The Kelly Criterion: A Simple Guide for Stock Investors

One of the hardest questions in stock investing is:

“How much should I invest in this stock?”

Many investors focus on which stock to buy,
but decide how much to invest based on intuition.

This is where the Kelly Criterion becomes useful.

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What Is the Kelly Criterion?

The Kelly Criterion is a mathematical formula that tells you:

“What percentage of your capital you should invest to maximize long-term growth.”

In other words,
it helps you grow your portfolio as fast as possible while controlling the risk of ruin.

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The Basic Formula

$$f = \frac{bp – q}{b}$$f=bbp−q​

Where:

• f = fraction of capital to invest
• p = probability of winning
• q = 1 – p (probability of losing)
• b = payoff ratio (average gain ÷ average loss)

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Stock Market Version

In investing, this is often written as:$$f = \frac{\mu}{\sigma^2}$$f=σ2μ​

• μ = expected return
• σ² = variance (volatility²)

👉 The higher the return relative to risk, the larger the position you can take.

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Simple Example

Assume a trading strategy with:

• Win rate: 55%
• Average gain: +4%
• Average loss: –2%

Payoff ratio: b = 4 ÷ 2 = 2$$f = \frac{2×0.55 – 0.45}{2} = 0.325$$f=22×0.55−0.45​=0.325

👉 Theoretically, the optimal position size is 32.5% of total capital.

(Practically, this is very aggressive.)

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How Professionals Actually Use It

Because markets are uncertain, most investors use:

• Half-Kelly (50%)
• Quarter-Kelly (25%)

These reduce risk while keeping most of the growth benefit.

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Pros and Cons

Advantages

• Provides a mathematical basis for position sizing
• Maximizes long-term portfolio growth
• Prevents emotional “all-in” decisions

Disadvantages

• Very sensitive to estimation errors
• Can lead to large drawdowns
• Psychologically difficult to endure

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One Key Takeaway

The Kelly Criterion is not about picking better stocks.
It is about deciding how much to invest.

Even a great stock can destroy your portfolio if the position size is wrong.

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Final Thoughts

The Kelly Criterion =
Investing based on risk-adjusted return, not just return.

If your goal is to survive and grow in the market long term,
this is one of the most powerful money-management tools you can use. 📈