The most crucial aspect of investment is knowing when to place significant bets.

The essence of substantial losses often lies in overcommitting to targets where significant bets shouldn't have been placed!

In 2022, the U.S. investment firm Archegos Capital Management incurred massive losses due to miscalculations in the valuation of Chinese internet companies. Founder Bill Hwang faced substantial losses as a result of overloading on a single high-valuation target, leading to a catastrophic fallout amid China's internet anti-monopoly actions.

In 2008, the U.S. Lehman Brothers bank suffered colossal losses due to misjudgments in the valuation of subprime mortgages. The bank's undervaluation in investing in subprime mortgages resulted in substantial losses.

These cases highlight that the root cause of massive losses is misplacing bets. Investors should carefully assess the value of investment targets and avoid excessive betting.

The Kelly Criterion, introduced by John L. Kelly Jr. in 1956, initially designed to address signal-to-noise issues in the telecommunications industry, was later found applicable in gambling and investment, especially in determining bet sizes or investment ratios.

The core of this formula lies in maximizing the long-term growth rate, attempting to balance risk and reward to avoid bankruptcy due to excessively large bets while simultaneously maximizing capital increase.

In simple terms, the Kelly Criterion calculates the proportion of funds you should bet to maximize the long-term expected growth rate. If the result is a positive value, you should place a bet; if it's negative, you should avoid betting.

The meaning of the Kelly Criterion is that, during each bet, investors should allocate funds to investment targets where the probability of success is higher than the odds.

In investments, investors can use the Kelly Criterion to calculate the optimal betting amount for individual assets or bets, considering both the odds and the probability of success. However, the formula has a drawback as it assumes investors are completely rational. In reality, investors are often influenced by emotions, leading to irrational decisions.

In the investment field, the Kelly Criterion helps investors determine how much capital to invest in individual assets or bets, considering both the odds and the probability of success. This can reduce risk and increase the potential for returns. However, in practical application, there are a few points to note:

1. Accuracy of estimation: The output of the Kelly Criterion highly depends on accurate estimations of win rates (p) and odds (b). If these parameters are inaccurate, the suggested amount by the Kelly Criterion might not be optimal.

2. Long-term application: The Kelly Criterion is designed for long-term growth. Short-term fluctuations may involve significant volatility, requiring investors to have corresponding risk tolerance.

3. Fractional Kelly: To reduce volatility and risk, many investors and gamblers choose to use a fractional Kelly strategy, betting only a portion (e.g., half or a quarter) of the recommended Kelly amount.

Although a powerful theoretical tool, the Kelly Criterion isn't always the practical choice, especially when an individual's risk preferences, capital, or ability to estimate probabilities don't align perfectly with the assumptions of the Kelly Criterion. Hence, many investors view the Kelly Criterion as one reference among many, not the sole decision-making tool.

Let's interpret the Kelly Criterion through a simplified investment example:

Imagine you have an opportunity to invest in a stock with a 60% probability of going up, providing a 50% return when it rises, and a 40% probability of going down, resulting in a 50% loss. Now, you need to decide the proportion of your total capital to invest in this stock.

First, let's define the parameters in the Kelly Criterion:

· b is the net win rate of the bet, here it's 50% or 0.5.

· p is the probability of winning, here it's 60% or 0.6.

· q is the probability of losing, here it's 40% or 0.4.

Plug these values into the Kelly Criterion:

Since the result of f∗ is negative, following the Kelly Criterion, you shouldn't invest in this opportunity because, in the long run, it is expected to result in losses.

However, let's change the conditions. If the probability of the stock going up remains 60%, but if it goes up, you can gain a 100% return; if it goes down, you lose 50%.

Now, the parameters for the Kelly Criterion are:

· b is 1 (or 100% return).

· p remains 0.6.

· q remains 0.4.

Plug in the values:

The result of f∗=0.2 indicates that if you want to maximize your long-term growth rate, you should invest 20% of your total capital in this stock.

