nicholas Taleb, Kaiser Partner Privatbank

Bulls and bears

This kind of asymmetric risk distribution is not a theoretical construct, but a reflection of a real, oft- misunderstood problem: the question of whether an investor should position him or herself for a bull or bear market. Or put succinctly: Is the market headed up or down? It seems logical at first glance to position oneself in line with one’s expectation about the market’s future direction. Whoever thinks that the market will rise will be inclined to invest correspondingly optimistically. But this approach is too short-sighted. The probability of a scenario occurring isn’t all that matters; so does the potential severity of its implications. A simple numerical example illustrates the dilemma. Let’s assume that there’s a 70% probability of the market rising by 1%. At the same time, there’s a 30% probability of it dropping by 10%. Even if the prevailing market view is bullish, this results in a negative expectation value of –2.3%. In this case, the statistics clearly show that a defensive, bearish positioning is more sensible in the long run even if the baseline scenario points to rising prices.

Bullish market outlook | Negative expectation value

Expectation value analysis

Sources: Nassim Nicholas Taleb, Kaiser Partner Privatbank

Like in the previous example with events A and B, the view here, too, is that there’s a high probability that the market will rise. Nevertheless, in some circumstances it makes sense to position oneself against the market because if the less probable case occurs and the market drops, the decline can be staggering. The losses in this scenario are so severe that they substantially outweigh the moderate gains in the other cases. Many investors focus too much on probabilities and disregard the severity of potential tail events. But financial markets in particular are precisely where it is crucial to ask not just what’s likely to occur, but above all what can happen if the improbable comes to pass. Those who understand this perspective make smarter decisions and protect their capital where others get lulled into a false sense of security.

The psychology of arrogance…

People’s biggest weakness in dealing with randomness is their inability to accept randomness. This inability gets coupled with other deep-rooted cognitive biases. Hindsight bias causes us to believe that we saw what happened coming. The narrative fallacy drives us to construct stories out of random courses of events. We want to recognize correlations where none exist. And overconfidence bias causes us to overestimate our own abilities, particularly within complex systems characterized by randomness. Those who fail see themselves as victims of adverse circumstances. But it’s precisely that mindset that obscures the view of what really matters: a well-structured decision-making process and not just the mere outcome.

…and the value of humility

In the context of finance, this frequently leads to grave mistakes. A person who believes that he or she has “figured out” the market is more prone to disregard his or her protective mechanisms and undertake risky maneuvers. Conversely, knowledge of one’s own limitations – i.e. genuine humility – guards against errors of that kind. Experienced investors who do well in the long run do not stand out due to clairvoyant powers, but by virtue of systematic thinking. They do not rely on intuition or short-term trends, but on robust processes, clear principles, and a profound understanding of risk. They know that in a world full of coin flips, it is senseless to bet on the next “heads.” Rather, the decisive question is: how many losing flips can one afford without getting wiped out of the game? A matter-of-fact look at long-term data shows what it really comes down to. Studies on large-scale pension plans verify that over 90% of differences in returns are attributable to the strategic asset allocation and not to tactical bets or individual asset picking.¹ So, whoever wants to invest successfully on a permanent basis should rely less on isolated market views and instead focus on the structure of his or her overall portfolio. It isn’t single brilliant decisions, but rather a clear and consistent allocation that performs soundly even in difficult times that makes the difference.

Monte Carlo casino

In our daily work, we deliberately employ Monte Carlo simulations to test the viability of investment strategies under realistic conditions. A portfolio can look very convincing on paper. Expected returns, clear risk parameters, and sound fundamental assumptions make everything seem plannable. But in reality, investments rarely follow a linear path. Gains and losses do not occur rhythmically, but in an unpredictable order. It’s precisely that succession that often determines whether a plan works out or falters. This is where Monte Carlo simulation comes into play. It enables one to work not just with single probabilities, but also allows one to simulate hundreds and sometimes thousands of possible future paths. Each path follows the same fundamental assumptions but evolves in its own way. What results from this is more than mere statistics. It’s a realistic glimpse into alternative visions of the future. Some of the paths lead to impressive wealth accumulation, and others end close to the zero line or even in negative territory. Each of the paths is hypothetical, but each one shows a possible future history that an investor might actually experience. We, together with our clients, do not write a single future history – we instead help to prep them for many possible scenarios.

Randomness writes histories | Monte Carlo simulations

One hundred hypothetical years (investment strategy with 15% return and 10% volatility)

Source: Kaiser Partner Privatbank

Structure rather than speculation

Randomness cannot be eliminated, but its impact can be contained through structure, discipline, and prudent risk allocation. This is exactly where the real added value of modern private banking lies. It’s not about foreseeing the future or finding the perfect entry point. It’s about advising and supporting investors in a way that enables them to survive in the market in the long run and maximizes their chance of earning sustainable profits over the long term. Professional private banking provides guidance during turbulent times. It helps clients to avoid making emotionally driven, impulsive decisions that often cost them dearly. It enables clients to build strategies that bet on resilience rather than on forecasts. At the same time, it’s not just about selecting individual products, but is also about comprehensive risk management that systematically takes randomness and asymmetry into account. A lighthouse does not avert a storm, but it prevents a ship from crashing and splintering on the rocks. An advisor analogously has just as little control over the markets, but an advisor can help one navigate them more wisely.

¹ Brinson, G. P., Hood, L. R., & Beebower, G. L. (1986). Determinants of Portfolio Performance. Financial Analysts Journal, 42(4), 39–44.