What is Risk?

Alex Stacy
7 min readApr 21, 2021


Story of my life.

If you asked a group of business school professors to define “risk”, they would dutifully reply, “beta”. Define “beta”, you may respond. “Well, it is the expected volatility of an asset relative to a collection of other assets (benchmark)”, they will describe. If a benchmark of assets possesses a beta of 1, and the stock of a company has a beta of 2, then the stock of the individual company possesses double the “risk”. The highest echelons of finance define risk as the covariance of one asset to a basket of others.

The average person would describe risk in basic, catastrophic terms: the destruction of a house from fire, death of a loved one in a car accident, termination of a job by an employer, etc. These descriptions come in stark contrast to the description of financial risk above. In the financial system, we experience risk as price volatility. In our everyday lives, we experience risk as binary downsides resulting from all sorts of common and uncommon actions. What explains the difference?

The concept of risk, while today inherent in Western culture, is relatively new in human history. Prior to advances in human understanding of risk, mystics and religious figures dictated the uncertain future to eager listeners. These religious leaders spoke on behalf of a multitude or singular deity, leaving no room for uncertainty and therefore risk. Several individuals in the past thousand years developed human capacity to define risk, which enabled us think critically about future outcomes. The ability to think critically about future outcomes enabled economic advances that contributed to our current circumstances.


European development of the concept of risk began with the import of the Hindu-Arabic numerical system a couple hundred years before the Renaissance. Prior to the numeric system we use today, the West relied on Greek and Roman numbering systems, which did not enable easy math. Imagine trying to use Roman numerals for complex equations.

In 1202, Leonardo Pisano wrote Liber Abaci after living in Algeria with his father — who spent time in the region as a merchant. The book became one of the first broadly distributed introductions to Hindu-Arabic numbers within the West, starting in Italy. The book included a series of practical applications for these new numbers in commercial bookkeeping — including revenue, margins, profit & loss statements. The introduction of this new numbering system equipped the West with the ability to manipulate numbers in ways not possible before.

While Leonardo wrote Liber Abaci roughly 200 years before the Renaissance took hold, the Hindu-Arabic numbering system caused mathematics to flourish, but after quite some time. Gambling, games of chance, formed one of the early applications of the imported numbering system. Often the rules of games of chance did not calibrate with the probable outcome of events. To satisfy a voracious appetite for gambling, a sixteenth century physician named Girolamo Cardano developed some of the first mathematical frameworks of probability in his book, Ars Magna (The Great Art). Ars Magna represented the first work during the Renaissance to focus on algebra — introducing the nomenclature a, b, c, and d that most people know today. Cardano followed up this work with calculations of probabilities of dice games — including the probability of certain outcomes over multiple rolls, with multiple die. Subsequently, three Frenchmen — Blaise Pascal, Pierre de Fermat, and Chevalier de Mere — pulled Cardano’s concepts forward into the first theory of probability — meant to measure the likelihood of outcomes in hard numbers. Europeans started framing events in terms of probable outcomes, applying these learnings from gambling to other decisions made in daily life.


Informed decisions on risk require not just proper frameworks of evaluation, but also data to plug into those frameworks. Cardano provided the framework of probabilities to evaluate risk, but systematic data collection on various daily activities came later. In 1662, a Brit named John Gaunt authored a breakthrough book that contained a compilation of births and deaths in London from 1604 to 1661, which included commentary that interpreted the data. While Gaunt did not use the word “probability”, Gaunt provided population data on a number of items that remained a mystery to society — including death rates at different ages, disease rates, birth rates, etc. Gaunt created the first actuarial tables that today define the insurance industry. Actuarial tables contextualize various forms of risk, enabling probabilistic decision making.


In 1687, Edward Lloyd opened a coffee house near the Thames on Tower Street favored by sailors of the ships moored at London’s docks. Recognizing the clientele and a demand for information, Edward started publishing “Lloyd’s List” in 1698 and filled it with information on arriving and departing ships, along with information gathered during voyages. Eventually, Edward’s coffee house became a place for those seeking and underwriting marine insurance to gather. The wall of the coffee shop contained shipping information and the shop acted as an exchange for risk. In 1771, 79 of the underwriters who did business at Lloyd’s subscribed to the Society of Lloyd’s — an unincorporated group of individuals that formed the Lloyd’s insurance house that still exists today (in virtually the same format). The concept of insurance encouraged risk takers to explore the world in ways not possible before.

