Risk Management & Position Sizing: An Engineer’s Guide to Trading

Trading can seem like a thrilling opportunity to achieve financial freedom, but the reality for most retail traders is starkly different. Statistics show that the vast majority of retail traders fail, not because they lack the ability to pick profitable trades, but due to inadequate risk management. Without a structured approach to managing losses and protecting capital, even a streak of good trades can easily be undone by one bad decision. The key to success in trading lies not in predicting the market perfectly but in managing risk effectively.

As engineers, we are trained to solve complex problems using quantitative methods, rigorous analysis, and logical thinking. These skills are highly transferable to trading risk management and position sizing. By approaching trading as a system that can be optimized and controlled, engineers can develop strategies to minimize losses and maximize returns. This guide is designed to bridge the gap between engineering principles and the world of trading, equipping you with the tools and frameworks to succeed in one of the most challenging arenas in finance.

Table of Contents

• Kelly Criterion
• Position Sizing Methods
• Maximum Drawdown
• Value at Risk
• Stop-Loss Strategies
• Portfolio Risk
• Risk-Adjusted Returns
• Risk Management Checklist
• FAQ

### The Kelly Criterion

The Kelly Criterion is a popular mathematical formula used in trading and gambling to determine the optimal bet size for maximizing long-term growth. It balances the trade-off between risk and reward, ensuring that traders do not allocate too much or too little capital to a single trade. The formula is as follows:

\[
f^* = \frac{bp – q}{b}
\]

Where:
– \( f^* \): The fraction of your capital to allocate to the trade.
– \( b \): The odds received on the trade (net return per dollar wagered).
– \( p \): The probability of winning the trade.
– \( q \): The probability of losing the trade (\( q = 1 – p \)).

—

#### Worked Example

Suppose you’re considering a trade where the probability of success (\( p \)) is 60% (or 0.6), and the odds (\( b \)) are 2:1. That means for every $1 invested, you receive $2 in profit if you win. The probability of losing (\( q \)) is therefore 40% (or 0.4). Using the Kelly Criterion formula:

\[
f^* = \frac{(2 \times 0.6) – 0.4}{2}
\]

\[
f^* = \frac{1.2 – 0.4}{2}
\]

\[
f^* = \frac{0.8}{2} = 0.4
\]

According to the Kelly Criterion, you should allocate 40% of your capital to this trade.

—

#### Full Kelly vs Half Kelly vs Quarter Kelly

The Full Kelly strategy uses the exact fraction (\( f^* \)) calculated by the formula. However, this can lead to high volatility due to the aggressive nature of the strategy. To mitigate risk, many traders use a fractional Kelly approach:

– **Half Kelly**: Use 50% of the \( f^* \) value.
– **Quarter Kelly**: Use 25% of the \( f^* \) value.

For example, if \( f^* = 0.4 \), the Half Kelly fraction would be \( 0.2 \) (20% of capital), and the Quarter Kelly fraction would be \( 0.1 \) (10% of capital). These fractional approaches reduce portfolio volatility and better handle estimation errors.

—

#### JavaScript Implementation of Kelly Calculator

You can implement a simple Kelly Criterion calculator using JavaScript. Here’s an example:

// Kelly Criterion Calculator
function calculateKelly(b, p) {
    const q = 1 - p; // Probability of losing
    const f = (b * p - q) / b; // Kelly formula
    return f;
}

// Example usage
const b = 2;  // Odds (2:1)
const p = 0.6; // Probability of winning (60%)

const fullKelly = calculateKelly(b, p);
const halfKelly = fullKelly / 2;
const quarterKelly = fullKelly / 4;

console.log('Full Kelly Fraction:', fullKelly);
console.log('Half Kelly Fraction:', halfKelly);
console.log('Quarter Kelly Fraction:', quarterKelly);

—

#### When Kelly Over-Bets

The Kelly Criterion assumes precise knowledge of probabilities and odds, which is rarely available in real-world trading. Overestimating \( p \) or underestimating \( q \) can lead to over-betting, exposing you to significant risks. Additionally, in markets with “fat tails” (where extreme events occur more frequently than expected), the Kelly Criterion can result in overly aggressive allocations, potentially causing large drawdowns.

To mitigate these risks:
1. Use conservative estimates for probabilities.
2. Consider using fractional Kelly (e.g., Half or Quarter Kelly).
3. Account for the possibility of fat tails and model robustness in your risk management strategy.

While the Kelly Criterion is a powerful tool for optimizing growth, it requires prudent application to avoid catastrophic losses.

### Position Sizing Methods

Position sizing is a vital aspect of trading risk management, determining the number of units or contracts to trade per position. A well-chosen position sizing technique ensures that traders manage their capital wisely, sustain through drawdowns, and maximize profitability. Below are some popular position sizing methods with examples and a detailed comparison.

—

#### 1. Fixed Dollar Method
In this method, you risk a fixed dollar amount on every trade, regardless of your account size. For instance, if you decide to risk $100 per trade, your position size will depend on the distance of your stop loss.

##### Example:
“`javascript
const fixedDollarSize = (riskPerTrade, stopLoss) => {
return riskPerTrade / stopLoss; // Position size = risk / stop-loss
};

console.log(fixedDollarSize(100, 2)); // Risk $100 with $2 stop-loss
“`

*Pros:* Simple to implement and consistent.
*Cons:* Does not scale with account size or volatility.

—

#### 2. Fixed Percentage Method (Recommended)
This method involves risking a fixed percentage (e.g., 1% or 2%) of your total portfolio per trade. It’s one of the most widely recommended methods for its adaptability and scalability.