Kelly’s Formula: How to Calculate the Size of Our Investments

Dasch
6 min readApr 5, 2022
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Every good investor must have a strong psychological balance that allows them to escape from euphoria or general fear.

In several articles in this section, we discussed some of the keys to becoming a good investor, keys that have a lot to do with the psyche of the person who wants to succeed, but not necessarily from today to tomorrow (aunque por supuesto, cuanto antes, mejor).

As workers, we must be clear that this aspect of our lives will be a long-term career that will consume our days and nights for a long time.

It would be a stretch to say that the reasons for which people invest are comparable and must be the same, but there are many who seek quick cash, more often than not with the fatal result of succumbing to the fracaso in an even more ferocious manner. As a result, one of the qualities we encourage investors to cultivate is patience, which allows them to plan ahead of time for bad times, invest for longer periods of time (on the margin of risk they are willing to accept), and invest with money they do not need in the short term.

To summarize, every good investor must have a strong psychological balance that allows them to escape from euphoria or general fear. It is necessary to understand aguantar y tener aguante en las bajas para entrar cuando el precio se hace muy atractivo o para evitar deshacer una buena posición solely due to fear. That same temple has to show up in the elevators, or else we’ll sell too soon, or else we’ll be too late to get into a car that’s already parked.

To begin with, as the value investing school teaches us, one of the most important keys to success is discovering the value of a company that is routinely overlooked by the market. This will be a significant purchasing opportunity. According to Warren Buffett, “the more absurd the market’s behavior, the better the opportunity for the systematic investor.”

After you’ve made a good purchase, the next step is to figure out when it’s time to sell. Sales commissions can come from a variety of sources. In the first place, the business may be exhibiting clear signs of deterioration, such as the arrival of competition, a lack of adaptability, changes in leadership, or strategic decisions that are detrimental to the interests of the shareholders, among other things. It is also possible that the market value has become excessive (as in the case of Terex, where we recommend selling positions).

Or, simply, that the journey to the summit is not as enticing as other activities that reveal significant investment opportunities. In addition, we can sell to adjust the risk of our portfolio, among other factors that support sales.
But the size of each of our positions is where we’ll be focusing our attention today. When an investor discovers a profitable opportunity, one of the first questions he or she asks is how much of their portfolio should be invested in it. Much of this has to do with two issues that are discussed in greater or lesser detail here: asset allocation and portfolio diversification.

To get a sense of the scope of this topic, let’s talk about the “Kelly criterion,” a system that Mohnish Pabrai mentions in his book The Dhandoo Investor. However, it is worth noting that the Pabrai has greatly improved its applicability, particularly since the 2008 crash. And, as we will see later, the Kelly formula is overly optimistic or, to put it another way, overly arried for many investors, including value investors.

In reality, this criterion gives us the percentage of our portfolio that we should invest in a specific action (or activity in general) given certain success probabilities. However, the percentages that the formula produces are so high that many investors (as well as the values that employ it) prefer to apply a correcting factor, whether it is a reduction factor (sistemically, invirtiendo only a fraction of the percentage that the formula produces), or it is a search for other activities that produce the same probability of success, up to dividing the total amount of investment that the formula produces.

Cabe detenerse en el matemático John Larry Kelly por unos instantes, quien da nombre a una fórmula que es empleada, entre otros y en alguna medida, no sólo por el propio Pabrai, sino por inversores como Warren Buffett. Kelly, acompañado por Claude Shannon, desarrolló para los laboratorios Bell una estrategia de apuestas o inversiones que podría englobarse dentro de la teoría de juegos. Lo que nos viene a decir esta fórmula es que existe una proporción óptima de capital a arriesgar en un suceso que se repite varias veces según la probabilidad que asignemos de acertar frente a la de errar. En el caso de una inversión, un acierto sería la obtención de una ganancia (o una ganancia superior al margen mínimo con que operemos).

Before we present the formula, we must first understand the budgetary implications of the Kelly criterion.

1.The investor’s goal is to maximize the total rentability of his portfolio over time. This is without a doubt the most significant flaw of the Kelly criterion, because almost none of us are willing to risk large volatility in order to gain greater long-term profitability from our portfolio (maximum when such a revaluation could occur when we have died or when we require a significant portion of our capital). Kelly’s criterion will imply the image of what Bernard Baruch said to the famous American gambler Jimmy, the Greek: “usted seguramente vaya an alternar el ser millonario y pobre hasta siete veces en su vida.”Keep an eye out for a rich finish in the seventh…”

2.Each investment has a unique potential for appreciation and depreciation. To put it another way, what one can win and lose depends on the circumstances. There will be instances where our price goal entails duplicating or tripling, while others require only a 15% increase. Similarly, if things go wrong, in some cases it is possible to lose everything, whereas in others it is possible to lose half, 15%, and so on.

3.Likewise, the likelihood of each scenario (success-failure) is distinct. For example, the odds of escaping the crisis in two years are 60–40, and the odds of a new competitor dethroning the sector’s most powerful companies in the new technology sector are high (comparando con otros sectores).

Kelly believes that applying the following formula yields the percentage that must be arried in each operation:

[(WP * WL) — (1 — WP)] / WL

Where WP (winning percentage) is the percentage of correct bets and WL (winning-loss ratio) is the winning-loss ratio.

As we can see, the Kelly formula takes into account all of the variables in point 3 and calculates the optimal percentage that we should invest in each opportunity (much higher when there is a high likelihood of a large revaluation, much lower when the expected revaluation is modest and there is a risk of loss).

We’ll look at how the formula is used in practice with an example. We believe that a price of 10 euros has a 50% chance of increasing to 20 euros (in reality, it could be the average of several possibilities, such as 25% of reaching 25 and 25% of reaching only 15 euros). Currently, the chances of it falling to 4€ are equal to 50 percent. As a result, the WL ratio will be 1,666 (10/6) and the WP ratio will be 0.

Using the formula, the percentage we must risk in this transaction is 19.98% of our capital.

[(0,5*1,666)-(1–0,5)]/1,6666=0,1998

As it can be seen, it is a large percentage to risk in a single operation, which is maximized when considering that it does not produce immediate results (in the case of value investing, it can take years) and that the chances of finding similar operations are not continuous.

Kelly’s criterion is nearly identical to the system used on the table by Edward O. Thorp — popularized in the film 21 Blackjack-, who increased or decreased his bets based on whether the remaining cards in the deck contained many or few figuras.

We’re returning to Earth. To summarize, our recommendation is to take advantage of what is good about Kelly’s criterion (significantly outperforming positions when opportunities are more clear), but to ignore it in a strict sense and to avoid concentrating more than 8 or 9 percent in any one value.

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Dasch

Tech and decentralization lover. I also love the art world in a lot of variants