Remember, the Kelly Criterion provides the theoretically optimal solution for maximizing capital growth. However, in reality, factors like risk tolerance and liquidity need to be considered. Many investors may choose to invest less than 20% of their capital to reduce risk.

The Kelly Criterion and Bayes' Theorem are both crucial decision-making tools in investment, although they are used for different types of problems. Let's explain their applications in investment decision-making through examples.

Example of applying the Kelly Criterion in investment:

Suppose you are considering investing in a startup technology company. This company could either succeed and bring high returns to investors or fail entirely, resulting in a total loss. After analyzing the company's business model, market potential, and team background, you estimate a 30% probability of the company's success, with returns on investment being three times the original investment. If it fails, you would lose the entire investment.

Here:

Example of applying Bayes' Theorem in investment:

Bayes' Theorem is a method for updating prior probabilities based on new evidence or information. Assume you are investing in a large-cap stock in an industry that typically correlates closely with macroeconomic indicators.

Initially, you may have a prior belief (probability) based on historical data and analysis, thinking that in the current economic environment, there is a 60% probability of the stock performing well this quarter. However, unexpectedly positive employment data, a strong indicator of the stock's favorable performance, emerges.

Using Bayes' Theorem, you can update the probability of the stock performing well. If historical data shows that, under similar employment data announcements, the probability of the stock performing well is 80%.

Therefore, considering the new employment data, after updating with Bayes' Theorem, you now believe there is a 96% probability that the stock will perform well this quarter.

In investment decision-making, the Kelly Criterion helps determine the optimal capital allocation based on your updated win rates and odds, while Bayes' Theorem assists in updating your probability assessments with new evidence. Both are powerful tools for making more informed decisions in the face of uncertainty.

From a probabilistic perspective, combining the Kelly Criterion with Bayes' Theorem aims to enhance the expected return of a portfolio and determine when to place substantial bets.

The Kelly Criterion and Bayes' Theorem are both important tools in decision theory, especially in investment decision-making. Combining these tools can enable a more sophisticated management of investment portfolios and potentially increase the expected return of the portfolio.

Combined usage:

1. Prior probability assessment: Use Bayes' Theorem to assess the prior returns and risks of each investment. This involves gathering market data, historical performance, economic indicators, and other relevant information as evidence to update your beliefs about asset returns.

2. Posterior probability updates: With changes in market conditions and the emergence of new information, continually update the posterior probability of asset returns using Bayes' Theorem. This helps you respond quickly to market changes.

3.Capital allocation: Use the Kelly Criterion to decide how much capital you should invest in each asset based on the updated probabilities. This way, you can optimize your investment portfolio according to the latest market information and your beliefs about future market performance.

4. Risk management: Utilize the Kelly Criterion to avoid overinvestment, maintaining risk control even in high-odds scenarios. This is because the Kelly Criterion considers the probability of failure and uses it as a crucial parameter for capital allocation.

Combining the Kelly Criterion with Bayes' Theorem can help investors increase the expected return of their portfolios while keeping risk under control. However, caution is needed in practical implementation, as it requires accurate estimations of returns and probabilities and the ability to adapt to new information, posing a significant challenge to investors' judgment and execution.

However, investment opportunities validated by both Bayes' Theorem and the Kelly Criterion are often the most worthwhile ones to place substantial bets on.

If the odds are high but the win rate is low, it may not be worth risking too much because, in the long run, you may lose more times than you win. Conversely, if the win rate is high but the odds are low, it's not worth investing too much because losses could be significant when you do lose.

Only when both the odds and win rate are relatively high does the Kelly Criterion recommend investing a significant amount. This is the time when it's worth placing substantial bets.

With such complex formulas, it's impossible to rely on individual calculations. Therefore, the Lane Club's super AI tool named "FinTech&AI Turbo" uses AI to accomplish this task, achieving excellent results.

Whether in the stock market or the cryptocurrency market, especially in the contract trading of the cryptocurrency market, maximizing profits can be achieved. Heavy emphasis on earnings!