Are Investment Losses Often Due to Overleveraging? The Kelly Formula Teaches You How to Bet Scientifically

Many investors have experienced the temptation of “going all in”—betting all their funds on a stock or trade they believe in. But what happens? A single misjudgment can cause serious damage. The root problem behind this phenomenon isn’t poor stock-picking ability but a lack of position management. The Kelly formula is the key to solving this issue.

Why “All In” Often Fails — Understanding the Essence of Position Sizing

Most investors make decisions based on two dimensions: whether the stock will “rise” or “fall.” But this binary thinking is precisely the root of losses. Even if your directional judgment is perfect, if you invest more than you can afford, a single downturn can wipe you out.

Imagine two investors both optimistic about a stock, each with a 70% chance of rising. One invests 10% of their account, the other invests 100%. When the stock drops unexpectedly by 30%, the second investor might be margin-called or forced to sell at a loss, while the first might have the opportunity to buy more at the lower price. This demonstrates the power of position sizing.

The Golden Rule of the Kelly Formula — Managing Risk with Probabilities

The core idea of the Kelly formula is simple: Not all good opportunities are worth going all in on; instead, you should scientifically calculate the optimal bet size based on win probability and potential gains or losses.

Factors considered in the Kelly formula include:

• Probability of increase — How likely do you think the price will go up?
• Upside potential — How much can you earn if correct?
• Probability of decrease — The chance of failure
• Downside risk — How much will you lose if wrong?

In stock or BTC investment scenarios, the application of the Kelly formula follows three principles:

First, don’t be overconfident. Even with a 90% win rate, you shouldn’t bet everything; an extreme move can wipe you out.

Second, don’t be overly cautious. If the opportunity is genuinely good, increasing your position appropriately is necessary to profit. Many people, driven by fear, hesitate and watch opportunities slip away.

Third, adjust dynamically. As your capital or market conditions change, your position size should be flexible—adding when funds are ample, reducing when tight.

How to Calculate the Optimal Bet Size Using the Kelly Formula

The mathematical expression of the Kelly formula is:

f = (p/g) - (q/l)

Where:

• f = optimal investment proportion (percentage of total capital to invest)
• p = probability of success (win rate)
• q = probability of failure (q = 1 - p)
• g = expected gain (upside)
• l = expected loss (downside)

Example: Suppose you are bullish on a stock:

• Win probability p = 60%
• Loss probability q = 40%
• Expected upside g = 30% (0.3)
• Expected downside l = 15% (0.15)

Plug into the formula: f = (0.6/0.3) - (0.4/0.15) = 2 - 2.67 = -0.67

A negative result indicates this isn’t a favorable bet. If you adjust parameters to be more conservative, say p = 55%, then:

f = (0.55/0.3) - (0.45/0.15) ≈ 1.83 - 3 = -1.17

Still negative, suggesting no edge. If you find parameters that yield a positive f, that indicates a favorable opportunity.

The Three Major Pitfalls of the Kelly Formula — Why Even the Perfect Formula Can Fail

While scientific, the Kelly formula has limitations.

First trap: Overreliance on predictions. Its accuracy depends entirely on your estimates of win probability and potential gains/losses. Overestimating your edge or underestimating risks can lead to overbetting.

Second trap: Extreme scenarios. When the formula suggests a position size over 100%, it indicates the trade is fundamentally flawed, not just a matter of position sizing. In such cases, you should abandon the trade rather than tweak parameters.

Third trap: Psychological capacity. Even if the formula recommends a 30% position, if that causes sleepless nights, you should use a “half-Kelly” approach—invest only half the suggested amount. Many professional investors do this to further reduce risk.

One Sentence Summary

The core lesson of the Kelly formula is: Bet big on good opportunities, but only if you have enough capital to withstand bad luck. It’s not about making more money but about surviving long-term in the markets—survival itself is already a major victory.