Kelly Criterion

The Kelly Criterion: A Beginner's Guide to Sizing Your Trades

Welcome to the world of cryptocurrency trading! Many new traders focus on *which* coins to buy, but a crucial, often overlooked aspect is *how much* of your capital to allocate to each trade. This is where the Kelly Criterion comes in. It's a formula designed to help you maximize long-term growth while minimizing the risk of ruin. This guide will break down the Kelly Criterion in a simple, practical way for complete beginners. It’s a complex idea, so we’ll take it slowly.

What is the Kelly Criterion?

The Kelly Criterion isn't a trading *strategy* itself, like Day Trading or Swing Trading. Instead, it's a *formula* for determining the optimal percentage of your capital to bet on a given trade. It’s a mathematical formula, created by John Kelly, originally for predicting horse races, but applicable to any situation where you have an edge. The goal is to find the sweet spot where you maximize your expected growth, but without taking on so much risk that you could wipe out your account.

Think of it like this: you want to grow a garden. You could plant *everything* as one crop (high risk, high reward), or spread it out across many different crops (lower risk, lower reward). The Kelly Criterion helps you decide how to ‘diversify’ your trading capital.

Key Terms Explained

Before we dive into the formula, let's define some important terms:

• **B:** The *net profit* expressed as a decimal. This is the amount you win minus the amount you lose, divided by the amount you bet. For example, if you bet $10 and win $12 (net profit of $2), B = 2/10 = 0.2.
• **p:** The *probability of winning*. This is your estimate of how likely you are to be profitable on a trade. Expressed as a decimal (e.g., 70% winning probability is 0.7). Estimating 'p' accurately is the hardest part! Technical Analysis and Fundamental Analysis can help with this.
• **f:** The *fraction of your capital to bet*. This is what the Kelly Criterion calculates – the optimal percentage.

The Kelly Criterion Formula

The formula itself looks like this:

f = (bp - q) / b

Where:

• f = fraction of capital to bet
• b = net profit
• p = probability of winning
• q = probability of losing (which is 1 - p)

Let’s break this down with an example.

Example: Trading Bitcoin

Let’s say you’ve analyzed Bitcoin (BTC) and believe:

• Your probability of winning (p) is 60% (0.6).
• If you win, your net profit (b) is 20% (0.2). So, for every $1 you bet, you make $0.20.
• Therefore, your probability of losing (q) is 40% (0.4).

Plugging these values into the formula:

f = (0.2 * 0.6 - 0.4) / 0.2 f = (0.12 - 0.4) / 0.2 f = -0.28 / 0.2 f = -1.4

Uh oh! A negative result! This means, according to the Kelly Criterion, you shouldn’t make this trade at all. Your expected value is negative.

Let’s adjust the example. Suppose your probability of winning is 70% (0.7) and your net profit is still 20% (0.2).

f = (0.2 * 0.7 - 0.4) / 0.2 f = (0.14 - 0.4) / 0.2 f = -0.26 / 0.2 f = -1.3

Still negative. Let’s increase the potential profit. What if your probability of winning is 70% (0.7) and your net profit is 30% (0.3)?

f = (0.3 * 0.7 - 0.4) / 0.3 f = (0.21 - 0.4) / 0.3 f = -0.19 / 0.3 f = -0.63

Still negative. This highlights the importance of having a significant edge (high probability of winning *and* a good profit margin).

Let's say your probability of winning is 80% (0.8) and your net profit is 20% (0.2).

f = (0.2 * 0.8 - 0.4) / 0.2 f = (0.16 - 0.4) / 0.2 f = -0.24 / 0.2 f = -1.2

Still negative. Finally, let's say your probability of winning is 90% (0.9) and your net profit is 20% (0.2).

f = (0.2 * 0.9 - 0.4) / 0.2 f = (0.18 - 0.4) / 0.2 f = -0.22 / 0.2 f = -1.1

Still negative. This shows how difficult it is to find a trade setup that meets the Kelly Criterion.

