When an investor puts their money into the market, their goal is to maximize returns while minimizing risk. In the labs where they do all the financial research, various scholars have tackled this investor’s dilemma, with Markowitz offering a well-known solution through the modern portfolio theory. Another notable approach comes in the form of the Kelly criterion.
Winning Strategies & Gambling – Kelly’s Criterion on Slot Machines
How do you decide what a bet is worth?
Imagine your clueless self trying your luck at a lively Vegas casino, filled with the clinks of slot machines, the cheer of roulette tables, and the bold spirit of risk-takers.
Among the odds stacked against you, suddenly you discover the deep wisdom of a calculative play with a better possibility of winning—that’s the essence of Kelly’s Criterion. It doesn’t matter if you’re investing or placing bets based on probability, this formula enhances your odds of avoiding financial setbacks and adds a protective layer to safeguard against unintended actions.
What makes this concept truly an area of interest is its absence from traditional textbooks, despite being embraced by some of the world’s top investors. Even billionaire investor Warren Buffett is an advocate.
Stemming from the Probability Theory of mathematics, this formula addresses the likelihood of various outcomes in unpredictable events. Kelly’s Criterion compliments the challenges most investors face in their worst-case scenarios, emphasizing that, despite conducting a comprehensive analysis to identify undervalued stocks, achieving absolute perfection is hard if not impossible.
Optimizing Bets- The Origins Behind Kelly’s Criterion
Surprisingly, the formula’s origin is not what you might think. Initially meant for communication, John L. Kelly Jr., a Texas-born computer scientist in the 1950s, created it at Bell Labs. Unbelievably, it later found a new life in finance.
Jump In 1952, economist Harry Markowitz shaped modern portfolio theory. Kelly’s concept, from information theory, later influenced casino gambling, online betting, and investments, as seen in his 1956 paper titled “A New Interpretation of Information Rate.”
Comparing it to modern portfolio theory, you’ll notice similarities in risk management. The difference? Kelly looks ahead at probabilities, while modern portfolio theory looks at past risks.
Understanding the Kelly Criterion Formula- The Geeky Stuff Begins
For the everyday investor, Kelly’s Formula might seem complex at first glance, but in reality, it’s quite simple.
The mathematics behind the Kelly Criterion relies on basic probability and manipulation. The crucial concept to grasp is its assumption of compounding bets.
In simpler terms, each bet and its profits contribute to the next bet. For instance, if you wager ₹1000 and receive ₹1100, the entire ₹1110 is reinvested in the subsequent bet. This compounding principle mirrors the one employed in compound interest.
To firmly establish this concept, let’s familiarize ourselves with four variables: (p), (q), (b), and (F). Don’t get intimidated by these symbols; they represent precisely what’s described below.
p — the probability that you win the bet
q — the probability that you lose the bet, which is just 1-p
b — the payout from a successful bet, determined from the betting odds
This is determined as follows: if the odds are “x-to-y”, then b = x/y
For example, if the odds of a bet are “3-to-1”, then b = 3/1 = 3.0
F — the optimal portion of your money you want to bet
With the variables at our disposal, let’s combine them in the following formula for a bet where losing means forfeiting the entire amount wagered.
F=p-(q/b)
Betting Amount= Probability Of Winning – (Probability of losing/Expected Payout)
A few examples from our imaginary gaming arcade illustrate the application of this formula better than anything else.
Heads or Tails? Applying Kelly’s Criterion to Coin Flips
1. Understanding The Game
- Imagine flipping a normal coin in our gaming ring.
- Heads and tails each have a 0.5 (50%) chance of occurring, making both p & q = 0.5.
2. Defining Probabilities
- p = 0.5 (probability of winning – getting heads)
- q = 0.5 (probability of losing – getting tails)
3. Determining Payout
- Winning (getting heads) has a “3-to-2” payout, meaning for every ₹20 you bet, you win ₹30 (total return of ₹50, including your original bet).
- Therefore, (b = 3/2 = 1.5) (the payout ratio).
4. Setting Up and Solving the Formula
- F= 0.5 – (0.5/1.5) = 0.1667
5. Final Result
This means that given the payout from winning the bet (landing heads) and the probabilities of winning and losing the bet, you should only bet 0.1667, or one-sixth or about 16%, of your money. So if you had ₹100, you’d only bet ₹16.67 of it.