Impact of Probabilistic Decision Making

Over a period of 500 years, Europe advanced significantly, aided in part by its conceptualization of risk. In 1200, religious thought dominated Europe, creating the perception that deities ordained future events. The concept of risk does not exist in a world of certainty. Beginning with Hindu-Arabic numbering, gamblers applied these numbers to games of chance. If the outcome of a game of dice relied on chance, then other aspects of life may rely on various probabilities (childhood death, disease, the prospects of a successful business venture, etc.).

Over time, theories of probability encompassed mathematical concepts. Normal distributions, standard deviations, law of large numbers, and reversion to the mean — gave a poetic harmony between the interplay of the observable world and mathematics. Height and weight follow normal distributions within society. 68.3% of the population fall within one standard deviation of the mean. With a large enough sample size or time period, results trend towards a normal distribution around the mean.

Wrong Turn

Implicitly, a probabilistic decision-making framework identifies and calculates alternatives that possess different probabilities and different utilities. The summation of these scores equals the expected value of any decision. Enter the 20th Century, where risk management in a world of growing compute power and observable data combined to create a deviation from the eight centuries of progress on the contextualization of risk. The development of computer-based frameworks for probabilistic decision-making tricked us into thinking we reduced uncertainty to a minimum. Metrics like “beta” or “value at risk” provide a false sense of security that since we can calculate the probability of various events occurring, the consequences of those events can be mitigated. University of Chicago economist Frank Knight, friend of John Maynard Keynes, rightfully pointed out our inability to comprehend all risks. In 1921 he wrote,

“Uncertainty must be taken in a sense radically distinct from the familiar notion of risk, from which it has never been properly separated. It will appear that a measurable uncertainty, or “risk” proper is so far different from an unmeasurable one that it is not in effect an uncertainty at all.”

Said plainly, uncertainty is unquantifiable, which means that measures of risk are imperfect. No perfect assessment of risk exists and therefore no perfect reflection of risks in any system society constructs.

HHC Method

At Hudson Hill, we do not believe that markets are efficient, nor that computers or spreadsheets predict the world around us. As Fischer Black, creator of a famous options pricing model, once said, “markets look a lot less efficient from the banks of the Hudson than from the banks of the Charles.” It certainly looks even less efficient in the fifty states in America and other countries in the world.

Risk in investing is not the degree of variance from a basket of other assets. Risk in investing is the probability of permanent impairment of capital or the opportunity cost of not investing our capital into something else. Hudson Hill believes it unknowable the ultimate probability of either occurrence, but quantifiable to some extent by assigning probabilities to a range of alternative outcomes determined by idiosyncratic due diligence. We only target situations where the range of possible outcomes likely preclude a permanent impairment of capital. We seek comfort not in our “diversification”, but rather in our investment analysis assessing the prospects of downside protection, coupled with likely asset appreciation throughout an investment. Just because computers possess substantial power to process enormous amounts of data creating complex frameworks for the world, does not mean computers are omnipotent. Overreliance on computers to dictate our understanding of risk dulls our intellect and leads to poor decision making. Just because you can measure something, does not mean it matters.

The problem with identifying risk as public market volatility is that investor psyche begins to track that of the herd. Allowing market perturbations to impact our conviction in an idea does not make a whole lot of sense to us. Owning a business should excite us at the price we paid and certainly not trouble us when the prices of random companies in different industries see price increases or declines. At HHC, we focus on notional value creation — growing our capital to the largest possible amount at the fastest possible pace. Losing money impedes both efforts. We develop idiosyncratic views on individual assets, fueled by a secular vision of the world coupled with that of fundamental due diligence on each opportunity. As a result, we also do not mind concentrating our investments in fewer opportunities we believe to possess substantial upside. We understand that in certain terrible circumstances, all assets possess no value and so diversifying to preserve capital for these rare instances where diversification ultimately fails sacrifices too much return in the meantime. We seek greater psychological strength in our convictions than relying on the stock price chart of unrelated businesses. Why? Because we operate in a world filled with chaos. Simplifying our decisions into basic beliefs represents the only enduring strategy to prosperity.

As Gottfriend Leibniz said in 1703, “Nature has established patterns originating in the return of events, but only for the most part.” In other words, the present rhymes with the past.