kelly-criterion

What Is The Kelly Criterion And Why It Matters In Business

The Kelly criterion is a formula-based approach to investing and gambling. For each investment or bet, the individual allocates funds as a percentage of the entire portfolio. The Kelly criterion was created by researcher John Kelly in 1956 as a means of analyzing long-distance telephone signal noise. In more recent times, the formula has been adopted by the gambling and investment industries as means of wise resource allocation to a bet or investment. 

For example:

  • A blackjack player determining how much of their bankroll to wager on the next hand.
  • A stock investor deciding on the percentage of their portfolio that should be devoted to speculative resource stocks.
  • A real-estate investor questioning how much of their portfolio to devote toward condominiums in Miami Beach.

In each example, the goal of the gambler or investor is to grow their capital. 

According to the Kelly criterion, the amount of money invested should be proportional to the knowledge of the bet or investment itself. 

Key components of the Kelly criterion formula

The Kelly criterion is expressed by the formula:

Here:

  • f* = the total percentage of wealth that should be risked.
  • p = the historical probability of a win. Ideally, the p-value needs to be above 0.50 or 50%.
  • b = the decimal odds minus 1, otherwise known as the amount that could potentially be won or lost. For investors, calculate the b value by dividing the total number of trades yielding a positive amount by the total number of trades.
  • q = the probability of failure (i.e. 1-p).

When interpreting the f* value, multiply it by 100 to get the percentage of total funds that should be risked. For example, if f* = 0.17 then the total percentage of funds allocated should be 17%.

Kelly criterion limitations

Earlier, it was stated that knowledge of the bet was proportional to the amount of money invested in that bet.

This begs the question: how is knowledge obtained and what does it constitute? 

The Kelly criterion defines knowledge as the perceived edge, itself defined as a betting advantage gained from exploiting bookmaker margins or possessing proprietary knowledge.

However, it is important to note that the formula is not foolproof. While it does define the point of maximum portfolio growth, the f* value is calculated from real-world probabilities that are best estimates only. Invariably, factors that influence the probability of winning are complex, obscured, or hard to define. 

To reduce variance, many choose to estimate returns that are 30 to 50% of the calculated f* value. This is known as a safety margin, where risks are assumed to be higher than stated.

Other limitations of the Kelly criterion include:

  • A focus on growth stocks. As growth stock profits are continually re-invested to encourage exponential growth, Kelly’s formula favors growth stock investors. Investors wishing to make smaller, more consistent income-stock profits may find the model too aggressive.
  • Higher margin for error. Given that the f* value is the point of maximum potential growth, a figure only slightly higher brings substantially more risk, variance, and decreased profit. This means that undisciplined gamblers or investors prone to greed could suffer larger losses by ignoring the stated f* value.

Key takeaways

  • The Kelly criterion is a mathematical formula that guides gambling and investment decisions by way of risk-managed resource allocation.
  • The Kelly criterion argues that the background knowledge of an investment or bet is directly proportional to the amount of money that should be allocated.
  • While useful in a variety of scenarios, the Kelly criterion is nevertheless based on mostly unquantifiable probabilities that increase variance. As a result, a conservative approach to calculating investment percentages should be taken.