Pushing Your Edge- Using Kelly’s Criterion at the Arcade
1. Understanding the Game
- You’re playing a coin pusher game at PlanB Arcade.
- Your observation suggests that four participants out of every 52 tend to win the game; a 4/52 (or 1/13) chance of winning.
2. Defining Probabilities
- p = 1/13 (probability of winning)
- q = 12/13 (probability of losing or the remainder, since (q = 1 – p)
3. Determining Payout
- Winning gives you a payout of “12-to-1,”
- Meaning for every ₹1 you bet, you win ₹12 (total return of ₹12, including your original bet).
- Therefore, b = 12/1 = 12 (the payout ratio).
4. Setting Up and Solving the Formula
F=1/13 – (12/13)/12 = 0
5. Final Result
The optimal portion of your money is essentially zero in practical terms.
In this specific scenario, the formula suggests you shouldn’t bet anything because the payout from taking the risk isn’t worth it. This indicates a cautious approach due to the observed probabilities and payout structure of the coin pusher game.
Kelly Criterion When Probabilities Are Unknown
When you’re making bets, it’s smart to think about both the chance of losing (risk) and the prize you could win (reward). If one is smaller than the other, it’s reasonable to bet some money because the odds are somewhat in your favor.
For lotteries, where the chances of winning are tiny, the prizes are usually big enough to attract participants and to make up for that huge risk of not winning. When flipping a coin, however, since the chances of getting heads or tails are the same, the prize should be worth it over many coin flips. In simple terms, it’s about ensuring that what you might win makes up for the risk you take in the bet.
Real-World Challenges– Where Kelly Criterion Falls Short
The limitation of Kelly’s formula lies in its sensitivity to inaccurate input estimates. Small errors in assessing probabilities or expected values can significantly impact the recommended bet size.
Additionally, the formula assumes that the probabilities and payoffs remain constant over time, which may not hold true in dynamic or changing environments. Therefore, users need to exercise caution and consider the potential for miscalculations when applying Kelly’s formula in real-world scenarios.
Conclusion
The Kelly Criterion is seen as a smart and disciplined way to bet, different from just betting the same amount every time. But, you need to be good at figuring out the chance of winning to use it well. You might want to try different scenarios to see how it works for you.
For more risk-averse investors, another option under Kelly’s Criterion is known as ‘Fractional Kelly’, where you only bet a part of the suggested bet.
For example, if the recommended bet turns out to be ₹16.67, you could choose to bet only half of that, which is ₹8.33.
This is a more careful approach that helps if you’re worried about overestimating your chances and losing too much money. If all the calculations seem too hard, there are online calculators and mobile apps for the Kelly Criterion that can do the work for you.
Feel free to take your time to revisit the article for better understanding. Additionally, if you have any questions, we’re happy to answer them in the comments section below.
Frequently Asked Questions (FAQs)
1. Why should I consider using Kelly’s Criterion in my investments?
Kelly’s Criterion helps you harmonize risks and rewards, enhancing your odds of avoiding financial setbacks and safeguarding against unintended actions, whether you’re investing or making bets based on probability.
2. How does Kelly Criterion differ from traditional risk management?
Unlike traditional risk management, Kelly’s Criterion looks ahead at probabilities rather than past risks. It assesses the likelihood of various outcomes in unpredictable events, offering a unique approach to managing risks.
3. Can you explain Kelly’s Formula in simpler terms?
Kelly’s Formula relies on basic probability and manipulation, assuming compounding bets. It considers variables like the probability of winning (p), the probability of losing (q), the payout from a successful bet (b), and the optimal portion of your money to bet (F).
4. How does Kelly’s Criterion apply to real-life scenarios?
Using examples like a coin flip game and a coin pusher game, the blog writeup above illustrates how to apply Kelly’s Criterion in practical situations. It guides investors in determining the optimal portion of their money to bet based on observed probabilities and payout structures.
5. What’s the significance of ‘Fractional Kelly’ for risk-averse investors?
‘Fractional Kelly’ is an option for more risk-averse investors, allowing them to bet only a part of the suggested bet. This approach is a more cautious way to manage risk, helping to mitigate concerns about overestimating chances and potential losses.