Let’s say your probability of winning is 60% (0.6) and your net profit is 50% (0.5).

f = (0.5 * 0.6 - 0.4) / 0.5 f = (0.3 - 0.4) / 0.5 f = -0.1 / 0.5 f = -0.2

Still negative.

Let’s say your probability of winning is 70% (0.7) and your net profit is 50% (0.5).

f = (0.5 * 0.7 - 0.4) / 0.5 f = (0.35 - 0.4) / 0.5 f = -0.05 / 0.5 f = -0.1

Still negative.

Let’s say your probability of winning is 80% (0.8) and your net profit is 50% (0.5).

f = (0.5 * 0.8 - 0.4) / 0.5 f = (0.4 - 0.4) / 0.5 f = 0 / 0.5 f = 0

So in this case, the Kelly Criterion says you should not trade at all.

Finally, Let’s say your probability of winning is 90% (0.9) and your net profit is 50% (0.5).

f = (0.5 * 0.9 - 0.4) / 0.5 f = (0.45 - 0.4) / 0.5 f = 0.05 / 0.5 f = 0.1

This means you should bet 10% of your capital.

The Problem with Full Kelly

While the Kelly Criterion provides an optimal fraction, blindly following it (known as "full Kelly") can be dangerous. It can lead to very large bet sizes, and a single losing trade can significantly impact your capital. This is why many traders use a *fractional Kelly* approach.

Fractional Kelly: A More Conservative Approach

Fractional Kelly involves multiplying the result of the Kelly Criterion by a fraction (typically 0.5, 0.25, or even 0.1). This reduces the bet size and lowers the risk of ruin.

Here's a comparison:

Criterion	Bet Size (Example: $1000 capital)
Full Kelly	$100 (if Kelly result is 0.1)		Half Kelly	$50 (if Kelly result is 0.1)		Quarter Kelly	$25 (if Kelly result is 0.1)

Using half Kelly in the previous example (Kelly result of 0.1) would mean betting $50 (10% of $500).

Practical Steps for Using the Kelly Criterion

1. **Estimate Your Edge:** Accurately assess your probability of winning (p) and your potential net profit (b). This requires diligent Market Research and understanding of Risk Management. 2. **Calculate the Kelly Fraction:** Use the formula above to calculate 'f'. 3. **Apply Fractional Kelly:** Multiply 'f' by a fraction (e.g., 0.5) to reduce risk. 4. **Adjust Based on Volatility:** More volatile assets might require a smaller fractional Kelly. 5. **Track Your Results:** Monitor your trades and refine your estimates of 'p' and 'b' over time. Learning from your past trades is crucial for improving your edge.

Important Considerations

• **Accuracy of Estimates:** The Kelly Criterion is only as good as your estimates of 'p' and 'b'. Be realistic and avoid overconfidence. Trading Psychology is very important.
• **Drawdowns:** Even with fractional Kelly, you will experience drawdowns (periods of losses). Be prepared for this and have a solid Trading Plan.
• **Transaction Costs:** Don't forget to factor in Trading Fees when calculating your net profit (b).
• **Diversification:** The Kelly Criterion doesn’t replace the need for diversification. Consider trading multiple assets.

Resources and Further Learning

• Risk Reward Ratio
• Position Sizing
• Volatility
• Trading Volume
• Candlestick Patterns
• Support and Resistance
• Moving Averages
• Bollinger Bands
• Fibonacci Retracements
• MACD
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• BitMEX

Conclusion

The Kelly Criterion is a powerful tool for optimizing your trading capital allocation. However, it's not a magic bullet. It requires accurate estimates, a conservative approach (fractional Kelly), and a solid understanding of risk management. By incorporating the Kelly Criterion into your trading strategy, you can potentially maximize your long-term growth while minimizing the risk of ruin.

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