Connected Business Heuristics

heuristic
As highlighted by German psychologist Gerd Gigerenzer in the paper “Heuristic Decision Making,” the term heuristic is of Greek origin, meaning “serving to find out or discover.” More precisely, a heuristic is a fast and accurate way to make decisions in the real world, which is driven by uncertainty.
recognition-heuristic
The recognition heuristic is a psychological model of judgment and decision making. It is part of a suite of simple and economical heuristics proposed by psychologists Daniel Goldstein and Gerd Gigerenzer. The recognition heuristic argues that inferences are made about an object based on whether it is recognized or not.
representativeness-heuristic
The representativeness heuristic was first described by psychologists Daniel Kahneman and Amos Tversky. The representativeness heuristic judges the probability of an event according to the degree to which that event resembles a broader class. When queried, most will choose the first option because the description of John matches the stereotype we may hold for an archaeologist.
take-the-best-heuristic
The take-the-best heuristic is a decision-making shortcut that helps an individual choose between several alternatives. The take-the-best (TTB) heuristic decides between two or more alternatives based on a single good attribute, otherwise known as a cue. In the process, less desirable attributes are ignored.
biases
The concept of cognitive biases was introduced and popularized by the work of Amos Tversky and Daniel Kahneman since 1972. Biases are seen as systematic errors and flaws that make humans deviate from the standards of rationality, thus making us inept at making good decisions under uncertainty.
bundling-bias
The bundling bias is a cognitive bias in e-commerce where a consumer tends not to use all of the products bought as a group, or bundle. Bundling occurs when individual products or services are sold together as a bundle. Common examples are tickets and experiences. The bundling bias dictates that consumers are less likely to use each item in the bundle. This means that the value of the bundle and indeed the value of each item in the bundle is decreased.
barnum-effect
The Barnum Effect is a cognitive bias where individuals believe that generic information – which applies to most people – is specifically tailored for themselves.
first-principles-thinking
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ladder-of-inference
The ladder of inference is a conscious or subconscious thinking process where an individual moves from a fact to a decision or action. The ladder of inference was created by academic Chris Argyris to illustrate how people form and then use mental models to make decisions.
six-thinking-hats-model
The Six Thinking Hats model was created by psychologist Edward de Bono in 1986, who noted that personality type was a key driver of how people approached problem-solving. For example, optimists view situations differently from pessimists. Analytical individuals may generate ideas that a more emotional person would not, and vice versa.
second-order-thinking
Second-order thinking is a means of assessing the implications of our decisions by considering future consequences. Second-order thinking is a mental model that considers all future possibilities. It encourages individuals to think outside of the box so that they can prepare for every and eventuality. It also discourages the tendency for individuals to default to the most obvious choice.
lateral-thinking
Lateral thinking is a business strategy that involves approaching a problem from a different direction. The strategy attempts to remove traditionally formulaic and routine approaches to problem-solving by advocating creative thinking, therefore finding unconventional ways to solve a known problem. This sort of non-linear approach to problem-solving, can at times, create a big impact.
moonshot-thinking
Moonshot thinking is an approach to innovation, and it can be applied to business or any other discipline where you target at least 10X goals. That shifts the mindset, and it empowers a team of people to look for unconventional solutions, thus starting from first principles, by leveraging on fast-paced experimentation.
bounded-rationality
Bounded rationality is a concept attributed to Herbert Simon, an economist and political scientist interested in decision-making and how we make decisions in the real world. In fact, he believed that rather than optimizing (which was the mainstream view in the past decades) humans follow what he called satisficing.
dunning-kruger-effect
The Dunning-Kruger effect describes a cognitive bias where people with low ability in a task overestimate their ability to perform that task well. Consumers or businesses that do not possess the requisite knowledge make bad decisions. What’s more, knowledge gaps prevent the person or business from seeing their mistakes.
occams-razor
Occam’s Razor states that one should not increase (beyond reason) the number of entities required to explain anything. All things being equal, the simplest solution is often the best one. The principle is attributed to 14th-century English theologian William of Ockham.
mandela-effect
The Mandela effect is a phenomenon where a large group of people remembers an event differently from how it occurred. The Mandela effect was first described in relation to Fiona Broome, who believed that former South African President Nelson Mandela died in prison during the 1980s. While Mandela was released from prison in 1990 and died 23 years later, Broome remembered news coverage of his death in prison and even a speech from his widow. Of course, neither event occurred in reality. But Broome was later to discover that she was not the only one with the same recollection of events.
crowding-out-effect
The crowding-out effect occurs when public sector spending reduces spending in the private sector.
bandwagon-effect
The bandwagon effect tells us that the more a belief or idea has been adopted by more people within a group, the more the individual adoption of that idea might increase within the same group. This is the psychological effect that leads to herd mentality. What in marketing can be associated with social proof.

Read Next: BiasesBounded RationalityMandela EffectDunning-Kruger EffectLindy EffectCrowding Out EffectBandwagon Effect.

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Published by

Gennaro Cuofano

Gennaro is the creator of FourWeekMBA which reached over a million business students, executives, and aspiring entrepreneurs in 2020 alone | He is also Head of Business Development for a high-tech startup, which he helped grow at double-digit rate | Gennaro earned an International MBA with emphasis on Corporate Finance and Business Strategy | Visit The FourWeekMBA BizSchool | Or Get The FourWeekMBA Flagship Book "100+ Business Models"